David & Guillaume

Quentin, François, Thibaut, Victor, Nicolas, Christophe David

Guillaume Philippe

The pipeline design codes and standards traditionally focus on the operational loadings such as internal and external pressures that are likely to exist over the entire lifetime of the pipeline. Existing Engineering Critical Assessments are mostly based on criteria developed in the seventies using stress-based considerations. In such approaches, the design margin is given as a percentage of the yield strength defined at 0.5 % total strain. In regions where ground movements can occur, pipelines may experience stresses beyond the yield point and plastic deformations up to 2.5 %. In such conditions, strain-based design (SBD) approaches shall be applied in order to certify that both the parent and weld materials are able to handle such loadings.

In this work, a literature review of the existing strain-based methods is proposed. In particular, ExxonMobil and PRCI (Pipeline Research Council International) multi-tier approaches are presented. Both are based on the tangency analysis where a tensile strain capacity is calculated equating the crack driving force of the structure with the material J or CTOD R-curve.

The use of the Single Edge Notched Tension (SENT) specimen to measure the material toughness is then studied. Different test protocols are compared and the essential parameters, such as the initial crack depth-tothickness ratio a 0 /W, are studied. This specimen is of particular interest for the pipeline operators as it is shown to be the closest to a pipe in terms of plastic constraint. Consequently, less conservative material R-curves are potentially measured.

The largest part of this PhD was dedicated to the study of the behavior of both parent and weld materials of an OD 323.8 mm / WT 22.2 mm seamless pipe supplied by Vallourec & Mannesmann. A compressive experimental campaign was carried out, including tensile tests under different stress triaxiality ratios, and fracture mechanics tests (SENT, SENB, CT) at room temperature, -20 • C and -40 • C . Both materials are shown to be isotropic with respect to plasticity and fracture. They remain fully ductile at low temperatures. The constitutive laws of these two materials are identified using an inverse analysis. Moreover, the ductile failure of such steels is 1 2 driven by the void growth followed by the void coalescence. These two mechanisms can be accurately represented using the Gurson Tvergaard Needleman (GTN) model. Its coefficients have been identified on axisymmetric notch specimens, and comparisons between simulations and experimental data derived from cracked specimens, mostly SENT, enable to validate the model. A four-point bending full scale test was carried out on a pressurized pipe containing one crack at the weld centerline of the girth weld, and one in the parent material. The pipe was fully instrumented, including strain gages and double-clip gages to measure both CMOD and CTOD. A three dimensional finite element analysis of the test was performed using the constitutive laws and GTN model determine on the laboratory-size test samples. Then, results are compared to the experimental data under the form of an axial remote strain-CTOD curve. Final failure is shown to be correctly predicted.

Finally, a similar procedure was followed to assess an OD 609.6 mm / WT 29 mm API X70 steel grade UOE-LSAW pipe supplied by Europipe. In that case the material is plastically anisotropic. A full-scale test was performed in tension.

Ces quatre années de thèse ont été effectuées au Centre des Matériaux Pierre-Marie Fourt de l'Ecole des Mines ParisTech, le CdM.

Je tiens à remercier en premier lieu Jacques Besson et Yazid Madi pour avoir co-encadré mon travail de thèse. Au cours de ces longues années, ils ont su me laisser une grande autonomie de travail et m'ont apporté leurs connaissances scientifiques dans le domaine de la mécanique de la rupture. Ils m'ont transmis avant tout une rigueur scientifique, qui me sera indispensable dans la poursuite de mon parcours professionnel. Je leurs également à les remercier pour leur aide très précieuse dans les dernières semaines de rédaction de ce manuscrit. Leurs nombreux conseils m'ont permis d'enrichir celui-ci.

Je tiens également à remercier Vincent Gaffard pour m'avoir fait confiance depuis mon stage de fin d'études en 2012. Il a toujours su se rendre disponible pendant ces cinq années, et a tout fait pour rendre mes travaux à la fois toujours plus riches et plus pertinents. Il a également tout fait pour que je profite de cette expérience de recherche pour enrichir ma connaissance du métier, au travers de ma participation à de nombreuses conférences. Je l'en remercie vivement, car j'ai aujourd'hui la chance de pouvoir valoriser ces différentes expériences dans mon travail d'ingénieur de Recherche. Il m'a également appris à constamment me dépasser. Je lui en suis très reconnaissant.

Je tiens ensuite à remercier Annie Audibert-Hayet (TOTAL) pour avoir initié cette thèse et m'avoir fait confiance. Je tiens également à la remercier pour les discussions toujours très intéressantes et enrichissantes que nous avons eu l'occasion de partager, et son soutien au cours de ces quatres années.

Je tiens à remercier l'ensemble des membres de mon jury de thèse. Je souhaite exprimer mes sincères remerciements aux rapporteurs Sebastian Münstermann et Sandrine Thuillier pour l'intérêt qu'ils ont porté à ce travail. Je remercie Fodil Meraghni et Benoit Tanguy qui ont également accepté de juger ce travail. Je leur suis reconnaissant pour leurs nombreuses remarques qui m'ont permis d'améliorer la qualité de ce manuscrit.

Mes plus vifs remerciements s'adressent à Abdennour Meddour pour sa disponibilité et sa grande implication pour les très nombreux essais mécaniques réalisés au bocal. Merci également à lui pour nous avoir accompagnés en Allemagne et en Italie pour la préparation et la réalisation des essais sur structure. Son sens de la débrouillardise et sa parfaite connaissance de son matériel m'a toujours permis de réaliser sereinement mes essais. Ce fut un réel plaisir de travailler avec lui.

Je tiens particulièrement à remercier René Cluzet, responsable de l'atelier du CdM pour sa disponibilité, sa gentillesse et sa patience au cours de ces quatre années. Il n'a jamais failli à mes innombrables demandes d'usinage, souvent de dernières minutes. Je lui en suis très reconnaissant car je n'aurais pas pu fournir autant de résultats sans lui.

Je tiens à remercier l'ensemble du personnel du CdM, qui font de ce laboratoire un lieu convivial et stimulant pour la réalisation de travaux de recherche. Je remercie également l'ensemble du personnal de l'EPF-Ecole d'Ingénieur(e)s pour leur soutien et leur aide.

Version française

Les codes et standards dédiés à la conception des oléoducs se concentrent tradionnellement sur les chargements mécaniques liés à leur fonctionnement classique en opération, tels que la pression interne et externe, qui sont susceptibles d'exister durant toute la vie de la structure. Les procédures d'analyse de défauts existantes reposent pour la plupart sur des critères développés dans les années 1970 et basés sur des considérations en niveaux de contraintes. Dans de telles approches, la marge de conception est donnée comme un pourcentage de la limite d'élasticité du matériau. Cependant, pour les régions dans lesquelles des mouvements de terrain sont susceptibles d'avoir lieu, les canalisations peuvent être soumises à des niveaux de contraintes au-delà de leur limite d'élasticité, et à des niveaux de déformations plastiques qui peuvent aller jusqu'à 2,5 %. Dans de telles conditions, des démarches de conception basées sur des critères en déformations doivent être utilisées pour garantir que le métal de base et le métal d'apport des zones soudées seront capables de résister à de tels chargements mécaniques : on parle alors de strain-based design, noté SBD.

Dans ce travail, une revue bibliographique des méthodologies SBD proposées par ExxonMobil et le PRCI (Pipeline Research Council International) est proposée. Ces dernières reposent sur le principe de l'approche tangentielle, selon laquelle le niveau de déformation critique est calculé en égalisant la courbe de chargement du défaut, appelée Crack Driving Force, et la courbe de résistance du matériau où la ténacité est exprimée en terme de CTOD ou de l'intégrale J.

L'utilisation de l'éprouvette Single Edge Notched Tension (SENT) pour mesurer la ténacité est alors étudiée. Différents protocoles d'essais sont comparés, et l'influence de différents paramètres expérimentaux, comme la profondeur d'entaille initiale, est étudiée. Cette éprouvette est particulièrement intéressante pour les opérateurs d'oléducs, car il est montré qu'elle est la plus proche d'une canalisation comportant un défaut, en terme de confinement plastique. Ainsi, les courbes de ténacité mesurées sont moins conservatives.

Une part importante de ce manuscrit est consacrée à l'étude du comportement mécanique des matériaux de base et d'apport d'un tube sans soudure en acier X65 fourni par Vallourec & Mannessmann. Celui-ci présente un diamètre extérieur de 323,8 mm et une épaisseur de 22,2 mm. Une riche campagne expérimentale est réalisée, incluant des essais de tractions sous différents niveaux de triaxialités des contraintes, ainsi que des essais sur éprouvettes fissurées (SENT, SENB et CT), aussi bien à température ambiante qu'à -20 • Cet -40 • C . Les deux matériaux de l'étude présentent un comportement isotrope en plasticité et rupture. De plus, ils conservent un comportement parfaitement ductile à basse température. Les lois de comportement de ces deux matériaux furent identifiées en utilisant l'analyse inverse. La rupture ductile de ce type d'aciers résulte de deux mécanismes : la croissante de cavités, suivie de leur coalescence. Ces deux évènements peuvent être représentés avec précision en utilisant le modèle Gurson-Tvergaard-Needleman (GTN), dont les coefficients peuvent être identifiíes grâce à des éprouvettes entaillées, et validés en comparant des courbes expérimentales et simulées d'essais réalisés sur des éprouvettes fissurées telles que des SENT. Les résultats d'un essai de flexion 4 points pleine-échelle réalisé sur un tube contenant un défaut dans sa zone de métal de base et dans son cordon de soudure de raboutage sont présentés. Le tube est instrumenté à l'aide de jauges de déformations et d'extensomètres d'ouverture pour la mesure du CMOD et du CTOD au cours de l'essai. Une modélastion élèments finis de l'essai fest réalisée en utilisant les lois de comportements et le modèle GTN identifiés sur les éprouvettes de laboratoire. Les résultats expérimentaux et numériques sont alors comparés, et il est montré que la rupture finale de la canalisation est correctement prédite par la simulation.

Pour finir, une démarche identique est déployée pour analyser un tube en acier X70 anisotrope en plasticité, soudé longitudinalement fourni par Europipe, dont le diamètre extérieur est de 609,6 mm et l'épaisseur de 29 mm. Pour ce dernier, un essai pleine-échelle en traction combinée à de la pression interne est réalisé.

ainsi que mes grand-parents qui m'ont toujours encouragé à poursuivre mon objectif et m'ont soutenu dans les moments les plus difficiles.

Je tiens également à remercier Djamila et Moumen, Adil ainsi que Leïla et Allal pour m'avoir aussi bien accueilli, soutenu dans mes efforts, et répondu présents le jour de ma soutenance de thèse depuis leur si beau Maroc. Je leur en suis profondément reconnaissant.

Enfin, je tiens à exprimer ma plus profonde gratitude à ma femme Yasmine pour son soutien indéfectible, son optimisme et sa joie de vivre contagieuse. Elle m'a permis de vivre pleinement cette expérience de thésard, et a su supporter les nombreuses soirées et nombreux week-ends consacrés à mon travail. Elle a été d'un courage exemplaire, et c'est uniquement grâce à elle que j'ai pu accomplir ce beau projet. Specimen compliance during the k load -unload sequence of a SENT test F (c) Load at the onset of the coalescence during a notched tensile test F max Maximum load reached during a tensile test f c

List of Symbols

Porosity value at the onset of the coalescence f F Porosity value at the end of the coalescence H Daylight between grips for SENT specimens

Part I

INTRODUCTION

INTRODUCTION

The growing needs for fossil energy oblige oil & gas companies to operate in areas where severe conditions of exploitation can be met, particularly in arctic areas. In such environments, pipelines which are classically designed to withstand the operating loads, i.e. internal and external pressure, are subjected to additional external loads, typically in tension or bending. These solicitations are mainly consequences of soil displacements as the results of different phenomenons: frost heave or thaw settlement due to the thermal cycles along the year; seismic events; or ground movements resulting from a sliding soil for example. Operating pipelines in arctic areas also implies to deal with temperatures which can be as low as -60 • C . At such temperatures, mechanical properties of metallic materials are likely to change, and a decrease of ductility or toughness is to be considered. It is therefore important for operators to challenge material properties through comprehensive experimental analyses to ensure that required minimum properties are met. In Chapter 4 and Chapter 7 of this document, the effect of the temperature on two grades of pipeline steels (X65 and X70) is studied, with testings carried out at room temperature, -20 • C and -40 • C . In addition to the parent material, the two corresponding girth weld materials are also studied.

When cracks are found on the network, operators have to determine their susceptibility to propagate within a stable or unstable regime. This is what is commonly called Engineering Critical Assessment (ECA). These approaches are traditionally stress based, meaning that the line pipes are designed so that the maximum stress which may be reached does not exceed a given percentage of the material yield stress (specified or actual). However, these approaches are necessarily overconsertive since the improvement of the material properties of the modern steel grades are not taken into account. Indeed, new steel grades show enhanced ductilities and a significant increase in toughness. As a remedy, new approaches based on strain considerations have been developed for the last ten years. In that case, structures are designed so that the strain (which is traditionally defined as a remote axial strain) does not exceed a given percentage of the material uniform elongation. It is also a priority to ensure that potential existing cracks will not propagate under such significant strain levels.

The use of strain-based design (SBD) approaches leads to new issues due to the high levels of plastic deformation that are likely to be met (up to 2.5 %). A proper characterization of the material toughness is mandatory since it is a key parameter of the failure analysis of structures. So far, this quantity could be measured using impact Charpy tests and ad hoc correlations providing toughness since stress-based approaches only requires the determination of the linear elastic fracture mechanics parameter K mat . This test is particularly adapted in the case of materials showing low ductility and low toughness. However, as said before, strain-based design implies materials with higher material properties for which correlations between Charpy fracture energy and toughness do not apply. Using test specimens such as Compact Tension (CT) or Single Edge Notch Tensile (SENT) specimens allows obtaining crack growth resistance curve (R curve) which can used to make the fracture assessment of structures beyond crack initiation. This point is discussed in Chapter 1 of this text.

The characterization of the tensile properties of girth weld materials are also challenging since classical tensile tests carried out on smooth round bars cannot be used as the weld material is more resistant than the parent material (so called weld overmatching). In such cases, the necking is likely to occur within the parent material which material properties are lower than the weld material. In Chapter 3, a procedure based on the use of notched specimens is proposed. The latter enables to ensure that necking will compulsorily occur within the weld material so that a full stress -strain curve is obtained. An additional work is then necessary to identify the material constitutive law using the inverse analysis.

Existing strain based design procedures have been identified in the literature. A first approach was developed by University of Ghent and proposes to calculate the tensile capacity of a line pipe based on tests carried out on sub-size specimens, called curve-wide plate. Two other procedures have been introduced by ExxonMobil and PRCI. They proposed two multi-tiered approaches which consist in assessment methodologies based on the "tangency" analysis. The later relies on the comparison between material R curve (toughness) and crack driving force (load condition at the crack tip). The multi-tiered procedures contain different assessment levels that shall be used depending on the required conservatism level and the available information on the material plastic and fracture behavior. First assessment levels are based on analytical formula whereas the most advance levels are based on detailed elastic-plastic finite element calculations to derive crack driving forces for the considered structure assuming various crack depths. These finite element calculations require a high level of expertise so that their use is not straightforward. In particular, the definition of an appropriate fracture parameter is not straightforward when dealing with simulations. The use of the crack tip opening displacement (CTOD) quantity is suggested by ExxonMobil, but its calculation using finite element analysis is not necessarily easy. This point is discussed in this Chapter 2.

There is currently no consensus on the strain based approaches, in particular regarding the methodologies for toughness characterization for which several specimen geometries exist. However, most of the industry agrees today on the relevance of the use of the single-edge-notch tension (SENT) specimen which is, in terms of plastic constraint, more representative of pipe loading conditions than more "standard" CT specimens. This point is studied in Chapter 1.

The existing recommended practices for the testing of SENT specimens proposed by ExxonMobil, DNV or CanMet are also discussed in Chapter 1. A major difference concerns the specimen geometry (square cross section vs. rectangular cross section), the specimen preparation before testing (fatigue precracking vs. narrow notch machining) and the processing of the experimental data (identification of the shape factor η for example) in order to derive the material R curves. Using results identified in the literature, it is shown that a simplified protocol can be introduced.

In this study, we propose the use of the local approach to fracture in order to investigate the transferability of toughness results obtained for the SENT specimens to actual structures. The local approach to fracture has been developed in the 80's and is based on several ingredients: (i) realization of fracture tests together with the observation (and possibly quantification) of the physical micro-mechanisms leading to fracture, (ii) development of physically based models to represent damage and fracture based on the observations, (iii) simulation of structures (tests specimens but also actual full size structures) using the damage/fracture models and integrating defect such as notches ans cracks. Within this framework, the Gurson model (and its numerous extensions) has been used by many authors to describe ductile fracture as it allows representing the different stages of ductile fracture (void initiation, void growth and coalescence) while remaining simple enough to allow conducting the simulation of complex flawed structures. The use of the local approach to fracture requires a good knowledge on the mechanical behavior of the material. Therefore, a comprehensive experimental campaign including tests under various stress triaxiality ratios must be conducted in order to study the fracture mechanism and properly calibrate the model using inverse methods. This work has been carried out for the four materials (including the effect of temperature) of the study and is presented in the two corresponding Chapter 5 and Chapter 8.

Finally two full scale tearing tests on the actual line pipe were carried out. This allows in particular to check the transferability of results obtained on SENT specimens to structures using the local approach to fracture methodology. A first pipe (X65 with an outer diameter of 323.8 mm and wall thickness 22.2 mm) is subjected to pure bending in addition to a high internal pressure. Two cracks are implemented within the girth weld and the parent material, and their propagation is studied. The other pipe (X70 with an outer diameter of 608 mm and a wall thickness of 29 mm) is tested in tension while a high internal pressure is applied. Again, cracks are inserted both in the weld and parent material. These two full size tests are then simulated using the local approach which is calibrated on small laboratory specimen to check that the transferability between specimens and the structure is possible. Finally, results from the so-called global approaches are benchmarked and compared to test result in Chapter 6 and Chapter 9.

Part II

LITERATURE Chapter 1

Fracture mechanics applied to pipe design

1.

Fracture mechanics applied to pipe design

Résumé en français

Dans ce chapitre, les fondamentaux de la mécanique de la rupture sont rappelés, en partant de la mécanique linéaire élastique de la rupture introduite par Griffith [9] jusqu'à son extension aux comportements élasto-plastiques des aciers pour oléoducs, en utilisant les concepts de l'intégrale J et du CTOD, pour Crack Tip Opening Displacement, correspondant à l'ouverture d'une fissure mesurée au niveau de sa pointe. Ces deux grandeurs mécaniques peuvent être mesurées expérimentalement, grâce à l'utilisation d'éprouvettes fissurées telles que les éprouvettes CT (pour Compact Tension), les éprouvettes SENB (pour Single Edge Notched Bending) ou les plus récentes éprouvettes SENT (pour Single Edge Notched Tension). De part leur géométrie et leur mode de chargement (flexion ou traction), ces éprouvettes présentent des indices de confinements plastiques différents, traduisant un développement de la plasticité plus ou moins important. Il est alors montré que l'intégrale-J et le CTOD ne sont pas des quantités intrinsèques du matériaux, mais que leur mesure dépend de la géométrie de l'éprouvette choisie. Notamment, les courbes de résistances à la fissuration mesurées à l'aide des éprouvettes fissurées sont classées dans un ordre croissant, la CT étant la plus basse et la SENT la plus haute, proche de la courbe de résistance d'un tube fissuré. Aussi, l'éprouvette SENT se veut moins conservative pour la conception de canalisation.

Ce chapitre se concentre sur cette éprouvette, pour laquelle différents protocoles expérimentaux sont disponibles dans la littérature. La norme British Standard BS 8571 -Method of test for determination of fracture toughness in metallic materials using single edge notched tension (SENT) specimens a fait son apparition en 2014. A noter que celle-ci repose principalement sur la procédure DNV-RP-F108 par ailleurs étudiée ici. L'effet de différentes conditions et techniques expérimentales est étudiée : géométrie de l'éprouvette, profondeur relative de la fissure (a 0 /W) ; mesure du CTOD via l'utilisation de deux extensomètres d'ouverture ; évaluation de l'avancée de fissure grâce à la mesure de la complaisance. De plus, des analyses basées sur l'utilisation de modèles éléments finis permettent l'évaluation de certaines recommandations de la littérature.

Fracture mechanics basics 1.Introduction

The major objective of fracture mechanics is the ability of predicting how cracks will behave in mechanical components subjected to internal (i.e. residual stresses caused by forming or welding) or external (i.e. tension, torsion, bending, internal and external pressure, etc..) loads.

At the beginning [START_REF] Irwin | Analysis of stresses and strains near the end of a crack traversing a plate[END_REF] only the linear fracture (LFM) mechanics, which involved only materials which behavior was linear elastic, has been considered. Thus, the calculations were relatively simple. The stress and strain field ahead of the crack tip is characterized by stress intensity factors K I,I I,I II . In the following only mode I loading will be considered so that one single parameter can be used: K I . The released energy rate G during crack growth can be related to K I so that a simple failure criterion which states that failure occurs when K I reaches a critical value K Ic which is a material property.

During the seventies, numerous studies arose to extend such an approach to elastic plastic materials [2,[START_REF] Kanninen | Elastic-Plastic Fracture Mechanics for Two-Dimensional Stable Crack Growth and Instability Problems[END_REF]. In particular, the J-integral approach (attributed to Rice [4] even if this point is discussed [START_REF] Eshelby | Energy Relations and the Energy-Momentum Tensor in Continuum Mechanics[END_REF]6]), was introduced. Then, Begley and Landes [7] derived a J-integral based failure criterion J C (for Critical J) that was extended to ductile tearing using the resistance curves J -∆a, where ∆a is the crack advance.

Linear Elastic Fracture Mechanics (LEFM)

In 1957, Williams [8] demonstrated that for an opening crack in mode I, the first order term of the Taylor's series for the stress field is directly proportional to a stress intensity factor, denoted K I . In a polar coordinate system centered on the crack tip (see Figure 1.1), the stress field for opening mode I writes:

σ xx = K I √ 2πr cos θ 2 1 -sin θ 2 sin 3θ 2
σ yy = K I √ 2πr cos θ 2 1 + sin θ 2 sin 3θ 2
σ xy = K I √ 2πr cos θ 2 sin θ 2 cos 3θ 2
σ zz = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩
ν σ xx + σ y y in plane strain 0 in plane stress (1.1) where the subscripts r, θ denote the polar coordinates with the origin at the crack tip, and K I depends on the geometry and the boundary conditions. The displacements fields writes:

u x = K I 2µ r 2π cos θ 2 κ -1 + 2 sin 2 θ 2 u y = K I 2µ r 2π sin θ 2 κ +1-2 cos 2 θ 2 κ = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩
3 -4ν in plane strain (3 -ν) / (1+ν)) in plane stress (1.2) Back in 1921, linear elastic fracture mechanics began with the work of Griffith [9] when he showed that the fracture of a elastic brittle material can be represented using a global scalar value G c , that will be later called critical Strain energy release rate (in J.m -2 ). This parameter corresponds to the energy release during the crack propagation related to the crack growth in a perfectly elastic solid.

To illustrate, let consider a solid with a constant thickness B and containing a crack of length a. For a given crack propagation value da and a given load P, one can observe a increase in the displacement d∆. The strain energy release rate is then proportional to the area between the two curves P(∆) corresponding to the cracks length a and a+da. An equivalent approach applies for a specimen under displacement control. For a crack propagation value da and an imposed displacement d∆, one can observe a decrease in force dP (see Figure 1.2).

Considering that the energy released during the opening of the crack is equal to the required work ∆W to open the crack on the length da, a relationship between K I and G exists, and writes:

∆W = B da 0 σ yy • u y dx = G • B • da (1.3)
where σ yy denotes the opening stress as defined in Equation 1.1. The following relationships are obtained:

G = K 2 I 1 -ν 2 E
in plane strain conditions, and

G = K 2 I E
in plane stress conditions (1.4) where E is the Young Modulus and ν is the Poisson's ratio.

However as stated herein before, these parameters are only valid in the case of a linear elastic material.

J-integral

Properties

This integral was shown independent of the path of integration on a closed contour. This property is of particular interest in the case of a finite element numerical study, since it allows to calculate J-integral on any contour defined by the mesh at the vicinity of a crack. The following development is valid only on the domain of validity of J defined for:

• The material behavior can be described using an non-linear elastic law. The case of an elasticplastic material can be considered, only for a purely monotonic increasing load. • The description of the deformation of the solid is based on the infinitesimal strain theory, i.e. small deformations theory.

In 1968, Rice [4] introduced the J-integral as:

J = Γ Wdx 2 -⃗ T. ∂⃗ u ∂x 1 ds (1.5)
where Γ is an arbitrary contour around the tip of a crack, and the traction vector applied to Γ writes ⃗ T = ⃗ n • σ ˜, with ⃗ n being the normal vector to Γ. These notations are defined in Figure 1.3. According to Figure 1.2 -Representation of the strain energy release rate (from [START_REF] Stéphane | Approche énergétique de la déchirure ductile[END_REF]) [4] W is the strain energy density which is calculated using the stress tensor σ ˜and the strain tensor ε ˜, using the relationship:

W = ε 0 σ ˜: dε ˜(1.6)
with ε ˜which writes following the small deformations theory: ε ˜= 1 2 ∇u + (u) t where u is the displacement vector (1.7)

Using index notation, Equation 1.6 becomes:

W = ε 0 σ ij dε ij with ε ij = 1 2
∂u i ∂x j + ∂u j ∂x i (1.8)
Now considering any contour Ω surrounding the crack tip that propagates in x 1 direction, Ω is obtained by adding the contour Γ + corresponding to the crack flanks, to the initial contour Γ (Ω = Γ∪Γ + ). In such case, J writes

J = Ω Wdx 2 -T ∂u ∂x 1 ds = Γ Wn 1 -n j σ ij ∂u j ∂x 1 ds (1.9) or J = Ω Wδ 1i -σ ij ∂u j
∂x 1 n j ds where δ 1i is the Kronecker symbol (1.10) Using Green theorem, Equation 1.10 becomes

J = A ∂ ∂x i Wδ 1i -σ ij ∂u j ∂x 1 dA (1.11) Γ Γ + =⋅ Closed contour Γ ∪ Γ + Γ 1 ∪ ∆ 1 ∪ Γ 2 ∪ ∆ 2 Figure 1.

-Integration contours for J-integral calculation

where A denotes the area of the surface delimited by Ω. Developing Equation 1.11 yields

J = A ⎛ ⎜ ⎜ ⎜ ⎜ ⎝ ∂ ∂x 1 W - ∂σ ij ∂x i ∂u j ∂x 1 -σ ij ∂ 2 u j ∂x 1 ∂x i ⎞ ⎟ ⎟ ⎟ ⎟ ⎠ dA (1.12)
Considering that Ω is free of external load, the equality ∇σ = 0 is verified, and then ∂σ ij /∂x i = 0. Considering Equation 1.8, Equation 1.12 becomes

J = A ∂ ∂x 1 W -σ ij ∂ε ij ∂x 1 dA (1.13)
The theory assumes that the material behavior is non-linear elastic. The path independence of J strongly depends on that hypothesis. In that case, tensor can be formulated as σ ij = ∂W /∂ε ij so that Equation 1.13 becomes :

J = A ∂ ∂x 1 W - ∂W ∂ε ij ∂ε ij ∂x 1 dA = 0 (1.14)
that states that the J-integral equals zero around a crack tip. Now considering a closed contour composed of Γ 1 , Γ 2 , ∆ 1 and ∆ 2 as depicted in Figure 1.3-b, Equation 1.5 becomes

J = Γ 1 ∪∆ 1 ∪Γ 2 ∪∆ 2 Wdx 2 -T ∂u ∂dx 1 ds = J Γ 1 + J ∆ 1 + J Γ 2 + J ∆ 2 = 0 (1.15)
Since the crack flanks are not subjected to any external loads:

∆ 1 Wdx 2 -T ∂u ∂dx 1 ds = ∆ 2
Wdx 2 -T ∂u ∂dx 1 ds = 0 (1.16) so that Equation 1.15 becomes:

J = Γ 1 ∪∆ 1 ∪Γ 2 ∪∆ 2 Wdx 2 -T ∂u ∂dx 1 ds = J Γ 1 + J Γ 2 = 0 (1.17)
Considering that J-integral is positive-definite for a contour oriented in the counter-clockwise direction [4], it is possible to write:

J = J Γ 1 -J Γ 2 =0 (1.18) or J Γ 1 = J Γ 2 (1.19)
and then:

Γ 1 Wdx 2 -T ∂u ∂dx 1 ds = Γ 2 Wdx 2 -T ∂u ∂dx 1 ds (1.20)
This result demonstrates the path-independence of the J-integral for a contour free of external loads and an elastic material.

Moreover, J-integral is equal to the variation of the potential energy Π during a crack extension. It is shown by considering a two-dimensional cracked body Ω which external contour is denoted Γ 0 , and Γ 0,F is the portion of Γ where external loads are applied, as depicted in Figure 1.3. Then, the potential energy Π writes:

Π = Ω W dΩ - Γ 0,F T i u i ds (1.21)
Now considering any contour Γ surrounding the crack tip, and Γ 0 which is consisting of Γ, Γ + and Γ -as defined in Figure 1.3. If the crack lips are free of load, then Γ 0 can be reduced to Γ. A crack of length a is now implemented in Ω in the direction x 1 . Considering the local coordinate system X i attached to the crack tip. In the global coordinate system x i , X i writes X i = x i -aδ i1 , where δ i1 is the Kronecker operator. Then, the derivative with respect to a writes:

d da = ∂ ∂a + ∂X 1 ∂a ∂ ∂X 1 = ∂ ∂a - ∂ ∂x 1 (1.22)
Then, assuming that the external loads are independent of the crack length a : Finally, the following relationship can be written:

dΠ
J = - dΠ da (1.27)
For a non-linear elastic material, this definition of J is equivalent to the strain energy release rate [9], corresponding to the variation of the elastic energy due to a crack extension. This property is depicted in Figure 1.4 in the case of a solid subjected to an imposed displacement (Figure 1.4-a) or load (Figure 1.4-b.).

Extension to elastic-plastic materials -J as a fracture parameter

Griffith theory (Figure 1.4) can be extended to elastic plastic materials in the case of a proportional loading only. In such cases, the behavior of an elastic plastic material can be considered as non-linear elastic. In order to respect this requirement, tearing tests should be carried out under a monotonic loading and avoiding any unloads generating plasticity.

Based on these theoretical developments, it was then proposed to introduce a material critical value for J, J c . Fracture is assumed to occur when J reaches this critical value. In the case of a non-linear elastic plastic material, the hardening under an uniaxial load writes:

ε = σ 0 E σ σ 0 n (1.28)
where E is the Young's modulus, σ 0 is a reference stress and n is the hardening exponent. In 1968, Hutchinson [START_REF] Hutchinson | Singular behaviorur at the end of a tensile crack in a hardening material[END_REF] and Rice and Rosenberg [START_REF] Rice | Plane Strain Deformation Near A Crack Tip In A Power-Law Hardening Material[END_REF] showed that the solutions field at the vicinity of a crack tip can be described using analytical solutions. These fields are denoted HRR fields in reference to their authors. Introducing ε 0 = σ 0 /E, the stress field writes:

σ ij = σ 0 J ασ 0 ε 0 I n r 1 n +1 σij (θ,n) (1.29)
The strain field writes:

ε ij = σ 0 E J ασ 0 ε 0 I n r n n +1 εij (θ,n) (1.30)
The displacement field writes:

u i = σ 0 E JE ασ 0 ε 0 I n r n n +1 r 1 n +1 ũi (θ,n) (1.31)
where functions σij , εij , ũi are tabulated, and parameter I n slightly depends on the hardening exponent n. In 1990, Sharma and Aravast [START_REF] Sharma | Determination of higher-order terms in asymptotic elastoplastic crack tip solutions[END_REF] added a second order term to Equation 1.29. It writes:

σ ij = σ 0 J ασ 0 ε 0 I n r 1 n +1 σij (θ,n) + Q rσ 0 J q σ(2) ij (θ,n) (1.32)
where the first term is denoted HRR term. In Equation 1.32, q is a quantity such as |q| ≪ 1, and r and θ are polar coordinates centered at the tip. In 1991, O'Dowd and Shih [START_REF] Noel | Family of crack-tip fields characterized by a triaxiality parameter -I. Structure of fields[END_REF] established that the q exponent is negligible. Moreover, they showed that the stress component σrθ equals 0 at the crack tip for |θ| < π/2, and σrr and σθθ are roughly equal and constant. Equation 1.32 can be simplified to become:

σ ij = σ ij (r,θ) HRR + Qσ 0 δ ij (1.33)
where δ ij is the Kronecker delta. In order to respect HRR field requirements, Q values are numerically calculated at a minimum distance of r 0 =2J/σ 0 from the crack tip, which corresponds to around four times the CTOD (see below), and given by

Q = σ FE ij -σ HRR ij σ 0 θ=0 r= 2J σ 0 (1.34)
where σ FE ij is evaluated using finite element analyses. Physically, the quantity Q can be seen as an uniform hydrostatic stress surrounding the crack tip which represent the difference between the reference stress field and the actual specimen stress field. Ma [START_REF] Ma | The effects of constraint on crack tip fields and fracture toughness[END_REF] showed that the effect of the geometry on the crack initiation toughness J c can be explained using the quantity Q. Taking the example of a HY80 steel tested using three-point bending (similar to SENB) and SENT-like specimens, it is shown that the smaller Q is, the higher J c is. However, even tough Ma demonstrated a clear effect of Q on J c , the relationship between these two quantities has not been clearly established. This leads to the possible definition of a J -Q fracture locus. Figure 1.5 shows a qualitative ranking of the specimens in comparison with a cracked pipe submitted to a bending load. As one can see, the SENT specimen has the constraint Q value the closest to the pipe. Figure 1.5 -Ranking of the classical fracture mechanics specimens in the J -Q plane. [START_REF] Chiesa | Efficient fracture assessment of pipelines. A constraint-corrected SENT specimen approach[END_REF] 1. Fracture mechanics applied to pipe design

Experimental measurement of J

In the case of a tearing test complying with the proportional load condition and in absence of crack extension, the J value can be expressed from the area below the experimental load-crack opening displacement curve, since this area corresponds to the energy received by the specimen. Then, it is possible to write a relationship between J and this area [START_REF] Rice | Some further results of J-integral analysis and estimates[END_REF][START_REF] Sumpter | Method for laboratory determination of Jc. In: Cracks and fracture[END_REF][START_REF] Ernst | Estimation on J-integral and tearing modulus T from a single specimen test record[END_REF]:

J = J e + J p = K 2 I E ′ + ηU p Bb with E ′ = ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩
E in plane stress E 1 -ν 2 in plane strain (1.35) where U p is the plastic component of the area under the curve load-crack opening displacement, B is the width of the specimen, b is the remaining ligament, K I is the stress intensity factor. η is a geometry dependent non-dimensional parameter. In the case of standardized CT or SENB specimens it is given by the ASTM-1820 standard [START_REF]Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness KIC of Metallic Materials[END_REF]:

η = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ 2+0.522(W -a)/W for CT specimens 2
for SENB specimens (1.36) where a is the crack length and W the specimen width (b = Wa). Values of η for SENT specimens will be discussed below. K I is expressed as a linear function of the load ; the proportionality factor depends on specimen geometry and on crack length.

In Equation 1.35, quantities J e and J p are valid for stationary cracks or for a limited crack extension only. In the case of a ductile tearing test, where crack extension is large, they must be corrected to take the modification of shape and actual material response into account. Therefore, an incremental formulation of J has been proposed in [START_REF]Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness KIC of Metallic Materials[END_REF]. One assumes that the updated crack length and dissipated plastic energy are available at various load steps referred to as (k) in the following. In that case J (k) can be J (k) = J e(k) + J p(k) (1.37) where the elastic component J e(k) is still given by

J e(k) = K 2 I(k) E ′ (1.38)
The plastic component J p(k) , is given by [START_REF]Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness KIC of Metallic Materials[END_REF] J

pl(k) = J p(k-1) + η (k-1) b (k-1) B N A p(k) -A p(k-1) • 1 - γ (k-1) b (k-1) a (k) -a (k-1) (1.39)
where the factor γ (k-1) is calculated from

γ (k-1) = ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ -1+η (k-1) - ⎛ ⎜ ⎜ ⎜ ⎜ ⎝ b (k-1) W η ′ (k-1) η (k-1) ⎞ ⎟ ⎟ ⎟ ⎟ ⎠ ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ (1.40) with η ′ (k-1) = W dη da (k-1) (1.41)
Simplified equations for γ are given by the ASTM standard [START_REF]Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness KIC of Metallic Materials[END_REF].

It is worth noting that Q cannot be experimentally determined and that it must be numerically evaluated.

CTOD concept

The CTOD concept has been introduced by Wells [START_REF] Aa | Application of fracture mechanics at and beyond general yielding[END_REF] as a quantity originally denoted Crack Opening Displacement (COD). The name has been changed later to distinguish the quantity from the Crack Mouth Opening Displacement (CMOD). When he introduced the J-integral concept in 1968, Rice [4] proposed a linear relationship between J and CTOD in the case of a elastic perfectly plastic material (no hardening):

J = σ YS δ (1.42)
where σ YS is the material yield strength. In the same year, Rice and Rosengren (using the HRR field) [START_REF] Rice | Plane Strain Deformation Near A Crack Tip In A Power-Law Hardening Material[END_REF] extended Equation 1.42 to elastic plastic materials, and obtained a general relationship between J and CTOD:

J = mσ YS δ (1.43)
where m is a parameter depending on the actual stress state (m = 1 for plane stress conditions). In their work, the CTOD was defined as the intersection between the deformed lips and the two 45 • angle lines from the crack tip. Using Compact Tension (CT) specimens, Hollstein and Blauel [START_REF] Hollstein | On the relation of the crack opening displacement to the J-integral[END_REF] showed that m has values between 1 and 2.

The CTOD may also be used as a fracture parameter. Fracture is then assumed to occur when the CTOD reaches a critical value CTOD c .

The SENT specimen 1.2.1 Introduction

Both Compact Tension (CT) and Single Edge Notched Bending (SENB) are common specimens. Their use is ruled by international codes and standards, more particularly the ASTM-E1820 [START_REF]Standard Test Method for Measurement of Fracture Toughness[END_REF] and British Standard 7910 [START_REF]Guide to Methods for Assessing the Acceptability of Flaws in Metallic Structures[END_REF]. These specimens are both deep cracked with an initial crack length-to-thickness ratio (a 0 /W) being in the range 0.5-0.7, and subjected to a bending load. It results in a high crack-tip constraint condition (i.e. high value of Q), whereas shallow surface crack in pipe are assumed to produce low constraint conditions. As a remedy, the Single-Edge-Notched Tension (denoted SENT) specimen has been introduced. Subjected to a tensile loading, this specimen presents a low crack tip constraint condition. A numerical analysis based on FEA is proposed in order to validate the consistency of the SENT specimen in the case of Engineering Critical Assessment for shallow notched pipelines.

As mentioned above, the use of the CT and SENB specimens is framed by international standards, such as the ASTM-E1820 [START_REF]Standard Test Method for Measurement of Fracture Toughness[END_REF] and BS-7448 [START_REF]Fracture mechanics toughness test. Pt. 1: Method for determination of KIc, critical CTOD and critical J values of metallic materials[END_REF]. However, these do not apply to the SENT specimen which makes its use not straightforward, especially because different recommended practices exist: Specimens. June, 2009. [START_REF] Shen | Measurement of J-R Curves Using Single-Specimen Technique on Clamped SE(T) specimens[END_REF] It is also important to note that a standard was published in year 2014 [START_REF] Pirsarski | Development of a british standard single edge notch tension (sent) test method (bs8571)[END_REF]. The latter is proposed by British Standard and is untitled BS 8571:2014 -Method of test for determination of fracture toughness in metallic materials using single edge notched tension (SENT) specimens. It was actually published to fill the lack of standard, and is mainly based on the recommended practice DNV-RP-F108. In the following the use and applicability of the SENT specimen is discussed.

Recommended practices in the literature

Specimen geometry

A typical SENT specimen is depicted in Figure 1.6. It appears like a SENB specimen with a cross section S = B × (Wa 0 ), where B is the specimen width, W is the specimen thickness and a 0 is the initial crack length.

1. Fracture mechanics applied to pipe design [START_REF]Recommended Practice RP-F108. Fracture control for pipeline installation methods introducing cyclic plastic strain[END_REF] suggests the use of a rectangular cross section with a thickness, denoted W , being half the specimen width, denoted B, whereas ExxonMobil and CANMET suggest using a square cross-section with B = W . The first configuration is more consistent with fracture mechanics considerations, since enlarging the width of the specimen enables to obtain a better plane strain state condition at the specimen middle width.

In [START_REF]Recommended Practice RP-F108. Fracture control for pipeline installation methods introducing cyclic plastic strain[END_REF], specimens may be either pin-loaded or clamped. This configuration was chosen by Exxon-Mobil and Canmet since it enables to avoid any rotation of the specimen within the loading device. A minimal distance between the clamped regions, denoted H, is required to ensure no effect of the boundary conditions of the stress state at the vicinity of the notch. In [START_REF]Measurement of Crack-Tip Opening Displacement (CTOD) Fracture Resistance Curves Using Single-Edge Notched Tension (SENT) Specimens[END_REF] and [START_REF] Shen | Measurement of J-R Curves Using Single-Specimen Technique on Clamped SE(T) specimens[END_REF], this distance is H = 10W . However, in cases where the amount of material is limited, it may be required to machine shorter specimens with H<10W . In such cases, the actual H distance shall be taken into account since it will have an impact on data processing (unloading compliance method, η parameter determination).

In addition, side grooves are required when the unloading compliance method is used to estimate the crack advance. More details are given in the following section. Typically, the distance between the root of the side grooves, denoted

B N , is B N =0.90 × B.

Loading condition

Clamped (H = 10W ) Clamped (H = 10W ) Clamped (H = 10W ) or pin-loaded

Testing procedures

DNV-RP-F108 is based on the multi-specimens method whereas ExxonMobil and CANMET are based on the single-specimen method. The first requires a minimum of six valid tests to described the material J-R curve, each test being a single point of the curve defined by its crack advance ∆a and toughness J. The determination of the initial crack size a 0 and ∆a is done by a series of post mortem optical measurements on the fracture surface. The procedure is described in ASTM-1820 [START_REF]Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness KIC of Metallic Materials[END_REF]. Basically, it consists in an average value of the crack lengths measured at nine points defined across the specimen width as depicted in Figure 1.8, where the light grey area represents the total crack advance during during the tearing process and the blue area represents the remaining ligament. The crack length a crack is calculated as the sum of the initial crack size a 0 , and the crack advance during the tearing process a tearing . Identically, a 0 is defined as the sum of the initial machined notch depth a notch and the crack advance during the fatigue precracking a precracking . Figure 1.8 -Measurement of the crack extension following ASTM-E1820 practices.

a precracking = 1 8 × ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ a precracking,1 + a precracking,2 2 + 8 i=2 a precracking,i ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ (1.44) a tearing = 1 8 × ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ a tearing,1 + a tearing,2 2 + 8 i=2 a tearing,i ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ (1.45) a 0 = a notch + a precracking (1.46) a f = a notch + a tearing (1.47)
In a single-specimen procedure, the material J or CTOD R-curve can be fully determined using a single valid test. In such case where the material toughness must be calculated for different amount of tearing, the crack advance is evaluated using the elastic unloading compliance method, based on the loss of rigidity of the specimen during the tearing process. Details are given hereinafter. DNV does not give strict recommendations about the initial crack-size-to-thickness ratio a 0 /W for the assessment of cracked pipes. According to DNV, the R-curve is crack size-independent, as long as 0.2 ≤ a 0 /W ≤ 0.5. This conclusion derived from a study by Nyhus et al [START_REF] Nyhus | Fracture Control-Offshore Pipelines: Experimental Studies on the Effect of Crack Depth and Asymmetric Geometries on the Ductile Tearing Resistance[END_REF] where the effect of the crack depth on the ductile tearing resistance has been studied.

In particular, SENT tests have been performed on a 12 inches X65 parent material with three different a 0 /W ratios (0.2, 0.35 and 0.5). The CTOD R-curves derived from these tests are depicted in Figure 1.9. One can see that for small value of tearing (approx. ≤1 mm), the CTOD R-curve is actually crack size independent. However, the curves seem to separate for higher values. As an example, for a tearing value of 1.5 mm, the difference for the CTOD values between a 0 /W =0 .25 and a 0 /W =0 .5 is approximately of 15%. An identical difference (about 15%) is shown in another study performed on a 13%Cr parent material for a 0 /W =0.25 and a 0 /W =0.5 (Figure 1.9-b). However, DNV recommendation for the maximum allowable crack extension being of 1 mm, this difference may be not significant since only low values of tearing are considered.

