Keywords: Spot welding, Adhesive bonding, Hybrid joining, Finite element, Constitutive modelling, Inverse identification, Cohesive zone

Spot welding and adhesive bonding are widely used in joining of sheet metals, such as assembling of car body-in-white. Recently, spot weld and adhesive are combined to make weld bonded joint, which is employed to join Advanced High Strength Steel to improve the stiffness and crashworthiness of car body. In industry, the assessment of designing prior to prototype requires reliable constitutive models in terms of the prediction of the mechanical behaviors. The FE model of weld bonded joint is a new challenge as it should combine the models of spot welding and the models of adhesive. This thesis focuses on the modeling of weld bonded joint by DP600 steel and structural adhesive SikaPower ® -498. The model of weld bonded joint consists of solid model and simplified model. The former is devoted to predict the behavior of weld bonded joint on smallscale specimen: KS2 and lap-shear. The latter can be used to predict the performance of large components with acceptable computational cost. As regards solid model, spot welded joint and adhesive bonded joint behaviors are separately identified by KS2 specimen under different loading path. The inhomogeneities in fusion zone and heat affected zone of spot weld are taken into account via the scaling of the flow stress of base metal. The scaling factors are calibrated by inverse identification. Gurson model is used to predict ductile fracture in heat affected zone and base metal while cohesive zone model is employed to simulate quasi-brittle fracture in the interface of fusion zone. The parameters of cohesive zone model are identified by the J-integral at the notch tip of spot weld crack. Cohesive zone elements with traction-separation-laws are also used to predict adhesive debonding. Model parameters are calibrated by Double Cantilevered Beam and End Notched Flexure specimens, corresponding to Mode-I and Mode-II fracture respectively. The model developed for spot weld is associated with adhesive model to predict weld bonded joint. As regards simplified model, connector elements are employed to predict the damage of spot weld. The parameters of connector element are identified by KS2 tests under different loading paths. Finally, the simplified model of spot welding, adhesive bonding, and weld-bonding are validated by T-joint which can represent the B-pillar of car body.

II III

Résumé:

Le soudage par point et le collage sont largement utilisés dans la jonction des tôles, telles que l'assemblage de caisses de voiture. Récemment, le soudage par point et le collage ont été combinés pour faire le joint hybrid soudé-collé, qui est utilisé pour joindre les aciers à hautes résistances et améliorer la rigidité et la résistance aux chocs des corps de voiture. Dans l'industrie, l'évaluation de la conception avant prototype nécessite des modèles fiables de comportement en termes de prédiction des comportements mécaniques. Le modèle élément finis de joint soudécollé est un nouveau défi car il doit combiner les modèles de soudage par points et les modèles de collage.

Cette thèse se concentre sur la modélisation du joint soudé-collé par de l'acier DP600 et avec l'adhésif structurel SikaPower ® -498. La modélisation peur utiliser un modèle solide ou un modèle simplifié (élément coque plus élément de connexion). Le modèle solide permet de prédire le comportement de spécimen à petite échelle: KS2 et cisaillement. Le modèle simplifié peut être utilisé pour prédire la performance des composants de grande dimension avec un coût de calcul acceptable.

En ce qui concerne le modèle solide, le comportement du joint soudé et du joint collé sont identifiés séparément calibrés sur un spécimen KS2 sous trajets de chargement différents. Les inhomogénéités dans la zone de fusion et la zone affectée par la chaleur du soudage par point sont prises en compte par l'intermédiaire de facteurs d'échelle applique à la contrainte d'écoulement du métal de base. Les facteurs d'échelle sont determinés par identification inverse. Le modèle de Gurson est utilisé pour prédire la rupture ductile en zone affectée par le chaleur et dans le métal base tandis que le modèle de zone cohésive est utilisé pour simuler la rupture quasi-fragile dans l'interface de la zone de fusion. Les paramètres du modèle de zone cohésive sont identifiés par l'intégrale J à la pointe de fissure de la soudure. Des éléments de zone cohésive avec une loi traction-séparation sont également utilisés pour prédire le décollement adhésif. Les paramètres du modèle sont identifiés par des essais du type « Double Cantilevered Beam » et « End Notched Flexure », correspondant aux mode I et mode II respectivement. Le modèle élaboré pour le soudage par est associé avec le modèle de collage pour prédire le comportement et la rupture du joint soudé-collé.

En ce qui concerne le modèle simplifié, des éléments de connexion sont utilisés pour prédire les endommagement des soudure par point. Les paramètres de l'élément de connexion sont identifiés IV par des tests de KS2 sous différents trajets de chargement. Enfin, les modèles simplifiés d'un soudage, d'un collage, et d'un soudé-collé sont validés sur une jonction en T qui peut représenter le pilier-B de carrosserie de la voiture. I would like to thank my collegues in the laboratories, Velluet Isabelle for the preparation of metallographic, Wtyklo Jean-Patrick for SEM analysis. I also thank to my colleagues and friends Kang YANG, Raoelison Rija, Xiongjie LIU for the encouragement and discussion. I would also like to thank the members of my reading committee: Prof. Farid ABED-MERAIM from ENSAM, Prof. Pierre-Olivier BOUCHARD, Prof. Daniel MARCEAU, Prof.

Said HARIRI, Eng. Roland JAEGGI, Prof. Gerard MOULIN, for your reading, correction and discussion during the defense.

At the end, I want to give my love to my parents for their support and comprehension, both of which were essential. My daughters Camille were invaluable for her laugh which relaxed me when I was tired from the work. I am especially thankful for my wife. They are most important to me and make everyday a wonderful experience.

VI VII

Symbols Explanation

A

Gaussian distribution function

A 1 Eutectoid temperature A 3
The lower-temperature boundary

Ac 1

The temperature at which austenite begins to form during heating

Ac 3

The temperature at which transformation of ferrite to austenite is completed during heating

A cm

The counterpart boundary for high-carbon contents which are finally assembled together to produce whole car body [START_REF] Rajput | A text book of automobile engineering[END_REF]. In addition, some lightweight structure materials are chosen to reduce car weight, such as aluminum, magnesium and composite materials. For these developments, the materials, their processing and joining processes play prominent role in the quality of car body.

Over the last decade, Advanced High Strength Steel (AHSS) were widely introduced in automotive industry due to the improvement in formability and crash worthiness compared to conventional steel grades. AHSS include dual phase (DP) steel, transformation induced plasticity (TRIP) steel, twinning induced plasticity (TWIP) steel, complex phase (CP) steel and martensitic steels (MART) steel [START_REF] Kuziak | Advanced high strength steels for automotive industry[END_REF]. Figure 1-1 shows the elongation versus tensile strength at fracture of several steels used in automobile industry. The strength of AHSS is increased in large amount meanwhile the formability remains acceptable. AHSS help reducing car weight by using high strength thinner sheet metal gauge gaining the same stiffness and strength that are obtained with thick conventional steels.

For the manufacturing of a typical family car, the possible joining technology could include welding (electrical resistance welding, arc welding, laser welding and soldering) and mechanical fastener (riveting, screw, bolts, clinching, hemming). However, welding is always difficult when dealing with dissimilar metals. Dissimilar metals joined by fastener are likely to cause galvanic corrosion. In addition, welding is not possible for non-metallic materials, e.g. plastic and composite. Hence, adhesive bonding is the optimal joining method for dissimilar materials in car body assembly. To design the above complex car frame, computer simulation is widely used by automakers in computer-aided engineering (CAE) analysis for crashworthiness in order to reduce the manufacturing cost and the development cycle by reducing the number of real crash tests. The crash test simulation, as illustrated in Figure 1-3, is used for design optimization on virtual prototype before a real prototype is manufactured. This simulation can predict the acceleration, the intrusions into the cabin and the risk of injury to the vehicle occupant. The car crash simulation is always facing problems of constitutive modeling when new materials and specific joining processes are used. As a consequence, material suppliers are requested to supply material input data and support for constitutive modeling of their materials.

In this context, several research projects were initiated by Sika for the development of adequate models to predict failure behavior of new adhesive and hybrid joint. Recently, adhesive constitutive models were investigated by Jousset in [START_REF] Jousset | Constitutive modeling of structural adhesives experimental and numerical aspects[END_REF]. The aim of our work is to extend the previous investigations to welded bonded joints. The microstructure of spot weld was firstly analyzed in order to investigate the spot weld structure and the interaction between the spot weld and the adhesive in hybrid joints. Material properties of welded metal and heat affected zone are calibrated based on the scaling of the base metal. Silicon is added to provide solid solution hardening and promote ferrite transformation [START_REF] Saha | Metallographic and fracture characteristics of resistance spot welded TWIP steels[END_REF].

Manganese in amount of 1% to 1.5% can stabilize super-cooled austenite (γ-phase), which can ensure sufficient hardenability.

Small amounts of microalloying additions (not show in Table 1-1), such as vanadium, niobiums, and titanium, are added to provide precipitation hardening. From the transformation line A 3 to melt temperature, the DP600 structure is a single phase γferrite. From the transformation line A 1 to the transformation line A 3 , it is mixture of γ-phase and α-phase. Below the transformation line A 1 , DP600 is in stable α-ferrite and Fe 3 C. Dual phase microstructure can also be obtained by continuous annealing after cold rolling process. Figure 234shows the schematic diagram of temperature changes in continuous annealing process. Steel is heated to intercritical temperature range between A c1 and A c3 and maintained for some time so that a small amount of ferrite and pearlite transforms to austenite. Then, the steel is quenched to a temperature lower than martensite start temperatures (Ms) so that the austenite phase transforms to martensite phase giving a ferrite-martensite dual phase structure [START_REF] Movahed | The effect of intercritical heat treatment temperature on the tensile properties and work hardening behavior of ferrite-martensite dual phase steel sheets[END_REF].

Spot welds

Resistance spot welding is a conventional joining technology to joint sheet metal due to its advantages in superior toughness, welding efficiency and suitability for automation [START_REF] Brauser | Deformation behaviour of spot-welded high strength steels for automotive applications[END_REF].

Consequently, it is widely used in many industrial products, such as aircrafts, automobiles bodies, truck cabins, and home applications [START_REF] Hou | Finite element analysis for the mechanical features of resistance spot welding process[END_REF]. For example, a typical car or truck may contain more than 2000 spot welds [START_REF] Lin | Failure loads of spot welds under combined opening and shear static loading condition[END_REF].

Spot welding process

Spot welding is the most common one of the various resistances welding [START_REF] Jeffus | Welding: Principles and Applications[END_REF]. Figure 2345shows spot welding pieces and machine, they consist of two or more sheet metal parts and two electrodes with adjustable forces and water cooling. The welding current is applied to the electrodes by alternative current power [START_REF] Gupta | Manufacturing Processes, 2ED[END_REF].

Figure 2-5. Illustration of spot welding machine [21]

The nuggets size is the most influential factor on the spot weld strength. A small nugget diameter usually results in low toughness and interfacial fracture [START_REF] Gayden | Development of requirements for resistance spot welding dual-Phase (DP600) steels part 1-The causes of interfacial fracture[END_REF][START_REF] Sommer | Modeling of the fracture behavior of spot welds using advanced micromechanical damage[END_REF]. The common criterion is that the average nugget diameter should be equal to or larger than 4 t (t is the sheet material thickness) [START_REF] Sun | Effects of fusion zone size and failure mode on peak load and energy absorption of advanced high strength steel spot welds under lap shear loading conditions[END_REF]. In spot welding procedure, some adjustable resistance welding parameters can affect the nugget size and welding quality, such as welding current, weld time, electrode pressing force and electrode geometry [START_REF] Pereira | Effect of process parameters on the strength of resistance spot welds in 6082-T6[END_REF].

Figure 2-6 shows welding stages to perform a spot weld. At first stage, proper pressure is applied on the electrodes for a short while (some seconds, squeeze time) to guarantee an effective contact between electrodes and the work piece. Then instantaneous welding current is applied.

The resistance heating makes the pieces temperature rise to their melting temperatures in the contact surfaces. Finally, welding force is decreased during the holding time. This post-welding time must be long enough to solidify the melted metal with the help of water cooling and base metal heat conductivity [START_REF] Tong | Deformation and fracture of miniature tensile bars with resistance-spot-weld microstructures[END_REF]. Due to high conductivity of metals, the cooling rate can be up to 10 5 °C/s [START_REF] Gould | Predictions of microstructures when welding automotive advanced high-strength steels[END_REF].