Kang et al [START_REF] Kang | Influence of Constraint on J-resistance Curves for an X100 Pipe Steel[END_REF] conducted a study on the constraint effect on the R-curve, and different results have been presented. In particular, the effect of the initial crack depth appears to be more pronounced. In this study, a series of SENT tests has been performed on shallow (a 0 /W =0.2) and deep (a 0 /W =0.5) specimens. The specimens were prepared by fatigue precracking and EDM notched with a fine wire of 0.10 mm diameter. When comparing the R-curves (see Figure 1.10), one can clearly see that shallow specimens produce higher J R-curves. Also, it is shown that the preparation of the specimen has a slight effect on the J R-curve, with EDM notch specimen producing slightly higher J R-curves.

From these results, the two main conclusions can be drawn:

• The a 0 /W ratio has an influence of the R-curve, in particular for tearing length greater that 0.8 mm. Based on existing experimental comparisons, the range proposed by ExxonMobil (0.25-0.35) seems to be the most relevant. For comparison, it is also of interest to remind that for workmanship type criteria, a 0 /W ratio is around 0.35 for onshore pipelines and 0.15 for deep water pipelines. • If the interest is in a ductile tearing criterion rather than an initiation criterion, Kang [START_REF] Kang | Influence of Constraint on J-resistance Curves for an X100 Pipe Steel[END_REF] and Moore [START_REF] Moore | The Effect of Notch Sharpness on the Fracture Toughness Determined From SENT Specimens[END_REF] demonstrated that very similar results are obtained with fatigue precracked and EDM notched specimens. However, before using EDM notched SENT specimen, one shall ensure that the minimum pipeline design temperature is in the upper-shelf by establishing the Charpy transition curve as EDM notches tend to generate lower stresses at low loading levels for which failure occurs in the brittle regime.

Experimental CTOD measurement

As introduced herein before, the CTOD is the measurement of the crack opening displacement at the intersection of the two 45 • lines and the crack flanks. It is denoted δ 90 , as depicted in Figure 1.11. Following this definition, it is not possible to experimentally measure δ 90 using conventional method. Therefore, the following alternative definitions are proposed:

• CTOD from J : CTOD = mJ/σ y • δ 5 : It corresponds to the opening displacement measured between two points located over a distance of 5 mm at the level of the initial crack tip. This measurement method is particularly adapted when the Digital Image Correlation (DIC) method is used (see [START_REF] Schwalbe | EFAM GTP 02 -The GKSS Test Procedure for Determining the Fracture Behaviour of Materials[END_REF] and [START_REF] Verstraete | Determination of CTOD resistance curves in side-grooved Single-Edge Notched Tensile specimens using full field deformation measurements[END_REF]). • CTOD double-clip : The CTOD measurement using the double clip gage method is introduced in the 2000 version of DNV-OS-F101 [START_REF]Submarines Pipelines Systems[END_REF], ExxonMobil [START_REF] Fairchild | A Multi-Tiered Procedure for Engineering Critical Assessment of Strain-Based Pipelines[END_REF] and Ghent University [START_REF] Verstraete | Determination of CTOD resistance curves in side-grooved Single-Edge Notched Tensile specimens using full field deformation measurements[END_REF].

CTOD from J

In the 2010 released version of the DNV-OS-F101, equations are provided to calculate the CTOD from J value. J is calculated using CMOD measurement according to DNV-RP-F108. However, according to DNV, Equation 1.48 gives a conservative measure of the CTOD and shall not be used the other way around to calculate J from CTOD. Indeed, this procedure is based on SENB tests results and not properly validated for SENT specimens [START_REF] Moore | Validation of Methods to Determine CTOD from SENT Specimens[END_REF].

Shen and Tyson [START_REF] Shen | Evaluation of CTOD from J-integral for SE(T) specimens[END_REF] offered a revision to the method proposed in DNV OS F101 [START_REF]Submarines Pipelines Systems[END_REF] and give a proper m definition for SENT specimens notched with a crack depth a/W between 0.2 and 0.5. Their method depends on the strain hardening exponent N of a elastic plastic power-law, and the ratio of the load P to the reference load P Y which writes:

P Y = B N (W -a) σ YS + σ UTS 2 (1.51)
where B N is the specimen net thickness (for side-grooved specimens). Then, m parameter takes values depending on the value of the current load P with regards to the reference load P Y :

m = m c forP ≤ P Y m = m c -m p P P Y -1 forP>P Y (1.52)
where

m c = A 1 a W + A 2 (1.53) m p = B 1 a W + B 2 (1.54)
where the coefficients A 1 , A 2 , B 1 and B 2 derived from a series of elastic-plastic FEA calculations [START_REF] Shen | Evaluation of CTOD from J-integral for SE(T) specimens[END_REF] and write:

A 1 = -0.1293 + 0.1152N -0.00986N 2 +0.000263N 3 (1.55) A 2 =3 .0867 -0.297N +0.0194N 2 -0.000427N 3 (1.56) B 1 =1 .0169 -0.0634N +0.00567N 2 -0.000200N 3 (1.57) B 2 =0 .6969 -0.1216N +0.01487N 2 -0.000393N 3 (1.58)
with N being again the hardening exponent of the material power-law that writes ε =(σ/σ 0 ) N .

Double-clip gage method

The double-clip gage method was first introduced in DNV-OS-F101:2000 [START_REF]Submarines Pipelines Systems[END_REF]. It enables to calculate the CTOD using a pair of clip gages mounted above the notch which measure the crack opening displacement at the heights h 1 and h 2 above the specimen crack mouth, as depicted in Figure 1.12. The equation introduced in [START_REF]Submarines Pipelines Systems[END_REF] writes

CTOD = 1 -ν 2 K 2 I 2σ Y E + V 1,p - a 0 + h 1 h 2 -h 1 V 2,p -V 1,p (1.59)
where K I is the stress intensity factor at the subject load, and V 1,p and V 2,p are the plastic parts of the clip gage displacements measured at h 1 and h 2 . Therefore, the CTOD can be understood as the sum of an elastic and a plastic component, ie CTOD = CTOD e + CTOD p with

CTOD e = 1 -ν 2 K 2 I 2σ Y E (1.60)
and

CTOD p = V 1,p - a 0 + h 1 h 2 -h 1 V 2,p -V 1,p (1.61)
CTOD p is therefore computed from simple geometrical considerations assuming that the initial crack (length a 0 ) does not deform. However, the relationship for the elastic component was developed for fracture toughness tests based on SENB specimens, and may not be adapted for SENT specimens. It is basically the relationship given in Equation 1.48 with m = 2.

Later, ExxonMobil introduced their procedure for a CTOD R-curve test based on SENT specimen (see [START_REF]Measurement of Crack-Tip Opening Displacement (CTOD) Fracture Resistance Curves Using Single-Edge Notched Tension (SENT) Specimens[END_REF]). They proposed to use the double-clip gage method but without separating in an elastic and a plastic component. The CTOD, or δ 0 , is then defined as the value of the crack opening displacement measured at the original crack tip position, which is directly given by:

CTOD = V 1 - h 1 + a 0 h 2 -h 1 (V 2 -V 1 ) (1.62)
where V 1 and V 2 are the crack opening displacements measured at h 1 and h 2 above the specimen surface. Moreover, the CMOD, or δ M , measurement is also directly given by:

CMOD = V 1 - h 1 h 2 -h 1 (V 2 -V 1 )
(1.63) [START_REF] Verstraete | Determination of CTOD resistance curves in side-grooved Single-Edge Notched Tensile specimens using full field deformation measurements[END_REF] proposed other relationships to determine both CMOD and CTOD from double-clip gage method. However, this definition of the CTOD is not the same as for ExxonMobil approach (which Figure 1.12 -An example of a double clip gages mounted on a fracture toughness specimen. From [START_REF] Moore | Validation of Methods to Determine CTOD from SENT Specimens[END_REF].

explains why different formulas are used.). Here, the CTOD is defined as the displacement measured at the intersection between the lips and the two 45 • angle lines from the current crack tip as defined by [4]. The CTOD value is given by:

CTOD = 2 V 2 (a 0 + h 1 ) -V 1 (a 0 + h 2 ) (V 2 -V 1 ) -2 (h 2 -h 1 ) (1.64)
where V 1 and V 2 are the crack opening displacements measured at h 1 and h 2 above the specimen surface. They also provided an equation identical to Equation 1.63 which enables to directly measure the CMOD:

CMOD = V 1 h 2 -V 2 h 1 h 2 -h 1 = V 1 - h 1 h 2 -h 1 (V 2 -V 1 ) (1.65)
The double-clip gage method is based on simple geometric assumptions, and trigonometric calculations. Equations 1.62-1.65 are valid only if the following assumptions are satisfied:

• there is no modification in shape of the initial crack flanks, i.e. the length between the crack mouth and initial crack tip remains constant, • the opening of crack is symmetrical with respect to the crack plane.

A demonstration of those equations is given in Appendix B. 1. Fracture mechanics applied to pipe design

Comparisons of the methods

It is difficult to a priori give any conclusions on the validity of each definition, or whether one is better to the other one. [START_REF] Moore | Validation of Methods to Determine CTOD from SENT Specimens[END_REF] conducted a comparative experimental campaign on SENT specimens in order to compare them.

The tests were performed on a API-5L X65 parent material representative of offshore pipelines, with SENT specimens of thickness W = 23 mm, and B =2W (rectangular cross-section). Details are given in the related paper. Comparisons are made between the CTOD obtained using the notch replica method (see Figure 1 From results given in Figure 1.15, [START_REF] Moore | Validation of Methods to Determine CTOD from SENT Specimens[END_REF] concluded that the methods which most closely matched the replica method were the double-clip method, finite element modeling and Shen and Tyson equation. However, this conclusion shall be put into perspectives, seeing as the scatter in the results and the significant relative errors between physical measurements and other methods. Thus, the relative error for the double-clip method is up to about 40% for shallow notched specimens (a 0 /W =0.1), and Shen and Tyson equation underestimates the CTOD by 25% for shallow notched specimens with a 0 /W =0.1, and 40% for deep notched specimens with a 0 /W =0.6.

From results depicted in Figure 1.16, they concluded that Shen and Tyson equation matches the most closely the double-clip method results for CTOD between 0.6 mm and 2.75 mm, and with a 0 /W of 0.3 and 0.5. On the other hand, they observed that both DNV-OS-F101 (2010) and Moreira and Donato equations considerably under-estimate the double-clip method. According to Moore and Pisarski, it reflects the fact that these methods have been developed to calculated CTOD from J using SENB specimens rather than SENT specimens.

In this study, two dimensional plane strain FEA simulations have been performed in order to compare methods that were not included in [START_REF] Moore | Validation of Methods to Determine CTOD from SENT Specimens[END_REF]. Two SENT specimens with W = 14 mm, and a 0 /W =0.25 and a 0 /W =0.5 were meshed. A constitutive law derived from tests on a X65 steel grade was used, and a GTN damage model was used so that the crack could propagate. More details on the material model and the simulation strategy are given in Chapter 5. The J-integral values were computed during the simulations using de Lorenzi method [START_REF] Delorenzi | On the energy release rate and the J-integral for 3d crack configurations[END_REF]. The convergence of J value was checked on the contour.

x y z Figure 1.17 -Mesh of the SENT for CTOD comparisons. The region highlighted in red corresponds to the contour where J is calculated. Fracture mechanics applied to pipe design with a good accuracy. However, it is also observed that CTOD calculated using DNV relationship underestimates δ 90 . Considering that, as shown in Figure 1.18, the level of plastic strain is greater than 15% within the area where J is calculated as soon as CMOD reaches 1 mm, the hypothesis of small deformations are not met. As a consequence, the independence of J is not guarantee, which may explain the significant error in the result.

Double-clip Ghent

Experimental J-integral calculation for SENT specimens

The method to compute J from experiments which was presented above, and which is well validated for CT and SENB specimens, can be applied to SENT specimens. Expressions for the determination of the stress intensity factor K I and shape factor η are however needed as well as functions relating compliance and crack length if the single specimen method is to be used.

Calculation of K I

Following CANMET K I can be expressed by:

K I (k) = P (k) √ πa (k) B N W F a (k) /W (1. 66
)
where P is the load. In Cravero and Ruggieri [START_REF] Cravero | Estimation procedure of J-resistance curves for SE(T) fracture specimens using unloading compliance[END_REF] the following expression is proposed:

K I (k) = P (k) ) B N √ W G a (k) /W (1.67)
F a (k) /W and G a (k) /W define non-dimensional stress intensity factor solutions which depend on the specimen geometry, the crack size and the loading conditions (clamped or pin-loaded). It was checked that both functions give very similar results.

Plastic factor η p

As presented before in the relationship 1.35, J p is related to U p , the plastic area under the load -CMOD curve, and the plastic factor η p . The evaluation of this factor is based on empirical expressions based on finite element analyses. In DNV-RP-F108 [START_REF]Recommended Practice RP-F108. Fracture control for pipeline installation methods introducing cyclic plastic strain[END_REF], two equations are given for both clamped or pin-loaded specimens for the calculation of η p . It is defined as a function of the ratio a/W and the ratio B/W for 1 ≤ B/W ≤ 5. For clamped specimen, η p is given as

η DNV,c = 196.719e
Cravero and Ruggieri [START_REF] Cravero | Estimation procedure of J-resistance curves for SE(T) fracture specimens using unloading compliance[END_REF] derived another set of expressions for η p , both for clamped and pinloaded specimens, from a series of three dimensional finite element analyses with initial crack length a 0 /W within the range 0.1 ≤ a 0 ≤ 0.7. These expressions are only functions of the ratio a/W . For clamped specimens, it is given by η However, one must take care in using Equation 1.74 which was developed in the context of the incremental method.

In this work, a FEM based study was conducted in order to benchmark the different definitions of η. Abaqus software has been used to perform three dimensional simulations a SENT specimens with both square (B = W ) and rectangular (B =2W ) cross sections. An elastic plastic constitutive law derived 1. Fracture mechanics applied to pipe design from tests on a X65 steel grade was considered, and meshes with the following crack length were built : a 0 /W = [0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.60, 0.70]. The models consisted in three-dimensional meshes with fully integrated linear 8-nodes brick elements C3D8, and only 1 /4 of the specimen was meshed, as depicted in Figure 1.20. In the literature the calculation of J-integral is not clear. In particular, it is not explicitly stated whether a maximum value or an average value along the crack front shall be used. Therefore, these two values were calculated in this study. The average J-integral value has been calculated taking into account the thickness of each element:

J average = 1 B Jdz (1.75)
where z corresponds to the coordinate of the integration contour in the specimen thickness direction, z = 0 mm being the free surface in plane stress conditions and z = 5 mm being the mid-thickness of the specimen close to plane strain conditions. Two configurations have been simulated: B = W and B =2W . Figure 1.21-b shows the evolution of J as function of CMOD. A significant difference (+26.5% at CMOD = 2.2 mm) is measured between the average value and the maximum value. However, results show that this difference is reduced for a B =2W specimen (+13.5% at CMOD = 2.2 mm) but should still taken into account when J is used in integrity analyses. In Figure 1.21-a, a comparison between the maximum and average J-integral values is depicted. It is shown that J value is maximal at the mid-thickness position where the highest constraint level is found. On the other hand, the J value is minimal at the free surface which exhibits the lowest constraint level. The calculated J-value by Abaqus, denoted here J Ab , is composed of both elastic and plastic components, such as J Ab = J e + J p . Since only J p is function of η p , a post-processing tool was developed in order to isolate J e from J p so that η p could be easily calculated solving Equation 1.35 for given J p , U p and a, where a is the crack length in the stationary crack simulations. Examples of simulations are shown in Figure 1.22 for B = W and B =2 W and various a 0 /W ratios. It is shown that the relation between J p B(Wa) and U p is linear for a given geometry. The slope corresponds to η. The obtained values for η are then plotted as a function of a/W for the clamped geometries (B = W and B =2W ) in Figure 1.23 (η corresponding to the maximum value of J p ) and Figure 1.24 (η corresponding to the average value of J p ). On the one hand, it is shown that the formulas proposed by DNV (1.23-a) correspond to the values of η based on the maximum value of J p (note that the agreement is good in the validity range proposed by DNV). On the other hand, the computed values of η based on the average value of J p closely correspond to the expression proposed by Cravero and Ruggieri (Figure 1

Crack growth measurement using the unloading compliance method

Different methods for the measurement of the crack extension exist, depending on whether the procedure implies the single-specimen or multiple specimens. In the case of a multi-specimen method, the measurement of the final crack extension ∆a is performed by means of optical observations, using the ASTM-1820 procedure. In the case of a single-specimen procedure, the measurement of the crack growth relies on the unloading elastic compliance method.

The compliance method relies on the decrease of the specimen stiffness due to the crack propagation. The compliance of the specimen is defined as

C (k) = ∆CMOD ∆F (1.76)
where ∆CMOD and ∆F are the variations of the CMOD and the load during the k th unloading sequence.

A non-dimensional effective compliance is introduced and writes

u (k) = 1 1+ B e C (k) E ′ (1.77)
where

C (k) = ∆CMOD (k) /∆P (k)
is the compliance for the k th unload reload sequence measured on the

CMOD-Load curve, B e = B -(B -B N ) 2 /B and E ′ = E/ 1 -ν 2 .
The corresponding a/W ratio at the k th load/ unload sequence is calculated using a polynomial function of u (k) in the form

(a/W ) (k) = 8 j=0 α j u j (k) (1.78)
where the coefficients α j mainly depends on the loading conditions. Cravero and Ruggieri propose in their paper different sets coefficients for Equation 1.78 derived from elastic FEA under plane-strain conditions. In their study both pin-loaded specimens and clamped specimens with different H/W ratios were considered. It is shown that for pin-loaded specimens, the compliance is independent on the distance between the two-loading points. However, for clamped specimens they show that the compliance is highly dependent on the clamping distance H/W, in particular for deep notched specimens (a/W ≥ 0.4), and essentially independent of H/W for shallow notched specimens (a/W ≤ 0.2). The coefficients are given in Table 1.1. [START_REF] Shen | Evaluation of CTOD from J-integral for SE(T) specimens[END_REF] proposes another set of coefficients derived from a series of FEA using a plane stress model instead of a plane strain model. They made that choice based on a previous study [START_REF] Guowu Shen | Estimation of 3-D SE(B) Fracture Parameters using 2-D Equations[END_REF] which showed that the actual CMOD compliance of a SE(B) specimen is closer to plane stress than plane strain. The coefficients are given in Table 1.2.

[27] also introduces a new set of coefficients, given in Table 1. [START_REF] Kanninen | Elastic-Plastic Fracture Mechanics for Two-Dimensional Stable Crack Growth and Instability Problems[END_REF]. No details are given on how they were obtained. A numerical study has been conducted to check the consistency of the proposed sets of parameters. Both plane strain two-dimensional and three-dimensional finite element analyses have been carried out. The 3D model consists in a SENT specimen following ExxonMobil recommendations with a square cross-section with B = W = 14 mm. Side-grooves were meshed so that a total width reduction equals to 10% was reached. A crack-tip radius representative of the EDM process was meshed so that the crack tip radius is of 55 µm. A view of a typical mesh is depicted in Figure 1.25. A purely elastic material was considered with an Young modulus of 207 GPa and a Poisson's coefficient of 0.3. The specimens were subjected to a force equal to the yielding load. The specimens were then unloaded to reach a zero force. Since no plastic deformation occurred, the loading path during the loading and unloading were perfectly superimposed so that an unique value of the slopes was obtained for the entire sequence. The compliance was then calculated by fitting a fifth order polynomial function. Coefficients are given in Table 1.4.

Results depicted in Figure 1.26 show that all the fitting polynomials functions properly evaluate the crack advances over the whole range. The best fit is obtained using the function fitted on the 3D FEA. Canmet equation slightly overestimates the actual a/W value, with an average error of about 2% over the range a/W = [0.2, 0.8]. Results obtained using Ruggieri and Cravero equation also show a good consistency with the actual values, with an average error of about 3.5%. The worst evaluation was obtained using ExxonMobil fitting polynomial function with an overestimation of 9% for small a/W = 0.2 and an overestimation of 6% for a/W = 0.7. Between these two values, the relative error is linearly decreasing.

However, as pointed out by [START_REF] Shen | Evaluation of CTOD from J-integral for SE(T) specimens[END_REF], it is important to keep in mind that these results are obtained considering an elastic material to measure the compliance. Such an approach does not take into account the development of a plastic strain field at the vicinity of the crack tip during the blunting process. Such a modification of the material properties (hardening) and the specimen geometry (blunting) produces an increase of the specimen stiffness. Considering Equation 1.78, this phenomenon will result in an underestimation of the actual experimental crack growth.

As a remedy [START_REF] Shen | Evaluation of CTOD from J-integral for SE(T) specimens[END_REF] proposes to correct the measured specimen compliance to take the plastic devel-

C c(i) = C (i) × F r(i) (1.79)
where C (i) is the experimental measured compliance on the Force-CMOD curve at the i th unloading, C c(i) is the corrected compliance, F r(i) is the correction factor depending on the current load at the unloading point. This correction factor writes:

F r(i) = 1 1 -0.165 a 0 W P (i) P Y (1. 80
)
where P Y = B N (Wa 0 ) σ Y is the limit load for the specimen. It derives from a series of both plane stress 2D and 3D FEA on clamped SENT specimen with H/W = 10 and a/W from 0.2 to 0.5. Three strain hardening exponents, namely n = 10, 15 and 30, were considered to investigate the effect of the material behavior. Results are given in Figure 1.27. They show a dependence on the strain hardening exponent n for P (i) /P Y ≥ 1.2 only.

A new series of 3D elastic plastic FEA was performed using Z-Set to evaluate the consistency of this correction factor. A SENT with a 0 /W was meshed as depicted in Figure 1.28 considering the geometry suggested by ExxonMobil and Canmet, i.e. a square cross section B = W = 14 mm. Side grooves were also meshed with a total width reduction of 10% (B N = 12.6 mm) so as to be as close as possible to the actual geometry. The crack type radius was set at 55 µm. Boundary conditions were applied so that the specimens were clamped. The plastic hardening behavior is described using the law than is presented hereinafter. The numerical CMOD vs load were post-processed with and without applying the Canmet correction for comparison. Figure 1.29 shows that using F r enables to limit the apparent negative crack growth. Figure 1.30 shows J-∆a curves obtained in [START_REF] Shen | Measurement of J-R curves using[END_REF] with and without correction evidencing a more consistent behavior in cases where the correction is applied (Figure 1.30).

Conclusions

In this chapter, the basis of the linear and non linear fracture mechanics have been used to justify the expressions used to evaluate the parameters of the global approaches(K, J, CTOD). The effect of the plastic constraint Q on the measured fracture toughness is observed, and justify the use of SENT specimens since these geometries show Q value close to that of a pressurized line pipe containing a defect.

The use of this specimen is relatively recent with regards to others standard geometries such as CT or SENB. Different recommended practices exist (ExxonMobil, DNV, CANMET). A norm dedicated to the SENT specimen, namely BS8571, has also been identified and is based on the multi-specimen procedure introduced in DNV-RP-F108 [START_REF]Recommended Practice RP-F108. Fracture control for pipeline installation methods introducing cyclic plastic strain[END_REF]. Finite element analyses were performed in this chapter in order to benchmark the recommended expressions:

• The evaluation of CTOD will be as per ExxonMobil definition, i.e. double-clip gages; • Cravero formulation for the determination of the shape factor η allows to correctly evaluate the average value of J-integral along the crack front. In the following, this expression is used. • Finally, the elastic unloading compliance method will be used to evaluate the crack advance during tearing tests on SENT specimens. A polynomial function has been identified based on finite element analyses, and is associated to a rotation correction factor to correctly measure the crack advance.

Résumé en français

Les méthodologies d'analyse de défauts dans les canalisations permettent de déterminer la taille maximale de défaut admissible pour des conditions de chargements définies, ou les conditions de chargement ultimes admissibles pour un défaut donné, en utilisant un critère prédéfini. L'utilisation de ces méthodologies, notées ECA en anglais pour Engineering Critical Assessment est classique pour la conception ou l'analyse d'oléoducs. Le British Standard BS 7910 et le standard Det Norske Veritas DNV-OS-F101 comptent parmi les plus utilisés dans l'industrie pétrolière. A l'origine issues des travaux sur le nucléaire, ces approches se montrent limitées pour la conception d'oléoducs pour lesquels des chargements en flexion peuvent être rencontrés et des niveaux de contraintes au-delà de la limite d'élasticité peuvent être atteints.

Les spécifications de conception permettent aux canalisations de résister aux chargements opérationnels tels que la pression interne ou externe, et aux chargements principalement en flexion liés à leur installation. Cependant, l'apparition de défauts dans les soudures de raboutage peuvent réduire la résistance d'une canalisation, et l'utilisation de procédures ECA garantit l'intégrité de la structure.

Ce chapitre introduit les méthodologies présentées par ExxonMobil et le Pipeline Research Council International (PRCI). Celles-ci consistent en différents niveaux d'analyse basés sur le concept de l'approche tangentielle, où la taille maximale de défaut admissible est identifiée en égalisant la courbe de chargements de la structure (dite crack-driving force) et la courbe de résistance du matériau (dite R-curve). Des modèles simplifiés et conservatifs sous forme de tableaux ou d'expressions analytiques ont été développés pour faciliter l'estimation de la déformation critique pour une canalisation comportant un défaut. Deux types d'approches existent : (i) celles qui cherchent à identifier le chargement critique à l'amorçage d'un défaut, et (ii) celles qui cherchent à évaluer le niveau de chargement qui conduira à la rupture de la structure. Ces dernières sont basées sur des modèles aux éléments finis, dont l'utilisation n'est pas simple et requiert un niveau d'expertise avancé. La question de la pertinence de ces méthodologies complexes est alors soulevée.

Engineering Critical Assessment

An Engineering Critical Assessment (ECA) is a procedure to define either the maximum allowable defect size for expected load conditions, or the maximum allowable stress or strain levels for an assumed defect acceptance criterion.

The use of ECA in pipeline projects is common practice. The British Standard BS 7910 [START_REF]Guide to Methods for Assessing the Acceptability of Flaws in Metallic Structures[END_REF] and DNV-OS-F101 [44] are considered as references in the Oil & Gas Industry. At the very beginning, ECA have been established for the assessment of pressure vessel or nuclear plants. The main difference in offshore pipelines is that the global bending is considered as a primary load condition, and the elastic limit may be exceeded in certain circumstances.

Minimum requirements for the strength capacity of the girth welds of offshore pipelines are mainly related to the need of withstanding bending loads both during installation and in operation where internal pressure causes a significant hoop stress. The strength capacity of the pipe, more specifically at the girth weld, may be reduced by circumferential defects that may result from the welding process. Common weld defects are typically lack of fusion1 , lack or excess penetration2 , gas cavities3 , slag inclusions 4 , cracks 5 , undercuts 6 , lamellar tearing 7 , or shrinking cavities 8 . Also, it is essential to perform ECA with appropriate Non Destructive Testing (NDT) methods, such a X-ray or Automatic Ultrasonic Testing (AUT).

Good Workmanship criteria mainly based on satisfactory operational considerations, have been used to define the allowable defect sizes. Good workmanship guidelines were originally developed in the late seventies for manual welding. Consequently, they do not reflect improvements over the last decades of line pipe material toughness and weldability, welding technology and equipment, etc. Then, the use of good workmanship criteria may result in over-conservative assessments that may lead to unnecessary costly and even dangerous cut-off and repairs. The adoption of ECA for defining allowable defects has met this challenge.

To simplify, an ECA is based on a relationships between a defect size and shape, material properties such as strength and toughness, and an applied load (see API-1104 [START_REF]API Standard 1104, Welding of Pipelines and Related Facilities[END_REF]). The ECA ensures that the calculated defect size limit is safe both from brittle fracture and plastic collapse using a Failure Assessment Diagram (FAD) that defines the boundaries into which unstable fracture will not occur for a given defect, material and load. Since pipelines today are manufactured using tough materials, brittle failure is no longer a potential problem, and the failure of pipelines is mainly driven by plastic collapse or cracks growth. In the first case, it means that the failure is due to the yielding of the ligament section. In the second case, it means that the material is not tough enough to contain the stable propagation of a crack. In both cases, large amounts of plastic strains are met.

Strain-Based Design

Definition

The design codes and standards traditionally focus on the operational loadings such as internal and external pressures that are likely to exist over the entire lifetime of the pipeline. Existing ECA ap-

Harsh environments

The frost heave phenomenon is an upward movement of the soil. It may occur in areas where the ground freezes during the winter months to a depth of several feet 9 . Such ground freezing can lead to the heaving of pipelines located above or adjacent to it. The forces involved can be very destructive (see Figure 2.2). The thaw settlement phenomenon is an downward of the soil. Contrary to frost heave, it may occur during the summer when ice contained in the soil unfreeze (see Figure 2.3). The seabed ice gouging occurs when floating ice parts (icebergs and sea ice ridges) drift into shallower areas and their keel comes into contact with the seabed.

Curved Wide Plate

The curved wide plate approach, mainly developed at the University of Ghent in Belgium, is based on the analysis of curved wide plate (CWP) test results. The CWP is a large scale weld tension specimen as depicted in Figure 2.5. The analytical model proposes a relationship between the average remote strain capacity ε c of 480 CWP tests and the defect area ration d = lh/Wt. Then, the tensile strain capacity is given by:

ε c = P c • R +1 1 -R 0.5 -C m • UEL• M FS C d lh Wt + C m • UEL• M FS (2.1)
where: P c is a correction factor to account for internal pressure effects within the range 0.5 -0.8 C d is a correction factor to account of the decreasing mismatch effect with increasing flaw size C m is a correction factor for weld strength mismatch variability R is the pipe metal Y/T ration UEL is the uniform elongation t is the wall thickness l is the flaw length (l =2c) h is the flaw heigth (h = a) W is the arc length of flaw or 300 mm for pipe diameter > 30 inch M FS is the weld strength mismatch factor based on flow stress (M FS = FS weld /FS pipe ) According to University of Ghent recommendations, this model can be applied only if the Charpy toughness of the weld metal and heat affected zone (HAZ) fulfil the Charpy impact requirement of 40 J average and 30 J minimum at the minimum design temperature. However, this requirement migth not be sufficient for Y/T ratios > 0.90 and UGhent suggests to replace the 40/30 J requirement by a 80/60 J requirement to cover high Y/T pipe and low thoughness girth welds. This approach does not require CTOD testing since it is assumed that the Charpy toughness requirement will ensure a CTOD of a least 0.10 mm. 2.4 ExxonMobil multi-tiered approach

Introduction

ExxonMobil introduced in 2011 [START_REF] Fairchild | A Multi-Tiered Procedure for Engineering Critical Assessment of Strain-Based Pipelines[END_REF] and revised in 2012 [START_REF] Fairchild | Advancements Regarding Capacity Prediction of Strain-Based Pipelines[END_REF] a multi-tiered procedure based on the tangency analysis to calculate the tensile strain capacity (TSC) of pipeline girth welds containing cracks, or reciprocally to determine a flaw acceptance criterion for a given remote strain. Three levels of assessment are defined, namely Level 1, Level 2 and Level 3. They shall be used in accordance with the level of accuracy required and the available data on the materials. Level 3 is based on the tangency analysis where the tensile strain capacity is determined by equating the crack driving and the resistance curve which is experimentally derived from SENT tests. On the other hand, the crack driving force is obtained from a series of finite element analyses on elastic plastic models with several fixed crack depths. Due to the complexity of performing such simulations, the simplified assessment levels 1 and 2 have been introduced under the form of sets of equations derived from Level 3 results and based on simplified assumptions regarding the material properties and geometrical parameters.

Calibration of ExxonMobil methodology

The model has been calibrated comparing the strain to failure experimentally observed and the strain to failure predicted using level 3 assessment. A limited number of six full-scale tests on line pipes were considered for calibration with diameters of 406.4 mm and 609.6 mm, and wall thickness equal to 16 mm and 20 mm. As depicted in Figure 2.7, level 3 assessments produced over-conservative results with a predicted strain capacity two or three times smaller than the measured one. It was observed that a deviation of the crack during the ductile tearing occured with an angle of about 45 • to the principle stress axis for the lower X60 grade line pipes (see Figure 2.8) leading to non-consistent and over-conservative FEA based predictions since such a phenomenon can not be predicted by the proposed FEA model.

Requirements and applicability ranges

The assessment level shall be selected depending on the available knowledge of the pipe materials and pipe geometry. Needless to say that the more data are known, the lower the conservatism is. It is important to note that at this stage, ExxonMobil model is based on the assumption that the material fracture behavior remains fully ductile. The brittle fracture mechanism is then no treated here. Other material and geometrical requirements are given hereinafter for assessment levels 1, 2 and 3.

Level 1

• The CTOD values in the weld material and the heat affected zone shall be greater than 0.1 mm at the minimum design temperature. • The misalignment shall be smaller than 3 mm.

Level 2

• Level 1 requirements. • Flaw depth: 3 mm to 5 mm. • Flaw length: 20 mm to 50 mm. • Wall thickness: 14 mm to 25 mm for X60 to X70 grades, and 15 mm to 25 mm for X80 grade.

• Hoop stress: 0 % to 80 % SMYS.

• Overmatch at tensile strength: 5 % to 60 %. • Uniform elongation: 6 % to 16 % for X60 to X70 grades, and 4.4 % to 8 % for X80 grade.

Level 3

• Level 2 requirements.

• Complete material stress-strain curve for the base material and the weld material.

Material testing of ExxonMobil approach

The basic material properties such as the elastic modulus, the yield stress, the tensile strength and the uniform elongation shall be known for the base material, the heat affected zone and the weld material. These mechanical quantities may be measured using a classical smooth round bar, except for the weld material due to the overmatching properties (see Chapter 3). The materials R-curves are obtained using SENT specimens following ExxonMobil recommendations [START_REF]Measurement of Crack-Tip Opening Displacement (CTOD) Fracture Resistance Curves Using Single-Edge Notched Tension (SENT) Specimens[END_REF], namely (see Figure 2.10):

• Clamping distance: L = 10W . • Cross section: B = W with W as close as possible to the wall thickness. • Side grooves: 5 % depth each side so that the final width is B N =0.9 × B.

• Crack depth (a 0 /W) ratio: target (a/t) + 0.1 where t is the pipe wall thickness.

• Notch location: surface notch from OD in WM or HAZ. • Fatigue precracking is not necessary as long as the EDM10 notch width is lower or equal to 0.2 mm.

According to [START_REF] Fairchild | Advancements Regarding Capacity Prediction of Strain-Based Pipelines[END_REF], the correction of 0.1 mm on the initial crack length for the SENT test results from the scatter than was experimentally observed during identical SENT tests and to ensure conservative material R-curve. Moreover, details on the SENT tests are given in Chapter 1 dedicated to the fracture mechanics for pipeline engineering applications.

Strain-based design

β i coefficients in Equation 2.5 depend on the material grades. For X60 to X70 grades, they write:

β 1 = (0.9+0.09λ) × {x 1 [Cε u λe] + x 2 [Cλe] + x 3 [Cε u e] + x 4 [Ce] + x 5 [Cε u λ] + x 6 [Cλ] + x 7 [Cε u ] + x 8 [C] + x 9 [ε u λe] + x 10 [λe] + x 11 [ε u e] + x 12 [e] +x 13 [ε u λ] + x 14 [λ] + x 15 [ε u ] + x 16 } β 2 = (0.9+0.09λ) × {x 17 [Cε u λe] + x 18 [Cλe] + x 19 [Cε u e] + x 20 [Ce] + x 21 [Cε u λ] + x 22 [Cλ] + x 23 [Cε u ] + x 24 [C] + x 25 [ε u λe] + x 26 [λe] + x 27 [ε u e] + x 28 [e] +x 29 [ε u λ] + x 30 [λ] + x 31 [ε u ] + x 32 } (2.8)
while for X80 grade they write In [START_REF] Fairchild | A Multi-Tiered Procedure for Engineering Critical Assessment of Strain-Based Pipelines[END_REF] and [START_REF] Fairchild | Advancements Regarding Capacity Prediction of Strain-Based Pipelines[END_REF], ExxonMobil presents a typical finite element model to be used in Level 3 assessments. It consists in a three dimensional model of the quarter of a line pipe with linear solid brick 13. An internal pressure is applied at the inner surface and the end cap effect is taken into account meshing end caps. Furthermore, a tensile load is applied under displacement control at the end on the structure to simulate a remote load. The CTOD, the load and the longitudinal strain are calculated after each time increment, where the longitudinal remote tensile strain is defined as an average engineering strain along a length of two diameters centered on the girth weld. ExxonMobil introduced an alternative definition of the CTOD so that it can be directly measurement during the simulations. The latter is defined as the displacement of two nodes located on the crack flanks 0.36 mm from the original crack tip. According to ExxonMobil, this particular position is proposed to avoid any trouble such as mesh distortion around the crack tip (see Figure 2.13-b.) due to high plastic deformations.

β 1 =y [ε u λe] + y 2 [λe] + y 3 [ε u e] +
(a.) View of the FE model (b.) Definition of the CTOD in ExxonMobil FEA calculation Figure 2.13 -Views of a typical mesh used in a ExxonMobil level 3 assessment [START_REF] Fairchild | A Multi-Tiered Procedure for Engineering Critical Assessment of Strain-Based Pipelines[END_REF] approaches where the tensile strain capacity is obtained by equating the crack driving force, denoted CTOD F , with the apparent toughness, denoted CTOD A or δ A . On the other hand, levels 3b and 4 are ductile-instability based limit state approaches where the tensile strain capacity is obtained by equating the crack driving force with the material resistance curve (see figure 2.16).

The model derives from a series of 1152 elastic plastic finite element analyses covering the ranges of parameters given in Table 2.5.

(a.) Initiation based limit state (b.) Ductile-instability limit state

Level 2

In Level 2, the tensile strain capacity TSC p is calculated using the following parametric relationship:

TSC = min ε u ,P f p G (t) TSC p (2.11)
where ε u represents the uniform tensile strain, G (t) characterizes the effect of the wall thickness t and P f p is the effect of the internal pressure f p defined as the ratio of the hoop stress and the material yield stress. G (t) is given by: G (t) = 15.9 t 0.8096(1+1.503Ψ 1.229 ) (2.12)

and P f p is given by:

P f p = ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ P max - 5 3 f p (p max -1) if 0 ≤ f p < 0.
TSC p = A F (δ A ) 1+F (δ A ) (2.15) with F (δ A ) = (Cδ A ) Bδ D A (2.16)
and where A, B, C and D are fitted functions of normalized geometry and material properties depending on the welding process.

GMAW:

A = a 1 e a 2 /β e a 3 ηβe a 4 /β (1+a 5 Ψ a 6 + a 7 Ψ (ηβ) a 8 )(1+a 9 ξ a 10 Φ a 11 + a 12 Ψ a 13 ξ a 14 ) (2.17) and and

B = β b 1 η b 2 β b 3 /η b 4 φ b 5 b 6 Φ b 7 ξ + b 8 Ψ b 9 (2.
B = β b 1 η b 2 β b 3 /η b 4 φ b 5 b 6 φ b 7 ξ + b 8 Ψ b 9 (2.22)
and • The weld material mismatch on the tensile strength: Φ = σ W u /σ u .

C = e c 1 /β e c 2 β (1+c 3 β) η 1+c 4 Ψ c 5 + c 6 Ψe -η + c 7 Ψe -β (c 8 + c 9 Φ c 10 + c 11 Ψ c 12 Φ ) (2.

Level 3a

Level 3a is based on the same approach as Level 2. The only difference is that the apparent toughness shall be measured using a series of low constraint test such as shallow-notched SENB, SENT and CWP tests.

Level 3b

Level 3b assessment is based on the tangency approach, with a parametric definition of curves to describe the crack driving force. They can be obtained by replacing δ A by δ F and TSC p by ε in Equation 2.15 and invert Equation 2.15 to Equation 2.24 in order to write δ F as a function of the applied strain ε and the normalized flaw depth η.

Level 4

Level 4 assessment is a more advanced level based on the same principle as level 3b assessment with the difference that the crack driving force curves are directly build using FEA calculations.

Limitations of ExxonMobil and PRCI approaches

ExxonMobil and PRCI approaches are both based on the tangency analysis which principle was introduced hereinbefore. Procedures under tabular form or based on sets of analytical expressions were developed so that it is possible to easily calculated the tensile strain capacity. Two types of approaches exist: (i) the initiation based procedures, and (ii) the failure based procedures.

If the first ones are proposed under a tabular or an analytical expressions form by PRCI, the failure based procedures (i.e., ExxonMobil level 3 and PRCI level 4) requires the use of finite element analyses in order to define the crack driving forces acting on the crack. The realization of such simulations is not straightforward and requires a high level of expertise. This raises the question of the relevance of using such procedures, considering that:

• The amount of material and geometrical data required to perform a finite element calculation of the cracked pipe is important (in particular, the true stress -strain curves for parent and weld material, and the actual geometry of the pipe). • The result may depend on the mesh quality.

• It is essential to define a proper mechanical quantity to plot the crack driving forces. However, it is not clear if the transferability between SENT and a pipe is validated. Therefore, comparing CTOD from finite element analyses on a pipe with a CTOD-R curve measured on a SENT specimen may not be relevant.

As said, the question of the transferability is not resolved, and therefore remains of the greatest importance considering the significant effect of the a 0 /W ratio on the material R-curves (see Chapter 1). Identically, the effect of the experimental procedure (ExxonMobil or CANMET for example) on the calculated tensile strain capacity was not studied. Therefore, further work shall be focused on the relevant use of the SENT specimen for global approach purpose.

Chapter 3

Justification of the weld overmatch in strain-based design applications • il n'est pas toujours possible de prélever une éprouvette dans la direction circonférentielle, notamment pour les tubes de faible diamètre (typiquement en-dessous de 168 mm) ; • ces éprouvettes ont une section rectangulaire de faibles dimensions au regard de l'épaisseur du tube ; • la direction de chargement n'est pas pertinente car les soudures de raboutages sont principalement sollicités en traction et en flexion lors de mouvements de terrain ; • le prélèvement de ces éprouvettes au coeur du tube exclut la racine et la face du cordon soudé.

Le DNV-OS-F101 suggère l'utilisation alternative d'éprouvettes prélevées dans la direction axiale de la canalisation, avec une section du fût réduite au niveau du matériau d'apport, de manière à y garantir la localisation des déformations. Cette méthodologie est intéressante, cependant :

• la géométrie ne respecte pas les recommandations formulées dans l'ASTM A370 en terme de rapport longueur de fût / diamètre du fût ; • seul un volume limité de matériau d'apport est testé, et une dispersion importante peut être observée.

Deux méthodes expérimentales alternatives sont alors présentées :

• La première repose sur l'utilisation de la technique de corrélation d'images numériques pour l'évaluation des champs de déformations dans le métal d'apport. • La seconde est basée sur l'emploi d'éprouvettes entaillées et l'analyse inverse pour l'identification des caractéristiques matériaux.

Introduction

In strain based design applications, it is necessary to demonstrate that the weld overmatches the parent metal properties to avoid strain localization at the pipeline girth weld. From an experimental point of view, it is always a challenge to accurately and consistently measure tensile properties in the weld metal area in particular in narrow-gap weld configuration and for low diameter pipes. This paper presents two experimental methods coupled with finite element analyses suitable for determining the weld material constitutive law.

A screening of all testing methods has been performed as part of PRCI project MATH-1 [START_REF] Quintana | Background of All-Weld Metal Tensile Test Protocol -Final Report[END_REF] and DOT Project BAA DTHP56-07-0001. It showed in particular that all developments have been focused on specimen type (strip or round), size, sampling location and direction in the girth-weld.

The recommendation of PRCI study was to sample strip specimens in the circumferential direction and to measure the "yield strength" at 1 % total strain to reduce variability in test results. However, PRCI recommendation can be challenged because:

• It is not always possible to sample tensile specimens in particular for low pipe diameters (typically below 6.625"); • the strip specimen geometry exhibits a highly reduced rectangular section; • the loading direction is not the relevant one as pipelines girth-welds experience tensile or bending loads in moving ground areas; • weld metal testing mainly covers fill passes (excluding hot, root and cap passes from the assessment).

The alternative option suggested by DNV-OS-F101 [44] is to use cross-weld tensile specimens with reduced gauge diameter in the weld metal area. This procedure has some attractive features but:

• the proposed specimen geometry does not fulfill the recommended ratio between specimen section and gauge lengths by ASTM A370-12a [START_REF]Standard Test Methods and Definitions for Mechanical Testing of Steel Products[END_REF] that shall be equal or greater than 4; • there are experimental issues to ensure a proper measurement of the yield strength; • a limited amount of weld metal is tested and high variability of tests results can be expected.