Spot welds microstructure

In spot welding process, the temperature distribution is not uniform in the nugget section.

Spot welds failure modes

Several researches were conducted in order to investigate the failure mechanism of spot welds by means of experiments and numerical simulation [START_REF] Zuniga | Resistance spot weld failure loads and modes in overload condition. Fatigue and Fracture Mechanics: ASTM SYP[END_REF][START_REF] Lin | A fatigue crack growth model for spot welds under cyclic loading conditions[END_REF][START_REF] Chao | Ultimate strength and failure mechanism of resistance spot weld subjected to tensile, shear, or combined tensile/shear loads[END_REF][START_REF] Lin | A general failure criterion for spot welds under combinated loading conditions[END_REF][START_REF] Radaj | Geometrically nonlinear behaviour of spot welded joints in tension and compressive in shear[END_REF][START_REF] Falko | Investigation of Spot Weld Behavior Using Detailed Modeling Technique[END_REF][START_REF] Sommer | Modellierung des Verformungs und Versagensverhaltens von Punktschweißverbindungen unter monoton ansteigender Belastung[END_REF][START_REF] Dancette | A finite element model for the prediction of advanced High Strength Steel spot welds fracture[END_REF]. All these researches evidenced three different failure modes in spot weld joint, e.g. interfacial fracture, pull-out (plug) failure and partial pull-out failure, as show in Figure 23456789. For a reliable spot weld joint, the pull-out failure is preferred because it ensures the higher peak loading and the largest energy absorption [START_REF] Donders | The robustness of dynamic vehicle performance to spot weld failures[END_REF].

Base Metal

Heat Affected Zone 1 Heat Affected Zone 2

A 1 A 3 Figure 2-9.
Spot welds fail in different modes [START_REF] Brauser | Deformation behaviour of spot-welded high strength steels for automotive applications[END_REF] Interfacial fracture and plug failure are two competitive processes. The cracks are caused by shear stress on faying surfaces in interfacial failure which generally leads to catastrophic damage.

Plug failure is inducted by excessive plastic deformation in the heat affected zone or base metal [START_REF] Nielsen | 3D modelling of plug failure in resistance spot welded shear-lab specimens (DP600-steel)[END_REF]. Cracks propagate towards base metal and then terminate at outer surface of one nugget in plug failure.

Adhesive bonding

Adhesive bonding technology has been widely used in the long history of human being, in order to join woods, bamboos, papers, metals, etc. This joining technique aims to connect different components by means of placing liquid or soft adhesive between them. The adhesive subsequently solidifies to produce an adhesive bonding. Adhesive bonding offers various advantages over conventional mechanical fasteners as it is easy to perform, it makes it possible to join dissimilar materials, it allows for continuous connection achievement that leads to uniform stress distribution, fatigue life improvement and corrosion prevention. [START_REF] Darwish | Critical assessment of weld-bonded technologies[END_REF][START_REF] Darwish | Characteristics of weld-bonded commercial aluminum sheets[END_REF][START_REF] Tripathy | Analytical studies for buckling and vibration of weld-bonded beam shells of rectangular cross-section[END_REF].

Structural adhesive

Structural bonding is gaining a competitive advantage compared to mechanical fasteners.

Nowadays structural adhesive is well developed and it can cover almost all industrial application from aircraft industry, aerospace, automobile, construction to microelectronic and packaging… [START_REF] Silva | Advances in numerical modelling of adhesive joints[END_REF]. Different structural adhesives are developed to meet various requirements. For example, in a typical family car, adhesive bonding allows flexible and durable connection between windshield and car body. In some shell parts assembly, like engine hoods, it permits to reduce system vibrations by soft connector between steel sheets. In order to reduce the cost and car weight, structural adhesive is more and more used to join structure components in car body-inwhite, especially for joining dissimilar metals. For example, the adhesive seams measure a total length of 83 m in the light-weight car body-Audi Q5 [START_REF] Audi | Audi Collision Frame Technology Guide[END_REF].

The properties of bonded structures are mainly affected by bonding procedure such as adhesive thickness, adherends surface preparation, curing process, etc [START_REF] Jousset | Constitutive modeling of structural adhesives experimental and numerical aspects[END_REF]. In order to match the optimal mechanical properties, adhesive thickness is restricted to range from 0.2 to 0.5 mm. The faying surfaces of adherends must be properly prepared to prevent adhesive failure. It should be pointed out that only cohesive failure is investigated in this work.

SikaPower-498

SikaPower ® -498 is a mono-component structural epoxy adhesive. It can resist dynamic loading by adding high tough inclusions to hard matrix, providing to adhesive a viscoplastic behavior [START_REF] Jousset | Constitutive modeling of structural adhesives experimental and numerical aspects[END_REF]. SikaPower ® -498 can be applied without surface pre-treatment. In order to gain an easy and efficient application, the adhesive must be pre-heated to 60℃.

Figure 2-10. Adhesive application in assembly chain of car body [6]

It is designed for automated automotive assembly chains as it can resist wash-out and the cataphoresis. It allows hardening the adhesive during drying process (curing at 180℃ for 30 min), as shown in Figure 2-10. SikaPower ® -498 has been selected by some automotive companies to fabricate new generation cars. In this thesis, SikaPower ® -498 is combined with spot welds to produce hybrid joint. The properties data of SikaPower ® -498 can be found in Appendix.

Weld-bonding

Motivations for weld-bonding

As shown in Figure 2-10, the adhesive may experience severe solicitations during the manufacture process of car body and sometimes before the final curing. Consequently, mechanical fasteners, such as spot welds, rivets, and bolts, are combined with adhesive bonding [44] [45-47]. Weld bonded joint is one typical hybrid joint which is mostly used in automobile industry since both spot welds and adhesive are largely used in car bodies manufactures [START_REF] Mazda | Skyactiv-body[END_REF][START_REF]Ford Motor Company provide weld bonding procedure. I-Car advantage-Tecnical information for the collision industry[END_REF].

On the one hand, the spot welds help to apply adhesive easily; on the other hand, the adhesive permits to reduce the number of spot welds. Some researchers show that weld bonded joints have higher strength than either spot welds or adhesive bonding, furthermore, the adhesive layer can increase stiffness of the assembled structure, reduce the vibration and corrosion of structure [START_REF] Darwish | Critical assessment of weld-bonded technologies[END_REF][START_REF] Darwish | Characteristics of weld-bonded commercial aluminum sheets[END_REF][START_REF] Tripathy | Analytical studies for buckling and vibration of weld-bonded beam shells of rectangular cross-section[END_REF], increases energy absorption and improves crashworthiness. Consequently, the use of weld bonded joints in white-car-body manufacturing is quickly increasing in recent years [START_REF] Chang | Studies on a computational model and the stress field characteristics of weld-bonded joints for a car body steel sheet[END_REF]. Then the sheets are spot welded together in the center of faying surface before the curing process.

The "flow-in" method requires low viscosity adhesive, which restrict the selection of adhesive.

As a consequence, the second method, which is chosen in this project, is more widely used. In this work, SikaPower ® -498 was selected to bond DP600 sheet and it is combined with spot welds.

(a) (b) Chapter 3. Joining procedures and joints characterization

In order to give an in-depth investigation into different joining methods, spot welded joint, adhesive bonded joint and hybrid joints are all investigated in this thesis. For each joint, tension, shear and complex loading are applied to calibrate the constitutive model. The so-called KS2

specimens are used to gain different loading conditions [START_REF] Hahn | Test specification for KS-2 specimen[END_REF]. As lap-shear specimens are widely used to evaluate spot welding failure in automobile industry [START_REF] Seeger | An investigation on spot weld modelling for crash simulation with LS_DYNA[END_REF][START_REF] Pouranvari | Failure mode transition in AHSS resistance spot welds. Part I. Controlling factors[END_REF], it is also investigated in this work. These specimens have benefits of simple geometry, limited experiment cost and limited experiment time. Moreover, the experiments results are reliable and reproducible. All the tests are carried out at Laboratorium für Werkstoff und Fügetechnik (LWF) in Paderborn using 1.6 mm thickness DP600 coated steel.

In this chapter, the specimen's geometries, preparation process, experiment configurations and results are discussed in detail. Spot welds microstructure and failure mechanisms are also investigated to get precise nugget diameter. Cross-comparisons are made between the different joints.

Description of joining procedures

Spot welding

As discussed in section 2.1 of Chapter 2, the nuggets diameter is the most important factor that affects the strength and the energy absorption of spot welded joint. In general, small diameter can result in interfacial fracture, which is not desirable in spot welded structures as interfacial fracture has lower strength than pull-out fracture [START_REF] Pouranvari | Failure mode transition in AHSS resistance spot welds. Part I. Controlling factors[END_REF]. Hence, the optimal diameter of spot weld is firstly investigated. Sommer [START_REF] Pouranvari | Failure mode transition in AHSS resistance spot welds. Part I. Controlling factors[END_REF] gives a critical diameter of approximately 5.4 mm for the transition from interfacial fracture to pull-out fracture under tension force on DP600 steel joint, but the sheet thickness is 1.5 mm. The experiment is achieved in accordance with the standard ISO 4063:

Figure 3-2 spot weld diameter with optimized current

Spot welding 5.78mm

Adhesive bonding

In adhesive bonded structures, the adhesive layer must have a controlled small thickness in order to have optimal mechanical properties [START_REF] Jousset | Constitutive modeling of structural adhesives experimental and numerical aspects[END_REF]. In this thesis, the adhesive layer thickness is set to 0.3 mm based on previous research works. To control the layer thickness and its uniformity,

Weld bonding (hybrid)

Hybrid joint combines spot weld with adhesive bonding. The presence of adhesive can significantly affect the spot welding process whereas the high temperature that results from spot welding deeply affects the adhesive in the vicinity of the spot weld. This will be discussed in detail in section 3.3.1. In this work, hybrid joining is performed in 4 steps: applying adhesive, assembling, spot welding and curing, as shown in Figure 34. Before applying, the adhesive should be heated at 60°C in order to reduce its viscosity. The optimized process parameters used for spot welded joints are no longer appropriate for hybrid joints performing because the adhesive layer may modify the contact resistance. To find the optimal welding parameters, the procedure is the same as the one used for spot weld joints.

Figure 3-4 Illustration of hybrid joint procedures

5.39mm

Weld bonding

Test results

The results of different joints are discussed separately in this section. The discussion focuses on the microstructure of spot weld, the interaction between spot weld and adhesive, the measurements of force-displacement of each tests and the cross comparison of ultimate strength and damage energy.

Test results of spot welded joints

Structure of spot welds with DP600

Spot weld microstructure has significant influence on its mechanical properties. In what follows, spot weld microstructure with DP600 steel is investigated to assess the welding quality and nugget's dimension. The macrograph of spot weld transverse section depicted in Figure 3-11 shows that the spot weld consists of WM, HAZ and BM. The investigated cross sections are free of any defect. In the WM zone, liquid metal transforms into solidification structure, which can be divided into columnar zone and equiaxed zone. The metal in contact with electrodes is rapidly cooled and forms columnar zone with growing orientation perpendicular to contact surface. Equiaxed crystal is acquired in the zone adjacent to BM which can affect the solidification process of WM. The splashed metal can be observed in the vicinity of spot welds.

The specimen is polished and then etched with 4% nital solution. The microstructure is investigated with the help of AFM in our laboratory. Figure 3

. Failure modes and load bearing capacity of spot weld joints

In spot welding, the plates are joined by welded zone. Hence, spot weld diameter is the key factor to influence the spot weld strength. Moreover, the HAZ and BM properties have significant influence on the fracture modes. Generally, a competition between two failure modes

Test results of adhesive bonded joints

Load bearing capacity and failure modes of adhesive bonded joints

The adhesive is applied on the faying surface of KS2 through the usual strictly prescribed procedure. The adhesive fillets are removed from both edges to reduce the fillet influence. The specimen is then heated at 180 °C for 3 min in resistant furnace. Adhesive layer thickness is set to 0.3 mm in order to ensure the optimal mechanical properties.

In tension test, the ultimate strength scatters from 7 kN to 10 kN. Test3 has the minimum force 6.8 kN while Test 5 has the maximum force 10.1 kN, as shown in Figure 3-17 (a). In Figure 3-18 (a), a dark black zone is observed in the center of fracture surfaces. This is probably due to the large strain rate in this zone caused by the release of the elastic strain energy stored in the adherends.