The aim of this paper is to propose two other experimental methods:

• One relies on digital image correlation and tracking by optical methods. It allows testing of the entire weld metal area and it provides full-field displacement measurements from which weld metal stress-strain behavior can be determined. • the second method is based on notched tensile specimens with various notch radii and requires finite element calculations of the test to determine weld metal yield strength from inverse analysis. This method is an improvement of the DNV method but does not address the possible variability issue.

However, it is not the aim of this paper to discuss about strain-based design procedures.

Weld overmatch and strain-based design 3.2.1 Objective

As a preliminary step, finite element analyses have been performed in order to quantify the effect of the weld mismatch on Engineering Critical Assessments (ECA). Two weld geometries that are typical of both onshore and offshore pipeline girth welds have been considered. Figure 3.1 depicts the schematics of a J-joint and a 60 • V-joint.

This study is based on the tangency analysis where the tensile strain capacity of the flawed girth weld is determined by equating the crack driving forces (CDF) and the material resistance curve, as depicted Figure 3.2. The CDF are usually based on FEA but analytical expression can be found for surface cracks in girth welds [START_REF] Fairchild | A Multi-Tiered Procedure for Engineering Critical Assessment of Strain-Based Pipelines[END_REF]. The R-curve is measured using fracture mechanics specimens, such as Single Edge Notched Tensile (SENT) specimens ( [START_REF] Cravero | Constraint evaluation and effects on J-R resistance curves for pipes under combined load conditions[END_REF]; [START_REF] Pisarski | Validation of Methods to Determine CTOD from SENT Specimens[END_REF] ; [START_REF]Recommended Practice RP-F108. Fracture control for pipeline installation methods introducing cyclic plastic strain[END_REF]; [START_REF] Shen | Evaluation of CTOD from J-integral for SE(T) specimens[END_REF]; [START_REF]Measurement of Crack-Tip Opening Displacement (CTOD) Fracture Resistance Curves Using Single-Edge Notched Tension (SENT) Specimens[END_REF]). For the exercise, the material R-curve was defined using ExxonMobil ( [START_REF] Fairchild | A Multi-Tiered Procedure for Engineering Critical Assessment of Strain-Based Pipelines[END_REF] and [START_REF] Fairchild | Advancements Regarding Capacity Prediction of Strain-Based Pipelines[END_REF]) exponential equation that writes CTOD = δ∆a η , where δ =0.9 and η =0.5 which are consistent values for an API-5L X65 steel grade.

FEA Model

The simulations consisted in three-dimensional analyses of a pipe containing an outer surface flaw at the weld centerline. The pipe is OD 323.8 mm and WT 22.2 mm and an overall length of 3 OD was modeled in order to avoid any perturbations due to the boundary conditions. Only 1 /4 of the pipe was actually modeled to take advantage of the two symmetry planes. The pipe is subjected to a tensile load applied at a rigid elastic plate at the end of the pipe. No internal pressure is applied.

The measurement of (half) the CTOD was performed following the displacement of a node located 0.36 mm away from the intersection of the crack tip radius and the crack flank, in accordance with ExxonMobil SBD procedure. This method enables to avoid an underestimation of the CTOD due to mesh distortion at the vicinity of the crack tip. Moreover, two points were defined distant of 400 mm to measure the remote strain, the first point being 50 mm away from the crack plane.

An isotropic hardening law under the form:

R (p) = R 0 [1+Q 1 (1 -exp (-b 1 p)) + Q 2 p] (3.1)
was used to describe the parent material hardening behavior and von Mises criterion was considered. Equation 3.1 was preferred to a more traditional Ramberg-Osgood formulation which introduces a dependency between Y/T and the uniform-elongation [START_REF] Stijn Hertelé | Weld Strength Mismatch in Strain Based Flaw Assessment: Which Definition to Use? Journal of Pressure Vessel Technology[END_REF].

The 0.2% proof stress (referred as the yield stress in the following) for the base material is R p0.2 =560 MPa, the ultimate tensile strength is UTS= 675 MPa and the uniform elongation is A % =18.6 %.

The weld material behavior was described using Equation 3.1 as well. Six different mismatch levels of the yield stress (-20 MPa, evenmatch, +20 MPa, +40 MPa and +80 MPa) have been considered and consisted in two different cases:

• Case 1: It consists in an offset of whole the stress-strain curve, meaning that both the yield stress and the ultimate tensile strength are offset. • Case 2: It consists in an offset of the yield stress only, keeping the ultimate tensile strength equal to 675 MPa, resulting in materials with 0.8 <Y/T <0.95. ) and V-weld with a 60 • angle. The base material is blue colored and the weld material is red colored.

Results

Simulations were post-processed in order to obtain the driving force curves for different levels of remote strains for J (figure 3.4) and V-welds (figure 3.5). CDF obtained for 0.4% and 1.5% remote strains are compared to the material R-curves. The critical defect sizes a c are determined using the tangency analysis basis as explained hereinbefore. In the first case where both R p0.2 and UTS are modified, it is shown that the mismatch level has a significant effect on the critical defect size for both OD and ID cracks (only OD cracks results are reported in this paper but conclusions are the same). The a c values are reported Figure 3.8 for the two weld geometries and for 0.4 % and 1.5 % remote strains. The effect of the weld overmatch is clearly shown in this Figure, with difference of about 26 % for the J-weld at 0.4 % and 1.5 %, and around 28-34 % for the V-weld.

In the second case which consists in a modification of R p0.2 only, simulations showed that there is no effect of the mismatch on the crack driving forces (see Figures 3.6 and 3.7) and therefore, the critical defect sizes are identical for the different mismatch levels.

To conclude, it is shown that the overmatch hardening behavior of the weld material up to the ultimate tensile strength must be determined to perform relevant strain based design Engineering Critical Assessments.

Specimens proposed in the literature

PRCI Specimen

The PRCI introduced a tensile test specimen in their final report 277-T-02 [START_REF] Quintana | Background of All-Weld Metal Tensile Test Protocol -Final Report[END_REF]. It consists in a strip specimen with a reduced cross-section that shall be machined in the circumferential direction, as depicted in Figure 3.9. According to PRCI, this geometry allows to incorporate a more representative section of the micro-structure present in the multiple pass welds. However, the tested direction does not correspond to the main loading direction for girth-welds subjected to tensile and bending loads, where the weld material is mainly loaded in the pipe axial direction. Furthermore, PRCI defines a minimum external diameter equal to 762 mm (30 in) due to the pipe curvature that would limit the specimen length and thickness so that there would be no interest in testing such specimens rather that conventional round bar.

DNV-OS-F101 Specimen

Two specimens are proposed in DNV-OS-F101:2013 [44]. The recommended specimen is a round allweld tensile bar that shall be machined in the circumferential direction and includes only weld material within its gage length. The specimen is of particular interest since it enables to fulfill ASTM-A370-12a requirement regarding the gage length-to-nominal diameter ratio (L 0 /φ 0 = 4). However, the tested direction is not consistent with girth-welds subjected to tensile loads as in the case of the PRCI specimen. Therefore, a cross-weld specimen is introduced. The latter is machined in the longitudinal direction with recommended geometry as depicted in Figure 3.10. This specimen contains a center part with a reduced cross-section that concentrates plastic deformations within the weld material. Therefore, it is possible to obtain a full stress-strain curve using such a specimen. Following DNV recommendations, this specimen should be machined only in weld with a width (denoted LW in Figure 3.10) greater or equal to 6 mm. This requirement would be hardly reached in the case of narrow girth weld, where widths are typically from 4 to 5 mm. Therefore, ASTM-A370-12a requirements are not fulfilled, and according to DNV such specimens produce stress-strain curves about 5 % higher compared with regular round tensile specimens.

A finite element based analysis was performed in order to investigate the effect of the gage lengthto-nominal diameter ratio (L 0 /φ 0 ) on the measured tensile properties. The meshes consisted in axisymmetric models with fully integrated axisymmetric eight-nodes elements using Z-Set code. Two sets of elements were defined and correspond to the Base Material (BM) and the Weld Material (WM), and node sets were defined in order to apply boundary conditions and measure the consistent nodal displacements and nodal reactions, as depicted in Figure 3.11. The nominal diameter was set equal to 6 mm, and meshes have been generated with varying LW values, so that the ratio LW/Φ 0 varies within the range from 1.4 to 16. The base material tensile strain was represented by an isotropic hardening law under the form given by Equation 3.1 with a typical API-5L X65 steel grade properties, and a material law derived from actual laboratory tests on a girth weld was assigned to the weld material. Figure 3.13 gives the ultimate tensile strength measured on each specimen configurations as an error to the actual material UTS. It shows that specimens fulfilling ASTM A370 requirement with L 0 /φ 0 > 4 is needed to retrieve the weld metal behavior. Also, it is shown that even with lower length-to-diameter ratii down to 4 /3 (L = 8 mm and φ 0 = 6 mm ) gave acceptable results with a maximum relative error equal to 3.4%. However, it must be noticed that for lower length-to-diameter ratii, the relative error strongly increases up to the significant value of 10 % for specimens exhibiting L 0 /φ 0 = 1 /3. Therefore, precautions shall be considered where the DNV specimen is used, in particular in the case of narrow girth welds.

Suggested approaches

Digital Image Correlation

In cases where the objective is to determine the mismatch level in terms of yield stress, a cross-weld flat tensile specimen may be used jointly with a Digital Image Correlation (DIC) system, in place of a classical mechanical sensor, such as a LVDT sensor. This approach allows to obtain an accurate measurement of the full-field displacements across the Parent Material (PM), the Heat Affected Zone (HAZ) and the Weld Material (WM).

Material and method

A flat specimen with a square or rectangular cross-section is proposed (see Figure 3.15). In this study, specimens with a 6x6 mm cross-section were machined from an line tube tube made of an API-5L X65 parent material. The specimen dimensions were intentionally reduced in order to comply with the tensile machine load capacity. However, when possible, they shall be sampled with dimensions as representative as possible of the weld joint, in order to incorporate the maximum welding passes as underline by PRCI report. Furthermore, since the sample is machined in the pipe axial direction, there is no restriction to the length due to pipe curvature. Therefore, the geometry satisfies the ASTM A370 requirements regarding the specimen dimensions (see Figure 3.13).

Prior to the test, a thin layer of a highly elastic white paint was sprayed on the surface of the specimen, and black speckles were added on top using an aerosol spray taking care to obtain black dots with an approximate average size of 50 × 50µm (see Figure 3.14).

The commercial software VIC-3D was interfaced with two high-definition cameras in order to measure both in-plane and out-of-plane displacements, and the load was recorded during the test using a 100 kN load cell.

Results

Four virtual strain gages were defined within the tracked surface. First, the strain gage denoted E 0 enables to measure the global strain within the specimen. Its initial gage length was set as the maximum possible regarding to the correlated surface, so that l 0,0 = 20.55 mm. Then, two strain gages E 1 and E 2 are located on each side of the weld to measure the tensile properties of each parent materials, with l 0,1 = 5.58 mm and l 0,2 = 6.63 mm. Finally, the strain gage E 3 allowed to measure the strain within the weld material region with l 0,3 = 3.08 mm. Obtained results are plotted in Figure 3.16. Several main observations are made from these curves:

1. The 0.2 % proof strength of the three materials are measured, and reported in Table 3.1. 2. The weld mismatch defined for the on the 0.2 % proof strength is measured, and reported in Table 3.1. 3. The two parent pipe steels have almost identical material properties. 4. Parent material 2 has a slightly lower yield stress so that necking occurs in this material. UTS can only be measured in this case and is equal to 600 MPa.

Discussion

It is shown that using the DIC method enables to capture well the behavior of both parent and weld material using a single specimen. The weld overmatch on R p0.2 is easily determined placing the virtual gages judiciously. Unfortunately, it is not possible to measure the weld overmatch on the UTS due to the strain localization into the parent material, with lower mechanical properties. Full thickness specimens (notched or not) can be used. In that case, as they are likely not to be compliant with codes and standards requirements, FE modeling of the test and material constitutive law identification by inverse analysis is

Notched Tensile Specimen

Material and method

The axisymmetric notched tensile specimens are denoted NT χ , where χ = 10r/Φ 0 with r being the notch radius and Φ 0 being the minimal diameter of the specimen. The use of such specimens allows to localize plastic deformations withing the material located at the notch, where the cross-section is minimal. It is therefore possible to obtain a full stress-strain curve of a weld material overmatching a parent material by simply machining the notch inside the weld material. The notch increases of the stress triaxiality ratio (τ= σ m /σ eq , where σ m is the mean stress, and σ eq the von Mises equivalent stress) which allows to reach locally a much higher level of stress than the one that would have been reached using a classical smooth tensile specimen. Furthermore, the main deformations are concentrated into the reduced crosssection making possible to measured the diameter reduction up to the complete failure, and derive a full stress-strain curve for strain levels higher than the uniform elongation (A % ). NT 10 and NT 4 specimens were machined from another X65 grade steel seamless pipe (see Figure 3.17).

The tests were conducted under displacement control loading. During the tests the load F, the longitudinal displacement ∆L and the diameter reduction ∆Φ in the transverse direction were monitored. A typical experimental curve is shown in Figure 3.18. On this diagram, three stages can be observed:

1. Up to C : containing elastic deformations and where plasticity develops into the notch. 2. From C to D : corresponding to the void nucleations in the steel micro-structure. Damage remains however limited and hardly affects the overall behavior. Figure 3.18 -A typical experimental stress-strain curve obtained with a NT test.

Inverse analysis

The inverse analysis lies on the comparison between experimental data and numerical results obtained using finite element analyses, as depicted in figure 3.19. A classical mean square error formula is used, and writes:

MSE = 1 n n i=1 Ŷi -Y i 2 (3.2)
where n is the number of experimental data points, Ŷ is the vector of predictions and Y is the vector of observed values. The simplex algorithm is used to minimize the cost function. In the case on NT specimens, 2D axisymmetric meshes as depicted in Figure 3.20 are used to take advantage of the two symmetries. Two sets of elements are defined and correspond to the parent material (in blue) or the weld material (in red). Boundary conditions are defined so that FEA are consistent with the experiments, and node sets are defined to follow the evolution of the load and the diametrical contraction during the simulations. Furthermore, the parent material constitutive law is considered as fully known and can be described by an isotropic hardening law which writes:

R (p) = max (R Lüders ,R 0 [1+Q 1 (1 -exp (-b 1 p)) + Q 2 p]) (3.3)
where R 0 = 413 MPa, R Lüders = 445 MPa, Q 1 =0.476, b 1 = 19.7 and Q 2 =0.6.80 are material parameters. The yield surface equation for the weld material writes:

f (σ) = σ -σ 0 -R(p) (3.4)
where p denotes the cumulative plastic strain. The function R(p) is defined as the combination of a linear and a nonlinear isotropic hardening term and writes:

R (p) = R 0,W 1+Q 1,W 1 -exp -b 1,W p + Q 1,W p (3.5) where R 0,W , Q 1,W , b 1,W and Q 2,

Validation

A test on a round bar including weld material was performed. The specimen geometry was machined as shown in Figure 3.22. Two LVDT sensors were used to measure the overall deformations (LVDT 1 with an initial gage length l 0 = 25 mm) and the weld material deformations (LVDT 2 with an initial gage

Conclusions

Two protocols to determine the weld mismatch are presented in this part. The first method relies on the DIC methodology coupled with standard tensile bars. It enables to determine the Young's modulus and the 0.2 % proof stress. It would also be possible to derive a full tensile curve from such a test by optimizing the test specimen geometry and identifying the material constitutive law by FEA.

A second method based on the use of notched tensile specimens coupled with the inverse analysis enables to derive full stress-strain curves. This approach requires finite element analysis in order to fully determine the constitutive equation of the material law behavior. Such simulations may be automated so that no particular engineering judgment is needed. From the authors point of view, such a protocol could conveniently replace the more classical tensile tests as suggested by DNV-OS-F101 and PRCI project. Geometry of the specimen does not correspond to codes and standards, but the use of FEA and inverse analysis makes the material constitutive law independent on the specimen geometry. It would then be recommended to perform tests on a number of specimen geometries, using different notch radii for example.

Part III ENGINEERING CRITICAL ASSESSMENT OF A SEAMLESS PIPE Résumé en français

Ce chapitre est consacré à l'étude expérimentale des deux matériaux du tube sans soudure (dit seamless) fourni par Vallourec : le matériau de base, noté ici X65, et le matériau d'apport de la soudure circonférentielle, noté X65W. Le diamètre extérieur de ce tube est égale à 323,8 mm (12.75 in) et son épaisseur est de 22,2 mm. Ces deux matériaux ont été caractérisés au travers d'une campagne expérimentale de plus de 150 essais sur éprouvettes, incluant des essais :

• de traction sur éprouvettes à section circulaire, notées ST ; • de traction sur éprouvettes à section prismatique, notées FT ; • de traction sur éprouvettes entaillées à section circulaire, notées NT χ ; • de traction sur éprouvettes entaillées à section prismatique, notées FN χ ; • de traction sur éprouvettes en déformations planes, notées PE ; • de ténacité sur éprouvettes Compact Tension, notées CT ; • de ténacité sur éprouvettes Single-Edge-Notched-Bending, notées SENB ; • de ténacité sur éprouvette Single-Edge-Notched-Tension, notées SENT.

Au préalable, des observations métallographiques ont été réalisées sur coupes polies (Nital 4%) dans les plans (LS), (LT) et (TS), ce qui a permis de conclure que :

• il n'existe pas d'orientation préférentielle des grains ; • les tailles et les formes des grains sont identiques dans les trois plans ; • seulement quelques inclusions sont observées dans les trois plans.

Cette étude se déroulant dans le contexte de canalisations soumises à des conditions extrêmes, des essais à basses températures ont été réalisés en complément des essais à température ambiante. Les températures de -20 • C et -40 • C ont été retenues. Cela fut possible grâce à l'utilisation d'une chambre climatique régulée en température dans laquelle est pulvérisée en fines gouttelettes de l'azote liquide.

Les essais sur éprouvettes entaillées ont permis d'évaluer l'effet de la triaxialité des contraintes τ sur le comportement des matériaux X65 et X65W. On observe en effet que l'augmentation de τ a pour conséquences une augmentation de la contrainte maximale admissible grâce à l'effet bénéfique du chargement multi-axial, et une diminution de la ductilité puisque la triaxialité des contraintes favorise le développement de l'endommagement. On observe également que les deux matériaux ont un comportement isotrope en plasticité et en rupture, et aucun mécanisme de rupture fragile ne fut observé, même à -40 • C . De plus, la comparaison entre le X65 et le X65W permet de valider l'overmatch de la soudure, nécessaire au déploiement de l'approche Strain-Based Design dans la suite de l'étude.

Des essais ont réalisés sur différentes éprouvettes fissurées (CT, SENB et SENT) pour la mesure de la ténacité de ces deux matériaux. Une comparaison de ces trois géométries d'éprouvettes sur le matériau X65 à température ambiante a permis de montrer que les courbes de ténacité obtenues (appelées Rcurves) se classent dans l'ordre suivant : R curve CT ≤ R curve SENB ≤ R curve SENT Cependant, la campagne expérimentale s'est particulièrement concentré sur l'utilisation de l'éprouvette SENT. Différents scénarios d'essais ont permis de conclure que :

• L'augmentation du rapport a 0 /W (profondeur de fissure initiale normalisée par l'épaisseur de l'éprouvette) a pour effet une diminution des courbes de ténacité mesurées, que ce soit en terme d'intégrale-J ou de CTOD. • Une entaille par électro-érosion (EDM notching) permet de judicieusement remplacer le long et délicat procédé de préfissuration par fatigue, à condition que :

-Le diamètre du fil d'usinage est suffisamment petit. Ainsi, ExxonMobil recommande un diamètre inférieur ou égale à 150 microns. Dans cette étude, un diamètre de 300 microns fut démontré être suffisamment petit pour le matériau de base. -A la température de l'essai, le matériau se situe sur le plateau haut de sa courbe de transition ductile -fragile, pour garantir une rupture 100 % ductile.

• Une diminution de la température d'essai conduit à des courbes de ténacité mesurées plus hautes, que ce soit en terme d'intégrale-J qu'en terme de CTOD. • Il est possible de normaliser les courbes de ténacité par la résistance ultime à la traction (R m ) pour regrouper les courbes obtenues aux différentes températures.

Pour aller plus loin dans l'étude de l'éprouvette SENT, il serait intéressant d'évaluer la robustesse du protocole expérimental en procédant à une campagne round-robin, c'est-à-dire étudier la dispersion des résultats expérimentaux obtenus par différents laboratoires d'essais. En effet, la réalisation des essais SENT n'est pas triviale que ce soit au niveau de la mise en place de l'essai en lui-même (phase de préfissuration si applicable) ou au niveau de l'interprétation des données pour l'obtention des courbes de résistance.

Introduction

This part is dedicated to the description of the materials of the first line pipe tube weldment of the study, which consists in a parent material of type API-5L X65 steel and a weld metal. Both base material, denoted X65 or BM, and weld material, denoted X65W or WM, have been characterized throughout a comprehensive experimental campaign including more than 150 small-scale tests. Samples were taken out a seamless pipe manufactured by Vallourec and Manessmann and provided by TOTAL S.A. The pipe external diameter is 323.8 mm (12.75 in) and the wall thickness is 22.2 mm. The tube contains a girth weld at its center that was realized by Serimax.

In the following:

1. X65 will refer to the parent material. 2. X65W will refer to the weld metal.

The material directions are denoted L, T and S as depicted in Figure 4.1:

• L : Axial direction of the pipe • T : Circumferential direction • S : Wall thickness direction In the manuscript, the following nomenclature is used for specimens: AAA_BBB_CCC_DDD_EEE where • AAA will refer to the material:

-X65 -X65W • BBB will refer to the temperature of the test:

-RT : Room temperature.

-20 : -20 • C.

-40 : -40 • C. • CCC will refer to the specimen geometry:

-ST : tensile tests performed on smooth round bars.

-FT : tensile tests performed on flat tensile specimens.

-NT : tensile tests performed on notched round bars.

-FN : tensile tests performed on flat notched specimens.

-PE : tensile tests performed on specimens loaded in a plane strain state. • DDD will refer to the loading orientation:

-L -T • EEE will refer to the specimen number in cases where tests are repeated.

Attention was first focused on the parent material which is a classical and widely used steel grade for pipeline applications demanding both mechanical resistance and good ductility properties. Evaluation of the mechanical properties was performed throughout tensile tests at room temperature and low temperatures. Such tests were performed at -20 • C and -40 • C using a cold room and liquid nitrogen. The laboratory campaign also included tests on axisymmetric or flat notched specimens allowing to investigate the material behavior under various stress triaxiality states, which is a damage governing parameter. Specimens allowing to reach a plane strain state were also used. The fracture behavior was then investigated throughout tests performed on three cracked specimens (CT, SENB and SENT). The results are compared and the use of the SENT specimen is discussed here.

Attention is then focused on the weld material. Its mechanical properties were determined at room temperature and low temperatures (-20 • C and -40 • C ) with a limited number of tests than for the parent material. Fracture mechanics tests were also conducted.

Manufacturing process

A seamless pipe is made one round at a time from single billets by one of the several possible multi-step hot-forming processes. However, the general process is basically the same:

• Heating of cylindrical billets (up to 1300 As a result, the seamless pipe is generally more expensive than seam welded pipe. It is made in sizes ranging from 2 3/8 inches diameter through 24 inches diameter, and in grades from Grade A through Grade X65. It may be obtainable in higher grades (X80 to X100) but such materials may require special heat treatment. If so the cost will likely be quite high relative to seam welded pipe.

• C) • Piercing of billets (1150 • C to 1250 • C ) (see
The seamless pipe is the pipe of choice for deepwater field development due to more and more demanding applications and performance. The optimized chemistry (homogeneous microstructure) and the correct process of quench and temper (Q&T) provide heavy wall pipe with increase strength without reducing toughness. The main stage of the process are hot piercing, hot rolling at a retained mandrel mill, and sizing. The subsequent Q&T consists of a first heating up (austenisation), internal and external quenching, followed by a second pipe heating (tempering).

Parent material 4.3.1 Metallurgical composition and general feature of the microstructure

The X65 steel pipe provided by TOTAL was manufactured by Vallourec and Mannesmann as a seamless pipe of 323.8 mm in outer diameter and 22.2 mm in wall-thickness. The pipe was reheated using a TMPC process at a temperature of 940 • C during 12 min and cooled down using water quenching. It was then tempered at a temperature of 620 • There is no preferred orientation of the grains in any plane.

• Sizes and shapes of the grains are identical in the three planes.

• Only a small amount of inclusions is observed in the three planes.

The chemical composition of this steel is shown in Table 4.2. In [START_REF] Maruyama | Strengthening mechanisms of creep resistant tempered martensitic steel[END_REF] Maruyama proposed a comprehensive review on the role of alloying elements on metallurgical and mechanical properties, given in Table 4 Classical tensile tests on ST specimens were performed in L and T directions. The specimens were taken out the pipelines at mid wall-thickness to avoid any heterogeneities due to the pipe manufacturing process. The specimen geometry, given in Figure 4.4 was chosen so that it complies with ASTM-E8 [START_REF]Standard Test Methods for Tension Testing of Metallic Materials[END_REF] requirements. Prior to the test, all the samples dimensions were fully measured using a numerical micrometer screw gage and a laser system in the case of cylindrical surfaces (Figure 4.5-a).

The tests were performed either on a 10 tons servo hydraulic MTS machine with a 100 kN load cell, or a 25 tons servo hydraulic Instron machine with a 250 kN load cell (see Figure 4.5-b). The tests have been carried out under displacement control so that a deformation rate of 5. 10 -4 s -1 was reached. The following parameters were recorded using the "MultiPurpose TestWare" software:

• The time in seconds (s) • The jack displacement in millimeters (mm) • The load in kilonewtons (kN) • The elongation in the axial direction using a LVDT extensometer in millimeters (mm) • The diametral contraction using a clip extensometer in millimeters (mm)

The engineering strain ε = ∆l/l 0 was measured using the LVDT extensometer with an initial gage length l 0 of 9.625 mm and the diametrical reduction was measured using a clip gage positioned along the S direction (see Figure 4.5-d). The engineering stress σ = F/S 0 was defined as the measured load F divided by the initial cross section S 0 . In addition, an analogical plotter (see Figure 4.5-c) was used so that it was possible to easily compare the experimental data during the tests. Figure 4.6-a depicts the stress-strain tensile curve at room temperature in L and T directions. It is shown that results are identical for both loading directions. The material exhibits a Lüders plateau in L and T directions up to elongations between 1.54 % and 1.89 % which is common for low-carbon steels. The Young's modulus was measured equal to 203 GPa which is in accordance with classical values for this kind of material. The pipeline industry usually considers a value of 207 GPa, which is slightly over the measured value. The 0.2 % proof stress, the tensile strength R m , the uniform elongation ε % and the reduction of area were also measured and reported in Table 4.6. From these resuls, it was also possible to determine the Lankford's coefficient. This scalar parameter was originally introduced to measure the plastic anisotropy of rolled sheet metal and is defined by:

L k = ε T ,p ε S,p (4.1)
where ε T ,p denotes the true plastic strain in the direction perpendicular to the rolling direction, and ε S,p denotes the true plastic strain in the sheet thickness direction. Here, alternative definitions of Lankford's coefficient are used depending on the loading direction.

L ′ k = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ε S,p ε L,p for L-loading tensile tests ε S,p ε T ,p for T-loading tensile tests (4.2)
Measured on an isotropic material, the Lankford's coefficient as defined in Equation 4.2 equals to -0.5 as it can be demonstrated using the property of constant volume transformation in plasticity which writes using the fact that plastic strain is isochoric so that:

∆V = ε L,p + ε T ,p + ε S,p = 0 (4.3)
The experimental values of the Lankford's coefficients in L and T directions are depicted in Figure 4.6b, where they are compared to the isotropic value (bold dot line). Experimental results do not exactly meet the theoretical isotropic Lankford's coefficient value, and it is believed that the relatively small difference may be explained by experimental issues only. Indeed, it is defined by the ratio of a local quantity (ε S,v ) by a non local (in the sense that it is averaged over the gage length l 0 ) quantity (ε L,v or ε T ,v ). 4.6. It is shown that the material remains fully ductile even at low temperatures, and that the main effect of the decrease in temperature is an increase of the tensile properties, especially with a significant increase in the yield stress and the ultimate tensile strength (+7 % at -20 The axisymmetric notched tensile specimens are denoted NTχ where the subscript is χ = 10r/Φ 0 with r being the notch radius and Φ 0 being the minimum diameter of the specimen. These specimens are used to characterize the fracture behavior of materials submitted to different levels of stress triaxiality. The use of a notch increases the stress triaxiality ratio, defined as τ = σ m /σ e where σ m =1/3Tr(σ) is the mean stress and σ eq is an equivalent stress (e.g. von Mises stress), which allows to locally reach higher level of stresses than the yield stress of the material.

The tests were performed either a 10 tons servo hydraulics MTS machine with a 100 kN load cell, or a 25 tons servo hydraulic Instron tensile frame with a 250 kN load cell. The tests were conducted under displacement control so that it was possible to obtain the full tensile curves even after the maximal load. A radial deformation rate of 5. 10 -3 s -1 was selected so that it was consistent with the smooth tensile tests. The following parameters were recorded using the "MultiPurpose TestWare" software:

• The time in seconds (s) • The jack displacement in millimeters (mm) • The load in kilonewtons (kN) • The elongation in the axial direction using a LVDT extensometer in millimeters (mm) • The diametral contraction using a clip extensometer in millimeters (mm) A typical experimental stress-strain curve is shown is Figure 4.10. The horizontal axis corresponds to the diametrical reduction, and the vertical axis corresponds to the normalized load. The curve can be The tensile stress-strain curves at room temperature are depicted in Figure 4.12a, and other quantities such as the maximum load F max , the load at the onset of coalescence F (c) and the diametrical contraction at the onset of the coalescence ∆Φ/Φ 0 were measured and are reported in Table 4.7. The tensile stress-strain curve measured on one of the ST specimens is added to the plot for comparison. It can be noticed that the maximum load is reached for an equivalent radial strain of about 7.1 % for all specimens and both loading directions. The failure of the notched specimens occurred far beyond the necking so that plasticity and damage widely developed inside the notches. One can see that the notch radius has a significant impact on the tensile curve. NT 2 specimens with the small notch radius reached higher levels of stress than NT 4 specimens, and even more than NT 10 . On the other hand, NT 2 specimens failed for strain levels smaller than NT 4 and NT 10 specimens. This was expected since the main notch effect is such that it increases the stress triaxiality at the center of specimens. Non significant difference can be observed between T and L loading. 4.17 and 4.18. Perfectly round shaped fracture surfaces are observed as it was already noticed from the uniaxial tests. Therefore, it is suitable to consider that both plasticity and fracture can be considered as isotropic for this material.

Six axisymmetric notched specimens were tested at -20 • C and -40 • C . The corresponding stressstrain tensile curves are depicted in Figure 4.13 and mechanical properties are reported in Tables 4.8 and 4.9. It is observed that the material remains fully ductile, as already seen in Figure 4.7 with ∆Φ/Φ 0 quantities almost equal to those measured at room temperature. RT

F max F (c) ∆Φ (c) Φ 0 F max /S 0 F (c) /S 0 Z (kN) (kN) (%) (MPa) (MPa ) (%) X65_RT_NT2_L_1
24. [START_REF] Besson | Modeling of crack growth in round bars and plane strain specimens[END_REF] Two different specimen geometries, namely FN 2 and FN 4 were tested at room temperature only. The testing protocol is similar to the NT χ specimens. During the tests, the load, the jack displacement and the opening of the specimens were monitored. The opening V was measured at both sides of the notches so that it was possible to check that specimens were correctly aligned with the loading direction. For flat notched specimens, damage develops at the center of the gage section so that the openings should be equal. Flat notched specimens enable to study the fracture of the material under different levels of stress triaxiality. The experimental stress-opening curves are depicted in Figure 4.20. Identical trends as for NT χ specimens are observed. As previously observed on the round notched specimens (although the effect is less pronounced), FN 4 samples show opening values slightly greater than for FN 2 specimens and the maximum loads reached by the FN 2 specimens is slightly over those for the FN 4 specimens.

Plane strain Specimens (PE)

The specimen geometry is depicted in Figure 4.21. The tests have been performed on a MTS servo hydraulic tensile frames using hydraulic grips and the specimens were loaded under displacement control at a strain rate of about 5. 10 -4 s -1 in the region of interest. During the test, the following values were monitored and recorded using the "MultiPurpose TestWare" software:

• The time in seconds • The jack displacement in millimeters • The load in kilonewtons • The elongation of the specimen in the loading direction using a LVDT extensometer Digital Image Correlation (DIC) was used together with a mechanical LDVT sensor so that it was possible to validate the DIC measurements. Two tracking points were defined at ±0.5 mm apart from the middle section of the specimen as depicted in Figure 4.21 so that the strain was accurately measured within the plane strain area. The LVDT sensors had a initial gage length l 0 = 10 mm. Two PE tests were performed at room temperature only. The main interest of this specimen is that the material at the center of the gage length is loaded under plane strain conditions (i.e. with a strain state (e.g. characterized by the Lode parameters) which strongly differs from the one obtained in axisymmetric specimens). The experimental tensile stress-strain curves in L and T directions are depicted in Figure 4. [START_REF] Hollstein | On the relation of the crack opening displacement to the J-integral[END_REF]. One can see that the specimen loaded in T-direction reached a slightly higher load than the specimen loaded in L-direction (+18.45 MPa at the maximum load). This phenomenon did not appear on the previous experiments. Moreover, the T-loaded specimen reached a slightly higher strain level. Three CT specimens were taken out of the seamless pipe so that they were loaded in tension L direction and the cracks propagated in the T direction. Such specimens are denoted LT specimens. A LS configuration would have been more consistent with cracks propagating through the wall thickness of a pipe subjected to a tensile load, but it was not possible to machine such specimens due to the reduce pipe wall thickness (22.2 mm). The dimensions of the specimens are given in Figure 4.23.

The specimens were precracked in fatigue in order to obtain an initial a 0 /W (a 0 : initial crack depth, W : specimen width) ratio equal to 0.5 to comply with ASTM-E1820 that requires: (1) ≤ a 0 /W ≤ 0.55 to measure the material toughness, and (2) 0.45 ≤ a 0 /W ≤ 0.7 to obtain the material R-curve. During the fatigue precracking process, the specimens were loaded within the range P min -P max where P min /P max equals 0.1. The loading was performed so that it never exceeded the limit load given by:

P limit = 0.4B(W -a 0 ) 2 σ Y (2W + a 0 ) (4.4)
where σ Y is the flow stress σ Y = 1 /2(σ YS + σ UTS ). P max is given by

P max = K (BB N W ) 1/2 f a W (4.5)
where K is the mode I stress intensity factor and where a is the actual crack length measured by an optical measurement system as depicted in Figure 4.24. K shall be chosen consistently depending on the material. For the X65 steel grade of the study, the fatigue precracking process was started with K = 18 MPa √ m for the first 0.2 mm, and decreased to 11 MPa √ m at the end of the process.

f (a/W ) =
The single specimen method was used to obtain the full material R-curve using one test, and the crack propagation was measured using the elastic unloading compliance method. Therefore, sidegrooves were machined after the fatigue precracking process with a total width reduction of 20 %, giving B N = 10 mm. The standard procedure allows for precracking with the side-groves. Using the proposed technique it becomes possible to check during crack propagation that crack advance is equal on both sides of the specimen. Furthermore machining of the side-groves eliminates a potential crack front curvature.

The specimens were pin-loaded under displacement control in order to obtain a full loaddisplacement curve even after reaching the maximum load. The displacement rate was chosen equals 1.5 mm.min -1 , and the diameter of the pin was 6 mm. The following outputs were recorded during the test:

• The time in seconds (s) • The jack displacement in millimeters (mm) • The load in kilonewtons (kN) • The CMOD in millimeters (mm) using a MTS clip gage The tests were interrupted at three increasing levels of CMOD values so that three final extension levels were reached. After completion of the test, the material toughness was calculated following ASTM-E1820. The J integral is partitioned into an elastic part J e and a plastic part J p that are calculated for each k th loading-unloading. J e(k) is given by:

J e(k) = K 2 (k) E/(1 -ν 2 ) (4.7)
The stress intensity factor K (k) writes

K (k) = P (k) (BB N W ) 1/2 f a (k) W (4.8)
with f (a k /W) given in Equation 4.6. J p(k) is given by:

J pl(k) = J p(k-1) + η (k-1) b (k-1) B N A p(k) -A p(k-1) • 1 - γ (k-1) b (k-1) a (k) -a (k-1) (4.9)
where

η (k-1) =2.0+0.522 1.0 - a (k-1) W (4.10) and γ (k-1) =1.0+0.76 1.0 - a (k-1) W (4.11)
which is a linear approximation of the original expression introduced in [START_REF] Ernst | Estimation on J-integral and tearing modulus T from a single specimen test record[END_REF] and defined by:

γ (k-1) = η (k-1) -1 - a W η ′ p(k-1)
η p(k-1) (4.12)

[62] showed the consistency of Equation 4.11 and Equation 4.11 for CT specimens over the range a/W ∈ [0.5, 0.8].

The elastic unloading compliance method was used to calculate the crack growth during the tests. The specimen compliance writes C (k) = ∆v (k) /∆P (k) , where ∆v (k) is the crack opening measured at the loading line (CLLOD) and ∆P is the unload during the k th loading-unloading sequence. a (k) /W can be calculated using the polynomial fitting function given by ASTM-E1820:

a (k) W =1.000196 -4.06319u (k) + 11.242u 2 (k) -106.042u 3 (k) + 464.335u 4 (k) -650.677u 5 (k) (4.13)
where u (k) is the normalized compliance u (k) , with

u (k) = 1 1+ ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ 1 B e EC c(k) ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ 1/2 (4.14)
where B e = B-(B-B N ) 2 /B is the effective width of the specimen, and C c(k) is the specimen load-line crack opening compliance on the k th unloading/ reloading sequence corrected for rotation. A correction factor was added to account for the rotation of the specimen during the test and writes:

C c(k) = C (k) H * R sin θ (k) -cos θ (k) D R sin θ (k) -cos θ (k) (4.15)
where The angle θ is

C (k) =
θ = sin -1 ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ d m 2 + D (D 2 + R 2 ) 1/2 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ -tan -1 D R (4.16)
where d m is the total measured load-line crack opening displacement. The experimental CMOD-Load curves depicted in Figure 4.27-a shows a very good reproducibility of the tests. The results were processed using ASTM-E1820 to determine the material J-R curves, where M = 2 but another value may be used based on the experimental data. The exclusions lines are then drawn parallel to the construction line with an offset of 0.15 mm and 1.5 mm along the x-axis.

Then, only the experimental points that lie inside the area define by this exclusions line are used to fit the determine the R curve. According to ASTM-E1820, these experimental points were fitted using a power law regression line under the form:

J = α∆a n (4.18)
where α and n are the coefficients obtained by minimizing the error between the experimental data and the regression line.

After completion of the tests, the specimens were broken using liquid nitrogen in order to observe the fracture surfaces. No brittle failure nor delamination were observed during testing where the temperature is -40 • C,-20 • C and +20 • C.

Single-Edge-Notched-Bending (SENB)

The tests were carried out following the testing protocol presented in ASTM-E1820 for SENB specimens. However, it was not possible to use the recommended B =0 .5W cross-section geometry, and specimens with square cross-section B = W = 14 mm were used instead. The specimens were fatigue precracked to obtain an initial a 0 /W ratio of about 0.3 which is slightly below the ASTM-E1820 current practice (a 0 /W = 0.5). This choice was made so that it was possible to compare the resulting material R curves with those obtained on SENT specimens tested for similar a 0 /W values. Side-grooves were machined so that the total width reduction equals 10 % of B, resulting in a net width B N equals 12.6 mm. The precracking process was carried out below the limit load given by:

P limit = 0.5Bb 2 0 σ Y S (4.19)
where σ Y is the flow stress σ Y = 1 /2(σ YS + σ UTS ) and S =4W is the span between the two bending points. P max is given by:

P max = K (BB N ) 1/2 W 3/2 Sf a W (4.20)
where K = K max precracking , and with:

f a W = 3 a W 1/2 1.99 - a W 1 - a W 2.15 -3.93 a W +2.7 a W 2 2 1+2 a W 1 - a W 3/2 (4.21)
According to ASTM-E1820, the maximum allowable stress intensity factor during the precrack, K max precracking , is given by:

K max precracking = σ f YS σ T YS 0.063σ f YS MPa √ m (4.22)
where σ f YS and σ T YS are the material yield stresses at the fatigue precrack and test temperatures. In the case of this X65 material, it results in K max precracking = 34.65 MPa √ m.

The tests were carried out on a servo hydraulic MTS machine with a 100 kN load cell. The pin diameters was equal to 8 mm and the span S =4W . A double-clip gages method was used to measure the CMOD and the CTOD during the test using ExxonMobil relationships. The following outputs were recorded during the test:

• The time, in seconds (s) • The jack displacement, in millimeters (mm) • The load, in kilonewtons (kN) • The crack opening displacement 2 mm above the specimen surface using a MTS clip gage, in millimeters (mm) • The crack opening displacement 8 mm above the specimen surface using a MTS clip gage, in millimeters (mm)

The J integral is partitioned into an elastic part J e and a plastic part J p for each k th loading-unloading. The elastic component J e(k) is given by Equation 1.38 (page 30) where the stress intensity factor K (k) writes:

K (k) = P (k) S (BB N ) 1/2 W 3/2 f a (k) W (4.23)
The plastic component J p(k) is calculated using the incremental method and given by:

J p(k) = J p(k-1) + η p(k-1) b (k-1)B N A p(k) -A p(k-1) • 1 - γ (k-1) b (k-1) a (k) -a (k-1) (4.24)
where A p(k) denotes the area under force versus CMOD record. The quantity γ (k) is given by Equation 4.12 and η (k) writes:

η (k-1) =3.667 -2.199 a (k-1) W +0.437 a (k-1) W 2 (4.25)
The crack growth is calculated using the elastic unloading compliance method by:

a (k) W =0.999748 -3.9504u (k) +2.9821u 2 (k) -3.21408u 3 (k) + 51.51564u 4 (k) -113.031u 5 (k) (4.26)
where u (k) is the normalized compliance for the k th unloading/ reloading sequence given by:

u (k) = 1 1+ B e WEC (k) S/4 1 /2 (4.27)
No correction rotation factor was applied in accordance with ASTME-E1820.

After completion of the tests, the specimens were cooled down by means of liquid nitrogen and broken into two parts. The actual initial crack length a 0 was then measured using ASTM recommendations as depicted in Figure 1 Two SENB tests (see Table 4.11 for details) were performed at room temperature. 4.12.

In [START_REF]Submarines Pipelines Systems[END_REF], a conversion factor m is proposed in Appendix A to convert J to CTOD. These relationships are given in Equations 1.48 to 1.50. No range of applicability is specified so it is interesting to plot the given relationships over the full range of CTOD during the test. Two quantities are compared: J-based CTOD and CTOD measured using the double-clip gages. Results depicted in Figures 4.30-b and 4. 30-c show that the m factor enables to obtain the CTOD with a good accuracy as long as only small CTOD values are considered.

As seen in Figure 4.30-d, the two evaluation split for a CTOD of about 1 mm, corresponding in these SENB tests to a crack propagation of about 0.225 mm. For greater values, the CTOD based on J is lower than the CTOD measured using the double-clip gages which will, in the case of a CTOD based ECA, conduct to conservative assessments. This result is in accordance with Moore [START_REF] Moore | Validation of Methods to Determine CTOD from SENT Specimens[END_REF]. More important, on the other hand the inverse relationships (J from CTOD) will not be conservative and shall not be used. As introduced in Chapter 1, no procedure is released yet, and only recommendations are found in the literature. Therefore, the tests were performed using "parts" of each recommended practice as follows:

• Specimen geometry:

- -Instrumentation: double-clip gages -ExxonMobil -Clamped with a specimen length between the grips H = 10W -ExxonMobil • Post-processing of the data:

-Crack growth evaluation: elastic unloading compliance -Cravero -Correction factor to avoid negative crack growth at the beginning of the test -Canmet -J-R curve:

* J p calculation: incremental method -Cravero * η p -γ p factors -Cravero -CTOD-R curve -ExxonMobil -J-R curve -Cravero b. Crack growth measurement:
As introduced in chapter 1, the single-specimen procedure enables to obtain a complete material Rcurve using only one specimen. This method implies that the crack advance can be accurately measured during the tearing test using the elastic unloading compliance. Three tests were performed to check the applicability of this method. The specimens were loaded under displacement control and a series of elastic unloads was performed so that it was possible to evaluate the specimen stiffness. After each unload, a silicon replica was realized to measure the current crack advance. Comparisons are depicted in Figure 4.31 where the x-axis represents crack advance estimated by the compliance method, and the y-axis represents crack advance measured using the silicon replica. It is observed that results obtained using the two methods can be considered as closed, with an average error of -8.44 % (underestimation using the compliance method) and a maximal error of 48.3 % (overestimation using the compliance method). However, the silicon replica procedure is difficult to use and might be the cause of such differences.

X65 RT SENT B10 X65 RT SENT B9 X65 RT SENT B7 ∆a measured using the unloading compliance method (mm) ∆a measured using the replica method (mm) 4 3.5 c. Effect of a 0 /W ratio on the material R-curve:

Kang et al [START_REF] Kang | Influence of Constraint on J-resistance Curves for an X100 Pipe Steel[END_REF] showed that the material R curve is highly affected by the initial crack depth to width ratio. SENT tests were performed with a 0 /W =0 .25, 0.35 and 0.50 in order to check for a potential effect of the crack depth. The deep notched specimens (a 0 /W = 0.35 and 0.5) were fatigue precracked following [START_REF]Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness KIC of Metallic Materials[END_REF] recommendation for SENB specimens (fatigue precracking in 3-point bending configuration), whereas the shallow notched specimens (a 0 /W =0.25) were EDM machined resulting in a initial crack width equals about 110 µm which is clearly higher than for a typical fatigue pre-cracked specimen, where crack tip radius is assumed to be about 4 µm. Specimens were also EDM with a larger wire resulting in an initial notch width of 300 µm. The effect of the notch sharpness was not directly investigated during this PhD, but Kang et al [START_REF] Kang | Influence of Constraint on J-resistance Curves for an X100 Pipe Steel[END_REF] and Moore [START_REF] Moore | The Effect of Notch Sharpness on the Fracture Toughness Determined From SENT Specimens[END_REF] showed that no significant effect was observed as long as the material is on the upper shelf of the transition curve, i.e. the material is fully ductile. Since results on the axisymmetric round notched bars and CT specimens demonstrated the fully ductile behavior of the X65 at room temperature, it is assumed that results for EDM notched specimens and fatigue precracked specimens are similar.

CMOD-load diagrams of nine SENT tests with various a 0 /W ratios from 0.25 to 0.592 are depicted in Figure 4.32-a. The actual a 0 /W are reported in Table 4.13, and the difference are due to the difficulty to control the crack growth during the fatigue precracking process. The actual initial crack lengths as well as the final crack lengths were measured post mortem in accordance with ASTM-E1820. The tests results were post-processed in order to obtain the material R curves using the procedure presented in Chapter 1, so that it was possible to derive both J and CTOD-R curves. These latter are plotted in Figure 4.32-b and Figure 4.32-d, respectively. First, one can see that the results are relatively reproducible. Then, these curves show identical trends with a high effect of the initial crack length on both J and δ values, confirming results of Kang et al [START_REF] Kang | Influence of Constraint on J-resistance Curves for an X100 Pipe Steel[END_REF]. The J based criteria J 0.2 and J 1 were determined as well as the δ based criteria δ 0.2 and δ 1 , and these values are plotted in Figure 4.33 and reported in Table 4.13. These quantities vary almost linearly as functions of the ratio a 0 /W within the range 0.25 to 0.565. Data obtained with EDM notches (a 0 /W ≈ 0.25) give results consistent with data obtained with fatigue precracks (a 0 /W > 0.35) as trends can be fitted using the same correlation.

As suggested in ExxonMobil SENT procedure [START_REF]Measurement of Crack-Tip Opening Displacement (CTOD) Fracture Resistance Curves Using Single-Edge Notched Tension (SENT) Specimens[END_REF], the material R curves were fitted using exponential functions of the form: where ∆a denotes the crack advance. The experimental curves were fitted for crack advances greater than 0.5 mm to avoid the inconsistencies for low ∆a values. Using this method, good fits were obtained as depicted in Figure 4.34. The J-R curves were fitted together according to their respective a 0 /W ratio, and the experimental CTOD-R curves were fitted independently, and average values of the fitting parameters, namely β average and n average are reported in Table 4.14.

J = α∆a m (4.

e. Effect of temperature on material R curves

A number of tests were carried out at -20 • C and -40 • C inside a cold chamber which was cooled down spraying liquid nitrogen. The temperature of the chamber was automatically maintained constant during the full test and monitored using a digital thermometer located inside the cooled chamber. It was also possible to read the temperature using a remote display placed outside the chamber. The temperature of the samples was also constantly measured at two points located on either side of the notch (see Figure 4.38-b). In doing so, it was possible to check the temperature through the entire specimen. Due to the relative important thickness of the SENT specimen, cooling down the specimen was very time consuming. For example, it took approximately 40 minutes to reach -20 • C and about 90 minutes to reach -40 • C for a 14 × 14 mm specimen. When the temperature of the test was met, a waiting time of about 10 minutes was observed to ensure that a plateau was reached. Moreover, a high volume of liquid nitrogen is required to performed a single test so that it was not possible to perform more than three SENT tests before refilling the reservoir, meaning that such tests are very time consuming.

Results of four tests carried out at -20 • C and -40 • C are given in the following and details of the tests are given in Table 4.15. For the sake of comparison, results of SENT tests performed at room temperature are also given. Load versus CMOD curves are plotted in Figure 4.39-a. As expected following the tensile tests results, decreasing the temperature resulted in an increase of the load reached by the SENT specimens.

It is shown that values of J for a given crack advance are higher at lower temperatures than at room temperature. This effect is partially due to the increase of the yield stress with decreasing temperatures as a higher energy is dissipated during crack advance provided that damage mechanisms and growth rates remain similar. Since J is a function of the area under the CMOD -load curve, and since the temperature mostly have an effect on the yield stress R p0.2 and the ultimate tensile strength R m of the material, it is instructive to normalized the load by R m to investigate on the temperature effect on SENT results. The comparison is depicted in Figure 4.40-a. where the load is also divided by the actual initial cross section of each specimen. It is observed that the curves nearly superimposed up to the failure, with respective maximal loads almost identical. In the same way, the J-R curves can be normalized by R m to take the effect of the temperature into account in the comparison, leading to the results depicted in Figure 4.40.

It is shown that it allows to practically gather the curves when compared to non-normalized R curves in Figure 4.39. Serimax developed a Mechanized Gas Metal Arc Welding Pulsed (mGMAW-p) 5G welding procedure using SATURNAX 09 equipment with passes from root to cap. This welding process shall be suitable for arctic applications and complies with the following requirements as defined by TOTAL S.A. (see Table 4.16):

-40 • C -20 • C RT CMOD (mm) F/((W -a 0 ) BR m )( -) 7
(a.) F/ [(W -a 0 ) BR m ] R curves (b.) J/R m R curves
• The filler metal shall be suitable for low temperature applications.

• The weld overmatch shall be minimum 80 MPa.

• The misalignement shall not exceed 3 mm.

• The Charpy V-notch energy absorption at -50 • C shall be at a minimum average of 56 J (and minimum single value of 50 J) for the weld metal and at the fusion line. • The shear area at -50 • C shall be at a minimum average of 85 % (and minimum single value of 75 %).

Metallurgical composition

Serimax determined the chemical composition of the weld material using optical emission spectrometry. Results are given in Table 4.18. As introduced in Chapter 3, it is always challenging to properly characterize the material properties of a girth weld. The use of classical round bar specimens does not able to obtain a full stress-strain tensile curve, due to the weld overmatching. The strain localizes in the softer material and only a limited amount of plastic deformation occurs in the weld material.

Notched Tensile tests were performed on specimens machined cross weld, so that the notch region contains only weld material as depicted in Figure 4.44. The raw material was etched using a 4 % Nital solution so that it was possible to machine the notch with accuracy. The testing protocol is identical to that of the parent material. The experimental tensile stress-strain curves at room temperature are depicted in Figure 4. [START_REF]API Standard 1104, Welding of Pipelines and Related Facilities[END_REF] and results are summarized in Table 4. [START_REF] Ernst | Estimation on J-integral and tearing modulus T from a single specimen test record[END_REF]. For each specimen, failure occurred after necking so that large values of diametrical reduction were reached. It is noted that this quantity is almost identical for NT 10 and NT 4 specimens with an average value of ∆Φ/Φ 0 equals 35.84 %, respectively 26.47 %. On the other hand, the NT 2 specimens show a larger scatter with value of ∆Φ/Φ 0 within the range 17.79 % to 20.50 %. Observations of the fracture surfaces indicate an isotropic behavior with perfectly round shape surfaces.

From these results, it is not possible to directly identify the mechanical properties of the material, such as the Young modulus, the yield stress and ultimate stress. Indeed due to the notch, the specimens does not comply with geometrical requirements as explained in Chapter 3. This point will be discussed in Chapter 6.

Comparison with X65 results in Figure 4. 45-b shows that the weld material highly overmatches the parent material since the maximal loads reached by each specimen is largely greater for X65W than for X65. However the ductility of the weld material, represented by the quantity ∆Φ/Φ 0 , is lower. Like for the parent material, it is observed that the temperature has only a slight effect on the material ductility. Ductility measured by ∆Φ/Φ 0 increases with decreasing temperature in particular for NT 2 and NT 4 specimens. This result is somehow surprising but is consistent with results obtained for the base metal (see Figure 4.14 on page 109). However the observed trend lies within the scatter band obtained at room temperature ; it is worth noticing that scatter is more important for the WM than for the BM.

For example at -40 • C , a value of ∆Φ/Φ 0 equals 22.5 % was measured using a NT 2 specimen, whereas tests at room temperature gave an average value equals 18.4 %.

Regarding the tensile properties, the material behaves as expected with an increase of the maximal load reached during tests at low temperatures. Moreover, comparisons with the parent materials at low temperatures depicted in Figures 4.46b

Single-Edge-Notched-Tension (SENT)

Tests were performed at room temperature as well as low temperatures, including -20 • C and -40 • C. Only one specimen geometry was considered and consisted in SENT with a square cross-section B × W with B = W =14 mm, and the initial crack length-to-thickness ratios were all equal to 0.25. The specimens were also side grooved to reach a total reduction of 10% of the initial width, i.e. B N = 12.6 mm. They were clamped using hydraulics grips with a daylight L = 10W as required in [START_REF]Measurement of Crack-Tip Opening Displacement (CTOD) Fracture Resistance Curves Using Single-Edge Notched Tension (SENT) Specimens[END_REF]. The experimental data were processed using the incremental method to calculate J with CANMET correction factor and Cravero definition of η. The material J-and CTOD-R curves as depicted in Figure 4.52a and Figure 4.53a. A large scatter is observed for both R-curves for crack advances smaller than 0.5 mm. This point has not been investigated.

The comparison with the parent material in Figures 4.52b and 4.53b show that the two materials have identical R-curves both in terms of CTOD and J. This point is surprising following results on NT specimens that show smaller ductilities for X65W. It as expected that the cracks would propagate faster in the weld material and therefore that the R-curves would be lower. 4.20, the maximal load reached at low temperatures is slightly greater than at room temperature, as it was expected following the results on NT specimens. Identically, it is observed that the material keeps a good ductility with CMOD-Load curves which slowly decrease after reaching F max as shown in Figure 4.54-a. The results are particularly reproducible as it was observed at room temperature. Identical conclusions are made regarding the material R curves, as depicted in These results are summarized in Table 4.20 so that the effect of the temperature on the weld material properties, particularly the toughness. It is shown that the maximal load, denoted F max , increases when the temperature decreases, with an average F max value being 91.95 kN at room temperature, 95.7 kN at -20 • C and 98.7 kN at -40 • C . On the contrary, decreasing the temperature yields to a decrease of the material toughness, either in terms of J value or CTOD.

Summary

In this section, the results of mechanical tests carried out on the seamless pipe are discussed. The scope of work included a great number of tests on both the parent material and the weld material.

A comprehensive experimental campaign was performed on the X65 steel. Classical tensile tests as well as notch tensile tests were performed in order to study the effect of the stress triaxility τ on the material behavior. It is observed that increasing τ yields to an increase of the maximal strength that can be handle by the material thanks to the multi-axial stress state, and to a decrease of the material ductility since high stress triaxiality rates favor the development of damage. The two materials are shown to have isotropic behaviors in plasticity and in rupture, and no brittle failure was observed even at -40 • C . Comparisons between parent and weld materials also allow the justification of the weld overmatch, which is a key requirement in strain-based design.

Tests were also carried out on cracked specimens such as CT, SENB and SENT to measure the material toughness. A comparison between these three geometries is proposed on the parent material at room temperature, and shows that the material R curves derived using these geometries are ranked as follows:

R curve CT ≤ R curve SENB ≤ R curve SENT

The experimental campaign particularly focuses on the use of the SENT specimen and comparisons arisen from Chapter 1 are presented. From these tests, the following conclusions are drawn:

• Increasing the ratio a 0 /W produces lower material R-curves both in terms of J and CTOD.

• EDM notching in place of fatigue pre-cracking is suitable for SENT tests as long as:

-The wire diameter Φ is small enough. ExxonMobil [START_REF]Measurement of Crack-Tip Opening Displacement (CTOD) Fracture Resistance Curves Using Single-Edge Notched Tension (SENT) Specimens[END_REF] suggests Φ ≤ 0.15 mm, but 0.3 mm is shown suitable in the case of the parent material. -The material is on the upper shelf of its ductile -brittle transition curve (100 % ductile failure).

• Decreasing the temperature results in higher material R curves both in terms of J and CTOD.

• Normalizing the J-R curves by the ultimate tensile strength R m given for the test temperature allows to practically gather the curves.

To go further in the SENT study, it would be interesting to evaluate the robustness of the protocol that has been used through a round-robin trial. Indeed, the testing of the SENT is not straightforward whether it be for the experimental process itself or the post-processing of the data to obtain the material R curve. The procedure is given in Appendix C.

Chapter 5

Modeling of X65 and X65W behaviors

Résumé en français

L'objectif final de l'étude étant la prédiction de la propagation ductile d'une fissure dans un cordon soudé grâce à l'approche locale de la rupture, il est essentiel de correctement évaluer les champs de contraintes et de déformations à proximité d'une fissure. Aussi, la bonne identification des lois de comportement des matériaux de l'étude, que ce soit en plasticité et face à l'endommagement, est impérative.

Ce chapitre propose la démarche déployée pour l'identification de ces lois de comportement, tout d'abord pour le matériau de base, puis pour le matériau d'apport.

Du fait de son comportement isotrope en plasticité, une loi d'écrouissage isotrope simple associée à un critère de von Mises permet une bonne simulation de l'ensemble des éprouvettes non fissurées à toutes les températures pour le matériau X65. Pour cela, les jeux de paramètres suivantes ont été identifiés grâce à l'analyse inverse : Le modèle dit de Gurson-Tvergaard-Needlman (GTN) permet la modélisation de la propagation de fissure pour l'ensemble des éprouvettes fissurées, en prenant en compte le développement de l'endommagement au cours du chargement. Ce modèle nécessite seulement trois paramètres qui peuvent être identifiés grâce aux résultats expérimentaux précédemment obtenus. Pour le matériau de base, les courbes de traction sur éprouvettes entaillées ont ainsi permis d'identifier le jeu de paramètres suivant :

Température R Luders (MPa) R 0 (MPa) Q 1 (MPa) b 1 Q 2 (
Matériau de base : q 1 =1.864 and q 2 =0.879 and h = 100µm

Celui-ci permet également la modélisation de la propagation d'une fissure dans une éprouvette SENT ou CT, avec une très bonne concordance entre les courbes expérimentales et simulées. En particulier, la simulation imite le protocole expérimental avec la simulation des cycles de charges et décharges élastiques pour l'évaluation de l'avancée de fissure par la méthode dite de la complaisance. Ainsi, les comparaisons entre les simulations et les essais sont d'autant plus pertinentes.

Puisque la valeur des paramètres q 1 et q 2 dépendent principalement de la microstructure du matériau et de ses propriétés métallurgiques (telles que la nature et la taille des inclusions), les résultats proposés dans ce chapitre montre qu'il est possible de simuler les essais aux différentes températures avec un même jeu de paramètres GTN.

Ces conclusions s'appliquent également au matériau d'apport, dont le comportement élastoplastique peut être correctement décrit en utilisant les paramètres suivants, associés au critère isotrope de von Mises : Matériau d'apport: q 1 =1.5 and q 2 =1.0 and h = 100µm On note cependant que la modélisation du matériau d'apport est plus délicate, et les comparaisons entre essais et simulations sont moins satisfaisantes. Ce résultat peut certainement s'expliquer par les hétérogénéités du matériau dans la soudure.

Temperature R 0 (MPa) Q 1 (MPa) b 1 Q 2 (

Introduction

As introduced herein before, the objective of the study is to correctly predict ductile tearing of a cracked pipe using the local approach to fracture. In such an approach, it is mandatory to accurately evaluate the stress and strain fields within the area where the crack initiation is likely to occur. Therefore, it is a priority to properly model the elastic-plastic behavior of the materials as well as their damage behavior.

The first part of this chapter is dedicated to the identification of a yield criterion and elastic-plastic material constitutive laws adapted to the X65 parent and weld material at room and low temperatures. The results on the uncracked specimens are used both to identify and validate the criterion.

In a second part, an identical work on the weld material is presented.

Description of the parent material elastic plastic behavior 5.2.1 Isotropic von Mises criterion

The von Mises criterion denoted σ eq or J 2 writes in a Cartesian system (⃗ x , ⃗ y , ⃗z ):

σ eq = √ 2 2 (σ xx -σ yy ) 2 +(σ yy -σ zz ) 2 +(σ zz -σ xx ) 2 +6σ 2 xy +6σ 2 yz +6σ 2 zx (5.1)
or in the eigenspace ( ⃗e 1 ,⃗ e 2 ,⃗ e 3 ) of the stress tensor σ :

σ eq = √ 2 2 (σ 1 -σ 2 ) 2 +(σ 2 -σ 3 ) 2 +(σ 3 -σ 1 ) 2 (5.2)
Using the stress deviator tensor denoted s ˜, the von Mises writes:

σ eq = J 2 (σ ˜)= 3 2 s ˜: s ˜(5.3)
where

s ˜= σ ˜-1 3 Tr(σ ˜) I ˜= σ ˜-σ m I ˜(5.4)
where s ˜is the stress deviator. This criterion is perfectly adapted to the isotropic plastic behavior of both X65 parent material and weld material. Note however that other isotropic yield criteria exist such a the Tresca or Hosford [START_REF] Hosford | Generalized isotropic yield criterion[END_REF] criteria.

Material constitutive equation 5.2.2.1 Formulation

The hardening behavior of the material was assumed to be isotropic as all tests were carried out using monotonic loading. The flow curve is represented as a function of the cumulated plastic strain p referred to as R(p). The plastic yield condition is then expressed as f (σ ˜)=σ -R(p) where σ is an equivalent scalar stress measure. In the case of the X65 parent material, the equivalent von Mises stress is used.

Results given in chapter 4 show that the change in temperature has a significant effect on both the yield strength and the ultimate tensile stress. These two values increase with decreasing temperature. Moreover, it is shown that the temperature also has a slight effect on the hardening properties of the material. Therefore, it is not possible to derive a single constitutive equation valid over the temperature range of interest. Three different flow curve were identified separately. It was also observed that the temperature has no effect on the elastic behavior of the material, meaning that both the Young's modulus E and Poisson's coefficient ν are constant. Then, it is possible to model the elastic part of the material law over the full temperature range using:

Results at low temperatures

Two sets of parameters are also obtained to describe the material behavior at low temperature (-20 • C and -40 • C ). They write: R(p) -20 = max 463, 420 + 251 1 -e -15.7p + 360p (5.11) and R(p) -40 = max 488, 466 + 291 1 -e -10.5p + 250p (5.12)

A comparison between equation 5.10-5.12 shows that the increase of the yield stress is correctly taken into account through the constant term, i.e. the stress measured along the Lüders Plateau. However the effect of temperature on hardening is not completely described by simply increasing the value of the plateau stress. Other hardening parameters (i.e. R 0 , Q 1 , b 1 and Q 2 ) must be expressed as function of temperature. Table 5.1 gathers the values of the hardening parameters at the different temperatures.

T R Lüders R 0 Q 1 b 1 Q 2 ( • C) (MPa) (MPa) (MPa) - (

Description of the parent material fracture behavior 5.3.1 Damage processus

In the case of the X65 parent material, the failure is driven by the ductile growth of the existing voids within the material matrix. This process is divided in three steps that are:

• Nucleation of cavities; • Growth of these nucleated cavities; • Coalescence leading to the final fracture.

Considering a material with an initial porosity f 0 , the void nucleation corresponds to the phase during the loading where micro voids are created and added to the already existing voids. At that point, a nucleation porosity, denoted f N is added to f 0 . The creation of such voids is mainly due to local cohesions between the matrix and particles, or to the fracture of these particles resulting in voids. This process is to be considered as continuous throughout loading, since all the particles will not lead to a void at the same time. The growing phase of these voids simply corresponds to the modification in volume and shape of the voids. Finally, coalescence corresponds to the moment where the remaining ligament between two adjacent porosities cannot sustain load anymore. At that time, these two voids joint together resulting in the initiation and propagation by coalescence with neighboring voids of a crack within the material matrix.

All these phenomenons can be described using a variety of models. Following [START_REF] Atkins | Fracture mechanics and metalforming: damage mechanics and the local approach of yesterday and today[END_REF] two types of approaches are now mainly used: (1) failure initiation criteria (un-coupled models), (2) fully coupled models. Failure criteria can be used to post-process elasto-plastic calculations to determine fracture initiation ; they can be based on purely empirical considerations (see e.g. the Cockcroft-Latham model [START_REF] Cockcroft | Ductility and the workability of metals[END_REF]) or on micromechanics (see e.g. the Rice-Tracey model [START_REF] Rice | On the ductile enlargement of voids in triaxial stress fields[END_REF]). Fully coupled models are able to describe the effect of damage on material yielding ; in particular they represent strong material softening caused by damage growth up to failure. They are either based on micromechanics and often referred to a porous-plasticity models (see e.g. the Gurson [START_REF] Gurson | Continuum Theory of Ductile Rupture by Void Nucleation and Growth. Part I. Yield Criteria and Flow Rules for Porous Ductile Media[END_REF] and Gurson-Tvergaard-Needleman (GTN) [START_REF] Tvergaard | Analysis of the cup-cone fracture in a round tensile bar[END_REF] models) or on phenomenology (see e.g. the Lemaitre [START_REF] Lemaitre | A continuous damage mechanics model for ductile fracture[END_REF] model). In this work, the use of the coupled model proposed by Gurson [START_REF] Gurson | Continuum Theory of Ductile Rupture by Void Nucleation and Growth. Part I. Yield Criteria and Flow Rules for Porous Ductile Media[END_REF] and modified by [START_REF] Tvergaard | Analysis of the cup-cone fracture in a round tensile bar[END_REF] is used.

Gurson Tvergaard Needleman model

In [START_REF] Gurson | Continuum Theory of Ductile Rupture by Void Nucleation and Growth. Part I. Yield Criteria and Flow Rules for Porous Ductile Media[END_REF], Gurson extends the work initiated by [START_REF] Rice | On the ductile enlargement of voids in triaxial stress fields[END_REF] where the growth of voids in a ductile matrix is studied. In this approach, the void consists in a hollow sphere of radius r at the center of an elementary volume of radius R. The matrix is supposed to be perfectly plastic with a yield stress σ 0 and to obey to the von Mises yield criterion. The void volume fraction f is simply defined as

f = r R 3 = V -V m V (5.13)
where V is the volume of the void and V m is the volume of the elementary volume. As in [START_REF] Rice | On the ductile enlargement of voids in triaxial stress fields[END_REF], the elementary volume is considered incompressible so that V m is a constant. [START_REF] Gurson | Continuum Theory of Ductile Rupture by Void Nucleation and Growth. Part I. Yield Criteria and Flow Rules for Porous Ductile Media[END_REF] introduced a new formulation to describe the yield surface Φ of the porous material that writes:

Φ = σ 2 eq σ 0 +2f cosh 1 2 σ kk σ 0 -1 -f 2 = 0 (5.14)
where σ eq is the equivalent von Mises stress and σ 0 is the yield stress.

The Gurson Tvergaard Needleman (GTN) model consists in a modification of Equation 5.14 as described in [START_REF] Tvergaard | Analysis of the cup-cone fracture in a round tensile bar[END_REF]. Then, it writes:

Φ = σ eq R 2 +2q 1 f cosh 3 2 q 2 σ kk R -1 -q 2 1 f 2 = 0 (5.15)
where q 1 and q 2 are two parameters added so that numerical results are in better agreement with experimental data. In literature, typical values for steels are q 1 =1.5 and q 2 = 1. R represents the flow stress of the undamaged matrix.

The GTN model as described in Equation 8.10 is limited to the growth process of the void. Coalescence was not taken into account in the original Gurson model. In [START_REF] Tvergaard | Analysis of the cup-cone fracture in a round tensile bar[END_REF], the phenomenon is captured with the substitution of the true porosity f by the term f * (apparent porosity) which writes:

f * = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ f if f ≤ f c f c + 1/q 1 -f c f F -f c (f -f c ) if f>f c (5.16)
where f c denotes the critical porosity value at the onset of the coalescence, and f F corresponds to the porosity at the end of the coalescence, i.e. the fracture. From this equation, it is noted that the apparent porosity f * at that fracture is equal to 1/q 1 .

The plastic strain rate tensor is given by the normality rule as:

ε ˜p = λ ∂Φ ∂σ ˜(5.17)
where λ is the plastic multiplier. It is related to the cumulated plastic strain p by the following equation:

σ ˜: ε ˜p = (1 -f ) ṗR (5.18)
which expresses the equality between the plastic dissipation at the macroscopic level (left handside) and the microscopic level (right handside) [START_REF] Gurson | Continuum Theory of Ductile Rupture by Void Nucleation and Growth. Part I. Yield Criteria and Flow Rules for Porous Ductile Media[END_REF]. The evolution of the porosity is controlled by void growth and nucleation of new voids:

ḟ = (1 -f )trace( ε ˜p)+A n ṗ (5.19)
where the first term on the right handside corresponds to void growth (and mass conservation) and the second term corresponds to void nucleation. Material parameter A n controls nucleation rate. A n may be expressed as a function of strain but also triaxiality (see e.g. [START_REF] Dalloz | Effect of shear cutting on ductility of a dual phase steel[END_REF]). In this work, based on the microstructural investigations, nucleation will not be used. It will be assumed that the initial void volume fraction is equal to the inclusion content.

The GTN model is implemented in the FE software Zebulon, developed at Ecole des Mines de Paris [START_REF] Besson | Large scale object-oriented finite element code design[END_REF][START_REF] Foerch | Polymorphic constitutive equations in finite element codes[END_REF]. An implicit scheme is used to integrate the constitutive equations. The consistent tangent matrix is computed using the method proposed in [START_REF] Simo | Consistent tangent operators for rate-independent elastoplasticity[END_REF][START_REF] Besson | Modeling of crack growth in round bars and plane strain specimens[END_REF]. An updated Lagrangian formulation was used in which Jauman stress rates are used [START_REF] Ladevèze | Sur la théorie de la plasticité en grandes déformations[END_REF]. Calculations were done using linear elements with full integration. In regions where the crack propagates, four node (AXI) and 8 node (3D) elements were used. To avoid pressure fluctuations within the elements, a selective integration technique was used [START_REF] Hughes | Generalization of selective integration procedures to anisotropic and non linear media[END_REF]. Usual symmetry conditions are accounted for in order to reduce the size of the calculations.

Identification of the GTN model parameters

Meshes

The identification of parameters q 1 and q 2 was carried out on the NT χ specimens only. The axisymmetric geometry enables to run the simulations on FE models with a reduced number of elements. The meshes are depicted in Figure 5.8.

Even though the GTN model is mesh size dependent. A simple rule is that the mesh size should be of the order of magnitude of the average distance between inclusions within the material matrix. Due to the very low number of inclusions (see Figure 4.3 page 101), a value of 100 µm was selected. The loading and the boundary conditions are the same as for elastic plastic simulations. The specimens are loaded under displacement control, and nodal displacements are recorded so that it complies with the actual measurements during the tensile tests. Due to the reduced size of the element at the plane of symmetry, the value for the ratio of convergence r must be calculated to ensure that results are consistent. A simple relationship in [START_REF] Bron | Simulation of the ductile tearing for two grades of 2024 aluminum alloy thin sheets[END_REF] gives:

r = bhR m 100 (5.20)
where b and h are the two smallest dimensions of the elements and R m is the ultimate tensile strength.

After the porosity f reaches the value f F =1 /q 1 at a least two integration points, the element is considered as broken. Then, its rigidity is numerically set at the low value of 1 MPa, meaning that it does not participate to the rigidity of the structure anymore. Using this method, it is possible to virtually propagate a crack in a specimen. Figure 5.9 shows the porosity at the onset of the coalescence, i.e. when the first element is considered as broken. As expected, the damage (porosity) mostly develops at the center of the specimens where the stress triaxiality is the highest. It results in a crack that propagates towards the external surface from the center of the specimen in the notched area.

The comparison depicted in Figure 5.10 shows the results of the simulations carried out using the set of parameters obtained from the identification process. The comparisons with the experimental data show a good agreement when the values for the GTN parameters are: q 1 =1.864 and q 2 =0.879 (5.21) with an initial material porosity taken equal to 5. 10 -4 . Values of the parameters q 1 and q 2 are mostly dependent on both the microstructure and the fracture mechanism. As shown in Chapter 4, the material remains on the upper shelf of the brittle-to-ductile transition curve even at the lowest considered studied which is -40 • C . Moreover, the material keeps a good ductility and no indication of brittle fracture was shown at low temperatures. Therefore, it is reasonable to formulate the assumption that the microstructure and the fracture mechanism of the X65 parent material remains the same at room temperature and low temperatures. Then, the values of the parameters q 1 and q 2 for -20 • C and -40 • C applications are identical to those given in equation 5.21.

GTN T-loading L-loading

Comparisons between the simulations and the experiments are depicted in Figure 5.11 and show these values of q 1 and q 2 enable to correctly predict the initiation of the crack propagation, even at low temperatures.

Simulation of the SENT specimens

The simulation of the SENT specimen is used as a validation of the GTN model parameters given in equation 5.21. The axisymmetric notched specimens are used to identify q 1 and q 2 so that the point corresponding to the beginning of the propagation of a macroscopic crack is in agreement with the experimental result. However, it does not necessarily ensure the crack extension phase to be correctly modeled. In particular, this phase is strongly mesh size dependent for pre-cracked specimens whereas mesh size has a much weaker effect on the simulations of NT specimens.

As a first guess, a size of 0.1 mm×0.1 mm was selected. A typical mesh of a SENT specimen is depicted in Figure 5.12. A blunted crack with an initial crack tip radius of 150 µm is modeled so that it is in agreement with the initial radius obtained using electro discharge machining. Side grooves are also modeled as depicted in Figure 5.12 to comply with the actual specimens. In addition, purely elastic elements are added to the mesh to model the double clip system as depicted in Figure 5.13. Two nodes located at +2 mm and +8 mm above the specimen surface are introduced and correspond to the position of the two clips. Monitoring their in-plane displacements, it is then possible to calculate the CMOD and the CTOD using the same protocol as during actual tests and to compare the computed values with the experimental measurements. A group of elements at the symmetry plane, highlighted in red in Figure 5.14 is created and corresponds to the crack extension path. The elements contained in this group are considered damageable and their behavior corresponds to the identified GTN model. The rest of the mesh is submitted to high level of plastic strain, but no crack was observed in this region. Therefore, the simple elasto-plastic law was assigned to these elements. Creating two partitions enables to decrease the computation time.

Simulations were carried out under displacement control, and loading-unloading sequences were performed so that it was possible to process the data, just like for the actual tests. A Z-Set plug-in has been developed so that it is possible to pilot the boundary conditions of the specimen according to the recommendations from ExxonMobil. Its principle is very simple: The tensile load is applied under displacement control at one end of the specimen at a jack displacement rate equal to the experimental x Figure 5.14 -View of the crack front as meshed for SENT calculation. The mesh size in the crack region is of 100 x 100 µm one. At the end at each increment, two quantities are monitored: the load F and the crack opening displacement V 1 measured 2 mm above the surface (see equation 1.62 page 38 for definition). Using ExxonMobil recommendations, it is then possible to start and stop each loading-unloading sequence for given ∆V 1 and ∆F values. At the end, a full CMOD-load curve is obtained which closely mimics the experimental protocol.

The comparison at room temperature in Figure 5.15-b shows that the numerical results are in a very good agreement with the experimental data up to the complete failure of the specimen. Figure 5.16 shows the evolution of the crack front during the simulation. In these pictures, the elements where the material is considered as broken are removed.

The numerical data are then processed using the same Python routine as for experimental data so that it is possible to obtain a simulated material CMOD, CTOD or J-R curves. Results depicted in Figure 5.17 show a good fit between the experimental and the numerical results again. This result is very interesting because it demonstrates the capability of the GTN approach to properly model the ductile crack tearing process. Moreover, a comparison between the predicted crack size and the actual fracture surface for CTOD = 3.4 mm is depicted in Figure 5.17-d. It shows that GTN model slightly overestimated the crack advance of about 0.200 mm, corresponding to two rows of elements at the crack tip at the center of the specimen. However, the global deformed shape of the specimen is well predicted, particularly the necking.

As already mentioned, the choice was made to keep the GTN parameters q 1 and q 2 constant for the three temperatures of the study, and it was shown in Figure 5.11 that the identified set of parameters enables to correctly predict the failure of the axisymmetric specimens. Simulations were carried out on SENT specimens using the appropriate hardening laws and the GTN model. Results are depicted in Figures 5. [START_REF] Sumpter | Method for laboratory determination of Jc. In: Cracks and fracture[END_REF] The comparison at -40 • C in Figure 5. [START_REF] Ernst | Estimation on J-integral and tearing modulus T from a single specimen test record[END_REF]-a shows that the model is not capable of representing the global CMOD -Load curve with a good accuracy after the maximal load is reached. After that point, the load is underestimated by the FEA. However, in spite of the scatter in experimental data, comparisons with the calculated J, CMOD and CTOD-R curves are good, as shown in Figure 5

CT specimen

The CT tests were also simulated. The same set of parameters q 1 and q 2 for the GTN model is used to describe the fracture behavior. Indeed, it was experimentally observed that the fracture mechanisms are the same for SENT and CT specimens. As for the simulation of SENT specimens, the loading / unloading method was used in the FEA so that it was possible to calculate the crack advance during the simulations. A three-dimensional mesh of the specimen is created and is is depicted in Figure 5.20.

Description of the weld material elastic-plastic hardening behavior

Once the behavior of the parent material is fully characterized, the same procedure is followed in order to model both material plastic and failure behavior of the weld material.

The elastic behavior of the weld material is described using the classical elastic parameters with values identical to the parent material.

• Young's modulus: E = 205,000 MPa • Poisson's coefficient: ν = 0.33 As developed in Chapter 3 and Chapter 4, the material constitutive law can not be determined using classical tensile tests on round bar specimens due to the weld material overmatching compared to the parent material. Therefore, only the experimental data measured on notched specimens are used.

The relationship between the true strain and the true stress is described by one of the three following equations:

R amb (p)=R amb 0 + Q amb 1 1 -e -b amb 1 p + Q amb 2 1 -e -b amb 2 p (5.22) R -20 • C (p)=R -20 • C 0 + Q -20 • C 1 1 -e -b -20 • C 1 p + Q -20 • C 2 1 -e -b -20 • C 2 p (5.23) R -40 • C (p)=R -40 • C 0 + Q -40 • C 1 1 -e -b -40 • C 1 p + Q -40 • C 2 1 -e -b -40 • C 2 p (5. 24
)
where p is the equivalent plastic strain, and Q 1 , b 1 , Q 2 and b 2 are the coefficients used to describe the hardening behavior.

The inverse analysis procedure is used in order to determine their numerical values which are given in Table 5.2. The Figure 5.22 shows a comparison between the experimental data and the numerical results on the X65W at room temperature. It is observed that the identified set of values for the hardening parameters enables to fit the experimental data with a correct accuracy. Identical comparisons are depicted in Figure 5.23 for tensile tests performed at lower temperatures.

One can observe that the identified set of parameters produces numerical results that hardly fit the experimental data. Tentatives to improve the results were made, but better fits at -20 • C and -40 • C could not be achieved because. As seen on Figure 5.23, simulations underestimate the load for NT 2 specimens, and underestimate the load for NT 10 specimens. Then, only an average "best" fitting set of parameters can be identified so that the simulations correctly fit the NT 4 specimens experimental data. This phenomenon can be explained by the non-homogeneity of the weld material across the pipe wall thickness or along the pipe circumferential. Therefore, since specimens were taken from the girth weld at different clock positions, it is possible that mechanical properties at the location of the NT 2 specimens are different (better in that case) than at the NT 10 specimens location. This result is of particular interest, since only the use of the inverse analysis enables to reveal such a distribution of the material properties. However, the phenomenon was not studied for a deeper understanding in this work. Table 5.2 -Weld material constitutive law parameters at room temperature and low temperatures.

Temperature R 0 (MPa) Q 1 (MPa) b 1 Q 2 (

Description of the weld material fracture damage behavior

As for the parent material, the Gurson-Tvergaard-Needleman damage model is used to describe fracture of the weld material. Parameters q 1 and q 2 are identified at +20 The best identified values are q 1 =1 .5 and q 2 =1 .0 (which correspond to the parameters initially proposed by Tvergaard and Needleman and very often used in the literature). The mesh height is taken equal to 100µm as for the base material. Using these values, the comparisons with the experimental data (figure 5.24) show that the void coalescence points are not always correctly predicted: the agreement is correct for NT 10 and NT 4 specimens and overestimated for the NT 2 specimens.

Using the same values for q 1 and q 2 , tests on axisymmetric notched bars conducted at -20 • C and -40 • C were also simulated. Results are shown in figure 5. [START_REF]Fracture mechanics toughness test. Pt. 1: Method for determination of KIc, critical CTOD and critical J values of metallic materials[END_REF]. Relatively good results are obtained although the match is not perfect. The fits are however better than for 20 • C . As mentioned above, this could be due to some heterogeneities in the weld material. Using the identified material parameters for both plastic and damage behaviors, SENT tests carried out at various temperatures were simulated using the same procedure as in the case of the base metal. In particular minimum mesh size was taken equal to 100µm in the crack propagation area.

Conclusion

For the X65 parent material, it was shown in this chapter that a simple isotropic hardening model (see Table 5.3) and a von Mises criterion allows to accurately represent the experimental data up to the crack initiation point for all the tests that were carried out at all temperatures. The Gurson Tvergaard Needleman model has been shown to consistently model crack advance for all the cracked specimens while taking into account the development of the material damage during loading. This model only requires three parameters that can be identified based on the experimental results. The stress-strain curves derived from the notched axisymmetric tensile tests at room temperature were used for the identification of the GTN parameters for the parent material. They write: Parent material: q 1 =1.864 and q 2 =0.879 and h = 100µm and they were shown to be suitable to accurately model the crack propagation in SENT and CT specimens, with numerical results that closely fit the experimental data at room temperature. In particular, the finite element simulations mimic the experimental unloading compliance method used to determine crack advance following the ASTM-E1820 standard. Comparisons of experiments and simulations are therefore more consistent.

Since q 1 and q 2 values mostly depend on the material microstructure and metallurgical properties (such as the nature and size of the inclusions), it has been shown that the same parameters can be used to describe the tests performed at -20 • C and -40 • C. These conclusions also apply to the weld material. The hardening coefficients to be used to describe the material constitutive laws are given in Table 5.4, and the GTN coefficients write:

Weld material : q 1 =1.5 and q 2 =1.0 and h = 100µm However, the weld material appears to be more difficult to model than the base metal as the match between experiments and simulations is less satisfactory. This could be caused by an heterogeneous distribution of the material properties within the weld leading to more experimental scatter. Table 5.4 -Weld material constitutive law parameters at room temperature and low temperatures. Pour cet essai, deux entailles furent créées à l'aide d'un disque à tronçonner : la première étant située dans le métal de base et la deuxième dans le cordon de raboutage. Ces deux entailles furent usinées avec un front rectiligne, avec pour profondeur mesurée au centre de l'entaille :

Temperature R 0 (MPa) Q 1 (MPa) b 1 Q 2 (
• pour le métal d'appport : a = 4.0 mm, de sorte que a/t = 0.180 • pour le métal de base : a = 2.8 mm, de sorte que a/t = 0.126 et distantes de 60 mm l'une de l'autre, de manière à éviter toute interaction. Des calculs éléments finis ont par ailleurs été réalisés de manière à garantir ce résultat. Le schéma d'implentation est donné sur la Figure 6.2.

Une instrumentation complète du tube fut réalisée, de manière à capter la cinématique de l'essai et le comportement mécanique sous l'effet des sollicitations externes. Les données suivantes furent enregistrées :

• Le déplacement des quatre vérins de manière indépendante (en mm) ; • La charge mesurée au niveau des quatre vérins de manière indépendante (en kN) ; • La pression interne (en bar) ; • Les CMOD et CTOD au niveau des deux entailles à l'aide de deux extensomètres d'ouverture, en s'inspirant de la méthodologie utilisée pour les essais sur éprouvettes ; • Les déformations axiales et circonférentielles en quatre points.

L'essai fut réalisé en contrôle de déplacement, de manière à garantir sa stabilité après avoir atteint la force maximale. La pression interne égale à 518 bar fut calculée de manière à atteindre une contrainte circonférentielle égale à 80 % de la limite d'élasticité du matériau de base. Cette pression fut appliquée avant le début du chargement en flexion, et fut conservée constante durant tout l'essai jusqu'à rupture de la canalisation. A noter toutefois que deux déchargements en flexion et pression interne furent réalisées de manière à :

• permettre la réalisation de répliques en silicone des entailles afin d'évaluer une éventuelle propagation de fissure (première décharge uniquement) ; • évaluer l'évolution de la complaisance de la structure due à une éventuelle propagation de fissure.

Après qu'une fuite fut observée au niveau de l'entaille dans le cordon de soudure, le chargement en flexion fut continué jusqu'à atteindre un déplacement vérin de 537 mm. La canalisation fut alors déchargée de manière à ce qu'il soit possible de sécher les surfaces de rupture et les protéger en utilisant un vernis spécial. La propagation circonférentielle de la fissure au niveau du métal d'apport est très importante, et aucune propagation n'est par contre observée au niveau du métal de base.

Une modélisation EF de l'essai est proposée dans ce chapitre. Dans un premier temps, celui-ci est modélisé avec l'hypothèse d'un comportement élasto-plastique et d'un tube sans défaut, de manière à évaluer la bonne prédiction du comportement globale de la canalisation sous l'effet des chargements externes. Cette étape de modélisation est très importante car elle permet d'évaluer la pertinence de la définition des conditions limites, et il est montré que la simulation sous-évalue constamment l'essai.

Une nouvelle expertise du matériau de base est alors réalisée, permettant de mettre en valeur un important gradient des propriétés mécaniques dans l'épaisseur du tube. En particulier, la surface ex-térieure montre une dureté très nettement supérieure qu'à coeur (220 HV2 en surface contre 180 HV2 à coeur), représentant une nette augmentation de la limite d'élasticité entre du coeur vers la surface (598 MPa en surface contre 445 MPa à coeur). La prise en compte de ce gradient de propriétés permet de légèrement recallé la simulation par rapport à l'essai.

Le recallage complet de la simulation est obtenu en modifiant les conditions limites, en faisant l'hypothèse que les appuis entre les vérins et la canalisation ne sont pas parfaitement surfaciques sur la totalité de la longueur des anneaux (voir Figures 6.25 à 6.27).

Dans un second temps, une simulation EF est réalisée en considérant le tube réel contenant une fissure dans le cordon soudé, et le modèle GTN identifié dans le chapitre précédent est utilisé pour modéliser la propagation de la fissure au cours du chargement. Les conditions limites sont identiques à celles identifiées sur le tube sans défaut, et une condition MPC4 (pour maillages incompatibles) est utilisée de manière à réduire le nombre de degrés de liberté du modèle. La comparaison entre l'essai et le calcul montre alors que le modèle GTN permet une bonne prédiction de la rupture de la canalisation.

En complément, les résultats des simulations EF et de l'essai sont comparés avec les résultats des approches SBD proposées par ExxonMobil et le PRCI. On constate que les niveaux de la déformation critique à initiation prédits par les modèles L1 et L2 du PRCI sont inférieurs à la mesure expérimentale pour 1,41 mm de propagation, démontrant le conservatisme de ces deux modèles. Cependant, on observe que la prédiction du modèle L1 du PRCI est très proche de ce qui est prédit par le modèle GTN pour 1 mm de propagation. (2.34 % pour le PRCI contre 2.32 % pour le GTN).

La prédiction de la déformation critique à rupture par le modèle GTN est cohérente avec la mesure expérimentale (5.10 % pour GTN contre 5.32 % pour l'essai). L'approche locale est donc légèrement conservative. Les modèles ExxonMobil L3 et PRCI L4 (6.10 %) se montrent eux non conservatifs.