In shear test, adhesive bonded joint shows noticeable mechanical property against shear force, up to 34 kN, as shown in Figure 3-17 (b). In peel, the adhesive exhibits the lowest ultimate

Test results of hybrid joints

Interaction between bonding and welding

The macrostructure of weld bonded joint is depicted in Figure 3-19. The typical solidification structure is formed in the center of spot weld nugget, as shown in Figure 3-19 (a) [START_REF] Gupta | Manufacturing Processes, 2ED[END_REF]. There are no visible defects or voids found in WM. There is no apparent difference of hardness in WM between SW and WB. Werber et al. [START_REF] Weber | Resistance spot welding and weldbonding of advanced high strength steel[END_REF] also reported that the hardness and microstructure of spot weld is not influenced by the adhesive in weld bonded joint.

In Figure 3-19 (b), the adhesive in WM is burnt by the heat of spot welding. In HAZ and its peripheral zone, adhesive is deteriorated by the heat of spot welding. Hence, the adhesive in these zones, with width of 2 mm, cannot effectively join the BM together. In addition, a channel, which connects HAZ with exterior edge of specimen, was found in adhesive layer. The adhesive in fusion zone was burnt into high pressure gas, which damages the viscous uncured adhesive layer and escapes from WM zone. The channel leads to discontinuity of adhesive layer. It should be noted that the effective bonding surface of weld bonded joint is smaller than that of adhesive bonded joint due to spot weld process.

(a) (b) (c) (d)

Comparisons between test results of different joints

In AB joint exhibits the highest ultimate strength among the three joints while its energy absorption is lower than that of SW joint.

The ultimate strength of WB joint is lower than that of AB joint due to the diminishment in adhesive surfaces by spot welding process and also some adhesive deterioration. It is notable that

Conclusion

Welding parameters are optimized for spot welding and adhesive bonding in terms of welding current, squeeze force and squeeze time. A complex structure of columnar grains and equiaxial grains is formed in molten zone of SW. The materials are hardened in HAZ due to phase transformation as evidenced by the hardness tests.

WB joint is successfully produced by combining SW with AB. The adhesive is burnt in the vicinity of spot weld nugget due to the heat of SW. Adhesive layer must have a controlled small thickness in order to have optimal mechanical properties, 0.3 mm for SikaPower ® -498 in this work.

KS2 and lap-shear specimens are used to assess the different joining techniques (SW, AB and WB) under tension, shear and peeling load.

SW joint always provides excellent energy absorption due to the large plastic deformation in base metal. SW joint exhibits the highest ultimate strength under tension among the three joints, whereas it lacks capacity to sustain pure shear force.

AB joint can provide high stiffness under complex loading condition while it exhibits noticeable high ultimate strength under shear force. AB joint has lower energy absorption due to the lack of ductility compared with SW joint. WB joint is a compromise solution between AB joint with SW joint. It exhibits two stages failure: adhesive failure and spot weld failure except KS2 pure shear. WB joint can benefit from the AB high stiffness and the SW large plastic deformation. As a consequence, WB joint offers largest energy absorption under tension and peeling among the three joints. In pure shear (KS2 shear), WB joint particularly exhibits the lowest energy absorption among the three joints.

λ μ ν λ ν ν - μ ν σ σ σ ′ - σ σ ε ε ε σ σ σ Φ - - σ ≤ - - - ε - ε ε ε ε ε π - - ε ε δ ε δ ε δ ε ε ε ν σ τ ξ -

Modeling strategy and results

In this section, the modeling and simulation results for SW joints, AB joints and WB joints will be discussed separately since the 3 kinds of joining methods are investigated for comparison purpose.

Modeling strategy and results for spot welded joint

FE model for spot weld joint

There are several models of SW joints used for failure analysis under static and dynamic conditions [START_REF] Sommer | Modeling of the fracture behavior of spot welds using advanced micromechanical damage[END_REF][36-37] [START_REF] Nielsen | 3D modelling of plug failure in resistance spot welded shear-lab specimens (DP600-steel)[END_REF]. Modeling spot weld is difficult, because many factors can influence spot weld properties such as geometrical irregularities, residual stresses, material inhomogeneities and defects in spot weld nuggets. These factors are even not taken into account by finite element modeling [START_REF] Chandra | Some issues in the application of cohesive zone models for metal-ceramic interfaces[END_REF].

Generally, spot weld models can be classified into two types: solid models and simplified models. In the former, detailed geometries and materials inhomogeneities of spot weld are taken into account. Material constitutive parameters of different zones must be calibrated and refined mesh must be used. Solid models can capture the stress distribution and concentration in vicinity of spot welds. Moreover, it can predict interfacial failure and pull-out failure. Seeger et al. [START_REF] Falko | Investigation of Spot Weld Behavior Using Detailed Modeling Technique[END_REF] developed a method to characterize the spot welded joint failure by using a highly detailed simulation model. Sommer [START_REF] Pouranvari | Failure mode transition in AHSS resistance spot welds. Part I. Controlling factors[END_REF] successfully predicted the peak loading and fracture modes under different loading combining Gurson model with shear induced fracture model. Dancette [START_REF] Dancette | A finite element model for the prediction of advanced High Strength Steel spot welds fracture[END_REF] et al.

introduced a finite element model combining cohesive elements and a ductile fracture model for the prediction of interfacial and pull-out fracture. Nielsen and Tvergaard [START_REF] Nielsen | Ductile shear failure or plug failure of spot welds modelled by modified Gurson model[END_REF] used a modified

Gurson model with shear prediction capacity to simulate shear failure or pull-out failure.

However, for a large structure which contains thousands of spot welds, e.g. car body in white, solid models are not appropriate as they require too high computational efforts to reach a useful solution [START_REF] Palmonella | Finite element models of spot welds in structural dynamics: review and updating[END_REF]. Hence, simplified models are introduced to reduce computational costs, such as connector elements [START_REF] Sommer | Fracture modeling of spot welds and rivets for crash simulation[END_REF], elastic or rigid beams models [START_REF] Heiserer | High performance, process oriented, weld spot approach. 1st MSC worldwide automotive user conf[END_REF] or brick elements [START_REF] Pal | Static and dynamic characteristics of spot welded sheet metal beams[END_REF].

In this section, both detailed solid models and simplified models are developed to simulate small-scale specimens.

The material in spot weld is heterogeneous. It can be split into three different zones in terms of materials properties: BM, HAZ and WM, as shown in Figure 456. WM has a radius of 2.9 mm

σ ασ σ α σ σ σ Δ ≤ λ μ ρ
Variable mass scaling are investigated on the whole models of KS2 tension. Three kinds of mass scaling are performed with different stable time step target values, 1.0E-3s, 1.0E-4s and 1.0E-5s, respectively. Figure 4-7 shows that the response does not exhibit significant change prior to fracture. The ultimate strength for t=1.0E-3s is slightly higher than the others. It can be concluded that even a high mass scaling value has only a slight effect on the response of our simulation under quasi-static loading. Hence, the mass scaling producing a stable time step value of 1.0E-3s is chosen for this research.

Mesh size

It was discussed that fine mesh in the vicinity of nugget is essential. However, too fine meshes will decrease the stable time step size and increase the computational time. The mesh sizes and simulation accuracy are investigated in spot weld firstly. In When the mesh size is refined up to 0.2 mm, the response does not show significant change.

Therefore, a 0.5 mm mesh size is used in nuggets for spot weld simulations. . There are 8 parameters to be calibrated for a given materials. In this work, the spot weld can be divided into 3 different zones; each zone has a set of parameters. Hence, there are totally 24 parameters that need to be calibrated. q 1 , q 2 and q 3 are constants introduced by Tvergaard [START_REF] Tvergaard | Influence of voids on shear band instabilities under plane strain conditions[END_REF]. Here, we take 1 q = 1.5 , 2 q =1and 2 1 3 q = q 2.25 = . The mean voids nucleation burst strain ε N and the standard deviation S N for DP600 can be found in [START_REF] Sommer | Modellierung des Verformungs und Versagensverhaltens von Punktschweißverbindungen unter monoton ansteigender Belastung[END_REF].

The volume fraction of particles available for new voids nucleation, f N , is related to the pre- existed voids or defects in materials. DP steels contain small fractions of hard martensite particle in soft ferrite matrix. The weak grain boundary between martensite and ferrite could be the sources of voids nucleation. In DP600, the martensite fraction ranges from 2% to 10%. In HAZ and WM, martensite fraction increases due to the heat affection of spot weld process. Hence, f N is set at 0.02 for base metal and 0.1 for WM. The volume fraction of particles f N of HAZ is considered close to that of WM, f N is 0.08 at this work.

f C is a material constant that can be determined experimentally. f F is the void volume fraction at final fracture. These two parameters can be calibrated by the so-called "trial-error" process which needs to run the simulation several times till the predicted result agrees with the measurement. The parameters of Gurson model for spot weld simulation are summarized in Table 4-1.

Material Constant Porous Nucleation and Distribution Porous Coalescence

BM q 1 =1.5 q 2 =1.0 q 3 =q 1 2 =2.25

f N =0.02 ԑ N =0.35 S N =0.5 f C =0.056 f F =0.10 HAZ f N =0.08 ԑ N =0.25 S N =0.5 f C =0.03 f F =0.06 WM f N =0.1 ԑ N =0.2 S N =0.5 f C =0.03 f F =0.08
K Ⅰ Ⅰ Ⅰ Ⅰ (N/mm 3 ) K Ⅱ Ⅱ Ⅱ Ⅱ (N/mm 3 ) σ 0 (MPa) G Ⅰ Ⅰ Ⅰ Ⅰc (mJ/mm 2 ) τ 0 (MPa) G Ⅱ Ⅱ Ⅱ Ⅱc (mJ/mm

Modeling strategy and results for adhesive bonded joint

FE models for adhesive bonded joints

The BM has the same geometry as in the case of spot welded joints, only a half of the model is . The energy release rate can be calculated using the J-integral [START_REF] Sørensen | Determination of cohesive laws by the J integral approach[END_REF]. Force (

The material parameters are identified by DCB and ENF specimens by Sika Techonology for the adhesive SikaPower ® -498. All parameters are summarized in Table 4-3.

Table 4-3. Cohesive parameters for fracture prediction of adhesive

Stiffness Mode I Mode Ⅱ Ⅱ Ⅱ Ⅱ K Ⅰ Ⅰ Ⅰ Ⅰ (N/mm 3 ) K Ⅱ Ⅱ Ⅱ Ⅱ (N/mm 3 ) σ 0 (MPa) G Ⅰ Ⅰ Ⅰ Ⅰc (mJ/mm 2 ) τ 0 (MPa) G Ⅱ Ⅱ Ⅱ Ⅱc (mJ/
TSLs can predict the ultimate strength under shear, but the predicted stiffness is far from the measured one. The difference is supposed to come from the error made when measuring local displacements during the test, which is difficult to measure. One reason is that the load direction could not align with the center of specimen. It should be noted that the whole displacement is 0.6 mm; any small rotation of specimens or sliding between specimen and grips can cause significant alteration in local displacement. In order to prove this assumption, simulations using Mahnken-Schilimmer model [START_REF] Jousset | Constitutive modeling of structural adhesives experimental and numerical aspects[END_REF] and J2 elastoplastic models are carried out, as shown in Figure 4-29. The different models predict the same stiffness in shear.

Under tension and peel, the ultimate strength and the displacement at fracture are accurately predicted.

TSLs cannot predict displacement of catastrophic fracture under shear and lap-shear as it inherently has bilinear shape, as shown in Figure 45. shown in Figure 4-31. It is common that the fracture occurs in substrate when adhesive is applied on large area or when low strength steels joints are tested [START_REF] Jousset | Constitutive modeling of structural adhesives experimental and numerical aspects[END_REF].

Modeling strategy and results for hybrid joint

FE model for hybrid joint

In this section, a model combining a spot weld model with an adhesive model is used to simulate weld bonded joints. As regards the AB joints, as shown in Figure 4-28 (a), the predicted elastic slope is not in accordance with measurement whereas it was matched in lap-shear, as shown in Figure 4-33 (d).

The load carriage capacity is overestimated due to the poor capacity of plastic prediction of TSLs under shear and lap-shear.