Material

The test was performed on a 6 m long API-5L X65 grade seamless pipe manufactured by Vallourec & Mannessman (OD 323.8 mm and WT 22.2 mm). The tested segment consisted of two segments that were butt-welded together by Serimax company. The behavior of both parent and weld materials, i.e. X65 and X65W, are described in Chapter 4 and Chapter 5 of this manuscript, and their mechanical properties at room temperature are recalled in Table 6.1.

The initial plan was to machine by means of electro discharge machining (EDM) two notches according to the machining sketch depicted in Figure 6.2. The first one at the weld centerline and the second one in the parent material, spaced 60 mm from each others in order to avoid any interaction and guarantee an identical applied strain on both cracks. Three-dimensional finite element calculations using Z-Set code were performed to ensure this requirement. Each crack was asked to be of constant depth a, except at its ends where quarter circles deflect the crack tip to the surface. The crack length was equal to 2C and the maximal initial opening equal to 0.150 µm (in order to be consistent with the SENT tests) as depicted in Figure 6.3-a. These parameters took the following values:

• Weld centerline crack: 2C = 50.0 mm and a = 5.0 mm, so that a/t = 0.225 with t = 22.2 mm • Parent material crack: 2C = 50.0 mm and a = 3.0 mm, so that a/t = 0.135 with t = 22.2 mm Figure 6.3-b depicts the actual shapes of the two cracks. The notches were machined using a hand disk grinder which resulted in notches as depicted in Figure 6.3 with an initial opening of about 0.600 µm (instead of 0.150 µm):

• Weld centerline notch: depth at the center a = 4.0 mm, so that a/t = 0.180 • Parent material notch: depth at the center a = 2.8 mm, so that a/t = 0.126 • The double-clip gage method was used in order to measure CMOD and CTOD at the two notch locations using four MTS clip gages (in mm), and ExxonMobil equations.

-Weld centerline crack: * Clip 1 to measure the crack opening displacement at a height of 2 mm above the crack mouth * Clip 2 to measure the crack opening displacement at a height of 8 mm above the crack mouth -Parent material crack: * Clip 3 to measure the crack opening displacement at a height of 2 mm above the crack mouth * Clip 4 to measure the crack opening displacement at a height of 8 mm above the crack mouth • The hoop and axial strains measured by the strain gages at four locations (in mm/mm):

-On the tensile side: * SG1 at 12 o'clock position between the two flaws * SG2 at 12 o'clock position to measure the remote strain -On the compressive side: * SG3 at 3 o'clock position on the neutral axis * SG4 at 6 o'clock position to measure the remote strain • The strain field at the vicinity of the two crack using DIC system (3D GOM ARAMIS)

The strain gages SG1, SG2, SG3 and SG4 were asked to be placed as depicted in Figure 6.5. In particular, the position of SG2 was chosen to ensure the capability to measure the actual uniform remote strain far away from both cracks. A distance of 500 mm from SG1 was considered, in agreement with FE calculation. However, SG2 was incorrectly positioned during the pipe preparation at SZMF with a spacing between SG1 and SG2 of about 100 mm only as seen in Figure 6.6-a.

In addition, the threaded holes to mount the knives for the double-clip gage method were mispositioned. Consequently, it was not possible to correctly (i.e., in parallel) position the knives. Therefore, a slight misalignment was observed for the weld material notch, and a greater misalignment was observed

Experimental results

Internal pressure

Figure 6.9-a depicts the evolution of the internal pressure during the test. The graph can be divided into seven sequences :

• Increase of the internal pressure up to 518 bars.

• Internal pressure kept as constant during the bending.

• Decrease of the internal pressure down to nearly 0 bar.

• Internal pressure kept equal to 0 bar during unloading in bending.

• Increase of the internal pressure up to 518 bars.

• Internal pressure kept constant during bending up to failure.

As one can see, the pressure was correctly maintained during each sequence.

Displacement -load curve

Figure 6.10 presents the load -jack displacement curve. As one can see in Figure 6.10-a, the loading is not symmetric with lower load levels for the left jacks (1 and 2) than for right jacks (3 and 4), with a difference of about 30 kN (3 tons or about 10 % of the load) which remains constant during the whole test. This difference may be explained by the geometry of the setup or the boundary conditions that might be not exactly symmetric with respect to the plane containing the girth weld.

Strain gages results

Figure 6.11 depicts the evolution of the strains in axial (L) and hoop (C) directions as a function of the jack displacement. Two mains remarks are formulated. First, comparing SG1 and SG4, one can observe that the pipe behaves unsymmetrically in the axial direction. Indeed, it was expected that the axial strain measured at the extrados would be the opposite of the axial strain measured at the intrados, due to the global bending load since the axial strain due the internal pressure is negligible. Two hypotheses can explain this result: 1. A global loading of the pipe not in bending.

2. An improper calibration or malfunction of at least one of the axial strain gages.

These hypotheses are discussed later using comparisons with finite element analyses. Furthermore, SG4 provided odd results in the hoop direction as seen in Figure 6.11-b. However, it is believed that it is only due to a material problem, therefore its results were not considered.

Predicted strain capacity using global approaches

The tensile strain capacity of the seamless pipe can be estimated using the global approaches developed by ExxonMobil and PRCI, presented in Chapter 2 of this text.

ExxonMobil multi-tier approach

Three assessment levels are proposed in ExxonMobil multi-tiered approach. It is reminded that the two first level, namely level 1 (L1) and level 2 (L2) are based on analytical formula. The main difference between L1 and L2 is the degree of conservatism in the result due to simplified hypotheses assumed for the calculation. All the details of this approach are given in Chapter 2.

ExxonMobil L1

This assessment level is the most conservatism but it requires the less amount of data concerning the geometry of the pipe and material properties. The following parameters are fixed. The actual values are given between parenthesis for comparison.

• Hi-lo misalignment is e = 3 mm (e = 0.22 mm) • Parent material uniform elongation is UEL = 6% (UEL = 14 %)

• Internal pressure is such as the hoop stress is σ h = 80 % of SMYS, i.e. σ h = 358.4 MPa ( σ h = 377.7 MPa) • Yield-to-tensile strength ratio of the parent material is Y/T = 0.9 (Y/T = 0.81)

In addition, only the actual size of the defect, given as its length 2C = 65 mm and its depth a = 4 mm, and the actual weld overmatch is λ =1.187. The tensile strain capacity ε c is then given by Equation 2.5 in Chapter 2:

ε c = PF β 1 ln aC (t -a) 2 + β 2 =1.52 %
where β 1 and β 2 coefficients are defined page 64.

ExxonMobil L2

In L2 assessment, the actual hi-lo misalignment (e =0.22 mm) and parent material uniform elongation (UEL = 14 %) are taken into account. Others parameters are kept identical to that of L1, except the weld material R curve that shall be defined using one out of three proposed analytical formulations, selected so that the actual material R curve is equal to or greater than the selected R curve. The three R curves proposed by ExxonMobil are plotted in Figure 6.12 and compared to the actual data derived from SENT tests on the weld material. One can see that actual weld material properties are significantly higher than that of the three R curves proposed by ExxonMobil. Therefore, R curve 3 is considering, but it is to be noted that the assessment is likely to be conservative even considering the highest R curve. Using identical equation as for L1 but with coefficients β 1 and β 2 defined in Equation 2.8, the tensile strain capacity is: The mismatch level is set at 1.15 which is slightly below the actual weld overmatch equals to 1.187. The misalignment is set at the minimal value which is 1.6 mm while the actual value is only 0.22 mm according. The crack depth is set at 4 mm which is identical to the actual value. However, the maximal tabulated value for the crack length is limited to 50 mm while the actual value is 65 mm. The CTOD A is set at 1.0 mm which is only slightly greater than the actual value equals to 0.986 mm according to PRCI procedure given above. Finally, the strain capacity is interpolated for the actual wall thickness value between the value reported for WT = 19.1 mm and WT = 25.4 mm. Finally, the strain capacity is given by: The tensile strain capacity at initiation calculated using level 2 assessment is based on Equations 2.15 to 2.20, considering the parameters set at the following values:

ε c =2.78%
ε c =2.0+ 2
• The normalized flaw depth, η = a/t = 0.18.

• The normalized flaw length, β =2c/t = 2.928.

• The parent material yield-to-tensile ratio, ξ = R p0.2 /R m = 0.82.

• The mismatch level measured on the tensile strength,

Φ = R weld m /R parent m = 1.187.
It leads to:

ε c =3.05%

PRCI L4

Level 4 is based on finite element analyses as ExxonMobil L3 to identify the strain level at failure. One can note that the finite element models is identical to that of ExxonMobil L3. Therefore, it is considered that the tensile strain capacity reported page 185 is the same, so:

ε c =6.10%
6.4 Elastic-plastic modeling of a free defect pipe

FEA model

One quarter of the pipe and the loading machine has been modeled in order to take advantages of the two symmetry planes. The mesh consists of 64,400 eight-nodes brick elements c3d8 with full gaussian integration using the "selective integration" technique to control pressure fluctuations within elements. Sets of elements have been defined so that the actual material constitutive laws are applied in the weld and parent material. Also, a purely elastic material is assigned to the loading rigs and the end cap. The FEA scenario consists of two successive loading steps:

1. Increase of the internal pressure up to 51.8 MPa 2. The internal pressure is kept constant, and the four-point bending load is simulated by applying a prescribed displacement (U2) along the vertical direction on the loading line located at the center of the rigs (see Figure 6.15).

The internal pressure is applied using the **hydro function in Z-Set. This boundary condition enables to apply the pressure while taking into account the deformation of the mesh.

Comparison with experimental data

A comparison between FEA and experimental results in terms of load -jack displacement is depicted in Figure 6.16. As one can see, the FEA highly underestimates the load level measured during the test. For example, the load is about 29 % lower in the FEA at the yield, and about 17 % for a displacement of 300 mm. From this first result, three hypothesis were made:

1. The material constitutive laws may have not been correctly identified, 2. the test rig kinematic may be not properly understood, and therefore modeled, 3. the actual geometry of the pipe shall be taken into account (misalignment, roundness, etc.)

These three points have been investigated and results are given hereinafter. The parent material was considered as homogeneous across the thickness of the pipe. Therefore, the mechanical properties have been derived from laboratory tests performed on specimens taken from the wall mid-thickness. However, with a 22.2 mm wall thickness, such an assumption may not be valid considering the manufacturing process of the pipe. The material may have cooled down faster at the outer and inner diameter surfaces resulting in a material with higher mechanical properties, especially in terms of yield stress and ultimate strength.

Hardness tests have been realized on a full-thickness flat specimen using an automatic microhardness material. A weight of 2 kg was selected in order to get marks of significant size with respect to the average grain size, and four series of measurements have been made. As one can see in Figure 6.17, a significant increase of the hardness has been observed close to the OD and ID. For example, for points at +/-20 mm from the weld centerline, the hardness is about 210 HV 2 at the OD, whereas it is only about 170 HV 2 at the wall mid-thickness.

Considering an elastic-plastic material, Francois [START_REF] François | Essais mécaniques des métaux Essais de dureté[END_REF] showed that the relationship between the ultimate tensile stress R m and the Vickers hardness writes:

R m ≃ 3.3 × HV30 (6.1)
where HV30 denotes the Vickers hardness for F=294 N. Considering Equation 6.1, a difference of about 132 MPa on the estimated ultimate tensile strength at wall mid-thickness and at pipe OD may exist. Such a difference is clearly not negligible. In order to determine the actual mechanical performance of the line pipe, full-thickness specimens have been machined as depicted in Figure 6.18, and tested using uniaxial tensile grips as depicted in Figure 6.19-a. The specimens were loaded under cross-head displacement control up to failure at a displacement rate of 1 mm.min -1 . The load has been measured using a 250 kN load cell, and the axial elongation has been measured using a LVDT extensometer. Furthermore, DIC was used in order to monitor the full-field displacement, as depicted in Figure 6.19-a. Figure 6.19-b shows the experimental stress-strain curve of the full-thickness test, compared with the experimental curve derived from tests performed on small-scale specimens ST 6 . As one can see, there is a significant impact of the specimen geometry, especially on the yield stress equal to 487 MPa (+ 40 MPa) and the ultimate tensile strength 572.5 MPa (+ 27.5 MPa). A slight effect on the ductility is also seen, with a loss of about 2.7 % on the uniform elongation. Furthermore, as observed on the small-scale specimens, the material exhibits a Lüders Plateau for small deformations up to 1.6 %.

Because of the difference in hardnesses across the pipe thickness, the parent material was considered as a composite material composed on a region which characteristics are those determined on small-scale ST 6 specimens and two regions of thickness 3 mm located at OD and ID, which mechanical characteristics are expected to be higher.

Therefore the hardening law for the "skin/surface" material was determined using inverse analysis of the full-thickness test. The "bulk" material is assumed to obey the law determined herein. The mesh is shown in Figure 6.20. The resulting constitutive law which has been identified by the inverse analysis writes as follows (the hardening law of the mid-thickess "bulk" material is recalled for comparison purposes): where p denotes the cumulative plastic strain. Figure 6.20-b shows the corresponding engineering stress-strain curve for the full thickness specimen (an excellent agreement with experiment is obtained) compared to the one obtained using small scale ST 6 specimens.

The pipe test was then simulated integrating the description of the "skin" material. The resulting mesh is shown in Figure 6.21-a. As expected the bending moment (Figure 6.21-b) is increased but remains below the experimental data.

Effect of the boundary conditions

A new modeling of the setup is proposed in order to simplify the mesh and lighten the simulation. The new mesh is shown in Figure 6.22. An internal pressure P equal to 51.8 MPa is applied at the inner diameter surface, and an axial force F is applied to the pipe to model the end cap effect, with F = πR 2 i P and R i being the inner radius (R i = 139.7 mm). The bending angle θ is then applied rotating a rigid plate attached to one pipe end. The rotation axis is allowed to move freely along the pipe axis to avoid generating spurious axial tensile forces. Using this FE model, the displacement cannot be directly calculated since only a rotation is applied. However, considering that the part of the pipe between the loading points A and B (see Figure 6.25) remains fully elastic, a relationship between the applied bending angle θ and the virtual applied jack displacement U writes:

U = L tan (θ) (6.3)
where L is the experimental lever arm as depicted in Figure 6.23, and the bending moment writes:

M = FLcos arcsin U L (6.4)
where F is the load measured on a pair of jacks, and the correcting factor cos (arcsin (U/L)) is used to taken into account the reduction of lever arm during the bending loading. A comparison between the two FEM depicted in Figure 6.24 shows that the two methods give to different results for displacement values greater than 100 mm. After that value, the relationships given in Equation 6.3 and Equation 6.4 may not applied anymore due to the change in geometry. However, it is observed that the rigid plate rotation model gives a better trend in terms of hardening. Therefore, this model is kept in the following development.

Since the material behavior is now correctly modeled and the hardening trend is consistent with the experimental data, only the geometry of the test rig may be reconsidered. Indeed, the knowledge on the boundary conditions is limited due to the complexity of the machine. In particular, the actual length of the lever arm was challenged since this parameter has a great influence on the global loaddisplacement curve. It was found that a lever arm distance L equal to 1300 mm (instead of 1600 mm) yields to a good agreement between the experimental data and the numerical results as depicted in Figure 6.26. This assumption was formulated considering that the contact between the rig and the pipe was not perfect across the width of the clamping parts. In the initial FE model, it was considered that the point of application of the loading was located at their centers which are 1600 mm spaced. The bending moment is then calculated using Equation 6.4 with L = 1300 mm and a comparison is depicted in Figure 6.26-a. However, since the simplified FEA model does not take the rigidity of the setup into account, the simulations slightly under-estimated the jack displacement. The experimental data can be easily corrected using a correcting factor on the displacement values using the relationships:

U corr = U + M K (6.5)
where M is the bending moment and K is a correcting factor found equal to 40 kN. The new comparison is depicted in Figure 6.26-b and shows that the FEM enable to fit the experimental data with a good accuracy.

Finally, a comparison in terms of axial strain -bending moment is of interest since the aim of the test was to measured the remote strain at failure. As depicted in Figure 6.11 (page 183), the experimental data were hardly exploitable. As a remedy, a linear relationship under the form ε axial,remote = α × U between the displacement and the remote axial strain was determined using FEA, with α =1.287e -4 m -1 . The use of the finite element to determine this relationship was necessary due to the multiple loads and the complex boundary conditions that does not allow to use analytical formulae.

Since that no vertical displacement U but a rotation is imposed in the simulation, a second relation- ship between the remote axial strain and the bending angle was determined using FEA. This one writes ε axial,remote = β × θ where β =3.014e -3. Figure 6.27 -Identification of the relationship between the displacement and the remote axial strain (a.), and remote axial strain-bending moment curves (b.).

To conclude, the FE model enables to accurately model the global behavior of the pipe. This was possible by taking into account:

• The gradient of material properties through the pipe wall thickness; • The effective boundary conditions during the loading; • The rigidity of the test rig; • The test kinematic to determine a relationship between the displacement and the remote axial strain.

Next step is the simulation of crack extension using a coupled damage model.

Flawed pipe modeling

In this section, results of simulations performed on the actual flawed pipe are presented. The aim is to show the capability of the GTN model to simulate the crack propagation process during the bending test.

laws are introduced: one without damage (outside of the crack path), and one with damage (within of the crack path).

Double-clip gage

The knives for the double-clip gage method are modeled so that the mesh is as closed as possible to the actual test.

Results

Figure 6.30 shows that this model enables to model the global behavior of the pipe during the four point bending test as accurate as with the free defect pipe, both in terms of remote axial strain -bending moment and jack displacement -bending moment. The presence of the defect does not affect the overall pipe behavior as the pipe central part is loaded under constant bending moment. Figure 6.31 shows the crack advance obtained for two CTOD values (CTOD = 3 mm and CTOD = 5.51 mm) during the finite element calculation. The main interest of the damage model is therefore its capability to describe the observed crack advance during bending and therefore to predict the jack displacement (or bending angle) at failure. Figure 6.32 depicts the comparison between the experimental data and the FEA numerical results. The experimental data consist in the strain -CMOD curve. The silicon replica provides one measurement of the CMOD corresponding to the first unloading. This point (blue triangle in Figure 6.32) is consistent with the continuous CMOD monitoring. The silicon replica also provides one evaluation of crack advance (orange triangle in Figure 6.32) which can be compared with simulations.

The comparison shows that the CMOD is slightly underestimated by the FEA and that the FEA predicts a quick increase of the CMOD occurs for about 5 % axial strain. The experimental data do not show such an increase, but the global trend is the same. However, it is to be noted that the FEA curve almost exactly matches the experimental measurement of the crack advance.

Since the interest here is to evaluate the capacity of the model to predict the ductile failure of the pipe, a comparison in terms of CTOD -strain is more consistent (see Figure 6.33). One can see that the fit between experimental and numerical values is not as good as it is for CMOD -strain curves depicted in Figure 6.32 even if the overall trend is respected.

It is observed that for low strain values up to 1 %, experimental data show a quick increase of the CTOD value. This phenomenon is absolutely not represented by the FEA. For strain values between 1 % and 5 %, the CTOD values given by the FEA underestimate the experimental data, but the curves are almost parallel. Then, the kinematic of the crack opening is assumed to be correctly described by the FEA. Finally, for strain values greater to 5 %, the FEA predicts a quick increase of the CTOD and highly overestimates the experimental data.

The three threshold values δ 0.2 , δ 0.5 and δ 1 , taken as the average of the values measured on SENT specimens are room temperature and reported in Table 4.20 page 146, are added to Figure 6.31 so that it is possible to check the suitability of these values as initiation criterial. One can observed that none of these values correctly predict the crack initiation. Indeed, according to the FEA results depicted in Figure 6.32, the crack initiation occurs for a remote axial strain of about 2.5%, and according to the silicon replica, a crack advance of about 1.4 mm was measured for a remote axial strain of 4.2%. However, if considering δ 0.2 as the initiation criterion, FEA predicts a value at initiation of remote strain of about 4.67 %. The comparison is even worse if δ 0.5 or δ 1 is selected. Therefore, none of this quantity can be considered as a criterion for initiation of the crack. Unfortunately, it was not possible to complete the calculation up to a crack advance through the entire wall thickness because of the considerable time calculation. However, the crack advance -axial strain curve in Figure 6.32 becomes almost vertical for an axial strain of 5 % indicating the onset of catastrophic crack advance. It leaves no doubt on the evolution of the crack advance rate which will obviously lead to the complete opening of the crack through the thickness for an axial strain between 5 % and 5.5 %, as observed during the full-scale test.

Comparison between local and global approaches

Table 6.2 proposes a comparison between the tensile strain capacities predicted using the local and global approaches. The single experimental point of reference is given as the measured crack advance using the silicon replica at a remote strain equal to 4.24 mm. Therefore, it is difficult to estimate the tensile strain at crack initiation. Also, it is important to distinguish the procedures based on initiation (PRCI L1 and L2) or ductile instability (others) control.

One can see that the tensile strain level reached at initiation predicted by PRCI L1 and L2 are lower than the tensile strain measured for an actual crack advance of 1.41 mm, meaning that these levels are conservative. Furthermore, PRCI L1 is very close to the strain at initiation predicted by the local approach (2.34 % vs 2.32 %).

Predictions of the tensile strain at failure are also in good agreement with the experimental final failure (5.32 %) for the procedures based on finite element analyses, particularly with the local approach being only slightly conservative (5.10 %). On the other hand, ExxonMobil L3 and PRCI L4 (6.10 %) are underconservative.

Conclusion

The possibility to perform such a full-scale has been of particular interest in this study. Indeed, due to the highly extensive costs of such a test, only few are carried out. In this chapter, the basis for the preparation of a four-point bending full-scale test are presented. It is shown that no matter how long the preparation is and how the test is carried out, experimental issues can show up. Therefore, this conclusion proposes to give advices on how to do a test.

At first, and as developed in Chapter 4 and Chapter 5, it is important to work on a structure (here a line pipe) for which material(s) is (are) known. It is important to have a sufficient knowledge on the material properties such as:

• The elastic modulus, or Young's modulus, E (MPa).

• The yield stress given at 0.2 % of plastic strain, R p0.2 (MPa).

• The ultimate tensile strength, R m or UTS (MPa).

• The uniform elongation (strain at maximal load), A % or UEL (%).

• The material anisotropy both in plasticity and fracture.

• The material toughness given as CTOD 0.2 or J 0.2 , or if under the form of R-curves if available.

It means that a sufficient experimental campaign shall be carried out. The values of parameters E, R p0.2 ,R m and A % can be directly measured using a classical round bar (see Figure 4.4 page 103). Such a test also allow to characterize the material anisotropic behavior looking at the fracture surface after the specimen fails (round shape: isotropic in plasticity ; oval shape: anisotropic in plasticity). For anisotropic materials, it is important to perform tensile tests in both axial and hoop directions. Indeed, API 5L steel grade requirements are given for the hoop direction, while mechanical properties with lower values can be met in the axial direction. Therefore, when dealing with full-scale tests that mostly load the line pipe in its axis direction, such as bending and tensile tests, the knowledge of the material properties in both direction is important.

This chapter shows that performing a full scale test can be challenging. Therefore, precautions shall be taken before, during and after the test.

Before the test:

• Geometrical measurements of the pipe:

-Outer diameter: min, max, average.

-Wall thickness: min, max, average.

-Out-of-roundness: min, max, average.

-Axial misalignment (hi-lo): min, max, average + value at the vicinity of the defects.

-Metal loss if corrosion: min, max, average. • Metrology of the defect(s):

-Overall shape: semi-elliptical / constant depth / straight front.

-Length.

-Depth: min, max, average.

-Initial crack opening (CMOD): min, max, average. • Geometrical measurement of the facility:

-Distance between the points of application of the loading(s).

-Characterization of the pieces used to transfer the load from the frame to the pipe (e.g. shape, surface of contact, friction coefficient, etc.). • Characterization of the strain gages: accuracy, operating strain range, etc. • Characterization of the sensors:

-Reference of the sensors (e.g. MTS 632-020-21 SN 1526).

-Calibration over the full range of interest. • Validation of the loading sequence:

-Each step shall be clearly defined (load, loading rate, etc.).

-The capacity of the loading device (pump, jack, etc.) shall be checked so that a safety margin exists. The displacement capacity of the jack shall be also checked. • Cameras shall be putted in place to ensure that all the critical areas are visible (e.g. defect areas, loading points, etc.) • The consistency of the results through an elastic trial load shall be checked. Simple formula from the linear elastic material mechanics can be used to assess the consistency of the hoop strain due to an internal pressure for example.

During the test:

• Consistency of the results with predicted values by means of analytical mechanics of material or finite element analysis.

• Consistency of the results comparing the redundant signals (e.g. strain gages).

After the test:

• Most important: Dry and clean the fracture surface as soon as the safety conditions permit. Doing so enables to perform further investigations on the fracture surface (e.g. optical observation and/or SEM). • Pictures of the final position of the different loading devices if possible (e.g. final jack displacement) • As much pictures as possible at any location.

Besides the recommendations, it is highly instructive to carry out a preliminary study based on finite element calculations in order to be capable of anticipating the structure behavior. For example, performing a simple elastic plastic simulation enables to predict the transition the elastic regime to the elastic plastic regime.

In this chapter, it is also shown that a more advanced model, such as the GTN approach, enables to accurately predict a complex four-point bending tests on a pressurized full-scale line pipe. Indeed, after a comprehensive experimental campaign to characterize the parent material and the weld, material constitutive laws as well as GTN model parameters were identified using the inverse analysis. The actual geometry of the crack shall be also well defined since the local behavior highly affects the crack propagation.

Part IV APPLICATION TO A UOE-LSAW LINE PIPE Résumé en français

Dans ce chapitre, les résultats d'une campagne de caractérisation complète réalisée sur le matériau de base (X70) et le matériau d'apport (X70W) sont présentés. Des essais de traction classiques ainsi que des essais sur éprouvettes entaillées ont été réalisés de manière à caractériser les propriétés élastoplastiques de ces deux matériaux. L'effet de la température fut également étudié. Concernant le X70, on note principalement :

• un comportement anisotrope en plasticité aussi bien en terme de déformations que de contraintes. Les propriétés mécaniques mesurées dans la direction de chargement T sont plus élevées que dans la direction de chargement L, avec une augmentation significative de la limite d'élasticité et de la limite ultime à rupture. La ductilité est cependant équivalente dans les deux directions. • un comportement isotrope en rupture sur les éprouvettes de traction entaillées, avec des valeurs de réductions diamètrales à l'initiation de coalescence pratiquement égales dans les directions de chargement L et T. • un effet de la température avec l'augmentation des propriétés mécaniques (limite d'élasticité et contrainte à rupture) lorsque la température de l'essai diminue. • une délamination sur les éprouvettes de traction entaillées pour les essais réalisés à -20 Les essais SENT ont également été réalisés à température ambiante et à basses températures de manière à déterminer les courbes de résistances des deux matériaux. L'effet de la température et de la profondeur de fissure initiale sur les courbes de résistance fut également étudié. Les principales conclusions sont :

• Comme observé sur le matériau X65, les courbes de résistance mesurées sur des éprouvettes SENT avec une faible profondeur d'entaille initiale sont plus hautes que pour les éprouvettes largement entaillées. • Aucune délamination ne fut observée, même aux basses températures.

• La diminution de la température de l'essai se traduit par une augmentation de la valeur de l'intégrale-J mesurée. Il est possible de normaliser les courbes de résistance en J par la valeur de la limite ultime à rupture à la température de l'essai, pour obtenir une courbe maîtresse indépendante de la température.

Le matériau d'apport fut également étudié, avec des essais à température ambiante uniquement. Les propriétés élasto-plastiques du matériau furent mesurées sur éprouvettes entaillées, du fait de l'overmatch entre matériau d'apport et matériau de base qui ne permet pas l'utilisation d'éprouvettes de traction classiques. Les résultats sur le X70W sont sensiblement reproductibles et la comparaison avec le X70 confirme l'overmatch. Cependant, la ductilité du X70W est deux fois inférieure à celle du X70.

Le dépouillement des essais SENT sur X70W montrent que les courbes de résistance exprimées en terme de CTOD ou CMOD sont quasiment identiques à celles mesurées sur le X70. Cependant, les courbes de résistance exprimées en terme de J sont nettement supérieures pour le X70W du fait de l'overmatch. The tensile curves at -40 • C are depicted in Figure 7.6. Again, the evolution of strains clearly shows the material anisotropy. The tensile curves are ranked in the same order as at room temperature and -20 • C in terms of mechanical strength. The increase of the yield stress due to the temperature decrease is about 100 MPa with regards to results at room temperature in T direction, and the ultimate tensile strength equals 51 MPa in T direction. It means that the ratio yield-to-tensile (i.e., R p0.2 /R m ) representing the hardening capacity of the material depends on the temperature. Still considering the T direction, it is equal to 0.84 at room temperature and 0.929 at -40 • C . This low hardening capacity at low temperature is explained by the Lüders plateau in T direction which is observed only at -40 • C. The mechanical properties are reported in Table 7.1. The normalized load -strain curves derived from the tests are depicted in Figure 7.8 where the tensile tests in L and T loading directions are compared. The ∆L/L 0 -F/S 0 curves are obtained using an axial LVDT type extensometer with an initial length L 0 equals 9.81 mm. Considering that the three specimens geometries have different notch radii, comparison based on this quantity is not consistent and are only given in Figure 7.8-a for information purpose only. A better comparison between these specimens is based on the ∆Φ/Φ 0 -F/S 0 curves (see Figure 7.8-b) derived from a radial extensometer measuring the diametrical contraction along the S direction which is a local response.

In this graph, the curves are classically ranked, with NT 2 specimens reaching higher stress values than NT 4 and NT 10 specimens. A higher ductility is indeed measured on the NT 10 specimens with the lowest stress triaxiality ratio. One can see a slight effect of the plastic anisotropy on the tensile response of the notched specimens: specimens loaded in the T-direction reach a higher maximum force than specimens loaded in the L-direction for both NT 2 and NT 10 specimens. The opposite effect is observed for NT 4 specimens. However the effect is very small. Moreover, one can notice that ductility in L direction is consistently larger than in T direction. SENT specimens were tested following the protocol described in Chapter 4. In the later, the effect of the initial crack depth-to-thickness ratio were studied, as well as the effect of the initial notch sharpness. It was concluded that :

• Shallow notch specimens produce higher material R curves than deep notch specimens;

• It is possible to replace the fatigue pre-cracking procedure by a notch using electro-discharge machining (EDM), as long as the wire diameter is not greater than 150 µm as the material is on the upper shelf of the brittle -ductile transition curve so that blunting before actual crack advance is larger that the EDM notch.

For the X70 material, all specimens were notched in T-S plane using EDM so that the initial crack tip diameter is not larger than 110 µm. The specimens were tested following the experimental protocol described in Chapter 4 and tested in the L-S configuration (i.e. loading along the L direction / crack propagation along the S direction). The L-S configuration was selected as it corresponds to the loading condition for the full size test reported in Chapter 9.

Effect of the initial crack depth-to-thickness ratio

Two sets of crack lengths, i.e. a 0 /W ≃ 0.25 and a 0 /W ≃ 0.35, are compared in order to study the effect of the initial crack length on the material R curve. The actual initial crack lengths are reported in Table 7.3.

Figure 7.12-a shows the comparison between both sets of SENT specimens in terms of CMOD-Load curves. As expected, ultimate loads reached by the shallow notched specimens (a 0 /W ≃ 0.25) are significantly higher than for the deep notched specimens (a 0 /W ≃ 0.35). The resulting J values (Figure 7.12-b) indicate a decrease with increasing a 0 /W ratios. Note that the J values are computed using the area under the CMOD-Load curve (which decreases with increasing a 0 /W) times η /(1a 0/W ) (an increasing function of a 0 /W). Consequently the evolution (if any) of J with a 0 /W is not obvious. One can see that the effect of the initial crack length on CMOD and CTOD-R curves is also clearly visible with an increase of the resisting curves as depicted in Figures 7. [START_REF] Sharma | Determination of higher-order terms in asymptotic elastoplastic crack tip solutions[END_REF]-c and d when the initial crack length is reduced. It important not outline that both CMOD and CTOD were measured using the ExxonMobil double-clip method so that these measures are independent of the J values. Therefore the CMOD/CTOD-∆a curves fully corroborate the J-∆a results. These results confirm the conclusions formulated in Chapter 4 based on the study of X65 parent material.

Effect of the temperature on the material R curves

Experimental CMOD-Load at -20 • C and -40 • C are depicted in Figure 7.13-a and compared to results at room temperature. An increase of the maximal load is observed while decreasing the testing temperature, but no effect is visible on ductility. Delamination observed on smooth and notched bars (see above) was not observed. This is likely due to the testing configuration (L-S) which does favor delamination of the T-L plane (a more favorable loading configuration would be L-T or T-L).

Figure 7.13-b shows comparison in terms of J-R curves. As for the X65 and X65W materials, the lower the temperature is, the higher the R-curve is. However, no particular effect of the temperature is seen on the CMOD and CTOD-R curves. This result confirms what was observed on the previous materials.

J-R curves can be normalized by the ultimate tensile strength R m at the testing temperature, as depicted in Figure 7.14-b. Based on these normalized curves, one can see that the material R-curves are almost superimposed, meaning that the fracture mechanism is identical at the three temperatures of this study. The resulting J/R m -∆a curves almost perfectly matches the CTOD-∆a curves.

Summary of the toughness properties

The results of the SENT tests at the three temperatures of this study are summarized in the following tables. In Table 7.3, fitted R-curves under the form J = α∆a m and CTOD = β∆ n are identified for all the specimens. Average fitting parameters are also reported for the analytical CTOD-R curves for the different testing conditions. Finally, the toughness values, given as J 0.2 , J 0.5 , J 1 , δ 0.2 , δ 0.5 and δ 1 are reported in Table 7.4.

Summary of parent material mechanical properties

Classical tensile tests carried out on smooth round bars and as well as axisymmetric notched tensile specimens at room and low temperatures enables to characterize the elastic-plastic behavior of the X70 parent material. The steel shows an anisotropic plastic behavior with mechanical properties better in T direction than in L direction, in accordance with API-5L requirements. This material also shows good ductility properties even at low temperatures. It is however to be noted that the hardening capacity is particulary decreased in T direction at -40 • C , with a yield-to-tensile ratio R p0.2 /R m equals 0.929 due to the presence of a Lüders plateau.

SENT tests enables to derive complete material R curves, where the toughness is expressed both in terms of J and CTOD. It is shown that toughness is not affected by the decrease of temperature and the fracture mechanisms remains identical at room and low temperatures, as seen in Figure 7.14 where the J-R curves are normalized by the actual ultimate tensile strength R m to get (J/R m )-R curves. Moreover, comparisons made at room temperature between shallow and deep notched specimens confirm ductility, in particular for NT 2 specimens where the stress triaxiality is the largest. As an example, the diametral contraction at the onset of coalescence measured on NT 2 specimens for X70W is only around 0.135. It is less than half of the value for the parent material which reaches a diametral reduction of about 0.368. SENT specimens were tested following the same procedure as for the previous materials (X65, X65W and X70). The notches were machined so that they are located at the weld centerline and that the crack propagate in TS plane from the outer diameter to the inner diameter. The specimen is loaded in the L direction and the crack propagates in the S direction (L-S loading configuration). It is however to be noted that due to the high strength of the material, the gripped length is increased to reach a daylight length between the grip H = 8 instead of H = 10W for the tests performed on the previous materials. It ensures the absence of sliding of specimens within the grips. Consequently, a new relationship between elastic compliance and crack advance was identified based on two dimensional finite element analyses using plane strain elements. Indeed, the previous equation given in Chapter where u represents the normalized compliance as defined in Chapter 1.

Material R curves

The tested specimens are room temperature were machined with initial crack length-to-thickness ratio within the range 0.25 -0.29. This small difference can be observed on the global CMOD -Load curves depicted in Figure 7.19-a, where the curves corresponding to the shallowest specimens have slightly higher loads, in particular after that the maximal load is reached. However, one can notice that the ultimate loads are close.

The material R-curves are depicted in Figures 7. 19-b-c-d. An important scatter is observed with two distinct sets of curves: specimens with a 0 /W =0.25 vs. specimens with a 0 /W =0. [START_REF] Shen | Measurement of J-R Curves Using Single-Specimen Technique on Clamped SE(T) specimens[END_REF] showing an important effect of the initial crack length on the R curves. Fitting power-law functions are identified on J-R and CTOD-R curves under the form J = α∆a m or CTOD = β∆a n . The sets of best fitting parameters are reported in Table 7.8. Corresponding toughness values are reported in Table 7.9.

Comparison with the parent material

It is interesting to compare these results with data derived from tests on the parent material. Only shallow specimens with a 0 /W =0.25 are considered. Results are depicted in Figure 7. [START_REF] Ernst | Estimation on J-integral and tearing modulus T from a single specimen test record[END_REF]. One can see that, due to the weld overmatch, the maximal load reached during the tests is greater for the weld than for the parent material (+9.4 kN). Consequently, Figure 7.19-b show that J-R curves are higher for the weld than for the parent material in particular for crack advances larger than 0.5 mm. However, it is interesting to see that the CMOD and CTOD-R curves are almost superimposed.

The previous result apparently indicate that fracture of the base and weld metals are very similar as the J-∆a curve of the WM scales proportionally with the ultimates stresses of both metals (as this is the case when test temperature is changed). This result is however not consistent with the results obtained for the NT χ specimens which are significantly less ductile in the case of the WM. As in both cases (NT and SENT) maximum forces are higher to cases where the base metal (BM) is loaded, it can be concluded that notches and cracks where properly located in the WM. It is however possible that failure could occur within the weaker ZAT in the case of notched bars ; however fractography could not reveal that fracture occured in the ZAT. The discrepancy between tests on NT χ and SENT could therefore not be explained.

Summary

In this chapter, the results of a comprehensive experimental campaign carried out on the parent material (X70) and weld material (X70W) are presented. Classical tensile tests as well as notched tensile tests were performed on the parent material in order to characterize its elastic-plastic properties. The effect of the temperature on X70 was also studied. The main conclusions on X70 are:

• An anisotropic plastic behavior is observed both in terms of stress and deformation. The mechanical properties in T loading direction are better than in L direction with a significant increase of the yield stress and ultimate tensile strength. However, ductility is identical in the two loading directions. • No anisotropy in fracture is observed on results of the notched tensile specimens, where the values of diametral contraction at the onset of coalescence is almost identical in L and T directions. • The main effect of the temperature is an increase of the mechanical tensile properties (R p0.2 and R m ) when the temperature decreases. • Delamination is observed on notched bars at both -20 and -40 • C . Delamination is never observed on SENT specimens which were all testes in the L-S configuration. Delamination leads to a sharp decrease of load.

SENT tests (L-S configuration) were also performed at room and low temperatures in order to derive material R-curves. The effects of the temperature and the initial crack length-to-thickness ratio were also investigated. Main conclusions are:

• As already observed on X65 material, shallow notched SENT specimens produces higher material R curves. • Delamination is never observed.

• The main effect of decreasing the temperature is an increase of J values. The J-R curves can be normalized by the effective ultimate tensile strength R m at tested temperature to get a master R curve independent from the temperature.

The weld material was also studied. The experimental campaign was reduced since only results at room temperature were obtained. The plastic hardening properties of X70W material were derived from tensile tests on notched tensile specimens due to the weld overmatch which does not allow the use of classical round bars. Results on the weld material are quite reproducible and comparison with X70 confirms the weld overmatch with very high tensile properties. However, the ductility of the weld is about the half to that of the parent material.

Results of SENT tests on X70W shows that the CMOD and CTOD-R curves are almost identical to that of X70 material. The overmatch leads to a significant increase of the CMOD -Load curves and J-R curves.

Chapter 8

Plastic and damage behavior of X70 and X70W materials Sommaire Résumé en français Dans ce chapitre, les lois constitutives pour décrire le comportement du matériau de base (X70) et du matériau d'apport (X70W) à température ambiante et à basses températures sont identifiées. Les essais sur éprouvettes ont révélé une anisotropie en plasticité du X70, avec des propriétés mécaniques mesurées dans la direction T supérieures à celles évaluées dans les directions L et D. Ainsi, contrairement au matériau X65, le comportement du X70 ne peut pas être décrit par le critère de plasticité isotrope de von Mises, et le critère anisotrope de Bron-Besson est utilisé. L'écrouissage du X70 peut être décrit en utilisant une formulation isotrope de l'écrouissage avec les paramètres suivants : En complément, on montre que le modèle d'endommagement GTN permet de simuler avec une bonne précision les essais réalisés sur éprouvettes SENT à température ambiante et à basses températures, en utilisant les valeurs suivantes : Matériau de base : q 1 =1.691 and q 2 =0.7886 and h = 100 µm Dû à un manque de temps à la fin de l'étude, le matériau d'apport (X70W) n'a pu être complétement caractérisé. En particulier, l'effet de la température sur les propriétés mécaniques et le comportement n'a pas été étudié. Aussi, l'identification du comportement du X70W est limité à la température ambiante, et les paramètres donnés ci-dessous permettent une bonne modélisation du comportement élasto-plastique. L'identification des paramètres du modèle GTN fut réalisé en utilisant les résultats des essais sur éprouvettes de traction entaillées. Cependant, il ne fut pas possible d'identifier un jeu de paramètres permettant une bonne modélisation des essais sur les éprouvettes SENT, bien qu'il faut vérifier que la rupture fut constamment localisée dans le matériau d'apport et non dans la zone affectée thermiquement. Des essais complémentaires seront à réaliser pour identifier l'origine de cette mauvaise modélisation. Le meilleur jeu de paramètres pour le modèle GTN est : Matériau d'apport : q 1 =1.603 and q 2 =1.090 and h = 100 µm The experimental tensile tests carried out on the X70 steel show that the material has an anisotropic plastic behavior at room and low temperatures. The isotropic von Mises criterion cannot be applied and the Bron-Besson criterion [START_REF] Bron | A yield function for anisotropic materials Application to aluminum alloys[END_REF][START_REF] Tanguy | Plastic and damage behavior of a high strength X100 pipeline steel: experiments and modelling[END_REF][START_REF] Shinohara | Anisotropic ductile failure of a high-strength line pipe steel[END_REF] is used. In that case, the yield surface is defined using an effective anisotropic stress measure expressed as:

Température R 0 (MPa) Q 1 (MPa) b 1 (-) Q 2 (
Température R Luders (MPa) R 0 (MPa) Q 1 (MPa) b 1 Q 2 (
σ = α σ 1 a + (1 -α) σ 2 a 1/a (8.1)
σ 1 = 1 2 S 1 2 -S 1 3 b 1 + S 1 3 -S 1 1 b 1 + S 1 1 -S 1 2 b 1 1/b 1 (8.2) σ 2 = ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ 3 b 2 2 b 2 +2 S 2 1 b 2 + S 2 2 b 2 + S 2 3 b 2 ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ 1/b 2 (8.3)
where S k i=1-3 are the principal values of a modified stress deviator σ ∼ k defined as :

s ∼ k = L ∼ ∼ k : σ ∼ k =1, 2 (8.4)
where the fourth order tensor L ∼ ∼ k is expressed as (using Voigt's notations): control the stress anisotropy on the shear stresses. Therefore, the yield criterion includes a total of 16 parameters. The material principal directions are ordered so that T≡ 1, L≡ 2 and S≡ 3 (and TL≡ 4, LS≡ 5, ST≡ 6). In this study, Equation 8.1 was simplified assuming a = b 1 = b 2 . As σ 5 = σ LS and σ 6 = σ ST shear stresses remain small for all tests included in the database, one also assumed: c k=1-2 6 = c k=1-2 6 = 1. Consequently only 10 parameters needed to be identified using the inverse analysis. The set of best parameters is given in Table 8.1, and comparisons with the experimental data are given hereinafter.

L k ∼ ∼ = ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ c k 2 + c k 3 /3 -c k 3 /3 -c k 2 /30 0 0 -c k 3 /3 c k 2 + c k 1 /3 -c k 1 /30 0 0 -c k 2 /3 -c k 1 /3 c k 1 + c k 2 /30 0 0 000 c k 4 00 000 0 c k 5 0 000 0 0 c k 6 ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ k =1, 2 (8

Hardening behavior and flow

Using the above defined effective stress (σ) the yield surface is then simply written as:

φ = σ -R(p)=0 (8.6)
where isotropic hardening is assumed. R(p) represents the flow stress expressed as a function of the cumulated plastic strain p. The plastic hardening function writes:

R(p)=R 0 + Q 1 1 -e -b 1 p + Q 2 1 -e -b 2 p (8.7)
where Q 1 , b 1 , Q 2 and b 2 are parameters of the non linear hardening law. Their fitted values are given in Table 8.2 for room temperature testing.

Plastic flow is assumed to obey the normality rule so that the plastic strain rate tensor is given by:

ε ∼p = ṗ ∂φ ∂σ ∼ = ṗ ∂σ ∂σ ∼ (8.8)
Finally the cumulated plastic strain rate is such that: ṗσ = ε ∼p : σ ∼ (8.9)

Simulation of the tensile tests and parameter identification

The identification of the hardening parameters as well as the parameters describing the anisotropic yield surface was carried out using the experimental data derived from ST and NT χ specimens. An inverse analysis was used following the same procedure as for the X65 parent and weld material.

According to the experimental results, the parameters describing the yield surface are considered to be identical both at room and low temperatures and only the hardening function is made dependent on the temperature. Parameters of the yield surface were fitted using results on tensile bars (ST) using both stress-strain curves and diametrical-axial strain curves and results on notched axisymmetric bars (NT) at room temperature. It results in the set of best parameters given in Table 8 The tensile curves derived from the notch tensile tests are added to the experimental data base in order to calibrate the parameters of the hardening function (see Equation 8.7). As already noticed, the use of these notched geometries is of particular interest in the inverse analysis since high strain levels are reached. Therefore, the constitutive law is not limited to the strain levels up to the uniform elongation.

R 0 Q 1 b 1 Q 2 b 2 (MPa) (MPa) (-) (MPa) (-) 447
68.43 29.52 269.52 2.67

The smooth tensile tests are simulated using a 3D single brick element (c3d8r) so that it is possible to take the plastic anisotropy into account. The simulation is carried out up to the onset of necking. On the other hand, full three-dimensional models are used for calculations on NT χ and PE geometries due to the notch. Only 1 /8 of theses specimens are actually meshed to take advantage of the three symmetry planes (see Figure 8.1 and Figure 8.2). Note that 3D meshes are relatively coarse so as to obtain relative short simulations. It was checked that the mesh size allows obtaining a converged macroscopic loaddisplacement curve. A finer mesh is indeed needed for simulations including damage development.

The calculated conventional stress-strain curves derived from ST specimens are depicted in Figure 8.3 for directions T, L and D. The diametrical plastic true strain (S direction)-axial true strain curves are also plotted. Their slope is related to the Lankford coefficient. These curves are compared to the experimental results (plain lines) up to the onset of necking and one can see that the identified set of parameters enables a good fit between experimental and calculated data. Identically good fits are obtained for NT χ and PE specimens as depicted in Figure 8.4 and Figure 8.5. As said before, it is considered that the anisotropic behavior at -20 • C and -40 • C is the same as at room temperature. Therefore, only parameters of the hardening function are identified using experimental results on ST and NT χ specimens. The best fitting parameters are given in Table 8.3. Table 8.3 -Parameters of the X70 parent material constitutive law at room temperature.

X70 at -20 • C R 0 Q 1 b 1 Q 2 b 2 (MPa) (MPa) (-) (MPa)
(-) 474.32 110.87 28.75 399. 13 1.22 The comparisons between calculated and experimental curves derived from ST specimens are depicted in Figure 8. 6. One can see that the numerical results are quite good in terms of stress-strain curves, with the difference in behavior in L, T and D directions being correctly taken into account. The comparison of the diametrical strains shows that the calculated strains in L and D directions are in good agreement with the experimental values over the entire considered strain range. However, a larger discrepancy is obtained for the T direction. Results of the calculations on the notch specimens are depicted in Figure 8.7. Both loading directions are plotted in separated Figures. On can see that the identified hardening law enables to fit most of the specimens with a good agreement. Only the NT 4 specimen in T direction are not correctly described. However, it is not clear if the experimental data are valid because the curves corresponding to NT 10 and NT 4 specimens cross each other while they should not (it is possible that the diametrical extensometer slipped during testing). 8.4. Again, the effect of the loading direction is correctly taken into account with the curves being ranked in the correct order in terms of stress values: T > L > D (see Figure 8.8). Moreover, it is shown that the calculated curves in L and T directions are in good agreement with the experimental data. The small Lüders plateau in T loading cannot be described the model. However, the calculated D loading stress-strain curve slightly underestimates the load over the full strain range.

Diametrical plastic true strains are plotted in Figure 8.8. One can see that only L-loading results show a good agreement between calculated and experimental values, while calculated strains for T and D directions underestimates the experimental values. Comparing to results of finite elements analyses carried out on axisymmetric notched specimens at room temperature and -20 • C , Figure 8.9 shows that the fit between experimental and calculated results is less good, even though it corresponds to the best fitting parameters in Table 8.4. Attempts to improve the results were made, but without success. One can observe in L direction that the calculated NT 10 results underestimate the experimental data, whereas the NT 2 simulations slightly overestimates the experimental results, preventing to improve the fit.

X70 at -40 • C R 0 Q 1 b 1 Q 2 b 2 (MPa) (MPa) (-) (MPa)

Identification of the damage model

As in the case of the X65 parent material presented in Chapter 5, the GTN model is used to describe the behavior of the X70 steel. The identification of the two parameters (q 1 and q 2 ) is based on the experimental stress-strain curves derived from the notched specimens NT χ depicted in Figure 7.8 of the previous chapter. As before f c =0.05 and f F =0.25 are used to describe the values of the porosity at coalescence and rupture.

The calculations were performed on three-dimensional meshes representing 1 /8 of the actual specimen to take advantage of the three symmetry planes. Finer meshes than in Figure 8.1 are used as depicted in Figure 8.10. The size of the elements within the notch region is 100 µm × 100 µm × 100 µm. Classical boundary conditions are applied so that the three symmetry planes are defined, and the specimens are loaded in displacement control so that it is possible to obtain the entire load-displacement curves up to the final failure. As the material is plastically anisotropic, it is necessary to use a modified version of the GTN model able to account for plastic anisotropy. Following the previous work by Rivalin [START_REF] Rivalin | Ductile tearing of pipeline-steel wide plates -II.: Modeling of in-plane crack propagation[END_REF] and Benzerga [START_REF] Benzerga | Plastic potentials for anisotropic porous solids[END_REF] who used the Hill model or Bron [START_REF] Bron | Simulation of the ductile tearing for two grades of 2024 aluminum alloy thin sheets[END_REF] and Tanguy [START_REF] Tanguy | Plastic and damage behavior of a high strength X100 pipeline steel: experiments and modelling[END_REF] who used the Bron model, the GTN yield surface is modified as follows:

Φ = σ R 2 +2q 1 f * cosh 3 2 q 2 σ kk R -1 -q 2 1 f 2 * = 0 (8.10)
where the von Mises equivalent stress (σ eq ) is simply replaced by any other stress measure (σ) (Bron model is the present work).

Simulations are performed in both L and T directions. The parameter fit was done for L loading only as it corresponds to the main loading during the full size test reported below (Chapter 9). Parameters providing the bst fit are reported in Table 8.5 with an initial porosity f 0 equal to 5. 10 -4 . Table 8.5 -GTN model parameters for X70 parent material X70 f 0 q 1 q 2 f c f F 5.e-4 1.691 0.7686 0.05 0.25 Using these values, the calculations of the NT χ specimens are in good agreement with the experimental data for both loading directions. The best fit is indeed obtained in L direction where the onsets of the coalescence is correctly predicted for the three geometries. On the other hand, results obtained for T loading specimens are less acurate, in particular for NT 2 specimens which failure prediction is underconservative: (∆Φ/Φ 0 ) exp = 31.9% < (∆Φ/Φ 0 ) fea = 38.1%. Identical simulations carried out at -20 • C and -40 • C show that the model also enables to correctly predict the failure at low temperatures. This results was expected since it was experimentally observed that the failure mechanisms are the same. In some cases (e.g. NT 2 T loading and -20 • C ) the simulation overestimate experimental failure. It is believed that the radial extensor did slip during testing this leading to a smaller diameter variation than the actual one.

Simulation of the Single-Edge-Notched Tension (SENT) specimens

A SENT test is simulated in order to check the validity of GTN parameters given in Table 8.5. The finite element model was already introduced in Chapter 5. Using this three-dimensional model, it is possible to take the anisotropy of the material into account, orienting the material local frame so that the SENT is of type L-S (loaded in tension in L direction, and the crack propagates in TS plane in S direction).

The comparison depicted in Figure 8.14-a shows that the calculated curve is in good agreeement with the experimental CMOD-Load curve. The maximal load is correctly predicted and the calculated load decreases along with the measured load, even though the calculated load slightly overestimates the experimental one at the end of the tearing test.

The calculated Load -CMOD curve is processed using identical procedure as for experimental data in order to obtain the calculated material J, CMOD and CTOD-R curves. Comparisons with experimental data are depicted in Figures 8.14-b-d. One observes that the simulated R curves accurately fit the experimental data along the entire ∆a range. These results confirm that the best fitting parameters given in Table 8.5 enable to properly simulate the crack growth process during a SENT test, even though some NT χ test calculations (see Figure 8 Identical calculations are carried out based on the identified constitutive laws at -20 • C , and results are compared to experimental data. Figure 8.16-a shows that the global CMOD-Load curve is correctly predicted for CMOD values up to 2.5 mm. However, the calculated load slightly overestimates the experimental one at the end of the test. As a consequence, the calculated J-R curve depicted in Figure 8.16-b also overestimates the experimental R curves for crack advances greater than ∆a = 1 mm, even though the order of magnitude of the error is quite small for reduced crack advances. At the end of the simulation (∆a ≃ 2.45 mm), the calculated J value is 3013 MPa.mm while the experimental measured J value is 2511 MPa.mm for an equivalent crack growth. An identical trend is observed concerning the CTOD-R curve in Figure 8.16-d. One can however note that the CMOD-R curve depicted in Figure 8.16-c is predicted with a very good accuracy, the calculated and experimental curves being almost superimposed. Results of the simulation using the material constitutive law derived from the tests at -40 • C are depicted in Figure 8.17. As for calculation at -20 • C , the global CMOD-Load (see Figure 8.17-a) is predicted with a good accuracy, even though the load is slightly overestimated for the greatest CMOD values. It results in calculated J-R and CTOD-R curves higher than the experimental data as depicted in Figure 8.17-b and d. This trend was already observed on the calculation at -20 • C but with a smaller error. However, the CMOD-R curve is correctly predicted as shown in Figure 8.17-c.

Weld material 8.2.1 Hardening function

The identification of the material constitutive law has been done using the results on NT χ specimens.

R(p,T )=R

0 + Q 1 1. -e -b 1 p + Q 2 p (8. 11
)
where p is the equivalent plastic strain, Q 1 and b 1 are parameters of the non linear part of the hardening law, and Q 2 is the parameter of the linear part of the hardening law. The identified values for the parameters Q 1 , b 1 and Q 2 are given in Table 8.6.

Table 8.6 -Parameters for the constitutive laws of X65W material room temperature and low temperatures.

X70W at RT

R Luders R 0 Q 1 b 1 Q 2 (MPa) (MPa) (MPa) (-) (

Gurson Tvergaard Needleman model 8.2.2.1 Model parameters

The GTN model used io describe to behavior of the X70W material is introduced in Chapter 5. It includes three parameters (q 1 , q 2 and f 0 )that must be identified depending on the actual material behavior. Since this model is mesh size dependent, it is also important to identify these parameters based on a fixed size of element. In the identification process, and according to the previous results obtained on the seamless pipe parent and weld materials, and the X70 steel, a size h equal to 100 µm is chosen. Table 8.7 -GTN model parameters for X70W weld material

X70W

f 0 q 1 q 2 f c f F 5.e-4 1.603 1.090 0.05 0.25

Simulation of the NT χ specimens

The methodology for the identification of the GTN model parameters has already been presented in Chapter 5 dedicated to X65W material, and the meshes used for finite element analyses are identical.

The result of the identifical process is depicted in Figure 8.19. One can observe that the overall behavior is well predicted for the three geometries. However, the predictions of final void coalescence to failure are incorrect. Hence, the ductility of the NT 10 specimens is underestimated whereas it is overestimated for NT 2 specimens. As a consequence, it is not possible to improve the result, since improving one geometry will necessary lead to make comparison on the other geometry worse.

Simulation of the SENT specimen

Even tough results on NT χ are not encouraging, simulation of a SENT tearing tests is performed. Geometry is identical to that for X65W material, and the elastic-plastic constitutive laws identified in this study are used to describe the true stress -strain relationship. The GTN parameters identified on the notched tensile specimens are used. It results to a significative underestimation of the actual material R curves, as depicted in Figure 8.20. This point must be clarified, since it is not in agreement with comparisons on NT 2 specimens.

Conclusion

In this Chapter, the material constitutive laws of the X70 parent material at room temperature and low temperature have been identified. The experimental campaign revealed an anisotropic plastic behavior, with material properties in T direction greater than in L and D directions. Therefore, unlike for X65 parent material, the material does not obey to the isotropic von Mises criterion, and the anisotropic Bron-Besson criterion is used instead. The anisotropic parameters of the criterion are given in Table 8.1, and the best hardening fitting parameters are reminded in Table 8.8, as well as the parameters corresponding the the constitutive laws at -20 Parent material: q 1 =1.691 and q 2 =0.7886 and h = 100µm Due to the lack of time at the end of this project, the weld material (X70W) could not have been fully characterize. In particular, the effect of the temperature on its material properties and behavior was not investigated. Therefore, the identification of the constitutive law for X70W is limited to room temperature. The best fitting parameters are reported in Table 8.9. The identification of GTN parameters was classically performed using results on the notched tensile specimens. However, it was not possible to identify values which allow to accurately predict the coalescence on NT χ specimens. It was verified that the failure occured within the weld material and not in the heat affected zone. Then, the simulation of the SENT specimen is obviously not close to experimental data. This poor result can not be explained here, and requires additional work including microscopic observations to better understand the failure mechanism of this steel. The best fitting values for GTN parameters are: Weld material: q 1 =1.603 and q 2 =1.090 and h = 100µm

Résumé en français

Ce chapitre est dédié à la description d'un essai de traction réalisé sur une canalisation contenant une soudure de raboutage. Trois entailles ont été usinées par électro-érosion : deux dans le cordon de soudure circonférentielle et une dans le matériau de base. Le tube fut ensuite soumis à un chargement en pression interne combiné à une sollicitation en traction. Malheureusement, une rupture inattendue au niveau du système de chargement mécanique interrompit l'essai avant rupture.

Le tube est pour le moment emmagasiné au Centre des Matériaux de l'Ecole des Mines de Paris, dans l'attente d'un éventuel nouvel essai. Pour cette raison, les défauts n'ont pas été extraits du tube pour réaliser des caractérisations destructives de ceux-ci.

Des simulations EF ont été réalisées, et les résultats sont comparées avec les courbes de chargement expérimentales. On constate que la simulation est en bon accord avec l'essai, que ce soit en terme de réponse globale, d'ouverture des défauts et de l'estimation de l'avancée de fissure.

Summary

An API X70 steel grade LSAW-UOE pipe containing a girth weld was tested using mixed tensile/internal pressure loading. The pipe contains three flaws: two located at the weld centerline of the girth weld (67 mm length × 7.5 mm height) and one in the parent material (60 mm length × 4.2 mm height). The line pipe was loaded first in internal pressure in order to reach a hoop stress equal 80 % of the material yield stress, and then an axial load was applied in addition to the internal pressure.

The objective of the test was to check the capability of the local approach (GTN model) to accurately predict both local and overall behavior of the line pipe during the test. The later was fully instrumented, including strain gages in axial and hoop directions, as well as clip gages to measure the opening of the different cracks (using Exxon double clip method).

An unexpected failure at the weld joining the line pipe and the end fixtures occurred during the second loading step, resulting in a fully and quick internal pressure release. At that point, a remote axial strain of about 1 % was reached, while a level of at least 3 % was aimed. NDE examinations were performed after the failure in order to measure potential crack advance. Results are in agreement with FE simulations.

Description of the test 9.2.1 Test rig

A full-scale test was carried out at CSM (Centro Sviluppo Materiali) facility in Cagliari (Sardinia, Italy) on an horizontal tensile frame as depicted in Figure 9.1. The machine consists in a frame composed on two high strength pipes that are used as the loading frame. They are located on each side of the tested line pipe. An high capacity hydraulic jack, capable to reach 2,200 tons and located at the center of the frame, is used to apply the tensile load on the pipe. Two extensions were welded on each end of the tested line pipe to allow both the pressurization using water and the application of the tensile axial load. Moreover, two roller devices (see Figure 9.2) were positioned below the line pipe along its length to ensure that no parasitic bending load is created under the pipe own weight. However, the axial displacement was not constrained.

Material

The tensile test was conducted on an API X70 steel grade LSAW-UOE line pipe (OD 600 mm and WT 29.3 mm) manufactured by Europipe and provided by TOTAL S.A. The tested segments contains a girth weld at its center that was made by Serimax. The behavior of both parent and weld materials, denoted X70 and X70W in this manuscript are described in Chapter 7 and Chapter 8 of this text.

Three constant depth flaws were machined using electro-discharge machining (EDM). Two of them were located at the weld centerline (length×depth: 67 mm × 7.5 mm. A third one was located within the parent material (length×depth: 60 mm × 4.2 mm) at a distance of 600 mm from the girth weld. This defect is less deep that the defects located in the girth weld so as to make sure that failure will occur in the weld. This configuration was selected after that three-dimensional FE analyses were performed to ensure that no interaction between the defects is possible. Moreover, the flaws were machined with the maximal angular spaces between them. Using EDM, it was possible to achieve values of the initial crack opening lower than 0.30 mm along the crack front. The actual crack sizes are reported in Table 9.1. CSM proceeded to a detailed verification of the dimensions of the line pipe. Six cross sections (C1, C2,. . . , C6) were defined as depicted in Figure 9.4, where both diameter (D1, D2, D3, D4) and thickness (S1, S2, ..., S8) measurements were performed as defined in Figure 9.5. Defect #1 is aligned with the angular position S1 and the axial distances between the cross sections are reported in Table 9.2. Table 9.3 reports the diameter measurements. The difference between the maximal and the minimal value is only 2 mm, corresponding to only 0.33 %. Table 9.3 gives the thickness measurements. One can see that the greatest difference between the maximal and minimal value is only 0.6 mm, corresponding to 1.93 %. As diameter and thickness are almost uniform, the mechanical simulation of the pipe can be conducted using constant values.

Monitoring

The line pipe was fully instrumented and the following outputs were recorded:

• The displacements of hydraulic jacks (in mm) • The load on the hydraulic jack (in kN) • The internal pressure (in bar) • The double-clip gage method was used in order to measure CMOD and CTOD at notch locations using four MTS clip gages (in mm), and ExxonMobil equations.

Analytical analysis of the test

It is possible to determine the critical axial force for a line pipe without defect. The axial load conducting to the collapse of the entire cross-section writes:

F = πR m R 2 -(R -t) 2 (9.1)
where R is the outer radius and t is the pipe thickness. An analytical formula is found in Miller [START_REF] Miller | Review of Limit Loads of Structure Containing Defects[END_REF] to determine the axial load to failure for thick pipes with or without internal pressure subjected to tension containing circumferential defects. It writes:

(

1 -2ξ) 1+λ 2 cos α - x sin β 2 + 2ξ 2 3 (1+λ) cos α x 3 sin β 1 -2ξ +2xξ = 0 (9.2)
where R is the outer radius λ is the ratio between σ y,tension and σ y,compression . λ = 1 in the present case ξ = t/(2R) x = a/t β is the crack angle with respect to the pipe centerline. α is the angle that neutral axis is away from the equator and where α is defined by:

α = 1 2 (1+λ) xβ 2 1 -2ξ 1 -ξ 1+ xξ 1 -2ξ + F σ y Rt (1 -ξ) - π (1 -λ) 2 (1+λ) (9.3)
where F is the axial remote load. It is possible to take into account the effect of the internal pressure in Equation 9.1 and Equation 9.2 considering that the end cap effect is the only contribution of the internal pressure to the axial collapse of the cross-section, which writes:

F axial,pressure = Pπ (R -t) 2 (9.4)
where P is the internal pressure. Numerical applications of Equation 9.1 and Equation 9.2 are reported in Table 9.5. Considering that the maximal tensile load reachable using the hydraulic jack is limited to 22,000 kN, these results show that the limit load is very close to the machine capacity. Therefore, the choice was made to perform the test with an internal pressure as high as possible to the onset of the yield.

Table 9.5 -Axial load to failure.

Internal pressure

Axial load due Axial load to failure the internal pressure Free defect pipe (Eq. 9.1) Miller (Eq. 9.

Unexpected failure

Details on the experimental results are given hereinafter, but it must be pointed out that an unexpected failure at one on the end cap girth weld occurred, as depicted in Figure 9.8. Consequently, the test could not be achieved and no significant crack advance was observed.

Figure 9.8 -Full cross section collapse at the joint between the line pipe and the end cap.

Experimental results

Internal pressure

.9 depicts the evolution of the internal pressure during the test. The targeted internal pressure equal to 476 bar was reached after a loading rate of 16 bar.min -1 . It is to be noted that a first maximal internal pressure equal to 488 bar was reached prior to the tension load. However, it was decided to slightly decrease the pressure after the hoop strain gages started to show a non linear response since no plasticity should be reached due to internal pressure only. Moreover, one can see that an internal pressure equal to 476 bar was hardly maintained during the tension part of the test, with several drop in pressure mainly because of the change in volume of the line pipe.

Load -displacement

The load -displacement curve, depicted in Figure 9.10 shows the variation of the tensile load measured at the load cell. The comparison with the internal pressure plotted in orange shows that these two quantities vary with opposite trends. Indeed, as said before, the volume of the line pipe increased during the test resulting in a decreased of the internal pressure. Now considering that the total axial load (depicted in blue) is equal to the sum of the force imposed by the jack (depicted in black) and the force resulting from the internal pressure (see Equation 9.4), one can obviously conclude that for an imposed displacement, the load measured at the jack increased while the internal pressure decreased. However, the total axial load follows a quite monotonic trend up to the final failure. The evolution of the hoop strain measured by the seven different strain gages is depicted in Figure 9.11, where the load corresponds to the total axial load (load measured by the load cell plus the load due to capped-end conditions). Several regimes are clearly visible for all strain gages (these three regimes are shown for the gage located on section C2 in Figure 9.11).

• First (regime 1), a small tensile load (about 3000 kN) was applied to check the gages. This results in a small negative hoop strain due to Poisson's effect. The load was then decreased. • The pressure is then increased up to 476 bar corresponding to an axial load equal to 11100 kN (regime 2). The hoop strain increases to a level slightly less than 0.2%. For this strain level, the response is slightly non-linear meaning that the line pipe was very close to the yield pressure. It is to be noted that the strain gage located at angular position S3 at cross section C5 measured a hoop strain slightly greater than 0.2 %, but its almost linear response shows that the strain is still elastic. • The axial load is then applied (regime 3). A small decrease of the hoop strain is first observed due to Poisson's effect but it starts to increase for a load a about 23,000 kN showing than plasticity becomes active in the pipe. Hoop strain increases sharping once an axial load of about 27,000 kN is reached.

One can see that the strain gages behaved differently during the tension load, with a minimal hoop strain measured in section C3 (about 0.25%), and a maximal hoop strain measured in section C5 (greater than 0.475%). Due to the axisymmetry of the structure, it was expected that all signals read the same. However, the difference can be simply explained by a bad positioning of the strain gages on the structure, i.e. the hoop strain gages were not perfectly aligned with the circumferential direction.

Axial strain

Figure 9.12 depicts the evolution of the axial strains measured by the strain gages located at the four cross section as function of the total applied axial load. As in Figure 9.11, the axial load corresponds to the sum of the load measured by the load cell, with the tensile load due to the end-cap effect. One can see that the signals are quite reproducible for small strain levels (up to approximatively 0.4 %) at all cross sections and angular positions. One can see that the axial strain measured evolves similarly at cross sections C3 and C4 (close to the girth weld), and at C2 and C5 (close to the end caps) where the strain is maximal with measured values larger than 1 % at angular position S3 at cross section C5. In the following, the signal corresponding to the strain gage located at angular position S3 at cross section C5 is taken as reference.

Clip gages

.13 depicts the openings of the three cracks measured using the double-clip gages fixtures. It is to be noted that cracks 1 and 2 were expected to open in the same way, since they were identically machined. The workshop in charge of defect machining (Chene) measured a slight different in crack depths but it was considered to be negligible (8.62 mm depth for crack 2 whereas crack 1 was only 8.56 mm deep). However, one can observe that crack 1 opened faster that crack 2. At the end, it resulted in a measured CMOD which is 18.6 % greater at crack 1 than at crack 2, and a difference of 39.9 % in terms of CTOD. This result was obviously not expected and is still to be explained.

Another surprise was to observe that the crack within the parent material opened faster than the other ones, even tough it was the shallowest with an initial crack depth-to-thickness ratio a 0 /W ≈ 0.17, in comparison to a 0 /W ≈ 0.28 for the cracks at the girth weld centerline. This crack is located at 600 mm from the girth weld in a region close to section C5 which in which the axial strain is larger that in the central area of the pipe (between C3 and C4). This could explain, together with mismatch, why the opening is larger that for cracks located in the girth weld. Another explanation could be that the initial crack is larger than requested.

Collapse of the full cross section

After reaching an axial strain value of about 1 %, the entire net section of the line pipe failed close to a girth weld joining the tube with a cap-end. This failure resulted in a complete and sudden depressurization of the pipe (see Figure 9.8) at about1 /3 of the expected final remote axial strain.

Geometrical measurement after testing

CSM proceeded to geometrical measurements after the testing of the line pipe. At first, they measured the axial distances between the different sections that were initially defined (see Figure 9.4). The postmortem distances are reported in Table 9.6. The axial elongation between the cross sections is also calculated. The accuracy of the measurements is about 1 mm so that strains evaluated between sections C3/C4 and the girth weld have the same magnitude as the error (≈ 1/55 = 2%) and cannot be used. The distance between sections C2/C3 and C4/C5 is much larger (900 mm instead of 55 mm) and a better precision is obtained (error ≈ 1/900 = 0.1%) so that the estimated elongation can be compared to the results obtained with the strain gages. A slight expansion of the tube (0.3 % between sections C2 and C5) due to the internal pressure is observed, and a slight thinning within a range between 0 % (no thinning) to 0.7 % is also measured at the center of the pipe (between sections C2 and C5). Deformation of end sections C1 and C6 is larger as they are close to the necking (C6) and failure (C1) sections.

Crack advance

Since the line pipe failed before the test was actually completed, the axial strain level that was reached was not high enough to ensure crack advance. Some silicon notch replica were made just after the test in order to check if any crack extension was visible. However, their realization was not easy after the elastic unloading due to the narrowness of the cracks. It resulted in hardly exploitable replica where mostly blunting of the crack front was seen.

In addition, CSM proceeded to crack depth measurements using both ultrasonic (US) and magnetic particle inspection (MPI) methods. They reported the following conclusions:

• Defect 1: there is no evidence of indications at the defect tip. The estimated defect depth is about 0.07 mm more than the nominal value. Such difference is small and then negligible compared to expected crack advance. • Defect 2: This defect differs from defect 1 as it appears 0.47 mm deeper than the measurement performed at Chene (EDM workshop). This difference is considered to be significant in particular since defects 1 and 2 had very similar initial depths (see Table 9.1). It is therefore concluded that defect 2 propagated over a distance of about 0.5 mm. • Defect 3: there is no evidence of advance of the defect tip. The estimated defect depth is about 0.04 mm more than the nominal value. Such difference is small and then negligible to the aim of the present work. It then remains difficult to interpret the larger CMOD/CTOD of the defect compared to defects 1 and 2.

Full reports are given in Appendix D. The model consists in a three-dimensional mesh of the line pipe using linear 8-nodes fully integrated C3D8 elements using selective integration. Due to the symmetries, only a quarter of the tube is actually meshed, as depicted in Figure 9.14-a. Two cracks are introduced in the mesh: (i) one at the weld centerline representing both cracks 1 and 2, (ii) one in the base metal at 600 mm from the girth weld representing crack 3. Both cracks are located at the same angular position so as to simplify mesh design (their actual position is given in figure 9.3). This simplification is made possible as cracks are not interacting as demonstrated by preliminary FE calculations performed before running the test. Solid elements are also added to the mesh to represent the double-clip gage system.

The size of the elements along the crack fronts, both at the weld centerline and within the parent material, is 0.1×0.1 mm×0.5 mm. The largest dimension corresponds to the crack front direction as stress/strain gradients are low along this direction.

Material constitutive laws

The material constitutive laws are given in Chapter 8.

Comparison with the experimental data

The simulation of the exact loading conditions on the line pipe during the tension test was difficult due to the variations of internal pressure, resulting in changes in both axial and hoop stresses. In the following the simulated macroscopic response as well as the local crack opening behaviors are compared to the experimental results. 9.4.2.1 Macroscopic response: hoop and axial strains, load Figure 9.15 compares the hoop/axial strain-load curves for section C5. A relatively good agreement is obtained. However the purely elastic behavior of the pipe is not perfectly represented which is for the time being difficult to interpret. Plastic yielding is reproduce with a similar degree of accuracy. Figure 9.16-a shows that a very good fit is obtained for crack 2 which is located at the weld centerline, considering either the raw clip opening, the CMOD or the CTOD. The curves are almost superimposed during the entire test. As said before, only one crack was actually modeled within the girth weld since they were identically machined. As expected from the experimental results, opening for crack 3 (base metal) is underestimated by the FE analysis.

Crack advance

As reported above, CSM measured an increase of the crack depth equal to 0.47 mm using an ultrasonic tool. Figure 9.17-a shows the elements that are considered as broken when the remote axial strain reaches 1.03 %. One can see that a single row of elements is broken, corresponding to a crack advance of only 0.1 mm. Therefore, the damage evolution is underestimated, and the simulation shows that an axial tensile strain of 1.43 % results in a calculated crack advance of about 0.5 mm on a length equal to 10 % of the initial crack front located in the middle section, as depicted in Figure 9.18. Crack advance is smaller on remaining crack front. However, considering the variations in the measured elongations reported in Table 9.6, it is reasonable to estimate that the simulation predicts crack growth with a good accuracy.

Conclusion

In this chapter, a full scale test performed on a pipe element containing a girth weld is reported. Three EDM flaws were introduced in the pipe which was submitted to internal pressure and axial tensile loading. The pipe failed prematurely close to the welded connection with the loading system. The pipe is presently stored at the Centre des Matériaux and could be possibly further tested. For this reason, cracks were not extracted for detailed (but destructive) examination in order, for instance, to check their initial geometry or potential crack advance.

Preliminary simulation of the pipe shows that a relatively good agreement is obtained with the experiment in terms of global response, crack opening and potential crack advance. A more detailed inspection of the pipe (as mentioned above) could help improving the pipe simulation.

Part V CONCLUSIONS AND PERSPECTIVES

This conclusion proposes a review of the different objectives that were proposed in the introduction of this text. We believe that most of them are reached and that lot of questions in relation with the strain based design find answers in this study. However, we are also aware that it was not possible to give a comprehensive answer to all the aspects of strain based design. Therefore we will try to formulate perspectives to continue the study.

Chapter 2 of this study is dedicated to a literature review of the existing strain based design procedures. Three approaches were identified. The first one, developed by University of Ghent, is based on the assumption of a full transferability between a line pipe containing a crack and a sub-size specimen, called curved wide plate (CWP). University of Ghent performed a series of tension tests with different configurations, and measured the corresponding tensile strain capacity. Then, an analytical empirical expression was developed in order to calculate the remote axial strain to failure depending on geometrical and material properties. Unfortunately, this method has not been studied in this PhD due to its high cost due to the difficulties to carry out such tests. However, it would be very interesting to benchmark this method by simulating both CWP tests and full size tests on pipes.

The two other approaches are the multi-tiered procedures proposed by ExxonMobil and PRCI. ExxonMobil method is based on the principle of the tangency analysis where the tensile strain capacity is calculated equating the material resistance curve, so-called R-curve and crack driving force curves. The first two levels out of three are based on analytical formula derived from a comprehensive campaign on full scale tests covering a wide range of geometrical and material properties. The third level is based on finite element analyses in order to determine the structure crack driving forces, assuming several fixed crack depth configurations, meaning that the simulations are elastic-plastic and that crack growth is not modeled. Therefore the strain/stress fields ahead of the running cracks and developed during crack propagation are not accounted for. In particular each finite element calculation corresponding to a given crack depth, is performed assuming an initial structure free of prestrain and stress. This point is questionable, in particular in the case of materials showing high blunting capacities. However, comparisons between finite element analyses and experimental full scale tests performed by ExxonMobil show that this approach predicts the strain capacity to failure with a good accuracy.

The PRCI procedure is based on a multi-tiered approaches as well. The first three levels out of four propose to calculate the tensile strain capacity as the remote axial strain leading to crack initiation. These levels are based either on a tabulated values which cover a large range of material and geometrical properties or on a series of analytical expressions derived from a comprehensive full-scale tests campaign. The material toughness is defined as the apparent toughness. The latter is to be measured for a crack advance equal 0.5 mm or 1 mm (depending on pipe geometry) using Charpy specimen or low constraint specimens such as shallow notched SENB, SENT or curved wide plates. Prediction of final failure is therefore not the purpose of these levels which are limited to initiation. As a remedy, a finite element analyses based procedure is proposed. The latter is very similar to the one presented by ExxonMobil using simulations with different constant depth cracks.

Beyond their specificities, PRCI and ExxonMobil agree on the capability of the SENT specimen to best characterize the material toughness for pipe applications. However, the absence of a standardized procedure makes its use not straightforward. ExxonMobil released its own procedure, whereas the PRCI approach is based on the experimental protocol proposed by CANMET. In addition, a recommended practice is suggested in DNV-RP-F108, and serves as the basis of British standard BS 8571:2014. Therefore, the use of SENT specimens is investigated in the Chapter 1 of this text, through the recommended practices identified during the literature review. Two types of procedure are proposed: the multi-specimens (DNV-RP-F108) and the single-specimen (ExxonMobil, CANMET, Cravero). In the first ones, the determination of the material R-curve requires testing a minimum of eight samples which are loaded up to increasing amounts of crack advance. On the other hand, single-specimen procedure allows to derive a full R-curve using only one sample. Previous studies already showed that they produce identical results, and this point is not investigated in this text, which focuses on singlespecimen procedures. The following conclusions are drawn:

• The time consuming fatigue pre-crack procedure can be replaced by the electro-discharge machining method in order to reach the initial crack depth-to-thickness ratio, at the conditions that: (i) the material is on the upper-shelf on the ductile-to-brittle transition curve (fully ductile failure), and (ii) the EDM wire diameter is sufficiently small. ExxonMobil advises not exceeding 0.150 mm, but tests show that a diameter of 0.300 mm is also acceptable. • The initial crack-depth-to-thickness ratio a 0 /W has a major effect of the material R curve, with a significant decrease of CTOD or J value for increasing values of a 0 /W. ExxonMobil suggests to perform SENT test with a 0.1 shift value on the actual ratio measured on the line pipe (i.e., a 0 /W = a/t +0.1) due to the scatter in the experimental database. This point was not investigated during this PhD, but it would be very interesting to do so. This can be done using finite element analyses where the crack growth mechanism is actually modeled, so that CTOD -∆a or J -∆a curves are obtained. However, it is important to note that ExxonMobil procedure limits the ratio a 0 /W between 0.25 and 0.35. As a result, only pipes containing shallow defects in the range 0.15 ≤ a/t ≤ 0.25 can be assessed. On the other hand, DNV-RP-F108 suggests performing tests with a 0 /W being between 0.2 and 0.5, but no recommendation on transferability is given. • The use of a double-clip fixture allows monitoring the evolution of CMOD and CTOD values during the tests, using a simple geometry based treatment. This method was validated based on a comparison with the classical 90 degree intercept method using finite element analyses. Moreover, this system was shown to be easily used in the context of a full scale test on a flawed pipe, where it was possible to compare the evolution of CTOD curves with material toughness expressed as CTOD for 1 mm crack advance (for example) during the test. • Other possibility to determine a CTOD-R curve is to use the relationship J → CTOD introduced in DNV-OS-F101:2013. In this work, a good agreement is found between CTOD estimated from J and CTOD calculated using double-clip gages for CTOD values up to 3 mm. However, as shown by results on our X65 steel grade, this value is low with regards to the high ductility and toughness of the new materials. • Procedures to post-processed and interpret the experimental results were compared. It is shown that formulation given by Cravero for the shape factor η used to calculate the J-integral from tearing tests is the most relevant with regards to comparisons based on finite element analyses, and also the most simple to use. Therefore, we recommend the use of the following definition: η =1.0398 + 0.687 a W for clamped specimens.

The literature review also pointed out that the use of J-integral as a fracture parameter is not straightforward. In particular, it is not clear how this quantity can be experimentally measured on a flawed pipe. Indeed, experimental J-integral estimations rely on a relationship between the plastic area under the CMOD -Load curve and J, plus geometry dependent parameters including the shape factor η which is not defined in the case of a line pipe. However, the CTOD was found to be a good candidate to replace J since it is based on a simple geometrical definition. Therefore, this quantity can be easily determine on both a laboratory specimen and a line pipe for comparison. It is also convenient to calculate CTOD by means of finite element analyses, based on the principle of the double-clip gages.

In this text, a large amount of experimental data obtained on various specimen geometries are presented. Chapter 4 of this text can be seen as a recommended procedure for a comprehensive material characterization. The elastic-plastic behavior was studied using classical tensile specimens, including round or flat bars which allowed to accurately identify the plastic anisotropy of the material with the measurement of the Lankford coefficients. In addtion, the use of notched specimens, so-called NT χ and FN χ , allowed to characterize the materials plastic behavior for high level of plastic strain (after necking). It is possible forcing the necking to develop inside the notch region and correctly instrument the sample. Using these specimens, it is moreover possible to evaluate the ductility of the material under various stress triaxiality τ. It is particularly important since it is known that τ is one of the driving parameters of damage development. Then, tests on specimens containing a crack allowed measuring the material toughness. These tests were carried out on compact tension (CT), single-edge-notched bending (SENB) and single-edge-notched tension (SENT) specimens for X65 parent material, and allowed to confirm the choice of the SENT geometry to be the less conservative.

The comprehensive experimental campaigns included tests performed at room and low temperatures (-20 • C and -40 • C ). These tests showed that for such steel grades, only the mechanical resistance is affected by the changes in temperature. It was observed that the yield stress R p0.2 and the ultimate tensile strength R m increase almost linearly while the temperature decreases. No effect on the ductility was however observed except in cases where delamination occurs. These two results explain why the J values are higher at low temperature for a given crack advance as forces (higher ultimate stress) are increased while local strain/displacements remain similar (same ductility). As J p is only function of the plastic area under the CMOD-Load curve (and J p ≫ J e ), J is a linear function of the yield/ultimate stress. On the other hand the CMOD/CTOD-∆a curves are almost temperature independent. Moreover, it is possible to confirm that a relationship under the form J = mR p0.2 CTOD exists, where m is a parameter weakly depending on geometry and material.

The experimental results also highlight difficulties in the realization of tests at low temperatures. In particular, it was observed that the use of the tempered room caused experimental issues: (i) vibrations due to the fan make the clips to oscillate and generate a significant noise in the data, (ii) the clip to measure the diametrical contraction seems to hardy follow the reduction of the minimum cross section, maybe due to presence of a thin layer of ice on the specimens surface. To go further and improve the experimental protocol, it would be interesting to develop a testing procedure based on the use of digital image correlation to monitor: (i) the diameter at the actual minimum cross section for NT χ specimens, (ii) the opening of the crack for SENT specimens. It would be then possible to directly measured CMOD and CTOD with a similar method to the double-clip gage method.

Another lesson from the experimental campaign is that it is essential to check the homogeneity of the material properties across the pipe wall thickness. Indeed, due to successive thermal treatments, it was observed that a few millimeters at the outer diameter show a significant increase of mechanical properties with the yield stress being about 150 MPa greater than the one measure at the mid-thickness. This phenomenon can be easily detected with the realization of a through thickness micro-hardness profile. In the future works, such a protocol must be systematically followed.

Chapters 5 and 8 are dedicated to the modeling of the materials behavior. This was performed in two steps. First, the elastic-plastic behavior of the four materials (X65/X65W and X70/X70X) was identified at the three temperatures (-40, -20 and 20 • C ) using experimental data from tensile tests and an inverse analysis. Then, the objectives was to be able to properly simulate all the specimens that were tested and presented in Chapter 4 and 7. The GTN damage model was found to be appropriate in the case of our four materials which failure mechanism is mainly driven by the growth and the coalescence of porosities. The identified sets of best GTN parameters for each materials are shown to allow finite element simulations very closed to the experimental data, except for the weld material from the UOE-LSAW for which simulations cannot predict the failure of NT χ specimens and correct R-curves from SENT tests.

The opportunity to perform full scale tests for validation is a chance in the context of a research project. Two full scale tests were carried out: (i) a seamless pipe of grade X65, outer diameter 323.8 mm and wall thickness 22.2 mm, was subjected to internal pressure up to 518 bar and four point bending, (ii) a UOE-LSAW pipe of grade X70, outer diameter 609 mm and wall thickness 29 mm, was subjected to internal pressure up to 476 bar and tensile axial load. Both line pipes contained cracks at the weld centerline and within the parent material, and geometries of the cracks were selected to ensure a crack propagation and final failure at the weld centerline. Unfortunately, only the four point bending test is exploitable since an unlikely failure occurred at one pipe end during the second test, while only 1 /3 of the targeted tensile strain was reached. For this test, no crack initiation was observed using silicon replica. On the other hand, non-destructive ultra-sonic testings measured a 0.4 mm propagation. However, such a value is not sufficient to allow comparison with global and local approaches. Therefore, only comparisons with the seamless pipe are reported.

Comparisons with global and local approaches show that these methods allow to predict with a good agreement the tensile capacity of the seamless pipe, both for initiation (PRCI levels 1, 2 and 3) and failure for the procedure based on finite element analyses (PRCI level 4 and ExxonMobil level 3). Furthermore, the local approach is shown to accurately predict the complete opening of the crack at the weld centerline where the experimental failure was observed. However, the results of assessments based on levels 1 and 2 from ExxonMobil are particularly overconservative, which can be explained by the fact that analyses are based on material R-curves being very low with regards to the actual material properties.

Performing these full-scale experiments also reveals the difficulties of such tests, related to both preparation and testing phases. As an example, errors during the machining of the flaws can significantly increase the amount of work during the interpretation of the results. Therefore, it is of the greatest importance to proceed to a quality control of the work done by contractors at each step of the test preparation. It is also essential to understand as much as possible the kinematics of the testing setup so that the actual applied loads and boundary conditions are known. As a matter of fact, several months were needed during this study to finally understand and properly interpret results of the four point bending test. To help, it is necessary to equip the pipe with as much sensors and extensometers as possible: strain gages, inclinometers, rigid body displacement indicator, etc. It is also mandatory to validate, prior to the test, that all these systems are correctly calibrated and recorded.

To conclude, we can say that this study can be seen as a procedure to investigate the transferability from laboratory specimens to complex structures of fracture parameters (either global of local). From the samples identified in the literature review, only the curved wide plate specimen was not investigated. To go further, considering that the local approach allows to predict with a good accuracy the result of the four point bending test, it would be interesting to simulate the testing of such a specimen and compare results with the procedure suggested by University of Ghent. There is no particular issue to do so, except the amount of time required to run the calculation. Reducing the simulation time is also an important goal to reach. where ϵ Sd is the design compressive strain. ϵ c is given by . p min is the minimum sustainable pressure with the associate strain. γ ϵ is a strain resistance factor in the range 2.0 to 3.3.1 ϵ c is given by:

ϵ c (

A.5.2 With external overpressure

In the case of a pipe subjected to longitudinal compressive strain due to bending moment or axial force, and external overpressure, the following criterion shall be verified at all cross sections of the pipe:

⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ϵ Sd ϵ c (t 2 , 0) γ ϵ ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟
δ 0 = V 2 - a 0 + h 2 a 0 + h 1 V 1 ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ 1 1 -a 0 +h 2 a 0 +h 1 ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ (B.4) δ 0 = V 2 - a 0 + h 2 a 0 + h 1 V 1 a 0 + h 1 h 1 -h 2 (B.5) then δ 0 = a 0 + h 2 h 2 -h 1 V 1 - a 0 + h 1 h 2 -h 1 V 2 (B.6) δ 0 = a 0 + h 1 + h 2 -h 1 h 2 -h 1 V 1 - a 0 + h 1 h 2 -h 1 V 2 (B.7
)

δ 0 = a 0 + h 1 h 2 -h 1 V 1 + V 1 - a 0 + h 1 h 2 -h 1 V 2 (B.8)
which yields the formula as given by ExxonMobil

δ 0 = V 1 - a 0 + h 1 h 2 -h 1 (V 2 -V 1 ) (B.9)
Following the same reasoning yields the following equality:

sin(α) = V 1 -δ M 2h 1 = V 2 -δ M 2h 2 (B.10) (V 1 -δ M ) h 2 = (V 2 -δ M ) h 1 (B.11)
which can be simplified as

δ M (h 1 -h 2 ) = h 1 V 2 -h 2 V 1 (B.12)
which gives after simplifications and finally

δ M = V 1 - h 1 h 2 -h 1 (V 2 -V 1 ) (B.
δ 90 (0.5V 2 + h 1 -0.5V 1 -h 2 ) = -V 1 a 0 -V 1 h 2 + V 2 a 0 + V 2 h 1 (B.
δ 90 =2 V 2 (a 0 + h 1 ) -V 1 (a 0 + h 2 ) (V 2 -V 1 ) -2 (h 2 -h 1 ) (B.18)
as defined in [START_REF] Verstraete | Determination of CTOD resistance curves in side-grooved Single-Edge Notched Tensile specimens using full field deformation measurements[END_REF].