HAZ

In Figure 4-34, spot weld rotation is also observed, however the angle is smaller than that of SW joint because the deformation of rotation in the spot weld vicinity is constrained by adhesive bonding. Figure 4-35 shows that rotation angle is 10.4° in SW KS2 while it is 5.6° in WB KS2.

This indicates that in KS2, sheared spot weld sustains more shear in WB joint than in SW joint.

Increasing shear force can lead to a premature failure of spot weld. In tension, peeling and lap-shear, two fracture stages (adhesive failure and spot weld failure) can be observed. Figure 4-37 shows the simulated damage process of WB joint under tension.

After adhesive layer firstly fails in

Connector model for spot weld

Automobiles body or aircrafts frames may contain more than thousands of spot welds or rivets [START_REF] Al-Samhan | Strength prediction of weld-bonded joints[END_REF]. The simulations of such structures are often faced with computational efficiency problems when using solid elements [START_REF] Al-Samhan | Finite element modeling of weld-bonded joints[END_REF][START_REF] Tumiluru | Resistance spot weld of coated high-strength in dual-phase steels[END_REF]. Hence, simplified models are developed to improve computation efficiency in crash simulation of whole car body. Various connector elements are available to represent different fasteners in Abaqus [START_REF] Hibbitt | Abaqus user manual[END_REF]. In this section, bushing type connector is selected to describe the spot weld behavior under complex loading condition.

Mesh independent fastener

The mesh-independent fastener is a convenient method to define point-to-point connection between two nodes. It can be easily applied to large structures such as spot welded car body since these systems contain large number of connections. The fastener can be located anywhere on the surface regardless of the mesh.

The fastener can be assigned variable connectors section for different purpose. Connector element modeling a spot weld (modified from [START_REF] Hibbitt | Abaqus user manual[END_REF]) Since experimental data are available only in shear, tension and peeling by KS2 specimen, the connector can be defined in terms of normal, shear and bending force, as shown in Figure 4-41.

Normal force can be defined by derived component f 1 :

1 = n f f (4.27)
Shear force can be derived from f 2 and f 3 :

2 2 2 3 = + s f f f (4.28)
Similarly, bending moment can be defined by moment around axis 2 and axis 3; torsion moment is defined by moment around axis 1. It can be concluded that the simplified model can predict the overall response of spot weld with compromise between accuracy and computational cost. The aim of simplified model is to simulate large components with reasonable computational cost. In Explicit method, the stable time step is the key factor that influence the total computational time. Jousset reported that the acceptable stable time step by BMW is t=1E-06 s for car body simulation [START_REF] Jousset | Constitutive modeling of structural adhesives experimental and numerical aspects[END_REF]. In this work, with the help of mesh-independent fastener and shell element, the stable time step can be increased. As regards the transversal loading, two-stage failure is observed as depicted in Figure 5-9 (b).

Test results from SW T-joint

Test 1 is again performed without any block inside the horizontal beam and the low strength exhibited by Test 3 is due to its small spot weld nugget diameter.

Cross comparison of different joining methods

The comparison between different KS2 and lap shear specimens reported in section 3.4

showed that the WB joints exhibit a distinctive behavior both in terms of strength and energy absorption. Similarly, cross comparisons are carried out to investigate the influence of joining method on the behaviors of large T-joints. The energy absorption was obtained by calculating the surface under force-displacement curves. shear on the vertical surface that causes large displacement with SW joint. Therefore, SW joint has higher energy absorption than AB joint. The energy absorption by WB joint is the highest one, 6.3 times than that of AB joint, and 2 times than that of SW joint, as shown in It should be noted that the "tear-out" mode can exhibit higher strength than "pull-out" mode. It should be also noted that although a small amount of adhesive is used, adding adhesive to spot welds deeply affects both the strength and the energy absorption of large scale component joints. Furthermore, WB T-joint shows the tendency of spot welds to change from pull-out fracture mode to mixed fracture mode. This brings benefit to joined structure as tearing fracture mode provides high energy absorption, especially in the case of crash.

FEM analysis of T-joints

Predictions from the spot welded T-joint model

Large structures are generally meshed with structural elements, such as shell element, beam, truss, etc…, for computational efficiency purpose. Meanwhile, the joints are represented by special elements. For each joining method, the simulations are carried out under longitudinal and transverse loading.

T-joint model

Previous research [START_REF] Jousset | Constitutive modeling of structural adhesives experimental and numerical aspects[END_REF] reported that the spew fillet can affect the response why the internal spew fillets, that are difficult to remove, are taken into depicted in Figure 5 As regards the transverse loading, the predicted strength is in good agreement with measurements, as shown in Figure 5 Only small stress concentration is observed in the vicinity of bonded area of base metal. The stresses within the faying surfaces are uniform in both loading cases.

Since adhesive can provide uniform stress distribution, it can be supposed that increasing faying surface can efficiently increase the strength of adhesive bonded joint. The connector stiffness along the direction 1, 2 and 3 for simulation are represented by E 1 , E 2 and E 3 , as summarized in Table 5-1. The rotation stiffness about each axis is denoted by E 4 , E 5 and E6. All the rotation stiffness is rigid in the analysis. The predictions with original and scaled parameters are compared with measurements under longitudinal and transverse loading, as depicted in Figure 5-21. The predictions using the original parameters and scaled parameters are denoted Sim-1 and Sim-2 respectively. Obviously, the predictions obtained with the original parameters under predict the results while the predictions obtained with the scaled parameters are in good agreement with the measurements. On one hand, the nugget of spot weld is heterogeneous. This needs additional material parameters to be calibrated for different zones (BM, HAZ and WM). On another hand, adhesive and spot weld can interact each other. Spot weld heat can diminish the effective surface of adhesive bonding, meanwhile adhesive increase the welding current of spot weld and affect the spot weld dimensions. All these can make the modelling of weld bonded joint a tricky task. Moreover, as regards car crash simulation that uses explicit codes, only the models with adequate stable time step can be acceptable due to the computational cost. Hence, simplified models should also be developed.

The aim of this work is to find adequate constitutive models to predict the failure of weldbonded joint under complex loading condition. The models intend to be used to simulate large industrial problems.

The adopted methodology consists in combining experiments with numerical models to investigate WB joints in relation to SW and AB joints. As regards the experimental aspects, welding parameters are firstly optimized for spot welding and weld bonding in terms of welding current, squeeze force and squeeze time. Optimal welding current for spot welding is 7.4 while this value is increased to 7.8 for weld bonding. Adhesive layer must have a controlled small thickness in order to obtain optimal mechanical properties. The optimized thickness for SikaPower ® -498 is 0.3 mm in this work. With the help of optimized parameters, SW joints, AB joints and WB joints are successfully produced on KS2 and lap-shear specimens.

The inspection of microstructure on specimens of weld bonded joints was carried out by AFM and OM to investigate the configurations and interactive effect between spot weld and adhesive.

Micro-hardness measurement was carried out to verify the microstructure change in spot weld.

The complex structure consisting in columnar grains and equiaxial grains are observed in molten specimen under tension and shear, respectively. The ultimate strength as well as the displacement at fracture of spot welds (KS2 tension, KS2 shear, peeling and lap-shear) is accurately predicted.

Secondly, as regards adhesive bonding, BM (the adherends) was meshed with 3D solid elements while adhesive was modeled by interfacial element-CZM with TSLs. The parameters of TSLs were calibrated using measurements from DCB and ENF specimen. TSLs have limited capacity to adequately predict the ultimate strength of AB joints with small scale specimens due to the lack of plasticity. The predicted ultimate strength is in good agreement with measurement for each test while the predicted initial stiffness on KS2 shear is higher than that of the tests. The error is supposed to come from measurements as the model can well predict the stiffness of lapshear tests.

  Mots clés: Soudage par point, Collage, Assemblage hybride, Eléments finis, Lois de comportement, Identification inverse, Zones cohésives. V steers me on the right way. During the report revision, he took his patience to fix the text problems raised by me. I would like to give my appreciation to the Chinese Scholarship Committee for the finance supports. Thanks Dr. Pierre Jousset, previously in Sika AG, for sponsoring this research and the contributions for adhesive modelling. I would like to thank Dr. Hein at Laboratorium für Werkstoff und Fügetechnik of the University of Paderborn for the tests and valuable information.

a 1 ,Damage evolution exponent α 1 Scaling factor of heat affected zone α 2 Scaling factor of welded metal zone ε 0 Chapter 2 . 1 . 2 .

 1120212 a 2 , a 3 , a 4 Parameter of damage potential function b 1 , b 2 , b 3 , b 4 Parameter of potential function of displacement C Fourth-order constitutive tensor c i (x) Computed response for inverse identification Energy along normal direction of model I G s Energy along the first direction of model II G t Energy along the second direction of model III G C Mixed model fracture energy G Ic Critical fracture energy of model I G IIc Critical fracture energy of model II K Strength coefficient of Swift's equation K n Stiffness of model I K s Stiffness along first direction of model II K t Stiffness along second directions of model III Rate of equivalent plastic relative motion. u i Connector displacement or rotation in the i th direction α Prior plastic strain ε N Mean voids nucleation burst strain ε n Normal separation of model I ε s Shear separation along first direction of model II ε t Shear separation along second direction of model III Table of content Chapter 1. Introduction ................................................................................................................. Bibliography ................................................................................................................ Dual phase steel ...................................................................................................................... Spot welds ...............................................................................................................................

4 . 4 . 1 .Chapter 3 . 1 .

 44131 Weld-bonding ....................................................................................................................... Motivations for weld-bonding ............................................................................................. Joining procedures and joint characterization ...................................................... Description of joining procedures .....................................................................................

4 .Chapter 6 . 1 Chapter 1 .

 4611 Conclusion ............................................................................................................................ Conclusion and perspectives ................................................................................... Appendix ...................................................................................................................................... References ....................................................................................................................................XVI IntroductionIn the world, there were about 1 billion cars and light trucks on the road in 2013 and the growing is still by roughly 40 million yearly. Based on current predictions, the number of cars in emerging and developing economies could increase by 1.9 billion from 2005 to 2050, bringing the world's total to nearly 3 billion automobiles[START_REF]Automobiles and Truck Trends[END_REF]. The exhaustion of non-renewable fossil energy and the environment pollution force us to continuously improve the vehicle in terms of fuel consumption efficiency and gas emission and also to develop electrical vehicles or hybrid cars. To meet these purposes, the main way is to reduce car weight. Most of modern cars opt for uni-body construction and advanced materials to gain light-weight, passenger safety and performance. This design needs a large number of steel sheet to form different substructures,

Figure 1 - 1 .

 11 Figure 1-1. Elongation versus tensile strength at fracture of different types of steels [4].Adhesive bonding has notable advantages like uniform stress distribution, fatigue life improvement and low cost[START_REF] Weber | Resistance spot welding and weldbonding of advanced high strength steel[END_REF]. When using adhesive for joining large structure in assembly line, it could be difficult to accurately position and maintain the parts in position. To overcome such difficulties, hybrid joints are developed by combining mechanical fasteners with adhesive bonding, such as spot welded bonded, bolted welded and laser welded bonded joints. Figure1-2

Figure 1 - 2 (

 12 a) shows a complex car body structure, in which several types of aluminum alloys are combined with high strength steels to reduce the car weight. To join these dissimilar materials, different joining technologies are used as illustrated in Figure 1-2 (b).

Figure 1 - 2 .

 12 Figure 1-2. A typical car contains (a) multi-materials and (b) diversified joining techniques.(SourceAudi)

Figure 1 - 3 .

 13 Figure 1-3. Crash simulation of whole car (Sourse:Volkswagen)

Figure 2 - 1 shows

 21 Figure 2-1 shows Fe-Fe 3 C equilibrium phase diagram, in which all the transformations occur in isothermal condition. DP600 steel is referred to as proeutectoid steel. It exhibits 3 types of phases depending on the temperature as shown by the Fe-Fe 3 C phase diagram (Figure 2-1).

Figure 2 - 1 .

 21 Figure 2-1. Fe-Fe 3 C equilibrium phase diagram Under non-equilibrium conditions, the phase transformation does not follow the equilibrium phase diagram in Figure 2-1. The microstructure can be estimated by continuous cooling transformation diagram, as shown in Figure 2-2. At high cooling rate, all the austenite can transform to martensite phase while an intermediate cooling rate could create a complex microstructure composed of ferrite, bainite and martensite. Finally, a low enough cooling rate produces the equilibrium structure consisting of ferrite and pearlite.

Figure 2 - 2 .

 22 Figure 2-2. CCT diagram of typical low carbon steel[START_REF] Zhang | Resistance Welding-Fundamentals and Applications[END_REF]

  be produced by hot rolling or cold rolling process. In hot rolling process, the final deformation is carried out at a temperature above A r3 , as shown in Figure2-3. After deformation, slow cooling is performed to obtain desirable ferrite by austenite decomposition, followed by the carbon enrichment in remaining austenite, which enhance the hardenability. The remaining austenite transforms to hard martensite by quick cooling before the final strip rolling.

Figure 2 - 3 .

 23 Figure 2-3. Hot rolling schedule in the production of the DP strips[START_REF] Saha | Metallographic and fracture characteristics of resistance spot welded TWIP steels[END_REF]

Figure 2 - 4 .

 24 Figure 2-4. Temperature changes during continuous annealing of DP steel sheets[START_REF] Bleck | Microalloying of Cold-Formable Multi Phase Steel Grades[END_REF]

Figure 2 - 6 .

 26 Figure 2-6. Illustration of spot welding stages

Figure 2 -

 2 Figure 2-7 shows a simulated temperature field. The steel is heated up to liquid phase in the center of nugget (in red); the yellow color covers a mushy zone and a heat affected zone, corresponding to the temperature range from A 1 to molting line, as shown in Figure 2-7.

Figure 2 - 7 . 10 Furthermore, as illustrated in Figure 2 - 8 ,

 271028 Figure 2-7. Temperature contour in spot weld section[START_REF] Raoelison | Étude et modélisation des conditions interfaciales dans le procédé de soudage par résistance par point de tôles d'acier revêtues[END_REF]

Figure 2 - 8 .

 28 Figure 2-8. Spot weld microstructures in different zones

Figure 2 -

 2 [START_REF] Asadi | Influence of martensite volume fraction and cooling rate on the properties of thermomechanically processed dual phase steel[END_REF] shows Audi Q7 car body containing a large part of weld bonded joints.

Figure 2 - 11 .

 211 Figure 2-11. Joining techniques in car body design (source Audi)

Figure 2 - 12 .

 212 Figure 2-12. Illustrations of Weld bonding process [40] Alternatively, as illustrated in Figure 2-12 (b), the adhesive is first applied on faying surface.

212.

  Single spot weld is performed on samples of 45×45 mm with 40 mm overlap using CuCrZr A16 electrodes, as shown in Figure 3-1. The smallest welding current I min is the one producing a minimum nugget diameter exceeding 4 t on 5 specimens [54]. The maximum current I max is the current setting, decreasing from the setting where first splashing occur, that produces 3 nonsplash welds, 7.6 scaled unit in Figure 3-1.

Figure 3 - 1

 31 Figure 3-1 Weldability of spot welded joint for DP600 steel with 1.5 mm thickness For 1.6 mm thickness DP600 steel, the optimized welding current, welding force, squeeze time, welding time and holding time are listed in Table 3-1. Under these welding conditions, the nugget diameter is within a range from 5.4 to 5.8 mm.

Figure 3 -

 3 Figure 3-2 shows a nugget metallographic cross section. The nugget diameter (ND) is 7.76 mm, the nugget height (NH) is 2.61 mm and the heat influenced zone diameter (HAZD) is 7.22 mm.

0. 3

 3 mm glass balls are added in the adhesive. It was found that the spew fillet between joined surfaces has important influence on the test result. To control this influence, the fillet is removed by specific tools as shown in Figure3-3. For the adhesive curing, the specimens are heated at 180 °C for 3 min in a resistance furnace.

Figure 3 - 3 A

 33 Figure 3-3 A KS2 specimen without fillet

Figure 3 -

 3 Figure 3-5 clearly shows that spot welding is not complete when the current is below 7.2 in weldbonded joint, whereas the minimum current in single spot weld is 6.8. It reveals that the adhesive increases the electrical resistance of welding parts. Additionally, the squeeze time increases from 300 ms to 500 ms to improve the conductivity.

Figure 3 - 5

 35 Figure 3-5 Weldability of weld bonded joint Spot welding parameters in weld bonding are listed in Table 3-2, corresponding to a nugget diameter within a range of 5 to 5.5 mm.

Figure 3 -

 3 Figure 3-6 shows a hybrid joint metallographic cross section. The measured nugget diameter is 5.39 mm but the investigations of several specimens reveal that the nugget diameter is ranging between 5 mm and 5.5 mm.

Figure 3 - 6

 36 Figure 3-6 Metallographic of spot weld in hybrid joint2. Description of simple characterization testsAll the tests are carried out using quasi-static loading with a velocity of 10 mm/min under room temperature on a universal tension and compression testing machine (Zwick Z100) with a capacity of 100 kN. The global displacement is measured by machine internal sensor. For each test, at least 5 specimens are tested to ensure the reliability of experiment. In order to calibrate constitutive model of different joints, KS2 specimen of SW, AB and WB joint are conducted in shear, tension and peeling.2.1. KS2 testKS2 specimens refer to combined tension-shear specimens. It is constituted by two "U" shaped parts, as shown in Figure3-7 (a). Different joining methods can be applied to the faying surfaces, e.g. adhesive bonding, spot welding and hybrid joining. The adjustable fixture system gives control on the load direction. In this work 0° (tension loading) and 90° (shear loading) load directions are investigated. With the specially designed fixture system[START_REF] Hahn | Test specification for KS-2 specimen[END_REF], local displacement is measured with the help of a digital image correlation (DIC) system between point 1 and point 2, as shown in Figure3-7 (a). The measurement of local displacement for peeling is not shown here.The reference points are in the same location as KS2 specimens. The specimens are tested using a universal tension-compression testing machine as shown in Figure3-7 (b). In fact, both global and local displacements are outputted but only the latter are used to be discussed and be compared with simulation.

Figure 3 - 7

 37 Figure 3-7 KS2 specimens, a) schematic of KS2, b) universal tension machine KS2 specimen geometry is depicted in Figure 3-8. The faying surface is 50mm×18mm. Four holes are drilled to fix the specimens on the clamps. The peeling test has the same faying surface as well as KS2 specimens. The geometry is depicted in Figure 3-9. The force is applied on the edges, as shown in Figure 3-7 (a) peeling.

Figure 3 - 8

 38 Figure 3-8 Geometry of KS2 specimen Figure 3-9 Geometry of peel specimen 2.2. Lap-shear tests Lap-shear test is widely used for assessment of mechanical characterization of joints, like spot weld and adhesive, due to its simple geometry [55-58]. In lap shear tests, spot welds or adhesive bonding is carried out on the over-lapping surface, which is 16mm×45mm in this work. Lap-shear has 100 mm free clamping length. The two ends of extensometer, with 22 mm gauge length, are fixed on both sides of the joint. Lap-shear geometry is shown in Figure 3-10. The faying surfaces can rotate with the loading in lap-shear differing from KS2 shear tests. In KS2 the faying surfaces are fully constrained by the grips.

Figure 3 -

 3 Figure 3-10 Lap-shear geometry

Figure 3 - 11

 311 Figure 3-11 Macrostructure in transverse section of spot weld

  -12 shows the microstructure in the different zones of spot welds.

Figure 3 - 12 .

 312 Figure 3-12. Sample distribution on macrostructure (left-up) and AFM microstructure images (a)Base metal, (b) Tempered zone, (c) Quenching zone, (d) the center of welded metal

Figure 3 -

 3 12 (c) shows the border of the welded metal (melted zone). It consists of bainite structure and a small quantity of ferrite. The center of melted zone generates a complex microstructure containing bainite and martensite, as depicted in Figure3-12 (d). The microstructures of spot weld are in accordance with the literatures[START_REF] Tong | Deformation and fracture of miniature tensile bars with resistance-spot-weld microstructures[END_REF] and[START_REF] Ghosh | Weldability of intercritical annealed dualphase steel with the resistance spot welding process[END_REF].

Figure 3 -

 3 Figure3-13 shows hardness tests results in the transverse section. It shows that the hardness distribution is in agreement with the microstructure observations. On average, WM has the maximum hardness 375 HV and it exhibits large hardness variations that result from the heterogeneities in solidification structure, e.g. dendrite and the solidification defects.Comparatively, soft base metal exhibits lower hardness in BM zone. In HAZ, the hardness is intermediate between those of BM and WM.

Figure 3 - 13 .

 313 Figure 3-13. Micro hardness distribution in spot weld transverse section 3.1.2. Failure modes and load bearing capacity of spot weld joints

  is observed. These modes are the pull-out (plug) fracture and the interfacial fracture. Figure3-14 shows the different fracture mode. The dotted lines represent potential crack path. In path (a), the strain localization leads to fracture in BM [60]. In path (b), (c) and (d), the crack initiates at the notch tip but it then propagates following different potential paths. Path (b) is located in the boundary BM/HAZ, path (c) is along the boundary HAZ/WM and path (d) produces partial pullout fracture. In this case the crack propagates along the front of dendrite structure but the path can change when crack meets some localized defects that are common in welding structure.

Figure 3 - 14 .

 314 Figure 3-14. Crack paths in different fracture mode of spot welded: (a) strain localization in BM, (b) pull-out in BM/HAZ, (c) pull-out in HAZ/WM, (d) partial pull-out in WM and (e) interfacial fractureIn this work, the pull-out fracture mode at the HAZ/WM interface and the interfacial fracture mode are observed corresponding to tension and shear loading. This will be discussed in details in the following section.

Figure 3 - 15 .

 315 Figure 3-15. Fracture modes of spot welded joint: (a) KS2 tension, (b) KS2 shear, (c) peel, (d) lap-shear

Figure 3 -

 3  shows that lap-shear test exhibits interfacial fracture mode. Further analysis reveals that in lap-shear test, the spot weld experiences complex loading combining shear and tension. In fact the spot weld can rotate about an axis perpendicular to loading direction. Figure3-16 (d)shows lap-shear force-displacement curve. The average ultimate strength is 15 kN, lower than shear force. Due to the rotation of spot weld, the displacement is larger than that of pure shear.

Figure 3 - 16 .

 316 Figure 3-16. Force-displacement curve of spot welded joint: (a) KS2 tension loading, (b) KS2 shear loading, (c) peeling, (d) lap-shear

  strength about 5 kN, as shown in Figure3-17 (c). Average ultimate strength of lap-shear joints is 23.1 kN, lower than that 34 kN in KS2 shear. The reason is that faying surfaces in lap-shear joint is smaller than shear KS2, 720 mm 2 compared with 900 mm 2 . Moreover, lap-shear joints undergo the component of tension load due to the rotation of faying surfaces.

Figure 3 - 17 .Figure 3 - 18 .

 317318 Figure 3-17. Force-displacement curve of adhesive bonded joint: (a) tension loading, (b) shear loading, (c) peeling and (d) lap-shearThe damaged specimens are depicted in Figure3-18. A dark black zone is observed in damaged interfaces of tension test, as shown in Figure3-18 (a). The reason is that the adhesive damaged under different strain rate. The adhesive layer has almost unique stain rate at the beginning of loading. However, when the adhesive layer remain a small zone before final damage, the strain rate may be large than the other zone. Similar phenomenon of damage can be observed in peeling test, as shown in Figure3-18 (b). As regards KS2 shear and lap-shear, the both damaged surfaces are in the same colour. This also indicates that adhesive bonded joint has uniform stress distribution than that of tension and peeling loading.

Figure 3 - 19 .

 319 Figure 3-19. Macrostructure of weld bonded joint: (a) transverse section, (b) in-plane section 3.3.2. Load bearing capacity and failure modes of weld bonded joints Weld bonding combines adhesive bonding with spot welding. The complex structure leads to two stage failure in WB: adhesive failure and spot weld failure. Two stage failures are observed in tension, peeling and lap-shear tests, as shown in Figure 3-20. Spot weld exhibits higher strength than adhesive under tension and peeling load. In tension test, the ultimate strength of Test 3 is 22.7% higher than the other tests, as depicted in Figure 3-20 (a). It is observed that in Test 3, the cracks initiate in BM/HAZ while it initiate in HAZ/WM in the other tests, as shown in Figure 3-21 (a). The ultimate strengths of peeling are scattered ranging from 3.7 kN to 5.4 kN. This could be explained by the variation of nuggets diameters, as shown in Figure 3-21 (c). Spot weld failure peak was not observed in force-displacement curve of KS2 shear tests, as shown in Figure 3-20 (b). This indicates that the spot weld fails prior to the adhesive layer. The reasons will be discussed in section 3.4. Pull-out fracture of spot weld was observed in tension, as shown in Figure 3-21 (a). It should be pointed out that the crack initiated from BM/HAZ in Test 3 while it takes place in HAZ/WM in the other tests. It indicates that spot welds in weld bonded joint are prone to damage in HAZ/WM. This phenomenon can be proved when investigating the T-joint test. Interfacial fracture was observed in shear and lap-shear tests, as depicted in Figure 3-21 (b) and (d). Pull-out

Figure 3 - 20 .Figure 3 - 21 .

 320321 Figure 3-20. Force-displacement curve of WB joint: (a) tension, (b) shear, (c) peel and (d) lapshear

  order to assess the behavior of different joining methods, tests results are compared in terms of load bearing capacity and energy absorption under the same loading condition. WB joint provides excellent properties in both load bearing and energy absorption under tension loading, as shown in Figure 3-22. WB joint combines high stiffness of adhesive and large plastic deformation of spot weld, as shown in Figure 3-22 (a). The energy absorption of WB joint is increased by 19.9% compared with SW joint while this value is increased by 8 times compared with AB joint, as shown in Figure 3-22 (b). A small amount of adhesive added to spot weld can markedly increases the ultimate strength and energy absorption.

Figure 3 - 22 .

 322 Figure 3-22. KS2 tension test: a) force-displacement curve, b) energy absorption

Figure 3 -

 3 Figure 3-23 (a) shows load capacities and energy absorptions of different joints under shear loading. SW joint exhibits the lowest loading capacity among the three joints but it has the largest displacement before complete failure. As a result, SW joint provides the largest energy absorption, increased by 1.46 times compared with that of WB joint.

WB joint has theFigure 3 - 23 .

 323 Figure 3-23. KS2 shear: a) force-displacement curve, b) energy absorption Force-displacement curve under peeling is depicted in Figure 3-24 (a). AB joint and WB joint acquire high stiffness from adhesive layer. Hence both them exhibit higher ultimate strength than that of SW joint. In addition, the large deformation of spot welds enables WB joint to improve the energy absorption, which is increased by 8.5 times compared with that of AB joint, as shown in Figure 3-24(b).

Figure 3 - 24 .Figure 3 - 25 .

 324325 Figure 3-24. Peel test: a) force-displacement curve, b) energy absorption In lap-shear, the joined zone has a slight rotation which leads to a combined load on the faying surface (shear and separation). As a consequence, lap-shear joint fails under tension and shear complex load. AB joint and WB joint exhibit higher ultimate strength than that of SW joint, as shown in Figure 3-25 (a). WB joint offers the highest energy absorption among the three joints, as shown in Figure 3-25 (b).

Figure 4 - 8 ,

 48 different mesh sizes are used in the HAZ and WM from 0.2 mm to 1.0 mm, while 1mm coarse meshes are used in base metal. The simulation is carried out on lap-shear test without considering damage.

Figure 4 - 8 .Figure 4 - 9

 4849 Figure 4-8. Different mesh sizes in spot weld in a lap-shear specimen

Figure 4 - 9 .

 49 Figure 4-9. Force-displacement curves obtained with different element sizes

Figure 4 - 10 .Figure 4 - 13 .

 410413 Figure 4-10. Force-displacement curves obtained with different nugget's diameters

Figure 4 - 14 .

 414 Figure 4-14. Flow stress of BM, HAZ and WM zone

Figure 4 -

 4 Figure 4-16. J-integral under (a) shear loading and (b) tension loading

5 .Figure 4 -

 54 Figure 4-17 shows the simulation boundary conditions used for spot welded joints: (a) KS2 shear, (b) KS2 tension, (c) peeling and (d) lap-shear. Because of symmetry, only half of specimen is discritized in all the simulations. In addition, the griped parts of specimens are not modeled as they do not experience noticeable deformation. The clamping effect is modeled using kinematic coupling constraints. The general contact is trigged with 0.1 friction coefficient between the two sheets. Displacement boundary condition is applied on the loading point to match the loading velocity at 10 mm/min. Smooth step amplitude is used to avoid discontinuities. Local displacement is outputted between point 1 and point 2 depicted in Figure 4-17.

Figure 4 -Figure 4 - 17 .

 4417  shows comparison between the predicted and the measured load-displacement responses. For shear test, the ultimate strength as well as the displacement at fracture is accurately predicted. For tension test, the simulation result gives good prediction of maximum strength. It should be noted that predicted crack is only located on one of spot welded sheets.

Figure 4 - 2 Figure 4 - 18 .Figure 4 - 19 .

 42418419 Figure 4-18. Prediction vs. measurement of load-displacement curve of SW joint: (a) shear, (b) tension, (c) peeling and (d) lap-shear As illustrated in Figure 4-19, strain localization leads to necking in BM while shear band located in faying surface. These two fracture mechanisms can occur simultaneously in one test.Necking leads to pull-out fracture whereas shear causes interfacial fracture.Spot weld rotates under bending moment resulting in an opening component in crack tip.Therefore lap-shear sustains tension-shear rather than pure shear in KS2 shear. In KS2 shear, spot weld exhibits limited rotation in simulation. Simulation results show that cohesive element damage in WM prior to the ductile fracture in BM; this leads to interfacial fracture in the spot weld.

Figure 4 - 20 .

 420 Figure 4-20. Main crack and kinked crack under tension loading of spot weld[START_REF] Wang | Stress intensity factors for spot welds and associated kinked cracks in cup specimens[END_REF]

Figure 4 - 57 Figure 4 - 21 .

 457421 Figure 4-21 shows that the crack initiates at the crack tip and propagates to the external surfaces. The elements in HAZ reached the critical value f F of Gurson model and were deleted.

Figure 4 - 22 .

 422 Figure 4-22. Stress contour of peeling: a) cracks initiation in HAZ, b) cracks propagation, c) pull-out damage.

  of lap-shear is similar to KS2 shear at the beginning of loading. The model can predict necking in WM and shearing in faying surface, as shown in Figure 4-23. Simulation results show interfacial fracture in lap-shear.

Figure 4 - 23 .

 423 Figure 4-23. Stress contour before fracture in lap-shear. Lap-shear exhibits a larger rotation angle (17.7°) than that of KS2 shear loading (10.4°), as shown in Figure 4-24. The amplitude of tension component increases when increasing spot weld rotation.

Figure 4 - 24 .

 424 Figure 4-24. Comparison of rotation angle between (a) lap-shear and (b) KS2 shear

  meshed due to symmetry reasons. The simulations were performed with 8-node, linear brick, reduced integration elements (C3D8R) in BM and cohesive element (COH3D8) in adhesive, as shown in Figure 4-25. Adhesive is modeled as a single layer with interface elements. The nodes in faying surfaces between adhesive and BM are tied together. The simulation boundary conditions are the same as with that of SW illustrated in Figure 4-17.

Figure 4 - 25 .

 425 Figure 4-25. FE mesh of adhesive bonded joint

Figure 4 - 26 .

 426 Figure 4-26.Schematic description of (a) DCB specimen and (b) ENF specimen

Figure 4 -

 4 Figure 4-28 shows the comparison between prediction and measurement of different joints loaded under different loading-paths.

Figure 4 - 28 .

 428 Figure 4-28. Simulation vs. measurement on load-displacement curve of adhesive bonded joint: (a) shear, (b) tension, (c) peeling and (d) lap-shear.

Figure 4 - 29 . 62 Figure 4 - 30 .

 42962430 Figure 4-29. Prediction from different constitutive models for KS2 shear loading Adhesive exhibits different failure modes under multi axial loadings. Figure 4-30 shows the scalar stiffness degradation of cohesive elements under different loadings. In KS2 shear, Figure 4-30 (a) shows that AB joint has a uniform stress distribution in the center where a maximum of elements were damaged simultaneously. Contrarily, under tension and peeling damage propagates progressively from external edges to the center as shown in Figure 4-30 (b) and (c). This can also explain the occurrence of different strain rate in the adhesive layer in tension test. Consequently, adhesive shows good ability to withstand shear loading.

Figure 4 - 31 .Figure 4 -

 4314 Figure 4-31. Mises Stress prediction of (a) shear, (b) tension, (c) peel and (d) lap-shear loadingFigure 4-31 shows predicted Mises stress and deformed BM under different loadings. Maximum stress is observed in BM in the vicinity of the crack fronts in all the simulations, as

Figure 4 -

 4 [START_REF] Chao | Ultimate strength and failure mechanism of resistance spot weld subjected to tensile, shear, or combined tensile/shear loads[END_REF] shows the mesh of the weld bonded joint. The adhesive is meshed with 0.3 mm single layer cohesive element using TSLs (in black). A 2 mm gap between adhesive layer and spot weld is created as the adhesive is burnt in this zone. BM is meshed with 1 mm coarse mesh while HAZ and WM are meshed with 0.4 mm fine elements with Gurson model.Cohesive elements are associated with TSLs used to predict shear failure of spot welds. The thicknesses of cohesive elements are 0.1 mm.

Figure 4 - 32 .

 432 Figure 4-32. FE model of weld bonded joint 2.3.2. Predictions from hybrid joint model The previously described finite element model is used to investigate shearing, tension, peeling and lap-shear tests. The comparisons between the predictions from the model and the measurement are presented in Figure 4-33.

Figure 4 - 33 .

 433 Figure 4-33. Predictions vs. measurements of load-displacement curves of weld bonded joints: (a) shear, (b) tension, (c) peeling and (d) lap-shear.Spot weld failure peak was not observed in shear loading. It indicates that spot weld was damaged prior to adhesive. This phenomenon can be explained by simulation of hybrid model.

Figure 4 -

 4 Figure 4-34 shows that spot weld fails in interfacial manner in KS2 shear. Adhesive remain in place and can bear additional loading.

Figure 4 - 34 .

 434 Figure 4-34. WB failure under shear loading

Figure 4 - 35 .

 435 Figure 4-35. Adhesive failure process under shear of weld bonded jointAs recalled in Chapter 3, the WB joint ultimate strength is lower than that of AB joint. This could be explained by the diminution in adhesive area caused by the spot weld process. In the simulation, adhesive in the periphery of spot welds can be the new source of crack initiation after spot weld failure. Figure4-36 shows element damaged near the spot weld.

Figure 4 - 36 .

 436 Figure 4-36. Adhesive failure under shear near spot weld of WB joint

Figure 4 -

 4 37 (b), cracks initiate at the notch tip of spot weld causing pull-out fracture, as shown in Figure4-37 (c). It is obvious that the spot weld is the major contributor to the plastic deformation in WB joint.

Figure 4 - 37 . 67 Figure 4 - 38 .

 43767438 Figure 4-37. Damage process of WB joint under tension loading Hybrid model gives good prediction for peeling load, as shown in Figure 4-33 (c). WB joint damage process is illustrated in Figure 4-38. Adhesive fails progressively till the front of cracks reached spot weld. Spot weld exhibits pull-out fracture with tearing of base metal.In WB lap-shear joints, the whole faying surface can rotate with loading. The rotation leads to increasing components of tension force in adhesive layers and spot weld, like the AB lap-shear joint, as discussed in Figure4-33. Adhesive has lower strength in pure tension than pure shear; hence WB lap-shear joints exhibit lower strength than KS2 shear.

Figure 4 - 39 .

 439 Figure 4-39. Fracture process of WB lap-shear joint

Figure 4 - 40 shows

 440 fastener configuration. The connector is attached to two parts A and B in the attachment point position. Radius of influence determinates the fastener region in which the points are kinematicaly coupled with attachment points.

Figure 4 - 40 .

 440 Figure 4-40. Schematic description of mesh independent fastener

Figure 4 -

 4 Figure 4-41 shows the schematic description of bushing to model spot welds. Bushing type connector has six available components of relative motion: three translations along each axis (components 1-3) and three rotations around each axis (components 4-6).

Figure 4 -

 4 Figure 4-41. Connector element modeling a spot weld (modified from [87])

Figure 4 - 45 .Figure 4 -

 4454 Figure 4-45. Prediction from shell connector model of spot welded KS2 specimen: (a) shear, (b) tension and (c) peeling Figure 4-46 shows connector damage and deformation of base metal in spot welded zone. Connector elements can fully capture the spot welds behavior including elasticity, plasticity and damage. The links between the two sheets are deleted when connector element are totally damaged. Simplified model can predict the rotation of spot weld in shear and base metal deformation of tension and peeling.

Figure 4 - 46 .

 446 Figure 4-46. Simulation of connector damage by shell connector model (a) tension (b) peeling and (c) shear Table 4-5 gives the comparison of CPU time between solid model and connector model.Connector element for spot welds can increase initial time increment and cut CPU time for the same KS2 simulation. Moreover, coarse meshes can be assigned to base metal by the help of mesh independent fastener.

  5-2 (a). The spot welds are numbered from 1 to 5. In the adhesively bonded joint, the spot welds are replaced by adhesive on the same surfaces, as shown in Figure5-2 (b). The thickness of adhesive layer is 0.3 mm. The dimension of the two horizontal faying surfaces is 16× 45 mm. The vertical faying surface is 18×50 mm. All the spew fillets are removed to control accurately the bonded surface.

Figure 5 -

 5 2 (c) shows weld bonded T-joint, in which spot welds are combined with adhesive to make hybrid joint.

Figure 5 - 2 .

 52 Figure 5-2. Illustration of T-joints: (a) spot welded, (b) adhesive bonded and (c) weld bonded

Figure 5 - 3 .

 53 Figure 5-3. Configuration of T-joint tests setup Preliminary investigation shows that excessive deformation took place on base metal in hybrid joints, instead of the damage of joints. Therefore, a block is placed inside the horizontal beam to increase the stiffness of T-joint, as shown in Figure 5-4.

Figure 5 - 4 .Figure 5 -

 545 Figure 5-4. Stiffness block placed inside the horizontal beam

Figure 5 - 5 .

 55 Figure 5-5. T-joint test setup under longitudinal loadingThe setup for the transverse loading is the same as that of longitudinal loading with the exception of the force direction that is perpendicular to the horizontal beam as depicted in Figure5-6. As the hybrid joint performance is assessed by comparison with adhesively bonded joint and spot welded joint, all three types of joints are tested.

Figure 5 - 6 .

 56 Figure 5-6. T-joint test setup for transverse loading

Figure 5 -

 5 Figure 5-7 (a) shows the measurements of force-displacement curve of SW T-joint under longitudinal loading. Except the spot weld N° 2, the other spot welds damaged successively at the different peaks of force. Both interfacial damage and pull-out damage modes of spot weld are observed in T-joint. Under transverse loading, as shown in Figure 5-7 (b), the two spot welds on horizontal surface (N°. 1 and N°. 2) are damaged almost at the same time while the spot welds on vertical surface (N°. 3, N°. 4 and N°. 5) remain undamaged.

Figure 5 - 7 . 2 . 2 .

 5722 Figure 5-7. T-joints test of SW: (a) longitudinal loading and (b)transverse loading2.2. Test results of AB T-jointAB T-joint tests are well reproducible in both transverse and longitudinal loading. Under longitudinal loading, adhesive layer on vertical surface (adhesive-3) undergoes shear loading while the layer adhesive-1 on horizontal surface undergoes complex loading combining tension and shear. The ultimate strength is about 13 kN, as shown in Figure5-8 (a).

Figure 5 - 8 . 2 . 3 .

 5823 Figure 5-8. AB T-joints test : (a) longitudinal loading and (b)transverse loading

Figure 5 - 9 .

 59 Figure 5-9. WB T-joints test: (a) longitudinal loading and (b)transverse loading

Figure 5 -

 5 10 (a) gives the comparison between SW, AB and WB joint under longitudinal loading. WB joint exhibits the highest strength and displacement, due to the combination of high stiffness conferred by the adhesive and large plastic deformation conferred by the spot welds. The strength of AB joints is higher than SW joint because of severe

Figure 5 -

 5 10 (b).

Figure 5 - 10 .Figure 5 -

 5105 Figure 5-10. Comparison between different T-joints under longitudinal loading: a) forcedisplacement curve, b) energy absorptionFigure 5-11 shows the damaged SW and WB T-joints. Spot welds on vertical surface exhibit same damage modes on both SW and WB T-joint.

Figure 5 - 11 . 3 Figure 5 - 12 .

 5113512 Figure 5-11. Images of damaged T-joints specimens: (a) SW T-joint (b) WB T-joints However pull-out fracture was observed on SW while mixed fracture mode combining pullout and tearing was observed on WB T-joints due to the adhesive, as shown in Figure 5-11 (a) and (b). In the mixed mode of WB T-joint, cracks initiate at the interface of HAZ/WM, and then propagate to the exterior edge by tearing the spot welds out of BM. Consequently, WB provides the highest strength and energy absorption among the 3 kinds of joints.

Figure 5 - 13 .

 513 Figure 5-13. Images of damaged T-joints specimens: (a) spot welds on vertical surface of SW Tjoints, (b) spot welds on vertical surface of WB T-joints The damaged specimens are depicted in Figure 5-13. All spot welds exhibit "pull-out" fracture mode over the 5 tests of SW T-joint, as shown in Figure 5-13 (a). As regards WB T-joint, only one of two spot welds (outlined in red) in Test 3 shows pull-out fracture while all the spot welds of other tests of WB T-joint exhibit "tear-out" mode (outlined in blue), as shown in Figure 5-13 (b).It should be noted that the "tear-out" mode can exhibit higher strength than "pull-out" mode.

  3 exhibits lower strength than the others in WB T-joints, as shown in Figure 5-9 (b).

Figure 5 -

 5 Figure 5-14 shows that the predictions are in good agreement with measurements both in terms of strength and displacement under both longitudinal and transverse loading. As regards longitudinal tests, spot welds failed consecutively with displacement and their damage results in a peak on force-displacement curve, as shown in Figure 5-14 (a). The two spot welds in horizontal surface are damaged simultaneously in transverse loading. This can be proved by single peak on the force-displacement curves, as shown in Figure 5-14 (b).

Figure 5 - 14 .

 514 Figure 5-14. Comparison between predictions and measurements of spot welded T-joint: (a) longitudinal load, (b) transverse loading

Figure 5 -

 5 Figure 5-15 shows the predicted spot weld failure under longitudinal loading. Right Y axis represents the damage of spot weld. Spot weld loses load carrying capacity when damage evolution reached its criteria. S1, S4 and S5 are damaged in different modes, as shown in Figure 5-15 (a) and (b).

Figure 5 - 15 .

 515 Figure 5-15. Failure of spot welds under longitudinal loading Simplified model of spot weld cannot predict the damage due to torsion force. Consequently the failure peak on test (red dash line) of spot weld outlined by red circle in Figure 5-15 (a) is not predicted by simulation. This spot weld is denoted S3 in Figure 5-15 (b).

Figure 5 -

 5 Figure 5-16 shows the deformed shape and the contour plot of equivalent plastic strain. It clearly shows that the deformed shape is well captured by the model. the vicinity of two damaged occurs close the spot weld S3.

Figure 5 - 16 .

 516 Figure 5-16. Predicted deformed shape T-joint under (a) transverse

Figure 5 -

 5 Figure 5-17. Modeling s

- 17 . 88 Figure 5 -

 17885 Figure 5-18 shows comparison between the predictions from the finite element model and measurements under longitudinal and transverse loading. The predictions are considered acceptable although the strength is slightly underestimates under longitudinal loading, as shown in Figure 5-18 (a).

  -18 (b), while the model cannot capture the plastic softening in base metal.

Figure 5 - 18 .

 518 Figure 5-18. Predictions vs. measurements of AB T-joint under (a) longitudinal loading and (b) transverse loading As regards AB T-joint, Figure 5-19 shows a comparison between the deformed shape from the finite element model and the damaged image from test. It clearly shows that rupture is limited to the adhesive layer. There is no significant plastic strain in base metals. Therefore stress contour is plotted to compare with experiments.

Figure 5 - 19 . 3 . 3 .

 51933 Figure 5-19. Predicted deformed shape vs. test picture of AB T-joint under (a) longitudinal loading and (b) transverse loading

Figure 5 - 20 .

 520 Figure 5-20. Modelling configuration of WM T-joint

Figure 5 - 21 .

 521 Figure 5-21. Simulation vs. measurement of WB T-joint: (a) longitudinal load (b) transverse load (a) (b)

Figure 5 -

 5 Figure 5-22 shows the predicted deformed shape and damaged T-joint image under different loading. It shows that large deformations occur in the vicinity of spot weld N° 3 on vertical faying surface, as shown in Figure 5-22 (a). Under transverse loading, the plastic deformation takes place on the two horizontal faying surfaces, as depicted in Figure 5-22 (b).

Figure 5 - 22 .Chapter 6 .

 5226 Figure 5-22. Predicted deformed shape vs. test picture of WB T-joint under (a) longitudinal loading and (b) transverse loading

  zone. The materials are hardened in HAZ due to phase transformation which is evidenced by the hardness tests. As regards WB joint, the hardness distribution of spot weld is not significantly affected by the adhesive. In all the investigated WB joints, an area of burned adhesive of about 2 mm width is observed in the vicinity of spot weld. The resulting diminution of bonded area is taken into account in FE model of WB joint. SW, AB and WB joints are tested on KS2 and lap-shear specimens under tension, shear and peeling load.AB joint exhibits by far the highest strength under shear load among the 3 kinds of joints while it performs the lowest strength under tension load. SW joint exhibits the highest ultimate strength among the three joints under tension load. Generally, SW joint provides excellent energy absorption through the plastic deformation in base metal. WB joint exhibits two stages failure: adhesive failure and spot weld failure except the case of KS2 shear. WB joint can combine high strength with high energy absorption. It offers largest energy absorption under tension and peeling among the three joints. As regards pure shear (KS2 shear), WB particularly exhibits moderate ultimate strength and the lowest energy absorption among the 3 joints. With contrast to pure shear, WB exhibits the highest strength and energy absorption in lap-shear tests. In reality, the damage mode of lap-shear joint is a common case for large component.For the numerical aspects, both solid and simplified models are developed in this work. The former can predict the response of joint under given configuration for small specimen (KS2 and lap-shear) and build some reference solutions. The latter is used to analyze large components, such as whole car body, to which solid model is inadequate due to the high computational cost.Firstly, the detailed models of spot weld and adhesive are investigated separately prior to the model of weld bonding. As regards spot weld, sensitivity analysis shows that HAZ and WM property have prominent effect on damage mode and strength of spot weld. Therefore, the heterogeneity of materials in WM and HAZ are taken into account by scaling the flow stress of BM. Inverse identification can be efficiently used to identify scaling factors. CZM with TSLs was associated with Gurson model to predict damage under complex loading (tension, shear and peeling). Different sets of parameters of Gurson model were calibrated for each zone (BM, HAZ and WM) of spot welds. TSLs are employed to predict the interfacial facture by shear in which Gurson model cannot predict damage adequately. J-integral can be used to assess the damage energy of TSLs. J-integral under tension and shear loading are calculated by simulation of KS2

Finally, the models

  for spot weld and adhesive were combined to predict WB joints under different loading condition. The burned adhesive is taken into account in the model with the help of a 2 mm gap between the adhesive layer and the spot weld. The model can predict two stages damage (adhesive failure and spot weld failure) of weld bonded joint. The ultimate strength of spot weld stage was accurately predicted by Gurson model and CZM. The strength of adhesive stage is not accurately predicted by TSLs as The TSLs model has limited capacity to estimate the plasticity of SikaPower ® -498.Simplified model was developed for the analysis of large spot welded structure due to its computational efficiency. The connector parameters were calibrated by KS2 specimens under shear, tension and peeling. In simplified model, BM was modeled with shell elements and adhesive with CZM. The spot welds were represented by mesh-independent fastener thereby enabling the use of coarse mesh in BM. Simplified models accurately predicted the ultimate strength as well as displacement for KS2 specimens. Simplified models for SW, AB and WB are validated by T-joint model which can represent the B-pillar of car frame. The T-joint tests are carried out under longitudinal and transverse loading condition. SW T-joint shows larger deformation than AB T-joint under both loading cases; consequently SW T-joints provide more large energy absorption than AB T-joints. SW T-joint

  2.1. Spot welds process ................................................................................................................ 2.2. Spot welds microstructure ................................................................................................... 2.3. Spot welds failure modes ...................................................................................................

3. Adhesive bonding .................................................................................................................

3.1. Structural adhesive ............................................................................................................. 3.2. SikaPower ® -498 ..................................................................................................................

  Conclusion ............................................................................................................................ Conclusion ............................................................................................................................

1.1. Spot welds joint .................................................................................................................. 1.2. Adhesive bonded joint ........................................................................................................ 1.3. Weld bonded (hybrid) joint ................................................................................................ 2. Description of simple characterization tests ..................................................................... 2.1. KS2 test ............................................................................................................................... 2.2. Lap-shear tests .................................................................................................................... 3. Test results ............................................................................................................................

3.1. Test results of spot welded joints ........................................................................................ 3.1.1. Microstructure of spot welds with DP600 ................................................................. 3.1.2. Load bearing capacity and failure modes of spot weld joints ................................... 3.2. Test results of adhesive bonded joints ................................................................................ 3.2.1. Load bearing capacity and failure modes of adhesive bonded joints........................ 3.3. Test results of hybrid joints ................................................................................................. 3.3.1. Interaction between bonding and welding ................................................................. 3.3.2. Load bearing capacity and failure modes of hybrid joints ....................................... 3.4. Comparisons between test results of different joints ..........................................................

XIV 4. Chapter 4. Numerical aspects ..................................................................................................... 1. Constitutive Models ............................................................................................................. 1.1. Elastoplastic model with damage ....................................................................................... 1.2. Cohesive zone model ........................................................................................................... 2. Modeling strategy and results .............................................................................................

2.1. Modeling strategy and results for spot welded joint ........................................................... 2.1.1. FE model for spot weld joint...................................................................................... 2.1.2. Sensibilities analysis in spot welds simulation .......................................................... 2.1.2.1. Mass scaling .................................................................................................... 2.1.2.2. Mesh size ........................................................................................................ 2.1.2.3. Nugget diameter ............................................................................................. 2.1.2.4. Scaling factors ................................................................................................. 2.1.3. Inverse identification ................................................................................................ 2.1.4. Sensibilities analysis in spot welds simulation .......................................................... 2.1.4.1. Parameter calibration of GTN model ............................................................. 2.1.4.2. Calibration of traction separation model for spot weld .................................. 2.1.5. FE Predictions of spot welded joint models ............................................................. 2.2. Modeling strategy and results for adhesive bonded joint ................................................... 2.2.1. FE model for adhesive bonded joint .......................................................................... 2.2.2. Calibration of traction separation model for adhesive ............................................ 2.2.3. Predictions from adhesive bonded model .................................................................. 2.3. Modeling strategy and results for hybrid joint ................................................................... 2.3.1. FE model for hybrid joint .......................................................................................... 2.3.2. Predictions from hybrid joint model ..........................................................................

3. Connector model for spot weld ........................................................................................... 3.1. Mesh independent fastener ................................................................................................. 3.2. Connector element .............................................................................................................. 3.2.1. Connector components ............................................................................................. 3.2.2. Connector elasticity and plasticity ............................................................................ 3.2.3. Connector damage ..................................................................................................... XV 3.3. Validation of connector element for spot weld ................................................................... 4. Chapter 5. Case study .................................................................................................................. 1. Description of T-joint .......................................................................................................... 2. Testing of T-joints ................................................................................................................

2.1. Test results from SW T-joint ............................................................................................... 2.2. Test results from AB T-joint ................................................................................................ 2.3. Test results from WB T-joint ............................................................................................... 2.4. Cross comparison of different joint methods .....................................................................

3. FE analysis of T-joints ......................................................................................................... 3.1. Predictions from the spot welded T-joint model ................................................................ 3.2. Predictions from the adhesive bonded T-joint model ......................................................... 3.3. Predictions from the weld bonded T-joint model ...............................................................

Chapter 2. Bibliography 1. Dual phase steel

	element associated with mesh independent fastener permit to simulate large component by saving
	computational time. Cohesive zone elements are also used to predict the adhesive failure. The
	material parameters are calibrated by DCB and ENF specimens, corresponding to Mode-I and
	Mode-II fracture. These two models are combined together to simulate hybrid joint. Advanced high strength steels (AHSS) are widely used in automobile industry for safety and
	Finally, the model was validated against T-joint benchmark that is representative of B-pillar of light weight body design [7]. Dual phase (DP) steels are referred to as advanced high strength
	car frame. The predictions from the models are in good accordance with the test results. The steel (AHSS). The microstructure of DP steels is composed of soft ferrite matrix and hard
	model developed is intended to be used together with large industrial applications such as full car martensite with small amounts of bainite, pearlite, or retained austenite. This type of
	bodies crash-test simulations. microstructure allows DP steels achieving high strength, continuous yield behavior, high work-
	This document is organized in 6 chapters. In Chapter 1, the backgrounds and the motivations hardening rate and superior ductility. Moreover, DP steel shows strong bake hardening effect
	of this work are presented. Chapter 2 is the chapter for bibliographies, in which dual phase steel, which is highly advantageous for car body bake process [8-11]. DP steel properties are
	spot welds, adhesive and weld bonding are introduced. Chapter 3 is devoted to introduce the significantly influenced not only by grain size but also by martensite phase volume fraction,
	specimens of KS2, peel and lap-shear. The force-displacement measurements and the results are distribution, morphology and carbon content [8] [12-13].
	discussed for each test. Chapter 4 introduces the numerical modeling, the material parameter
	calibration and the finite element analysis of simple tests. The obtained results are discussed. In
	Chapter 5, the simplified model is validated by different T-joint under longitudinal and transverse
	loading cases. Chapter 6 summarizes the main conclusions of this thesis and also present future
	work to be continued following this work.
	The modeling of spot weld behavior is carried out on two different scales with a solid finite
	element model and a simplified shell connector model. In the solid model, Gurson model is used
	to predict ductile fracture (pull-out fracture) of spot weld, while cohesive zone model is adopted
	for the simulation of interfacial fracture in the interface as Gurson model cannot predict voids
	coalescence under nearly zero stress triaxility. The parameters of cohesive zone model are
	calibrated using J-integral at notch tip of spot weld nugget. In the simplified model, connector

Table 1 -1. Chemical composition of DP600 steel

 1

	Elements	C	Si	Mn	Cr	Al	S	P
	Content in Weight %	0.08	0.5	1.4	0.42	0.42	0.008	0.085
	Table 1-1 shows typical chemical composition of DP600 steel. Adequate carbon weight
	fraction (<0.1%) can provide adequate martensite fraction (about 20%) without diminishing the
	weldability [8].

Table 3 -

 3

	Welding Current In	Welding Force	Squeeze Time	Welding Time	Holding Time
	Scale Unit	(kN)	(ms)	(ms)	(ms)
	7.4	5	300	140	160

1. Spot welding parameters

Table 3 -2. Welding parameters in weld bonding Welding Current In Scale Unit Welding Force

 3

			Squeeze Time	Welding Time	Holding Time
		(kN)	(ms)	(ms)	(ms)
	7.6	5	500	140	160

Table 4 - 1 .

 41 Parameters of Gurson model for simulation 2.1.4.2. Calibration of traction separation model for spot weld Cavalli et al. introduced the cohesive zone model to predict the interfacial and pull-out fracture of spot weld in aluminum alloy [90]. Then, Zhou et al. used the same model to simulate ultrasonic spot weld on same metal [91]. These two authors calibrated cohesive parameters with the help of experiments under different loading modes. Dancette et al. predicted interfacialfracture of spot weld using cohesive element on the faying surface[START_REF] Dancette | HAZ microsructure and local mechanical properties of high strength steel resistance spot welds[END_REF]. For casting aluminum, spot weld keep the same materials properties, and parameters can be calibrated on base metal. For DP steel, fracture mechanics is employed to calculate the energies to create the new damage

surface. J-integral, proposed by James Rice in 1968, is used to calculate energy release rate in fracture surface by means of path contour integral around the crack

[START_REF] Rice | A path independent integral and the approximate analysis of strain concentration by notches and cracks[END_REF]

. Rice also showed that if

Table 4 - 2 .

 42 Cohesive parameters for interfacial fracture prediction of spot weld

	Stiffness	Mode I	Mode II

Table 4 - 5 .

 45 CPU time for KS2 analysis comparison between solid model and connector model

Minimum element length Initial time increment Total CPU time

	Solid model	0.5 mm	1.36966E-09 s	1.23s
	Simplified model	2 mm	1.507481E-07s	0.34s
	4. Conclusion
	The Gurson model and CZM are used to predict spot weld rupture under different loading
	conditions. Additionally, simplified model (shell+connector) is developed for large spot welded
	structure simulations because of their computational efficiency. The adhesive behavior is

Table 5 - 1 .

 51 Stiffness of connector for translation and rotationAs regards WB T-joint, it was observed that spot welds on horizontal surface exhibit pull-out fracture with fracture initiation in HAZ/BM rather than in HAZ/WM as in SW T-joint. The ultimate strength in former is higher than latter as discussed in section 3.3.2 in Chapter 3. Hence, the force for damage initiation in pure tension is scaled by 22.7% for WB T-joint simulation, as shown in Table5-2.

	E 1 (N/mm) E 2 (N/mm) E 3 (N/mm)	E 4 (N•mm/rad)	E 5 (N•mm /rad) E 6 (N•mm /rad)
	3.47e+06	1.33e+06	1.33e+06	Rigid	Rigid	Rigid

Table 5 - 2 .

 52 Parameters of connector for damage initiation and evolution of spot welds in WB joint

	F n (kN)	F s (kN)	M n (N•m)	M t (N•m)	a 1	a 1	a 1	a 1	r inf (mm)
	14.7	20.7	16500	10 6	2	2	2	2	2.9
	U n (mm)	U s (mm)	U b (Rad)	U t (Rad)	b 1	b 2	b 3	b 4	α
	5	1	2	10 6	2	2	2	2	3.5

Acknowledgements

I would like to thank my advisor Mohamed Rachik, for his encouragement, instruction, and understanding. His broad level of knowledge, expertise, and interests are unmatched. He always

monotonic loading is assumed then the J-integral could be used to compute the energy release rate of plastic materials. The J-integral calculation is implemented in Abaqus. Figure 4-15 shows the model used to calculate J-integral. Here, we suppose that the crack tip is embedded into WM guarantying isotropic material surrounding the tip. Very fine meshes are required around the crack-tip.

Figure 4-15. FEM model for the computation of J-integral

The simulation is carried out under shear and tension loading, as shown in Figure 4-16. For each loading condition, 5 contours of J-integral are outputted. The one close to crack tip is neglected due to plastic deformation. The average value of the rest is used to calibrate energy release rate for cohesive zone model.

In Figure 4-16, the vertical black dash lines represent the maximum load from experiment; the corresponding J-integral at notch tip is read following the corresponding horizontal dash line.

The cohesive zone model parameters for interfacial damage of spot welds are summarized in Then the T-joints are analyzed using finite element models. The predictions from the models are compared with measurements for validation purpose.

Description of T-joint specimens

The so-called T-joints are widely used to assess the behaviors of different joints [START_REF] Sommer | Fracture modeling of spot welds and rivets for crash simulation[END_REF] [104] in However, the extra CZM model will bring additional parameters to calibrate. Therefore, extended

Gurson model with shear damage prediction could be developed to analyse spot weld under pure shear loading.

Adhesive behaviour is temperature-, thickness-and strain rate dependent. The models taking all these effects into account can be implemented to predict the performance of adhesive under more complicated condition.

The CZM model for adhesive has bi-linear shape which can capture the maximum force at damage. However, under shear or lap-shear, the predicted response cannot match with the actual data from experiments. Different CZM models can be found in the literature. It is interesting to implement them to improve the prediction for the adhesive behaviour under shear.

All the models in this work are used for quasi-static loading condition. However, constitutive models with strain rate dependant are required for car crash simulation. As regard simplified models, the model taking strain-rate dependency into consideration is also an interesting issue.

Moreover, simplified models with prediction of torsion damage could be developed because some spot welds in T-joint can sustain torsion force under certain loading conditions. It would also be necessary to develop adequate test to calibrate the model parameters for torsion.