The demonstration of Equation 1.65 is the same as for ExxonMobil formulation.

C.3 Symbols and designations

Symbol Definition a 0 average original crack depth from the optical measurement a p 0 crack depth measured at one of the nine equally spaced points along the pre-crack front a i crack depth measured from one of the nine equally-spaced points along the final crack front a p physical final crack depth ∆a p ∆a p = a p -a 0 B Specimen thickness in the direction parallel to the crack front

B

C.4 Sent specimen

• The SENT specimen has a square cross-section B x W, where B denotes the specimen width and W denotes the specimen thickness. The specimen thickness shall be as close as possible to the pipe wall thickness. • The fatigue pre-cracking procedure as per ASTM-E-1820 [START_REF]Standard Test Method for Measurement of Fracture Toughness[END_REF] can be replaced by electrodischarge machining as long as the material is demonstrated to be on the upper-shelf of the brittleductile transition curve. Wire diameters up to 0.50 mm. • The SENT specimens shall be notched from the outside diameter surface to reach an initial crack depth-to-thickness ratio between 0.25 % and 0.35 %. • Side grooves shall be machined to reach a total width reduction of 10 % (i.e. B N = 0.9 x B).

• The side-grooves shall be machined after the machining of the notch, with their root centered on the specimen length and perpendicular to the long direction of the specimen. • The root radius of the side-grooves shall be equal to 0.5 mm ± 0.2 mm. • The specimen length shall be sufficient to ensure a clamping distance L = 10 x W.

C.5 Instrumentation

The following quantities shall be monitored and saved during the test:

• the load F over the range [0,F max ] where the maximal load can be estimated by P UTS = B N (Wa 0 ) UTS ; • the openings V 1 and V 2 of the two clip gages that measure the CMOD at the heights h 1 and h 2 .

Note 1: Opening displacements greater than 10 mm can be reached in the case of highly ductile materials. Then, it is necessary to ensure a proper calibration up to the maximal opening of the clips.

Note 2: It is necessary to set a sufficient writing rate of the signals to ensure a proper post processing of the data for R-curve determination. A frequency of 10 s -1 was demonstrated being suitable.

D.2 Ultrasonic testing

R ésum é

Les standards consacr és à la conception des ol éoducs se concentrent principalement sur les chargements op érationnels, tels que les pressions internes et externes, et les proc édures d'analyse de d éfauts actuelles n'exploitent pas les capacit és d' écrouissage du mat ériau. Pourtant, dans des conditions extr êmes, les ol éoducs peuvent être soumis à des contraintes audel à de la limite d' élasticit é jusqu' à atteindre 2.5% de d éformations plastiques. Ici, les proc édures propos ées par ExxonMobil et PRCI bas ées sur des crit ères en d éformation sont pr ésent ées, et l'utilisation de l' éprouvette SENT (Single Edge Notched Tension) pour caract ériser la t énacit é est étudi ée, en comparant les diff érentes proc édures d'essais recommand ées. Les r ésultats d'une importante campagne exp érimentale r éalis ée pour caract ériser deux aciers pour ol éoducs à temp érature ambiante et à basses temp ératures sont pr ésent és.

Les comportements m écaniques des mat ériaux de base et d'apport sont identifi és gr âce à l'utilisation de l'analyse inverse, et il est montr é que le mod èle d'endommagement GTN permet de mod éliser finement les essais sur éprouvettes de laboratoire. Enfin, les r ésultats de deux essais sur structures (pression et flexion, puis pression et traction) sont pr ésent és de mani ère à comparer les approches globales et le mod èle d'endommagement GTN. Ce dernier d émontre une bonne transf érabilit é de l' éprouvette vers la structure.

Mots Cl és ol éoduc, crit ères en d éformations, X65, X70, m écanique de la ruptutre, éprouvette SENT, t énacit é, transf érabilit é, CTOD, int égrale J, mod èle d'endommagement GTN, cordon de soudure Abstract Pipeline design codes and standards traditionally focus on the operational loadings such as internal and external pressures that are likely to exist over the entire lifetime of the pipeline. Existing Engineering Critical Assessments are mostly based on stress considerations, where the design margin is given as a percentage of the yield strength. In extreme environments, pipelines may experience stresses beyond the yield and plastic deformations up to 2.5 %. In such conditions, strain-based design procedures apply. In this work, a literature review of the existing strainbased methods is proposed, including ExxonMobil and PRCI multi-tier approaches. The use of the Single Edge Notched Tension (SENT) specimen to measure the material toughness is then studied, benchmarking the recommended testing procedures from literature. A comprehensive experimental campaign was carried out to fully characterize two actual line pipes at room and low temperatures. The mechanical behavior of parent and weld materials are identified using an inverse analysis, and GTN damage model is shown to allow accurate modeling of the laboratory testings. Finally, two full scale tests (pressure + bending or pressure + tension) were carried out to benchmark the global approaches and GTN damage model. The latter showed a very good transferability from specimens to the structure. Keywords pipeline, strain based design, X65 steel grade, X70 steel grade, fracture mechanics, SENT specimen, toughness, transferability, CTOD, Jintegral, damage model GTN, girth weld, oil & gas

Sommaire 1 . 1

 11 Fracture mechanics basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Linear Elastic Fracture Mechanics (LEFM) . . . . . . . . . . . . . . . . . . . . . . . 1.1.3 J-integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.4 Experimental measurement of J ............................. 1.2 The SENT specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Recommended practices in the literature . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3 Crack size and crack sharpness effect . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.4 Experimental CTOD measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.5 Experimental J-integral calculation for SENT specimens . . . . . . . . . . . . . . . 1.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 1 . 1 -

 11 Figure 1.1 -Definition of the polar coordinates used in Equation 1.1 and Equation 1.1 .

1 .Figure 1 . 4 -

 114 Figure 1.4 -Representation of J-integral

Figure 1 . 6 -ΔFigure 1 . 7 -

 1617 Figure 1.6 -Drawing of a typical SENT specimen.

Figure 1 . 9 -Figure 1 . 10 -

 19110 Figure1.9 -CTOD R-curves obtained for different crack sizes on (a.) a 12 inches X65 parent material and (b.) a 13% Cr parent material[START_REF] Nyhus | Fracture Control-Offshore Pipelines: Experimental Studies on the Effect of Crack Depth and Asymmetric Geometries on the Ductile Tearing Resistance[END_REF]

Figure 1 .

 1 Figure 1.13 -(a.) ExxonMobil and (b.) UGhent drawings defining the double-clip gage method.

  .14), the double-clip method, FEA results and the relationships from DNV-OS-F101, Shen and Tyson, and Moreira and Donato. Results are given in Figures 1.15 and 1.16.

Figure 1 . 14 -

 114 Figure 1.14 -Notch replica by Moore and Pisarski to accurately measure the CTOD (A-A) and determine the amount of tearing (B-B) [37].

Figure 1 . 15 -

 115 Figure 1.15 -Comparisons by Moore and Pisarski of CTOD values obtained using the notch replica method and other methods [37].

Figure 1 . 16 -

 116 Figure 1.16 -Comparisons by Moore and Pisarski of CTOD values using the double-clip method and J-based methods [37].

Figure 1 . 18 -

 118 Figure 1.18 -Evolution of the plastic area during the tearing test.

Figure 1 .

 1 Figure 1.19 shows a comparison between the different experimental definitions of CTOD and δ 90 definition. One can see that the double-clip gages methods and δ 5 method enable to evaluate the CTOD

Figure 1 . 19 -

 119 Figure 1.19 -Comparison of the different experimental methods for δ measurement.

Figure 1 . 20 -

 120 Figure 1.20 -Views of a typical mesh for η p calculation.

Figure 1 . 21 -

 121 Figure 1.21 -FE analyses of two configurations, B = W and B =2W : (a) normalized J/J average through the thickness; (b) Evolution of J as a function of CMOD.

7 a0B 7 a0

 77 .24-a). The DNV correction accounting for the effect of weld mismatch (Equation 1.70) does not improve the correspondence between the present FE simulations and the DNV equations (Figures 1.23-b and 1.24-b). The 0.85 coefficient should only be considered as a safety factor. Based on these results, the values for η used in this work will be computed based on the correlation proposed by Cravero and Ruggieri for clamped SENT specimens, i.e.: η =1.0398 -0.697 a W Furthermore, this expression can be corrected for large extension using incremental expression 1.40 taking into account the γ coefficient. The latter will be calculated using the above expression and Equation 1.40. B = W specimens -0.25 ≤ a0/W ≤ 0.=2W specimens -0.25 ≤ a0/W ≤ 0.) B = W SENT specimens (b.) B =2W SENT specimens.

Figure 1 . 22 - 5 (Figure 1 . 23 -

 1225123 Figure 1.22 -Linear relationship between U p and J p B (Wa). η p is directly given by the slope.

1 .Figure 1 . 24 -

 1124 Figure 1.24 -Comparison between DNV and Cravero and Ruggieri η formulations and calculated values by means of FEA, when considering J as the mean value of J along the crack front.

Figure 1 . 26 -

 126 Figure 1.26 -Results of the comparison between compliance expressions in the literature and the numerical results.

Figure 1 . 27 -

 127 Figure 1.27 -Evolution of the correction factor Fr during a typical SENT test (from [43]).

Figure 1 . 28 -

 128 Figure 1.28 -Views of a typical SENT mesh -(a.) Global and (b.) close-view .

Figure 1 .

 1 Figure 1.29 -(a.) CMOD vs load graph with unloading for increasing displacement and (b.) calculated crack advance without and with the correction factor.

Figure 1 . 30 -

 130 Figure 1.30 -Canmet results (a.) without and (b.) with the rotation correction factor F r .

Figure 2 . 2 -

 22 Figure 2.2 -An example of how frost heave works. From [46].

Figure 2 . 3 -

 23 Figure 2.3 -An example of how thaw settlement works. From[START_REF]Buried Alaska gas line could face powerful bending forces[END_REF]

Figure 2 . 4 -

 24 Figure 2.4 -Iceberg and pressure ridges. From http://officerofthewatch.com

Figure 2 . 5 -

 25 Figure2.5 -Description of a curved wide plate (CWP) tension test.[START_REF] Hertelé | Parametric finite element model for large scale tension tests on flawed pipeline girth welds[END_REF]

Figure 2 . 16 -

 216 Figure 2.16 -Representation of the limit states as defined by the PRCI. From [51].

Figure 3 . 1 -

 31 Figure 3.1 -Typical J-weld (left) and V-weld with a 60 • angle (right). The base material is denoted by BM, and the weld material is denoted by WM. Two crack locations were considered: OD surface cracks, and ID surface cracks.

Figure 3 . 2 -

 32 Figure 3.2 -Principle of the tangency analysis. ε c denotes the critical remote strain for an initial defect size a 0 -From [48].

Figure 3 . 3 -

 33 Figure 3.3 -Meshes of the J-weld (a.) and V-weld with a 60 • angle. The base material is blue colored and the weld material is red colored.

Figure 3 . 4 -Figure 3 . 5 -

 3435 Figure 3.4 -Effect of the mismatch on the crack driving force curves measured on a J-weld. Results of the post-processing for a remote strain equal to 0.4 % (a.) and 1.5 % (b.).

Figure 3 . 6 -Figure 3 . 7 -

 3637 Figure 3.6 -Effect of the mismatch on the crack driving force curves measured on a J-weld. Results of the post-processing for a remote strain equal to 0.4 % (a.) and 1.5 % (b.).

Figure 3 . 8 -

 38 Figure 3.8 -Critical defect sizes as defined by the tangency analysis for the five different mismatch level and weld geometries, for OD cracks.

Figure 3 . 9 -

 39 Figure 3.9 -PRCI tensile strip specimen. In [54].

Figure 3 . 10 -

 310 Figure 3.10 -Tensile specimen for weld material stress-strain curve determination as proposed in DNV-OS-F101. LW value corresponds to the specimen length including only weld material.

Figure 3 . 11 -Figure 3 . 12 -

 311312 Figure 3.11 -Typical meshes used in the numerical analysis. The base material is blue colored and the weld material is red colored.

Figure 3 . 13 -

 313 Figure 3.13 -Effect of the L 0 /φ 0 ratio on the measured ultimate tensile strength using DNV-OS-F101 cross-weld specimen. The vertical axis indicates the error with respect to the actual material ultimate tensile strength (R m = 675 MPa).

Figure 3 .

 3 Figure 3.14 -Specimen mounted in the hydraulic grips on a MTS tensile frame. Two LVDT sensors are used in order to compare with DIC.

Figure 3 . 15 -

 315 Figure 3.15 -Position of virtual gages E0, E1, E2 and E3.

Figure 3 . 16 -

 316 Figure 3.16 -Tensile stress-strain curves obtained using the DIC methodolgy.

3 .

 3 From D to failure: where a macro crack develops in the center of the notch up to failure. The parameters F(c) and ∆Φ (c) s denote the load and the diameter reduction at void coalescence and crack initiation. The slope δF/ (δΦ/Φ 0 ) reflects the speed of the crack propagation through the specimen cross-section.Experimental results for NT 4 and NT 10 specimens are plotted in figure3.21 where the material shows a good reproducibility in terms of plasticity (up to point D).

Figure 3 . 17 -

 317 Figure 3.17 -View of notched tensile specimens with a nominal diameter φ 0 = 6 mm, and two different notch radius: NT 10 and NT 4 .

Figure 3 . 19 -

 319 Figure 3.19 -Inverse analysis flow chart.

  W are material parameters to be adjusted. The use of such an expression comes out the comparison with the experimental data. Any other formulation may be preferred, such as classical Ramberg-Osgood or Hollomon formulations. The optimizer gave the following values for the parameters: R 0 = 525 MPa, Q 1 =0.645, b 1 =7.11 and Q 2 =0.164. Comparisons between experimental and FE results are given in Figure 3.21.

Figure 3 . 20 - 4 NT 10 ∆ΦFigure 3 . 21 -

 320410321 Figure 3.20 -Meshes of NT 10 and NT 4 specimens (left to right). Parent material in blue ; weld material in red.

Figure 3 . 22 -Figure 3 . 23 -

 322323 Figure 3.22 -Schematic of the round bar specimen.

Figure 4 . 1 -

 41 Figure 4.1 -Definition of the material orientations.

  Figure

  4

  .

  Figure 4.2 -Billet piercing process (from [59])

  Heat treatment 12 min at 940 • C Water quenched 22 min at 620 • C Air quenched Chemical etching using a 4 % Nital solution was realized on (L,S), (T,S) and (L,T) planes to reveal the microstructure. Results are depicted in Figure 4.3. X65 steel shows a bainite microstructure, and the following is observed:

Figure 4 . 3 -

 43 Figure 4.3 -Microstructure of X65 material after a 4 % Nital etching. The scale represents 20 µm.

Figure 4 . 4 -

 44 Figure 4.4 -Geometry of ST specimens.

Figure 4 . 5 -

 45 Figure 4.5 -(a.) Measurement of the specimens using a numerical micrometer screw gage and a laser system for cylindrical surfaces ; (b.) view of the MTS 100 kN tensile machine ; (c.) view of the analogical plotter ; (d.) View of a ST specimen clamped in the hydraulics grips of the tensile machine, fully instrumented with a LVDT extensometer to measure the axial deformation and a clip gage to measure the diametrical reduction in S direction.

Figure 4 . 6 -

 46 Figure 4.6 -Results of the ST specimens on X65 material at room temperature. ∆φ denotes the diameter change and φ 0 the initial diameter. The p subscript indicates that the quantity is a plastic strain.

  and 4.8. Moreover, the mechanical properties derived from these tests are given in Table

Figure 4 . 7 -Figure 4 . 8 -

 4748 Figure 4.7 -Results of the smooth tensile tests on the X65 material at -20 • C.

Figure 4 . 9 -

 49 Figure 4.9 -View of a NT 2 specimen mounted into the hydraulic grips, and fully instrumented with a LDVT extensometer and a clip gage.

Figure 4 .

 4 Figure 4.10 -NT typical curve and experimental load-diameter reduction curves

Figure 4 . 11 -

 411 Figure 4.11 -Notched tensile specimen (NT χ )

  ,

Figure 4 .

 4 Figure 4.14 shows a comparison of the results measured on NT 10 at the three temperatures of the study and enables to observe the effect of temperature on mechanical resistance and ductility of the material. A slight increase of the maximum load in observed with decreasing temperature as reported in Tables 4.7, 4.8 and 4.9. Figure4.15 also shows that the material keeps a good ductile performance even at low temperatures, with ∆Φ/Φ 0 ratios at -20 • C and -40 • C almost equivalent to those was measured at room temperature. Moreover, no delamination was observed on the fracture surfaces of the notched specimens even at -40 • C.

Figure 4 . 2 (Figure 4 . 13 -Figure 4 . 14 -

 42413414 Figure 4.14 shows a comparison of the results measured on NT 10 at the three temperatures of the study and enables to observe the effect of temperature on mechanical resistance and ductility of the material. A slight increase of the maximum load in observed with decreasing temperature as reported in Tables 4.7, 4.8 and 4.9. Figure4.15 also shows that the material keeps a good ductile performance even at low temperatures, with ∆Φ/Φ 0 ratios at -20 • C and -40 • C almost equivalent to those was measured at room temperature. Moreover, no delamination was observed on the fracture surfaces of the notched specimens even at -40 • C.

Figure 4 . 15 -

 415 Figure 4.15 -Effect of the temperature on the ductility measured on NT χ specimens. The circle denote the tests performed in L direction, and the triangles the tests in T direction.

Figure 4 . 19 -Figure 4 . 20 -

 419420 Figure 4.19 -Flat notched tensile specimen (FN χ )

Figure 4 . 21 -

 421 Figure 4.21 -Plane strain specimen (PE)

  Figure 4.22 -Stress-strain curves derived from plane strain (PE) tests at room temperature.

Figure 4 .

 4 Figure 4.23 -Compact Tension specimen CT

Figure 4 .

 4 Figure 4.24 -Optical measurement of the crack growth during the fatigue pre-cracking procedure.

  measured specimen elastic compliance (at the load-line), H * = initial half-span of the load points (center of the pin holes). Here H * = 8.87 mm, R = radius of rotation of the crack centerline, (W + a)/2, where a is the updated crack size, D = one half of the initial distance between the displacement measurement points. Here D = 1.5 mm, θ = angle of rotation of a rigid body element about the unbroken midsection line (see Equation 4.16)

Figure 4 .

 4 Figure 4.25 -Elastic compliance correction for CT specimen rotation (from ASTM-E1820 [20]).

Figure 4 .

 4 Figure 4.26 -CT tearing test performed on a 100 kN servo-hydraulic MTS machine.

Figure 4 .

 4 Figure 4.27 -(a.) CMOD-Load curves of the CT tests on X65 material at room temperature, and (b.) J-R curves.

Figure 4 .

 4 Figure 4.28 -Definitions of the exclusion lines in [20].

  .8.

Figure 4 . 29 -

 429 Figure 4.29 -View of a SENB specimen (a.) prior to the test and (b.) during the test.

  Figure 4.29 shows views of a SENB tests prior to the test and during the test. The experimental CMOD-load curves are depicted in Figure 4.30-a showing that they are perfectly reproducible, as well as the J and CTOD-R curves given in Figures 4.30-b/c, where the CTOD is directly measured using the double-clip gages method. The experimental R curves were fitted using exponential functions of the form: J = α∆a m (4.28) and δ = β∆a n (4.29) where ∆a denotes the crack advance. The fitting R curves are depicted in Figures 4.30-b/c in thin black lines. Values fitted for α and m are respectively 1433 and 0.561 with J being expressed in kJ.m -2 and ∆a in mm. Similarly β and n are equal to 2.103 and 0.637. Moreover, crack initiation criteria were determined and values are reported in Table

Figure 4 . 30 -

 430 Figure 4.30 -Results on SENB specimens at RT.

  Cross section: BxB -ExxonMobil, Canmet and Cravero -Notch preparation: * EDM notch -ExxonMobil * Fatigue precrack -DNV, Canmet and Cravero -Crack depth: * shallow notch with a 0 /W =0.25 -ExxonMobil * deeper notches with a 0 /W =0.35 and a 0 /W =0.5 for comparison • Testing:

Figure 4 . 31 -

 431 Figure 4.31 -Comparisons of crack growths measured by the unloading compliance (horizontal axis) and the silicon replica (vertical axis). The unloading method shows a good accuracy on most of the measurement points.

Figure 4 . 32 -

 432 Figure 4.32 -SENT tests on X65 at room temperature clearly show the effect of the initial a 0 /W on the material R-curve. The non effect of the notch sharpness is also observed between 110 µm and 300 µm edm notched specimens.

Figure 4 . 33 -

 433 Figure 4.33 -Effect on the initial crack length on the measured material toughness.

  Figure 4.34 -SENT fitting material R curves according to the initial crack length.

Figure 4 .Figure 4 . 35 -

 4435 Figure 4.35 -Comparisons between CTOD measured using double-clip gages method and CTOD derived from J values, using DNV-OS-F101:2010 relationships.

Figure 4 . 36 ) 1 m=1. 5 MeasuredFigure 4 . 37 -

 43615437 Figure 4.36 -Estimation of the CTOD from J using DNV-OS-F101:2010 relationship.

  Figure 4.38 -Views of the SENT setup for testing at low temperatures.

Figure 4 . 40 -

 440 Figure 4.40 -Effect of the temperature on the material toughness -Normalized curves.

Figure 4 . 41 -Figure 4 . 42 -Figure 4 . 43 -

 441442443 Figure 4.41 -View of the welding procedure: (a.) the two pipes are positioned so that the hi-lo is minimal ; (b.) and (c.) the region at the vicinity of the girth weld is pre-heated to reach 100 • C ; (d.) operators manually control the positioning of the welding trolley using a remote.

Figure 4 .

 4 Figure 4.44 -NT specimens were machined so that the notches are located within the weld material.

Figure 4 . 45 -

 445 Figure 4.45 -Results on X65W NT χ specimens at room temperature.

  and 4.47-b confirm what was already observed at room temperature: greater maximal loads and lower ductilities for the weld material. All the results are gathered in Table 4.19, and Figure 4.49 summarizes the differences in terms of tensile properties measured at +20 • C,-20 • C and -40 • C for NT specimens for X65 and X65W materials.

Figure 4 . 46 -Figure 4 . 47 -Figure 4 . 48 -Figure 4 . 49 -

 446447448449 Figure 4.46 -Experimental results on X65W NT χ specimen at -20 • C.

Figure 4 . 4 . 4 . 5 . 1

 44451 Figure 4.50 -X65W SENT specimen. The specimens were machined so that the crack is at the weld centerline.

Figure 4 .

 4 Figure 4.51a shows that the CMOD-Load diagrams are reproducible over the entire testing range. The curves slowly decrease after reaching the maximal load, showing good capacities of the material to resist to the crack propagation. This property was not expected following the results on the NT specimens at room temperature (Figure 4.45-a) where the diameter reductions at void coalescence were particularly low in comparison with parent material properties. Therefore, it is interesting to compare the SENT results with those obtained on the parent material with identical specimens depicted in Figure 4.51b. Unlike what was observed on NT results, the two materials show almost identical CMOD -Load curves, meaning that the processing of the data should lead to identical R-curves. This point is confirmed hereinafter.

Figure 4 .Figure 4 . 53 -

 4453 Figure 4.51 -SENT CMOD-Load diagrams at room temperature on X65 and X65W.

Figure 4 .Figure 4 . 54 -Figure 4 .Figure 4 . 56 -

 44544456 Figure 4.54 -SENT CMOD-Load results on X65W at low temperatures.

Figure 5 . 3 -Figure 5 . 4 -Figure 5 . 5 -

 535455 Figure 5.3 -Results of the identification of the material constitutive law for the tensile tests at room temperature.

Figure 5 . 6 -Figure 5 . 7 -

 5657 Figure 5.6 -Results of the identification of the material constitutive law for the tensile specimens (ST) and the notched tensile specimens (NT χ )at-20 • C , with a consistent hardening law.

Figure 5 . 8 -

 58 Figure 5.8 -Axisymmetric meshes for NT χ specimens with mesh size of 100µm

Figure 5 . 9 -

 59 Figure 5.9 -Axisymmetric meshes for NT χ specimens with mesh size of 100µm

Figure 5 .

 5 Figure 5.10 -X65 axisymmetric notched specimens at room temperature: Comparisons between experimental and GTN simulations

Figure 5 . 11 -

 511 Figure 5.11 -X65 axisymmetric notched specimens at low temperatures: Comparisons between experimental and GTN simulations

Figure 5 . 12 -

 512 Figure 5.12 -View of the crack front as meshed for SENT calculation. The mesh size in the crack region is of 100 x 100µm

Figure 5 . 13 -

 513 Figure 5.13 -View of the SENT specimen mesh with the two elastic rigid parts for CMOD and CTOD calculations. The two measurements points are highlighted.

Figure 5 . 15 -

 515 Figure 5.15 -Numerical CMOD-Load curve measurement on the parent material SENT using the GTN model.

CMODFigure 5 . 18 -

 518 Figure 5.18 -X65 material. R-curves derived from FEA using GTN model at -20 • C

Figure 5 . 19 -

 519 Figure 5.19 -X65 material. R-curves derived from FEA using GTN model at -40 • C

Figure 5 . 20 -

 520 Figure 5.20 -Mesh for CT calculation with GTN model. Mesh size is 100 × 100 µm. The experimental data of the CT tests have already been presented in Chapter 4. Comparison with experiments (figure 5.21) show a good agreement. It is worth noting that the J-∆a obtained from CT and SENT specimens have very different shapes which is well represented by the simulations.

Figure 5 . 21 -

 521 Figure 5.21 -Comparison between experimental and numerical load-displacement curves obtained for CT specimens on X65 material in LT direction

Figure 5 . 22 - 2 NT 4 NT 10 ∆ΦFigure 5 . 23 -

 5222410523 Figure 5.22 -Comparison between experimental data and simulations of the axisymmetric notched tensile specimens on X65W at room temperature

Figure 5 . 24 -

 524 Figure 5.24 -Comparison between experimental data and simulations of the axisymmetric notched tensile specimens on X65W at room temperature

X65W at -20 o C NT 2 NT 4 NT 10 ∆ΦFigure 5 . 25 -

 2410525 Figure 5.25 -X65W material: Comparison between experimental data and simulations of the axisymmetric notched tensile specimens on X65W at -20 • C and -40 • C.

Figure 5 . 26 -Figure 5 . 27 - 5 .CMODFigure 5 . 28 -

 5265275528 Figure 5.26 -X65W material: measured material R-curve using FE simulations with GTN model

6. 1

 1 Description of the test 6.1.1 Test rig The full-scale test was carried out at SZMF (Salzgitter Mannesmann Forschung GmbH) in Duisburg (Germany) on a vertical four-point-bending facility LiSA (for Limit State Analyzer) as depicted in Figure 6.1.

Figure 6 . 1 -

 61 Figure 6.1 -Overview of the vertical four-point bending facility LiSA (from [78])

  ) As required before machining (left: notch inside the girth weld ; right: notch in the base metal). ) As provided after machining (left: notch inside the girth weld ; right: notch in the base metal).

Figure 6 . 3 -

 63 Figure 6.3 -View of the notches in the weld material (left) and the parent material (right).

Figure 6 . 5 -

 65 Figure 6.5 -Location of the four strain gages as required for the test.

  Figure 6.6 -Views of the instrumentation on the pipe.

Figure 6 . 7 -

 67 Figure 6.7 -Geometry of the setup and positioning of the four jacks.

Figure 6 . 8 -

 68 Figure 6.8 -View of the the crack after the test. The weld centerline crack propagates through the whole wall thickness and circumferentially (a.). Only a limited blunting was observed for the base material crack (b.).

Figure 6 . 9 -

 69 Figure 6.9 -Evolution of the internal pressure during the test

Figure 6 . 10 -

 610 Figure 6.10 -Load -jack displacement curves for each cylinders (a.), and average load-displacement curve (b.)

Figure 6 . 11 -

 611 Figure 6.11 -Evolution of the axial and hoop strains measured at each strain gage locations as a function of the average displacement.

Figure 6 . 12 -

 612 Figure 6.12 -Comparison between ExxonMobil R curves for L2 assessment and actual material properties derived from SENT tests on X65W.

6. 3 . 2

 32 PRCI multi-tier approach 6.3.2.1 PRCI L1 PRCI level 1 assessment is used to predict the tensile strain at initiation under a tabular form. The input parameters are: • The yield-to-tensile ratio, Y/T = 0.82 • The weld overmatch, λ = 1.187 • The misalignment, e = 0.22 mm • The flaw depth, a = 4 mm • The flaw length, 2C = 65 mm • The pipe wall thickness, WT = 22.2 mm • The apparent toughness, CTOD A The apparent toughness was not measured during the experimental campaign at room temperature. However, according the PRCI procedure, it is possible to derive CTOD A from the upper-shelf Charpy impact energy using the relationship given in Equation 2.10 page 72. Serimax carried out Charpy impact tests at -20 • C . Assuming that the material remains on the upper-shelf at -20 • C , it is possible to calculate the apparent toughness: CTOD A = (0.0080 * Y/T -0.0014) CVN upper-shelf =0.986 mm Tabulated results are given in Figure 6.14, and the line highlighted in blue correspond to the configuration which is the closest to the actual configuration.

Figure 6 . 14 -

 614 Figure 6.14 -Tabulated results reported for PRCI level 1 assessment. The line highlighted in blue is the closest to the actual properties.

Figure 6 . 15 - 1 / 4

 61514 Figure 6.15 -1 /4 mesh of the pipe. The displacements are applied on the highlighted nodes (U2= 0 on the left and U2> 0 on the right).

Figure 6 . 16 -

 616 Figure 6.16 -Comparison of experimental and simulated pipe responses (left: force ; right: bending moment). The FEA highly underestimated the load level.

Figure 6 . 17 -

 617 Figure 6.17 -Micro-hardness HV2. Location (a.) and results (b.)

RFigure 6 . 18 -Figure 6 . 19 -

 618619 Figure 6.18 -View of the full-thickness specimen after the preparation for DIC.

Figure 6 . 20 -Figure 6 . 21 -

 620621 Figure 6.20 -View of the mesh used for the inverse identification. The elset in red corresponds to the bulk region, and the elset in blue to the surface region (a.). Stress-strain tensile curves (b.).

Figure 6 . 22 -

 622 Figure 6.22 -FEA model of the pipe bending applying a rotation (a). View after bending (b.).

Figure 6 . 23 -

 623 Figure 6.23 -Rotation of the pipe during the loading.

Figure 6 . 24 -Figure 6 . 25 -

 624625 Figure 6.24 -Comparisons between full test rig model and rigid plate model.

Figure 6 . 26 -

 626 Figure 6.26 -Correction of the experimental data using a modified lever arm, L = 1300 mm (a.) Correction on the rigidity (b.).

Figure 6 . 29 -

 629 Figure 6.29 -Elsets used to assign the material properties.

Figure 6 . 30 -

 630 Figure 6.30 -Displacement-Bending moment (a.) and Remote axial strain-Bending moment (b.) computed using the FEM with GTN model.

Figure 6 . 31 -Figure 6 . 32 -Figure 6 . 33 -

 631632633 Figure 6.31 -Views of the crack extensions during the FE calculation: CTOD = 3 mm (left) and CTOD = 5.51 mm (right). The colors correspond to the field of the opening stress σ 11 with the associated scale.

Figure 7 . 5 -

 75 Figure 7.5 -Experimental stress -strain curves and evolution of the Lankford's coefficients measured using tensile tests on ST specimens at -20 • C.

Figure 7 . 6 -Figure 7 . 7 -

 7677 Figure 7.6 -Experimental stress -strain curves and evolution of the Lankford's coefficients measured using tensile tests on ST specimens at -40 • C.

Figure 7 . 8 -Figure 7 . 9 -Figure 7 . 10 -Figure 7 . 11 -

 7879710711 Figure 7.8 -Experimental stress -strain curves derived from tensile tests on NT χ specimens at room temperature. Experimental results for the tests at low temperatures are depicted in Figure 7.9 (-20 • C ) and Figure 7.10 (-40 • C ). Ductilities significantly differ from those measured at room temperature. Many specimens shows a very quick load decrease which is associated with delamination as evidenced in Figure 7.11. Delamination cracks lie in the T-L plane ; their normal corresponds to the S direction.Note that this phenomenon was not observed on the X65 material. As delamination was not observed on SENT specimens tested at low temperature (see below), this phenomenon was not investigated in details in this work.

Figure 7 . 12 -

 712 Figure 7.12 -SENT tests on X70 at room temperature clearly show the effect of the initial a 0 /W on the material R curve.

Figure 7 . 13 -Figure 7 . 14 -

 713714 Figure 7.13 -Comparisons between SENT tests at room temperature and low temperatures clearly show the effect of the temperature on the material R curve.

Figure 7 . 17 -Figure 7 . 18 -

 717718 Figure 7.17 -Experimental stress -strain curves derived from tensile tests on NT χ specimens at room temperature.

Figure 7 . 19 -

 719 Figure 7.19 -X70W material R curve derived from SENT tests at room temperature

Figure 7 . 20 -

 720 Figure 7.20 -Comparison between parent and weld materials from SENT tests at room temperature.

8. 1

 1 Parent material 8.1.1 Identification of the material constitutive law 8.1.1.1 Plastic anisotropy

. 5 ) 1 , c k=1- 2 2and c k=1- 2 3 4 ,

 51224 where the four parameters a, b 1 , b 2 and α are material parameters that modify the shape of the yield surface, and the parameters c k=1-2 control the stress anisotropy on the principal directions, and c k=1-2

Figure 8 . 1 -Figure 8 . 2 -Figure 8 . 3 -Figure 8 . 4 -Figure 8 . 5 -

 8182838485 Figure 8.1 -Three-dimensional meshes of the NT χ specimen used for the identification of the elastic plastic behavior of the X70 parent material.

8. 1 . 1 . 4

 114 Plastic behavior at -20 • C

FEAFigure 8 . 6 -

 86 Figure 8.6 -Results of the identification of the material constitutive law for the tensile tests (ST) at -20 • C.

Figure 8 . 7 -

 87 Figure 8.7 -Results of the identification of the material constitutive law for the notched tensile tests (NT χ )at-20 • C.

Figure 8 . 8 -

 88 Figure 8.8 -Results of the identification of the material constitutive law for the tensile tests (ST) at -40 • C.

Figure 8 . 9 -

 89 Figure 8.9 -Results of the identification of the material constitutive law for the notched tensile tests (NT χ )at-40 • C.

Figure 8 .

 8 Figure 8.10 -Three-dimensional meshes for NT χ specimens with mesh size of 100µm

Figure 8 . 11 -

 811 Figure 8.11 -Results of the identification of the material constitutive law for the notched tensile tests (NT χ ) at room temperature.

Figure 8 . 12 -

 812 Figure 8.12 -Results of the calculated stress-strain tensile curves derived from NT χ specimens at -20 • C.

Figure 8 . 13 -

 813 Figure 8.13 -Results of the calculated stress-strain tensile curves derived from NT χ specimens at -40 • C.

  .10) poorly fit the experimental data in T direction. Stress fields after partial unloading are shown in Figure 8.15 ; they also clearly indicate crack advance.

Figure 8 . 14 -

 814 Figure 8.14 -Calculated CMOD-load curve and material R curves using GTN model for X70 material at room temperature, and comparison with the experimental data.

Figure 8 . 15 -

 815 Figure 8.15 -Evolution of the calculated opening stress σ 22 during the SENT test (MPa).

Figure 8 . 16 -

 816 Figure 8.16 -Calculated CMOD-Load curve and material R curves using GTN model for X70 material at -20 • C , and comparison with the experimental data.

Figure 8 . 17 -

 817 Figure 8.17 -Calculated CMOD-load curve and material R curves using GTN model for X70 material at -40 • C , and comparison with the experimental data.

Figure 8 . 18 -

 818 Figure 8.18 -Results of the identification of the GTN parameters on the NT_χ specimens in L direction on the X70 weld material.

Figure 8 . 19 -

 819 Figure 8.19 -Results of the identification of the GTN parameters on the NT_χ specimens in L direction on the X70 weld material.

Figure 8 . 20 -

 820 Figure 8.20 -Comparison between experimental data and calculated R curves on X70W using the GTN model, at room temperature.

Figure 9 . 1 -

 91 Figure 9.1 -Overview of the tensile frame at CSM in Cagliari, Sardinia.

Figure 9 . 2 -

 92 Figure 9.2 -Overall and zoomed views of the roller devices under the line pipe to avoid any bending moment.

- 2 Figure 9 . 6 -

 296 Figure 9.6 -Double-clip gage fixtures.

Figure 9 . 7 -

 97 Figure 9.7 -Locations of the strain gages. Crack 2 at the weld centerline is visible in (a.).

Figure 9 . 9 -

 99 Figure 9.9 -Evolution of the internal pressure during the tensile test

Figure 9 . 10 -

 910 Figure 9.10 -Load -displacement evolution during the tensile test.

9. 3 . 3

 33 Strain gages 9.3.3.1 Hoop strain

Figure 9 . 11 -

 911 Figure 9.11 -Evolution of the hoop strain as a function of the axial load.

Figure 9 . 12 -

 912 Figure 9.12 -Evolution of the axial strain as a function of the axial load. Note that for section C2, gages S1 and S5 failed during testing.

Figure 9 . 13 -

 913 Figure 9.13 -Opening of the three cracks: CMOD (left) and CTOD (right).

Figure 9 . 14 -

 914 Figure 9.14 -View of the mesh used for GTN calculations.

FEAFigure 9 . 15 -Figure 9 .

 9159 Figure 9.15 -Hoop and axial strain in section C5 as a function of the load.

Figure 9 . 16 -

 916 Figure 9.16 -Comparison between experimental data and calculated crack openings. A good fit is obtained for crack 2.

( 11 Figure 9 . 18 -

 11918 Figure 9.18 -Results of the FE analysis. Focus on the weld centerline crack: broken elements (a.) and opening stress field at ε remote, axial =1.43 %

13 )B. 2

 132 Ghent University Equation 1.65 and Equation 1.64 can be easily demonstrated by considering a right-angle triangle as defined in Figure B.2. Simple trigonometry relationships give:sin(α) = V 1 -δ 90 2 (a 0 + h 1 -l 1 ) (B.14)andsin(α) = V 2 -δ 90 2 (a 0 + h 2 -l 1 ) (B.15)where l 1 = δ 90 /2.

Figure B. 2 -

 2 Figure B.2 -Ghent double-clip gage method

17

 17

  )

Table 1 .

 1 1 -Cravero and Ruggieri coefficients for Equation 1.78 -Valid for 0.1 ≤ a/W ≤ 0.7

			α 0	α 1	α 2	α 3	α 4	α 5
	Pin loaded all H/W	1.0056 2.8744	5.442	12.51	16.102 7.0642
		H/W =4	2.3928 14.074 47.881 104.58 124.20 59.423
	Clamped	H/W =6	2.1263 13.461 51.229 120.47 147.83 71.812
		H/W = 10 1.6485 9.1005 33.025 78.467 97.344 47.227

Table 1 .

 1 2 -Canmet coefficients for Equation 1.78 -Valid for 0.05 ≤ a/W ≤ 0.95 -16.411 79.600 -211.670 236.857 27.371 -179.740 -86.280 171.764

	α 0	α 1	α 2	α 3	α 4	α 5	α 6	α 7	α 8
	2.072

Table 1 .

 1 3 -ExxonMobil coefficients for Equation 1.78 -Valid for a/W ≥ 0.25

	α 0	α 1	α 2	α 3	α 4	α 5
	1.64461 -8.7084 30.31342 -69.60922 83.52325 -39.11201

1 .

 1 Fracture mechanics applied to pipe design

Table 1 .

 1 4 -Sets of parameters derived from 3D FEA on clamped SENT -Valid for 0.20 ≤ a/W ≤ 0.70

		α 0	α 1	α 2	α 3	α 4	α 5
	H/W =8 H/W = 10	-2.58419 64.86691 -440.22 1.60887 -9.91131 39.4674 -102.559 1404.87	-2187.09 140.665	1338.14 -76.8264
	Figure 1.25 -Typical mesh for the determination of polynomial coefficient of Equation 1.78.
	opment into account. It writes:

  y 4 [e] + y 5 [ε u λ] + y 6 [λ] + y 7 [ε u ] + y 8 β 2 =y [ε u λe] + y 10 [λe] + y 11 [ε u e] + y 12 [e] + y 13 [ε u λ] + y 14 [λ] + y 15 [ε u ] + y 16

						(2.9)
	where x i parameters are given in Tables 2.3 and 2.4.
	Table 2.3 -x i coefficients in Equation 2.8 for Level 2 assessment for X60 to X70 grades.
			Level 2 for X60 to X70 grades
	R-Curve 1	R-Curve 2	R-Curve 3	R-Curve 1	R-Curve 2	R-Curve 3
	x 1 x 2 -6.550e --8.922e -04 -9.999e -04 x 19 -8.978e -04 -1.477e -03 -1.990e -03 2.495e -05 4.458e -05 5.876e -05 x 17 9.885e -05 1.679e -04 2.312e -04 x 3 6.162e -04 2.187e -04 -3.023e -04 x 19 6.453e -06 -4.338e -05 -1.856e -04 x 4 -3.869e --2.443e -03 -5.374e -04 x 20 2.485e -02 3.014e -02 3.520e -02 x 5 -4.777e --8.082e -05 -9.424e -05 x 21 -3.683e -04 -6.264e -04 -8.563e -04 x 6 2.082e -03 2.659e -03 2.815e -03 x 22 2.967e -03 5.094e -03 6.957e -03 x 7 -1.120e -1.160e -03 2.576e -03 x 23 -8.599e -04 -9.935e -05 9.168e -04 x 8 1.377e -03 -1.600e -03 -4.717e -03 x 24 -6.224e -02 -8.585e -02 -1.089e -01 x 9 -6.873e --1.169e -03 -1.508e -03 x 25 -2.687e -03 -4.540e -03 -6.242e -03 x 10 1.899e -02 2.577e -02 2.920e -02 x 26 2.135e -02 3.513e -02 4.744e -02 x 11 -6.961e -2.408e -03 1.430e -02 x 27 -1.139e -02 -1.758e -02 -2.021e -02 x 12 1.821e -01 2.074e -01 2.197e -01 x 28 -7.034e -01 -8.193e -01 -9.348e -01 x 13 8.783e -04 1.721e -03 2.037e -03 x 29 1.019e -02 1.724e -02 2.355e -02 x 14 -5.926e --7.885e -02 -8.730e -02 x 30 -6.830e -02 -1.199e -01 -1.652e -01 x 15 -3.306e --8.203e -02 -1.310e -01 x 31 8.513e -02 9.647e -02 9.596e -02 x 16 -4.634e --4.634e -01 -4.634e -01 x 32 1.778e + 00 2.370e + 00 2.963e + 00
	2.4.6.3 Level 3
	Level 3 is the most advanced level. It requires a series of elastic plastic FEA calculations to define the
	crack driving force curves. It also requires SENT tests to obtain the actual material R-curve. Its use
	is not straightforward and therefore requires engineering judgment in particular regarding the FEA
	calculations.

Table 2 .

 2 4 y i coefficients in equation 2.9 for Level 2 assessment with X80 grade.

				Level 2 for X80 grade
		R-Curve 1 R-Curve 2 R-Curve 3		R-Curve 1 R-Curve 2 R-Curve 3
	y 1 y 2 y 3 y 4 y 5 y 6 y 7 y 8	0.0010 -0.0040 -0.0043 0.1839 -0.0016 -0.0064 -0.0116 -0.6597	-0.0014 -0.0057 -0.0067 0.2168 -0.0029 -0.0012 -0.0073 -0.7703	0.0018 -0.0072 -0.0090 0.2466 -0.0041 0.0034 -0.0028 -0.8694	y 9 y 10 y 11 y 12 y 13 y 14 y 15 y 16	0.0008 -0.0119 -0.0340 -0.0222 -0.0001 0.0373 0.1539 -0.0872	0.0014 -0.0165 -0.0388 -0.0328 -0.0016 0.0508 0.1748 -0.0717	0.0020 -0.0205 -0.0430 -0.0431 -0.0030 0.0626 0.1924 -0.0539
	elements, as depicted in figure 2.

Table 2 .

 2 5 -Ranges covered by the 1152 PRCI finite element analyses

		Parameters	Values	No. of cases
		Pipe	YS (ksi) Y/T	80 0.75, 0.81, 0.87, 0.94	1 4
	Material	Weld	Lüder's strain OM	1% 0%, 15%, 30%	1 3
		HAZ	Softening	10%	1
		Pipe	OD (in) WT (in)	42 5/8	1 1
	Geometry	Flaw	Depth (mm) Length (mm)	2, 4, 6, 8 25, 50, 75, 100	4 4
		Weld	High-low (mm) Type	0.0, 1.6, 3.2 GMAW, FCAW	3 2
	Load	Pressure	Design factor	0.72	1
			Total cases		1152
	2.5.2 Model validation
	The model has been validated through a comprehensive large scale tests campaign including 24 full-
	scale tests and 30 curved wide plate (CWP) tests, covering the ranges of parameters:
	• Outer Diameter: 323.8 mm (12.75 in).
	• Wall Thickness: 12.7 mm.
	• Internal Pressure: Such as the hoop stress σ h is in the range 0 % to 80 % of the SMYS. • Temperature: 20 • C. • Flaw location: Base material, heat affected zone and weld material.
	• FST on X65 grade with a low yield-to-tensile ratio:

  Ψ c 5 + c 6 Ψe -η + c 7 Ψe -β (c 8 + c 9 Φ c 10 + c 11 Ψ c 12 Φ ) A = a 1 e a 2 /β e a 3 ηβe a 4 /β 1+a 5 Ψ a 6 + a 7 Ψ a 8 (ηβ) a 9 (1+a 10 ξ a 11 Φ a 12 ) (2.21)

	and	c 2 β
	C = e c 1 /β e	(1+c 3 β) η 1+c 4 (2.19)
	and		d 3 β
		D = d 1 β d 2 η	1+d 4 β 1+d 5 Ψ d 6 1+d 7 ξ d 8 + d 9 Φ d 10	(2.20)
	FCAW / SMAW:
				18)

Table 2 .

 2 [START_REF]Standard Test Method for Measurement of Fracture Toughness[END_REF] andD = d 1 β d 2 η d 3 1+d 4 Ψ d 5 + d 6 ηβΨ 1+d 7 ξ d 8 + d 9 Φ d 10 (2.24)where the coefficients a i , b i , c i and d i take values as given in Table2.6. 6a i , b i , c i and d i coefficients in Equations 2.17 to 2.24

	a 1 a 2 a 3 a 4 a 5 -5.005e + 00 b 5 2.084e + 00 b 1 -5.005e -02 2.812e -01 b 2 -5.139e -03 -4.950e -01 b 3 4.485e -01 7.373e -01 b 4 1.417e + 00 2.217e + 00 a 6 1.186e + 00 b 6 1.029e + 00 a 7 1.644e + 00 b 7 -2.598e + 00 a 8 7.374e -01 b 8 -2.679e + 00 a 9 -9.829e -01 b 9 1.694e + 00 a 10 8.655e -02 a 11 -1.029e -01 a 12 -1.500e -01 1.025e + 00 a 13 a 14 5.557e + 00	c 1 c 2 c 3 c 4 c 5 c 6 -5.384e + 00 1.409e + 00 2.345e -01 1.125e + 00 4.181e + 00 1.201e + 00 c 7 2.406e + 00 c 8 -2.154e -01 c 9 -5.237e -03 c 10 9.889e + 00 c 11 3.547e -01 c 12 -7.513e -01	d 1 d 2 d 3 d 4 d 5 d 6 d 7 d 8 -2.240e + 00 2.209e -02 1.156e + 00 1.601e + 00 8.964e -01 1.383e + 00 1.333e + 00 9.313e -02 8.559e + 00 d 9 d 10 -3.719e + 00
	Others parameters are defined by:
	• the normalized flaw depth: η = a/t ;
	• The normalized flaw length: β =2c/t ;
	• The normalized weld high-low misalignment: Ψ = h/t ;
	• The base material Y/T ratio: ξ = σ y /σ u ;

  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Weld overmatch and strain-based design . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 FEA Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

	Résumé en français
	Il est impératif de démontrer que les caractérisques mécaniques des soudures sont supérieures à celles
	du matériau de base en préalable de toute utilisation d'approches SBD, pour éviter une concentration
	des déformations plastiques au niveau de ces zones soudées. D'un point de vue expérimental, la mesure
	des caractéristiques mécaniques d'un matériau d'apport peut se révéler difficile, notamment dans le
	cas de cordons soudés de faible largeur et pour les tubes de faibles diamètres. Dans ce chapitre, il
	est montré que les méthodologies classiques d'essais ne permettent pas de répondre correctement à la
	problématique.
	Une étude du PRCI recommande le prélèvement d'un échantillon prismatique dans la direction
	circonférentielle et de mesurer la limite d'élasticité du matériau d'apport pour 1 % de déformation
	totale afin de diminuer la variabilité dans les résultats d'essais. Cependant, cette procédure peut être
	remise en cause car :
	Sommaire
	3.1 3.3 Specimens proposed in the literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
	3.3.1 PRCI Specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
	3.3.2 DNV-OS-F101 Specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
	3.4 Suggested approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
	3.4.1 Digital Image Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
	3.4.2 Notched Tensile Specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
	3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Table 3 .

 3 1 -Mechanical properties measured using DIC method on a single multi-materials specimen.

						E (GPa) (MPa) R p0.2		Mismatch
	Parent material 1	207	524	9.0 % (+ 47 MPa)
	Parent material 2	207	504	13.3% (+ 67 MPa)
		Weld material		207	571		-
		600
		500
	F/S 0 (MPa)	400 300
		200
		100
		0	0	0.05	0.1	0.15	0.2	0.25	0.3	0.35
						∆L/L 0 (mm/mm)

Table 4 .

 4 • C during 22 min and cooled down by air. The heat treatment is summarized in Table 4.1. 1 -Heat treatment of Vallourec and Mannesmann line pipe of the study.

  .3. In this table, D designates the austenite grain size ; MX designates carbon-nitrides type elements (M=V, Nb and X=C, N) and M 23 C 6 designates carbides type elements (M=Cr).

			Table 4.2 -Chemical composition of the X65 steel (wt %)
	C	Si	Mn	P			S		Cr			Mo	Ni	Al	Cu	Nb
	0.09	0.28	1.28	0.009 0.0014	0.07		0.09	0.16	0.030	0.18	0.02
	Ti	V	Sn	Pb			Ca		B			N	As	Bi	Sb	V+Nb
	0.1	0.00 0.016 0.010	0.001	0.0003 0.005 0.003 0.003 0.003	0.03
	Nb+V+Ti	CE	Pcm	Al/N
	0.03	0.36	0.19	6
				CE = C +	Mn 6	+	Cr + Mo + V 5	+	Ni + Cu 15
			Pcm = C +	Si 30	+	Mn + Cu + Cr 20	+	Ni 60	+	Mo 15	+	V 10	+ 5B

Table 4 . 3

 43 Mechanical tests were performed by Vallourec & Mannesmann on the parent material prior to delivery. Tensile tests were carried out at room temperature on flat specimens having a cross-section of about 25 mm×22 mm in both longitudinal and transverse directions. Charpy tests were also performed at -20 • C on specimens having a 10 mm × 8 mm cross section(width × thickness) machined in the transverse direction. Results from Vallourc are given in Table4.4. Those values are typical of a X65 grade steel.

	Element Merit	Demerit
	B	Imprve creep strength and quench hardenability. Stabilize M 23 C 6 particles and delay their coarsening.	Reduce impact toughness
	Cr Cu Mn Mo	Improve oxidation resistance. Lower M s , raise A 1 . Suppress δ-ferrite. Lower M s . Raise A 1 . Solid solution hardening.	Increase D. Promote precipitation of Fe 2 M. Increase D and reduce creep strength. Lower A 1 . Promote M 6 C precipitation. Accelerate growth of M 23 C 6 .
	N	Necessary to make VN.
	Nb	Form MX. Contribute to strengthening. Promote precipitation of Z phase.
	Ni Si	Improve oxidation resistance.	Increase D and reduce creep strength. Lower A 1 .
	V	Form MX. Contribute to strengthening.

-Role of elements according to in [60] C Necessary to make M 23 C 6 and NbC. Co Suppress δ-ferrite. Decrease D.

Table 4 .

 4 4 -Mechanical properties measured by Vallourec & Mannesmann. (The minimal value corresponds to the minimal requirements). so that only a limited number of tests were carried out at -20 • C and -40 • C . Table4.5 summarizes the performed tests.

	Orientation	Temperature	YS (MPa)	TS (MPa)	Elongation YS / TS (%) ratio
	Longitudinal Transverse	+20 • C +20 • C	516 508	607 612	--	0.85 0.83
	Orientation	Temperature	Charpy Impact Energy (J) average test 1 test 2	test 3
	Transverve	-20 • C	296	296	300	292
	4.3.3 Tests on uncracked specimens

A comprehensive test campaign was carried out in order to fully characterize the mechanical properties of the X65 steel of the study. It included classical tensile tests performed on smooth round bars, but also specimens allowing to reach different stress triaxiality states. The tests were carried out at room temperature (about 22 • C ) and low temperatures to study the influence of this parameter on the material behavior.

Testing at low temperature is very time consuming (between 1 hour to 1 hour 1 /2 of preparation only),

Table 4 .

 4 5 -Tensile tests performed on X65 material.

	Test temperature ST	RT -20 • C -40 • C L,T L,T L,T
	FT	L,T	-	-
	NT 2 , NT 4 , NT 10 FN 2 , FN 4 , FN 10 PE	L,T L,T L,T	L,T --	L,T --
	4.3.3.1 Smooth Tensile (ST)

Table 4 .

 4 • C and +11.7 % at -40 • C .) 6 -Mechanical properties of X65 material at room and low temperatures.

	Temperature Direction ( • C)	R p0.2 (MPa)	R m (MPa)	ε % (%)	R p0.2 /R m (-)
	RT	L T	445.40 548.35 13.50 446.50 552.25 14.00	81.23 80.85
	-20 • C	L T	467.50 594.30 11.00 461.60 582.30 16.00	78.67 79.27
	-40 • C	L T	488.50 610.60 16.00 468.30 619.10 13.00	80.00 75.64

Table 4 .

 4 7 -X65 NT χ test results at room temperature.

Table 4 .

 4 8 -X65 NT χ test results at -20 • C

		18.60 27.55	859	646	27.55
	X65_RT_NT2_L_2	24.68 18.90 27.73	866	663	27.73
	X65_RT_NT2_T_1	23.89 18.42 26.34	863	666	26.34
	X65_RT_NT2_T_2	23.86 18.15 26.64	856	651	26.64
	X65_RT_NT4_L_1	21.82 14.58 35.69	776	519	35.69
	X65_RT_NT4_L_2	21.96 15.01 34.26	779	532	34.26
	X65_RT_NT4_L_3	21.74 14.73 34.95	771	523	34.95
	X65_RT_NT4_T_1	21.27 14.34 35.63	761	513	35.63
	X65_RT_NT4_T_2	21.32 14.16 36.16	757	503	36.16
	X65_RT_NT10_L_1	20.01 12.34 41.64	710	438	41.64
	X65_RT_NT10_L_2	19.89 12.21 41.23	700	430	41.23
	X65_RT_NT10_T_1 19.52 11.97 42.09	691	424	42.09
	X65_RT_NT10_T_2 19.67 12.03 41.56	689	422	41.56
	-20 • C	F max (kN)	F (c) (kN)	∆Φ (c) Φ 0 (%)	F max /S 0 F (c) /S 0 (MPa) (MPa )
	X65_20_NT2_L3	25.99 19.69 28.51	919	697
	X65_20_NT2_T3	26.19 19.53 25.51	928	692
	X65_20_NT4_L4	22.91 15.48 36.00	820	542
	X65_20_NT4_T3	22.93 15.10 37.65	821	541
	X65_20_NT10_L3	21.50 13.28 41.96	766	473
	X65_20_NT10_T3 21.21 13.35 42.47	749	471

Table 4 .

 4 10 -CT tests at room temperature on X65 material.

	Specimen	a 0 /W (-)	F max (kN)	F final CMOD final (kN) (mm)	J 0.2 (kJ.m -2 )	J 1.0 (kJ.m -2 )
							extrapolation
	X65_RT_CT_1 0.522 15.92 15.16	3.87	1017	not applicable
	X65_RT_CT_2 0.528 15.57 13.92	4.65	958	1444
	X65_RT_CT_3 0.525 15.58 12.49	5.89	1072	1520

depicted in Figure

4

.27-b. As required by the standard, two exclusion lines were defined as explained in Figure

4

.28. The initial slope is built in accordance with J = Mσ y ∆a (4.17)

Table 4 .

 4 [START_REF] Hutchinson | Singular behaviorur at the end of a tensile crack in a hardening material[END_REF] -SENB results at room temperature.

	Specimen	a 0 /W F max (-) (kN) (kN) F f	CMOD f (mm)
	X65_RT_SENB_C3 0.321 20.4 18.5	4.02
	X65_RT_SENB_C4 0.323 19.6 18.3	4.07

Table 4 .

 4 [START_REF] Rice | Plane Strain Deformation Near A Crack Tip In A Power-Law Hardening Material[END_REF] -SENB results at room temperature.

	Specimen	J 0.2 (kJ.m -2 ) (kJ.m -2 ) J 0.5	J 1.0 (kJ.m -2 )	δ 0.2 (mm) (mm) δ 0.5	δ 1.0 (mm)
				(extrapolation)		(extrapolation)
	X65_RT_SENB_C3	800	1185	1639	0.959 1.487	2.264
	X65_RT_SENB_C4	864	1162	1616	1.072 1.507	2.264

Table 4 .

 4 13 -Effect of the crack length

	Specimen	a 0 /W (-)	J 0.2	J 0.5 (MPa.mm)	J 1	δ 0.2	δ 0.5 (mm)	δ 1
	X65_RT_SENT_B13	0.25	1665 1932 2174 2.56 3.14 3.75
	X65_RT_SENT_B14	0.25	1604 1862 2174 2.62 3.19 3.90
	X65_RT_SENT_B25	0.25	1806 2065 2341 2.97 3.54 4.30
	X65_RT_SENT_B27	0.25	1611 1828 2054 2.67 3.10 3.62
	X65_RT_SENT_B19	0.385 1192 1426	-	2.11 2.57	-
	X65_RT_SENT_B20	0.407 1028 1279 1538 1.85 2.37 2.93
	X65_RT_SENT_B18	0.440	937	1175 1419 1.75 2.22 2.79
	X65_RT_SENT_B17	0.555	387	616	834	0.61 1.17 1.72
	X65_RT_SENT_B21	0.565	345	559	760	0.55 1.09 1.62

Table 4 .

 4 [START_REF] Noel | Family of crack-tip fields characterized by a triaxiality parameter -I. Structure of fields[END_REF] -Coefficients of the fitting J and CTOD-R curves.DNV-OS-F101:2010[START_REF]Submarines Pipelines Systems[END_REF] (in Appendix A -F106) introduces a conservative [sic] relationship to estimate a CTOD based fracture toughness from the J value. It writes:The validity of Equation4.33 was checked using the experimental data obtained on the SENT tests summarized in Table4.13.

	Specimen	a 0 /W (-)	α (MPa.mm)	m (-)	β (mm)	n (-)	β average n average (mm) (-)
	X65_RT_SENT_B13	0.25			2.741 0.456
	X65_RT_SENT_B14 X65_RT_SENT_B25	0.25 0.25	1670.	0.408	2.775 3.034 3.034 0.463	2.837	0.455
	X65_RT_SENT_B27	0.25			2.799 0.404
	X65_RT_SENT_B19	0.385			2.397 0.456
	X65_RT_SENT_B20	0.407	1191	0.476	2.248 0.473	2.265	0.467
	X65_RT_SENT_B18	0.440			2.150 0.473
	X65_RT_SENT_B17 X65_RT_SENT_B21	0.555 0.565	681	0.595	1.356 0.655 1.286 0.682	1.321	0.668

Table 4 .

 4 [START_REF] Ma | The effects of constraint on crack tip fields and fracture toughness[END_REF] -Effect of temperature on the material toughness.

	Specimen	a 0 /W F max (-) (kN)	J 0.2	J 0.5 (MPa.mm)	J 1	δ 0.2	δ 0.5 (mm)	δ 1
	X65_RT_SENT_B13	0.25	87.8 1665 1932 2174 2.56 3.14 3.75
	X65_RT_SENT_B14	0.25	85.8 1604 1862 2174 2.62 3.19 3.90
	X65_RT_SENT_B25	0.25	88.4 1806 2065 2341 2.97 3.54 4.30
	X65_RT_SENT_B27	0.25	88.4 1611 1828 2054 2.67 3.10 3.62
	X65_20_SENT_B1	0.25	93.7 2274 2477 2696 3.67 4.14 4.79
	X65_20_SENT_B2	0.25	95.3 1888 2262 2629 2.47 3.67 4.22
	X65_40_SENT_B1	0.25	94.8 2280 2365 2699 3.13 3.76 4.56
	X65_40_SENT_B2	0.25	96.0 2286 2471 2633 2.48 3.45 4.13
	4.4 Weld material
	4.4.1 Welding process

Table 4 .

 4

		16 -Weld material mechanical requirements
	Main specifications : GS EP PLR 421 Rev.09 / API 1104th Edition
	Item	Code/ Standard	Temp	Property	Units Min	Max
	AWMT	GS EP PLR 421 Rev.09 ASTM A 370	RT	YS Break location	MPa	530		-
	CWTT	API 1104 20th Ed GS EP PLR 421 Rev.09	RT	TS Break location	MPa	530 Base material	-
	Side Bends	GS EP PLR 421 Rev.09	RT	Weld quality	Acceptance per
						API 1104 §9
		ASTM A 370		Energy each	J	50		-
	CVN-WM	ASTM E23 GS EP PLR 421 Rev.09	-50 • C	Energy av. Shear each Shear av.	J % %	56 75 85		---
		ASTM A 370		Energy each	J	50		-
	CVN-FL	ASTM E23 GS EP PLR 421 Rev.09	-50 • C	Energy av. Shear each Shear av.	J % %	56 75 85		---
	CVN FL+2	ASTM A 370 ASTM E23 GS EP PLR 421 Rev.09	-50 • C	Energy each Energy av. Shear each Shear av.	J J % %	50 56 75 85		----
	CVN -Transition curve (WM/FL/ FL+2 / FL+5) CTOD WM/HAZ SSC root mid-thickness	-20 • C -30 • C -40 • C GS EP PLR 421 Rev.09 -50 • C ASTM A 370 ASTM E23 -60 • C BS 7448 GS EP PLR 421 Rev.09 -30 • C GS EP PLR 421 Rev.09 24 • C A NACE TL0177 Std ± 3 • C ASTM G 39 Std	Energy each Energy av. Shear each Shear average CTOD Macro	J J % % mm	For information TBD TBD WM & HAZ No crack
	Hardness WM/HAZ/BM	ASTM E 384 GS EP PLR 421 Rev.09	RT	Weld Quality	HV5		250
	Macro	GS EP PLR 421 Rev.09	RT	Weld quality	Acceptance per GS EP
	Evaluation				PLR 421 Rev.09
	Chemical	AWS A5.18	RT	Root zone &	Ni < 1%, variation of
	Analysis	GS EP PLR 421 Rev.09		filler passes	Mn < 30% & Si < 20%
	Views of the welding process are depicted in Figure 4.41.
	4.4.2 Preliminary tests

Mechanical tests were performed on the two girth welds by Serimax prior to the PhD work to certify the welding process. The experimental campaign consisted in tensile tests, toughness tests (Charpy, CTOD) and hardness tests. Others tests such as SSC (Sulfide Stress Corrosion crack) and chemical analysis were also carried out. The exhaustive list is reported in Table

4

.17.

Table 4 .

 4 [START_REF] Sumpter | Method for laboratory determination of Jc. In: Cracks and fracture[END_REF] -Chemical composition of the X65W steel (wt %)

	Al	C	Cr	Cu	Mn	Mo	Ni
	0.005 0.10	0.03	0.14	1.43	0.01	0.03
	P	Si	S	Ti	V	Zr
	0.008 0.64 0.008 < 0.005 < 0.01 < 0.01
	4.4.4 Notched Tensile (NT χ )
	4.4.4.1 Tests at room temperature

Table 4 .

 4 [START_REF] Ernst | Estimation on J-integral and tearing modulus T from a single specimen test record[END_REF] -X65W NT χ test results at room and low temperatures.

	RT	F max (kN)	F (c) (kN)	∆Φ (c) Φ 0 (%)	F max /S 0 F (c) /S 0 (MPa) (MPa )
	X65W_RT_NT2_L_1	29.47 25.30 20.50	1043	896
	X65W_RT_NT2_L_4	29.38 26.18 16.90	1038	925
	X65W_RT_NT2_L_5	29.34 25.89 17.79	1043	921
	X65W_RT_NT4_L_1	25.55 19.96 28.49	916	716
	X65W_RT_NT4_L_4	25.48 21.22 23.43	899	749
	X65W_RT_NT4_L_5	24.65 19.54 27.50	876	695
	X65W_RT_NT10_L_1 22.07 15.28 35.13	830	574
	X65W_RT_NT10_L_5 23.04 15.85 36.54	815	561
	X65W_20_NT2_L2	30.75 25.86 22.27	1097	922
	X65W_20_NT4_L2	26.89 20.97 29.58	950	741
	X65W_20_NT10_L4	23.41 15.60 37.68	827	551
	X65W_40_NT2_L2	31.47 26.62 22.51	1153	943
	X65W_40_NT4_L3	27.33 21.09 30.12	964	744
	X65W_40_NT10_L3	24.83 17.95 35.79	879	635

Table 4 .

 4 [START_REF]Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness KIC of Metallic Materials[END_REF] -Effect of temperature on the material toughness.

	Specimen	a 0 /W F max (-) (kN)	J 0.2	J 0.5 (MPa.mm)	J 1	δ 0.2	δ 0.5 (mm)	δ 1
	X65W_RT_SENT_B1	0.25	90.9 1407 1720 2018 2.12 2.66 3.20
	X65W_RT_SENT_B4	0.25	91.5 1366 1664 1982 2.12 2.61 3.20
	X65W_RT_SENT_B6	0.25	92.7 1431 1647 1912 2.21 2.56 3.05
	X65W_RT_SENT_B11	0.25	92.7 1325 1692 1940 1.97 2.46 2.90
	X65W_20_SENT_B9	0.25	95.7	902	1512 1866 1.80 2.37 2.92
	X65W_20_SENT_B13	0.25	95.7	787	1499 1876 1.89 2.39 3.03
	X65W_40_SENT_B8	0.25	98.7	840	1453 1794 1.74 2.23 2.70

Table 4 .

 4 [START_REF] Aa | Application of fracture mechanics at and beyond general yielding[END_REF] -Coefficients of the fitting J and CTOD-R curves.

	Specimen	a 0 /W (-)	α (MPa.mm)	m (-)	α average (MPa.mm)	m average (-)
	X65_RT_SENT_B1	0.25		1909	0.301
	X65_RT_SENT_B4	0.25		1883	0.247	1792	0.267
	X65_RT_SENT_B6	0.25		1854	0.258
	Specimen		a 0 /W (-)	β (mm)	m (-)	β average n average (mm) (-)
	X65_RT_SENT_B1	0.25	2.60	0.378
	X65_RT_SENT_B4	0.25	2.56	0.448	2.53	0.403
	X65_RT_SENT_B6	0.25	2.43	0.382

  Sommaire 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 5.2 Description of the parent material elastic plastic behavior . . . . . . . . . . . . . . . . . 151

5.2.1 Isotropic von Mises criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 5.2.2 Material constitutive equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 5.3 Description of the parent material fracture behavior . . . . . . . . . . . . . . . . . . . . 156 5.3.1 Damage processus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 5.3.2 Gurson Tvergaard Needleman model . . . . . . . . . . . . . . . . . . . . . . . . . . 156 5.3.3 Identification of the GTN model parameters . . . . . . . . . . . . . . . . . . . . . . 157 5.4 Description of the weld material elastic-plastic hardening behavior . . . . . . . . . . . 165 5.5 Description of the weld material fracture damage behavior . . . . . . . . . . . . . . . . 166 5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

Table 5 .

 5 1 -Hardening parameters for the X65 material.

	MPa)

  • C using the experimental tensile curves measured on the axisymmetric notched tensile specimens given in Chapter 4. The inverse analysis is used.

	NT 2	X65W at RT

Table 5 .

 5 3 -X65 parent material best fitting parameters at room temperature, -20 • C and -40 • C.

	Temperature	R Lders (MPa) R 0 (MPa) Q 1 (MPa)	b 1	Q 2 (MPa)
	Room temperature	445	412	196	19.7	280
	-20 • C -40 • C	463 488	420 466	251 291	15.7 10.5	360 250

  La question de la transférabilité de l'éprouvette de laboratoire vers la structure est au coeur de cette thèse. Aussi, un essai pleine échelle a été réalisé sur un tube identique à celui ayant fait l'objet de la caractérisation expérimentale présentée dans les chapitres 4 et 5 précédents. Cet essai fut réalisé au SZMF (pour Salzgitter Mannessmann Forschung GmbH) à Duisbourg (Allemagne) sur le banc d'essai dénommé LiSA (pour Limit State Analyzer) dont les caractéristiques sont les suivantes :

	Résumé en français
	Chapter 6 • Quatre vérins hydrauliques de 2 500 kN chacun, de sorte qu'une force totale de 10 000 kN (1 000 t)
	puisse être atteinte
	• Déplacement maximal de 1 100 mm • Portée maxmimale entre les deux supports centraux d'environ 15,5 m • Tubes de diamètre externe jusqu'à 1 422,4 mm Four-point bending test at SZMF • Nuance d'acier jusqu'à l'API-5L X100
	Sommaire
					MPa)	b 2
	Room temperature	559.9	364.4	6.271	104.9	5.694
	-20 • C -40 • C	566.3 521.9	340.3 231.5	8.862 24.92	281.7 85.52	6.968 s 0.8545

Table 6 .

 6 2 -Comparison between global and local approaches, and experimental results.

			ExxonMobil			PRCI
	Full-scale test		Failure		Initation	Failure	Local approach
		L1	L2	L3	L1	L2	L4
	∆a =1.41 mm						2.32% (initiation)
	at ε =4.24 % Final failure	1.52 % 2.78 % 6.10 % 2.34 % 3.05 % 6.10 %	4.06 % (1 mm advance) 5.10 % (final failure)
	at ε =5.32%

  • C et -40 • C . Cependant, aucune délamination ne fut observée sur les éprouvettes SENT testées dans la direction L-S.

Table 7 .

 7 1 -Mechanical properties of X70 parent material at room and low temperatures.In addition to the classical tensile tests, axisymmetric notched NT χ specimens were tested in L and T directions. The experimental protocol is described in Chapter 4. Three different geometries, namely NT 2 , NT 4 and NT 10 as depicted in Figure4.11 page 108, are used with three notch radii in order to reach different stress triaxiality states.

	Temperature Direction ( • C)	R p0.2 (MPa) (MPa) (%) R m ε %	R p0.2 /R m (-)
	RT	L T	447 488	560 582	11.0 12.0	0.798 0.839
		D	450	547	12.5	0.823
	-20 • C	L T D	467 519 476	599 630 585	13.0 12.0 12.0	0.779 0.824 0.814
	-40 • C	L T D	485 588 477	622 633 588	12.0 12.0 12.0	0.780 0.929 0.811
	7.2.1.2 NT specimens

Table 7 .

 7 2 -Maximal load and diametral contraction at the onset of the coalescence measured on NT χ on X70 material.

	Specimen	Tensile direction	(F/S 0 ) max -∆Φ (c) /Φ 0 (MPa) (-)
	X70_RT_NT10_L1	L	698	0.558
	X70_RT_NT10_L2	L	703	0.553
	X70_RT_NT10_T1	T	723	0.492
	X70_RT_NT10_T2	T	721	0.487
	X70_RT_NT4_L2	L	800	0.422
	X70_RT_NT4_T1	T	781	0.409
	X70_RT_NT4_T2	T	782	0.421
	X70_RT_NT2_L1	L	880	0.357
	X70_RT_NT2_L2	L	888	0.378
	X70_RT_NT2_T1	T	905	0.305
	X70_RT_NT2_T2	T	913	0.326

Table 7 .

 7 3 -Coefficients of the fitting J and CTOD-R curves.

	Specimen	T ( • C)	a 0 /W (-)	α (MPa.mm)	m (-)	β (mm)	n (-)	β average n average (mm) (-)
	X70_RT_SENT_B1		0.24	1803	0.306	3.036 0.464
	X70_RT_SENT_B9		0.33	2008	0.309	3.421 0.377	3.170	0.419
	X70_RT_SENT_B10		0.25	1772	0.320	3.054 0.416
	X70_RT_SENT_B12	+20	0.39	1336	0.338	2.429 0.431
	X70_RT_SENT_B13 X70_RT_SENT_B14		0.39 0.38	1190 1217	0.382 0.351	2.100 0.489 2.153 0.483	2.230	0.471
	X70_RT_SENT_B15		0.37	1283	0.356	2.235 0.482
	X70_20_SENT_B3 X70_20_SENT_B4 X70_40_SENT_B5	-20 -40	0.28 0.28 0.29	2048 1924 2113	0.320 0.299 0.272	3.203 0.385 2.897 0.391 3.246 0.300	3.050 3.246	0.388 0.300

Table 7 .

 7 4 -Effect of temperature on the material toughness.

	Specimen	T • C	a 0 /W F max (-) (kN)	J 0.2	J 0.5 (MPa.mm)	J 1	δ 0.2	δ 0.5 (mm)	δ 1
	X70_RT_SENT_B1		0.24	86.9 1811 2040 2260 3.51 3.82 4.39
	X70_RT_SENT_B9		0.33	86.9 1626 1912 2265 2.66 3.23 4.02
	X70_RT_SENT_B10		0.25	84.3 1447 1740 2061 2.47 3.04 3.76
	X70_RT_SENT_B12	+20	0.39	71.9 1013 1233 1503 1.82 2.27 2.87
	X70_RT_SENT_B13		0.39	72.7	948	1218 1453 1.77 2.27 2.79
	X70_RT_SENT_B14		0.38	69.7	919	1176 1394 1.60 2.15 2.68
	X70_RT_SENT_B15		0.37	73.2	983	1227 1492 1.68 2.22 2.80
	X70_20_SENT_B3 X70_20_SENT_B4 X70_40_SENT_B5	-20 -40	0.28 0.28 0.29	89.9 1870 2104 2373 2.95 3.38 4.00 92.7 1750 1960 2256 2.60 3.11 3.65 94.7 2042 2248 2477 3.05 3.50 3.98

Table 7 .

 7 7 -Maximal load and diametral contraction at the onset of the coalescence measured on NT χ on X70W material.

	Specimen	(F/S 0 ) max -∆Φ (c) /Φ 0 (MPa) (-)
	X70W_RT_NT10_L1	846	0.379
	X70W_RT_NT10_L2	856	0.372
	X70W_RT_NT4_L1	989	0.189
	X70W_RT_NT4_L2	978	0.217
	X70W_RT_NT2_L1	1114	0.122
	X70W_RT_NT2_L2	1106	0.154
	7.3.3 SENT specimens
	7.3.3.1 Testing protocol

  1 is only valid for specimens with H = 10W . The best fitting polynomial function writes:

	a W	= -49.1887 + 1159.5u -11327.7u 2 + 60532.8u 3 -191660u 4 + 359839u 5 -371132u 6 + 162295u 7

Table 7 .

 7 8 -Coefficients for the fitting of J and CTOD-R curves.

	Specimen	a 0 /W	α	m	β	n	β average n average
		(-)	(MPa.mm)	(-)	(mm)	(-)	(mm)	(-)
	X70W_RT_SENT_B2 X70W_RT_SENT_B3	0.25 0.25	2022 2045	0.413 0.332	3.037 0.519 3.000 0.418	3.019	0.469
	X70W_RT_SENT_B9 X70W_RT_SENT_B10	0.28 0.29	1470 1604	0.438 0.420	2.140 0.501 2.194 0.516	2.167	0.509

Table 7 .

 7 9 -X70W material toughness.

	Specimen	a 0 /W F max (-) (kN)	J 0.2	J 0.5 (MPa.mm)	J 1	δ 0.2	δ 0.5 (mm)	δ 1
	X70W_RT_SENT_B2	0.25	94.7	1026 1589 2099 1.54 2.38 3.26
	X70W_RT_SENT_B3	0.25	95.3	1379 1724 2077 2.00 2.53 3.13
	X70W_RT_SENT_B9	0.28	93.6	937	1154 1507 1.35 1.69 2.25
	X70W_RT_SENT_B10	0.29	93.1	764	1214 1694 1.00 1.65 2.38

Table 8 .

 8 .1 and Table 8.2. 1 -Parameters of the Bron-Besson model to describe the anisotropy of the X70 parent material at room and low temperatures.

Table 8 .

 8 2 -Parameters of the X70 parent material constitutive law at room temperature.

	X70 at room temperature

Table 8 .

 8 4 -Parameters of the X70 parent material constitutive law at -40 • C.

Table 8 .

 8 8 -X70 parent material best fitting parameters at room temperature, -20 • C and -40 • C. In addition, it was shown in this chapter that the Gurson Tvergaard Needleman model allows to simulate the SENT tests with a very good accuracy. The set of best fitting parameters is:

	Temperature	R 0 (MPa) Q 1 (MPa) b 1 (-) Q 2 (MPa) b 2 (-)
	Room temperature	447	58.43	29.52	269.52	2.67
	-20 • C -40 • C	474.32 490.59	110.87 187.44	28.75 11.51	399.13 284.69	1.22 0.92

Table 8 .

 8 9 -Weld material constitutive law parameters at room temperature and low temperatures.

	Temperature	R Lders (MPa) R 0 (MPa) Q 1 (MPa)	b 1	Q 2 (MPa)
	Room temperature	539.06	634.49	239.35	6.79	193.22

Table 9 .

 9 1 -Actual crack sizes after electro-discharge machining.

	Crack	Location	Length Depth Width
			(mm)	(mm)	(mm)
	1	Girth weld	67.06	8.56	0.30
	2	Girth weld	67.06	8.62	0.31
	3	Parent material	60.64	5.23	0.25

Table 9 .

 9 6 -Axial distances between the cross sections where the diameters and thicknesses were measured.CSM also proceeded to diameter and thickness measurements in order to compare with the initial values reported in Table 9.3 and Table 9.4. The post-mortem values are given in Table 9.7 and Table 9.8.

	Start Failure C1 1	End C1 1 C2	Axial distance (mm) Elongation (%) --800 -
	C2	C3	906	0.7
	C3	Girth weld	56	1.8
	Girth weld	C4	57	3.6
	C4 C5 C6 1	C5 C6 1 Necking	910 800 -	1.1 --

Table 9 .

 9 7 -After testing diameter measurements at each cross section locations and average values.

		Failure	C1 1	C2	C3	C4	C5	C6 1	Necking
	D1 (mm)	609.0	616.5 609.6 609.0 609.6 610.6 612.6	609.2
	D2 (mm)	612.3	615.3 609.9 610.3 610.5 611.4 613.8	611.6
	D3 (mm)	608.5	614.7 611.0 609.4 609.0 610.6 612.3	611.6
	D4 (mm)	608.2	615.1 611.0 611.4 611.8 612.0 613.0	610.5
	Mean value (mm)	609.5	615.4 610.4 610.0 610.2 611.2 612.9	610.7
	Expansion (%)	-	1.2	0.3	0.3	0.3	0.4	0.8	-

Table 9 .

 9 8 -After testing thickness measurements at each cross section locations and average values.

		Failure C1 1	C2	C3	C4	C5	C6 1 Necking
	S1 (mm)	19.4	29.3 30.3 30.2 30.5 30.4 28.9	28.6
	S2 (mm)	21.0	28.5 30.5 30.9 31.1 30.5 28.8	28.6
	S3 (mm)	20.8	28.1 30.4 30.6 30.8 30.6 28.9	28.3
	S4 (mm)	17.2	28.0 30.5 30.8 30.4 30.7 29.3	28.7
	S5 (mm)	21.5	28.2 30.7 30.8 30.8 30.7 29.4	27.4
	S6 (mm)	20.8	28.1 30.6 30.7 30.7 30.6 28.9	28.1
	S7 (mm)	19.5	28.9 30.7 31.3 31.0 30.4 29.2	28.1
	S8 (mm)	18.0	29.0 30.6 31.3 31.0 30.3 29.1	28.2
	Mean value (mm)	19.8	28.5 30.5 30.8 30.8 30.5 29.1	28.2
	Thinning (%)	-	7.0	0.4	0.0	0.1	0.7	5.2	-

  a.) broken elements depicted in yellow (b.) Opening stress σ 11 Figure9.17 -Results of the FE analysis. Focus on the weld centerline crack: broken elements (a.) and opening stress field at ε remote, axial =1.03 %

	0	0.167	0.333	0.5	0.667	0.833	1	1.17	1.33	1.5	1.67	1.83	2	-4e+02 -1.9e+02	10	2.1e+02 4.2e+02 6.2e+02 8.2e+02 1e+03 1.2e+03 1.4e+03 1.6e+03 1.8e+03	2e+03
				broken map:120.000 time:1107.33	min:0.00000 max:1.00000						sig11 map:120.000 time:1107.33	min:-397.097 max:2046.58
	0	0.167	0.333	0.5	0.667	0.833	1	1.17	1.33	1.5	1.67	1.83	2	-4.5e+02 -2.5e+02	-47	1.6e+02	3.6e+02	5.6e+02	7.7e+02	9.7e+02	1.2e+03	1.4e+03	1.6e+03	1.8e+03	2e+03
					broken map:179.000 time:1137.24	min:0.00000 max:1.00000							sig11 map:179.000 time:1137.24	min:-454.365 max:1989.63

(

  t 2 ,p min -p e )=0.78 = R p0.5 /R m max is the strain hardening, and α gw is a girth weld factor. Equation A.22 is applicable for D/t 2 ≤ 45 and p i ≥ p e .

	t D	-0.01 1. +5.75	p min -p e p b (t)	α -1.5 h	α gw	(A.23)
	where α h

  Equation A.24 is applicable for D/t 2 < 45 and p min <p e .

	0.8
	⎠ ⎟	+	γ m γ c p e -p min p c (t 2 )	≤ 1	(A.24)

Strain-based design

The lack of fusion results from too little heat input and/or too rapid traverse movement of the welding torch (gas or electric).

The lack of penetration or excess penetration arises from a too high heat input and/or too slow movements of the welding torch (gas or electric).

Gas cavities occur when gases are trapped in the solidifying weld metal, resulting in porosities.

Slag inclusion is of different types. It can be of any shape in any direction: slag lines (elongated cavities containing slag or other foreign matter), wearing faults, faults from bad chipping, faults at electrode change, faults at junction of seams.

Cracks are often caused by sulphur and phosphorus and are more likely to occur in higher carbon steels.

Undercut is due to the reduced thickness of one (or both) of the sheets at the toe of weld, due to inaccurate settings/procedure.

Lamellar tearing is mainly a problem with low quality steels. It occurs in plates that have low ductility with laminar segregation.

 8 Shrinkage cavities are due to thermal shrinkage or due to a combination of steam accompanying phase change and their shrinkage cavities.

1 foot = 304.8 mm

Electro Discharge Machining

Mechanical testings

Due to the failure and the necking at both ends of the line pipe, the C1 and C6 cross sections defined in Figure9.4 are replaced by sections moved by 100 mm towards the pipe center.

Depending on the safety classe (low, medium, high).

Remerciements

The Ph.D thesis focused on the failure of pipeline due to the propagation of existing cracks, either in the parent or weld material. The study of such failure mode is developed in "Engineering Critical Assessments" methods. However, one shall keep in mind that a pipeline tube safe from crack propagation may experience others failure modes, such as buckling, internal or external pressure, or compression load. Therefore, these limit states shall be considered using the following international codes:

• DNV OS F101, Rule for submarine pipeline systems, 2013 The following sections propose a brief reminder on the analytical methods which are available to assess these limit states.

A.2 Pressure containment (bursting)

The pressure containment of a pipe shall verify the two following relationships: is the material strength factor equal to 1 for pressure test 4 . α mpt is the mill pressure test factor in the range 1 to 1.251 5 t 1

is the pipe wall thickness as defined in Table A.1.

p li and p lt are local pressures calculated in order to take the the fluid column weight due to difference in elevation into account. They write:

where p d is the design pressure at the reference elevation p t is the system test pressure at the reference elevation γ inc is the incidental to design pressure ratio ρ cont is the density of the relevant content of the pipeline ρ t is the density of the relevant test medium of the pipeline g is the gravity h ref is the elevation of the reference point (positive upwards) h 1 is the elevation of the local pressure point (positive upwards)

The pressure containment resistance p b (t) is given by

with

where t is the pipe wall thickness, D is the pipe nominal outside diameter,

is the de-rating value of SMYS due to the temperature f u,temp is the de-rating value of SMTS due to the temperature 1 γ m =1 for in fatigue design. 2 Depending on the safety classe: low = 1.046, medium = 1.138, high = 1.308. 3 Depending on the safety classe: low = 1.03, medium = 1.05, high = 1.05. 4 In other cases, α U =0.96 which corresponds to an allowable hoop stress of 96% of SMYS. 5 Depending on the safety classe: low = 1, medium = 1.088, high = 1.251.

A.3 Collapse due to external pressure only

Following DNV-OS-F101, the external pressure at any points along the pipe shall verify the following relationship:

where p min is the minimum internal pressure that can be sustained. Furthermore, the external pressure at collapse f c can be calculated by For pipes subjected to bending moment, effective axial force and internal overpressure, the following relationship shall be verified:

where Moreover, the parameters used in the case of combined loading criteria write:

and where α pm is the plastic moment reduction to take the point load into account that writes:

where R is the reaction force from the point load and R y writes: R y =3.9f y t 2 2 (A.20)

A.4.2 With external overpressure

For pipes subjected to bending moment, effective axial force and external overpressure, the following relationship shall be verified:

A.5 Collapse due to combined loads in displacement controlled conditions A.5.1 With internal overpressure

In the case of a pipe subjected to longitudinal compressive strain due to bending moment or axial force, and internal overpressure, the following criterion shall be verified at all cross sections of the pipe:

and

Combining Equation B.1 and B.2 yields This SENT testing protocol is a modified version of ExxonMobil recommended practice [START_REF] Fairchild | Advancements Regarding Capacity Prediction of Strain-Based Pipelines[END_REF]. The main modification consists in the addition of a rotation correction factor from CANMET work [START_REF] Shen | Evaluation of CTOD from J-integral for SE(T) specimens[END_REF].

C.2 Definitions

Term Description CMOD Crack mouth opening displacement (CMOD). The opening displacement at the mouth of the machined notch (specimen surface) CTOD Crack tip opening displacement (CTOD). The opening displacement at the location of the original crack tip Net thickness Net thickness (B N ). The distance between the roots of the side grooves Note 3: Following [START_REF] Fairchild | Advancements Regarding Capacity Prediction of Strain-Based Pipelines[END_REF] recommendations, the vertical distance between the two knives shall be at least equal to 0.25 W.

C.6 Testing protocol

The testing protocol presented here derived from the recommended practice that were proposed by ExxonMobil [START_REF] Fairchild | Advancements Regarding Capacity Prediction of Strain-Based Pipelines[END_REF] and Canmet [START_REF] Shen | Evaluation of CTOD from J-integral for SE(T) specimens[END_REF], and from the work done by Cravero et al. [START_REF] Cravero | Structural integrity analysis of axially cracked pipelines using conventional and constraint-modified failure assessment diagrams[END_REF].

• The specimen shall be tested following the single-specimen method, in order to derive a full material CTOD R-curve from a single test. • The unloading compliance method is used in order to continuously measured the crack advance during the test (see details hereinafter). • Each loading / unloading cycles k is divided into 2 phases:

-Loading: The specimen is loaded under displacement control up to an opening displacement measured on the lower clip ∆V 1,k =0.01W . The current load is measured and denoted F max,k . -Stress relaxation: The specimen shall be maintained under a constant displacement as long as need so that stresses are relaxed. It was experimentally observed that 5 s were sufficient. -Unloading: The specimen is unloaded under displacement control to reach 0.75 F max,k .

-Reloading: Next cycle k + 1, etc. • The test is complete when a certain amount of crack growth is achieved.

• After completion of the test, the specimen shall be cooled down using liquid nitrogen, and broken using a three point bending devices, so that it is possible to investigate on the fracture surfaces.

C.6.1 CMOD and CTOD determination

Both the CMOD and CTOD can be measured using triangular geometrical considerations on the crack opening displacements V 1 and V 2 :

C.6.2 Crack advance measurement

The compliance method relies on the decrease of the specimen stiffness due to the crack propagation. The compliance of the specimen is defined as

where ∆CMOD (k) and ∆F (k) are the variations of the CMOD and the load during the k th unloading / reloading sequence. A non-dimensional effective compliance is introduced and writes: