Li Ma

Frédéric Wiame
email: frederic.wiame@chimie-paristech.fr

Vincent Maurice
email: vincent.maurice@chimie-paristech.fr

Philippe Marcus
email: philippe.marcus@chimie-paristech.fr

Stainless Steel Surface Structure and Initial Oxidation at Nanometric and Atomic Scales

Keywords: Alloys, Corrosion protection, Nanostructures, Oxidation, Scanning probe microscopy, Surface structure

HAL is

Stainless steels (SS) constitute one of the most technologically important class of alloys. Their durable use in our industrial society relies on the self-protection against corrosion brought by a surface barrier oxide film, the passive film, only a few nanometers thick and isolating the metallic substrate from the aggressive environment. However, the local failure of the corrosion protection can lead, in the absence of self-healing of the passive film, to localized corrosion with costly consequences and environment-and even health-jeopardizing risks.

Surface analytical studies of passivity of various stainless steels at macroscopic level have shown that the passive film is markedly enriched in Cr(III) oxide/hydroxide species, which is the key for the stability of the corrosion protection [START_REF] Macdonald | Passivity -The key to our metals-based civilization[END_REF][START_REF] Strehblow | Passivity of metals[END_REF][START_REF] Marcus | Oxide Passive Films and Corrosion Protection[END_REF][START_REF] Olsson | Passive films on stainless steels -chemistry, structure and growth[END_REF][START_REF] Strehblow | Passivity of metals studied by surface analytical methods, a review[END_REF][START_REF] Maurice | Progress in corrosion science at atomic and nanometric scales[END_REF][START_REF] Maurice | Current developments of nanoscale insight into corrosion protection by passive oxide films[END_REF]. However, the pre-passivation mechanism by which the surface oxide film initially grows may produce nanoscale chemical and structural weak points at the origin of the subsequent loss of stability [START_REF] Maurice | Progress in corrosion science at atomic and nanometric scales[END_REF][START_REF] Maurice | Current developments of nanoscale insight into corrosion protection by passive oxide films[END_REF][START_REF] Massoud | Nanostructure and local properties of oxide layers grown on stainless steel in simulated pressurized water reactor environment[END_REF][START_REF] Maurice | Effects of molybdenum on the composition and nanoscale morphology of passivated austenitic stainless steel surfaces[END_REF]. Therefore, the development of the comprehensive insight of the stability of the corrosion protection requires not only to better understand at small length and time scales the surface reactivity in the early oxidation stages, but also to characterize in detail the structure of the surface in the metallic state prior to the formation of the surface oxide.

Ultra-high vacuum (UHV) conditions provide the environmental control necessary to investigate surface structure and oxide growth mechanisms, as shown by previous studies [START_REF] Lince | Interaction of O2 with the Fe0.84Cr0.16(001) surface studied by photoelectron spectroscopy[END_REF][START_REF] Lin | A consistent method for quantitative XPS peak analysis of thin oxide films on clean polycrystalline iron surfaces[END_REF][START_REF] Roosendaal | The oxidation state of Fe(100) after initial oxidation in O2[END_REF][START_REF] Grosvenor | Examination of the oxidation of iron by oxygen using X-ray photoelectron spectroscopy and QUASES[END_REF][START_REF] Lampimäki | Morphology and composition of nanoscale surface oxides on Fe-20Cr-18Ni(111) austenitic stainless steel[END_REF][START_REF] Davies | The oxidation of Fe(111)[END_REF][START_REF] Ali-Löytty | Infuence of CrN surface compound on the initial stages of high temperature oxidation of ferritic stainless steel[END_REF]. Some works investigated stainless steel single crystals under UHV [START_REF] Maurice | X-ray photoelectron spectroscopy and scanning tunneling microscopy study of passive films formed on (100) Fe-18Cr-13Ni single-crystal surfaces[END_REF][START_REF] Jussila | Inuence of minor alloying elements on the initial stages of oxidation of austenitic stainless steel materials[END_REF], but most studies adressed the chemical composition and structure at macroscopic level by non-local techniques. Few scanning tunneling microscopy (STM) experiments have been carried out on ferritic stainless steel to characterize at the nanometric scale the single-crystal surface upon annealing [START_REF] Yuhara | The role of nitrogen in the preferential chromium segregation on the ferritic stainless steel (111) surface[END_REF][START_REF] Fujiyoshi | Segregation and morphology on the surface of ferritic stainless steel (001)[END_REF] but direct observation at atomic resolution has been reported neither on ferritic nor austenitic stainless steel surfaces.

Here, we discuss the very first characterization of the structure of the oxide-free stainless steel surface at the nanometric and atomic scales, and the very first modifications related to early reaction with oxygen. We applied surface analysis at high resolution using STM under UHV conditions on a (100)-oriented Fe-18Cr-13Ni single crystal (see experimental details in Supplementary Information). This material is a good model for the most common AISI 304 austenitic stainless steel.

Figure 1 shows the surface structure of our model Fe-18Cr-13Ni stainless steel surface as repeatedly observed by STM. At the nanometric scale, it is characterized by terraces of nominal (100) orientation alternating with bunches of steps of monoatomic height hereafter referred to as multi-steps (Figure 1(a)). The terrace width is about 10-20 nm. The total height of the multi-steps is of about 3-6 atomic planes (0.54-1.07 nm) (Figure 1(b)), in agreement with the reticular distance of 0.18 nm calculated from the bulk lattice parameter of the fcc lattice (0.359 nm). The residual misorientation, at the origin of this terrace-step topography, is 2.5±0.2° with respect to the (100) plane. On the terraces, parallel lines constituted of dark spots are mostly aligned along the [001] direction (Figure 1(a)), with an average periodicity of about 7.6 nm. These line features were reproducibly observed after sample preparation by Ar + ion sputtering followed by annealing under UHV. They always appeared lower than the terraces independently of the imaging bias conditions, meaning that they correspond to actual topographic depressions. Their apparent depth is about 50 pm (Figure 1(c)), and could slightly vary depending on the tip used for imaging. An electronic effect may contribute to the difference of apparent height if, inside the vacancy rows, the terminating structure is bulk-like and unreconstructed, i.e. (1×1), as proposed below. The observed lattice is periodic and forms a square structure with a lattice parameter of 0.359 nm. This structure of the topmost plane, confirmed by low energy electron diffraction (LEED), is reconstructed and denoted (√2×√2)R45° with respect to the unreconstructed structure, denoted (1×1), of the underlying (100) planes (lattice parameter of 0.254 nm). The apparent height range between the atomic protrusions is about 20 pm (Figure 1(e)), and was observed to slightly vary with tunneling conditions and tip structure. The atomic protrusions, appearing individually brighter or darker, are randomly distributed on the square lattice but some larger areas including several protrusions also present contrast difference. These variations of apparent height of the atomic protrusions are attributed to the chemical contrast between the Fe, Cr and Ni atoms present in the topmost reconstructed plane. This kind of chemical contrast has been observed by STM on various alloys [START_REF] Schmid | Direct observation of surface chemical order by scanning tunneling microscopy[END_REF][START_REF] Wouda | Chemically resolved STM on a PtRh(100) surface[END_REF][START_REF] Gauthier | Chemical ordering and reconstruction of Pt25Co75(100): an LEED/STM study[END_REF][START_REF] Hebenstreit | Pt25Rh75(111), (110), and (100) studied by scanning tunnelling microscopy with chemical contrast[END_REF][START_REF] Wiame | Brass surface nanochemistry: The role of alloying Cu with Zn[END_REF]. In the present case, it seems quite difficult to obtain a simple and clear identification of the different elements at the surface due to the rather small difference of apparent height and to the complexity of sample composition. A systematic study as a function of tunneling bias may help in identifying specific surface states of the different elements, as previously done for Fe and Cr [START_REF] Davies | Atomic-Scale Observations of Alloying at the Cr-Fe(001) Interface[END_REF][START_REF] Choi | Surface alloy formation of Fe on Cr(100) studied by scanning tunneling microscopy[END_REF]. It was attempted in the present work but uncontrolled changes of the imaging tip impacted the data, which supports the view of the variations of contrast being dominated by electronic effects. Future density functional theory (DFT) simulations, as done for other alloys [START_REF] Ondracek | Chemical ordering and composition fluctuations at the (001) surface of the Fe64Ni36 invar alloy[END_REF][START_REF] Wiame | Zn effect on STM imaging of brass surfaces[END_REF] may also help us in the interpretation of the chemical contrast. It cannot be excluded that slight variations of the actual topographic height also contribute to the observed contrast. The periodicity of these vacancy rows can be explained thanks to the elasticity theory [START_REF] Ibach | Physics of Surfaces and Interfaces[END_REF][START_REF] Wiame | Strategies for the growth of large-scale self-organized structures[END_REF]. Indeed, any metallic surface is subject to a tensile stress caused by the electron density rearrangement induced by the discontinuity of the crystal structure. In order to minimize the surface total energy, which is the sum of the elastic energy due to surface stress and of the vacancy rows creation energy, the vacancy rows self-organize by forming a periodic pattern in the [010] direction (i.e. perpendicular to [001]). † The small width of the terraces in the [001] direction may explain the low amount of vacancy lines in the perpendicular [001] direction due to the limited stress in that direction. Combining all information above, the structural model shown in Figure 2 is proposed. The topmost plane is reconstructed with an atomic density half that of the underlying (100) planes.

It adopts a (√2×√2)R45° superstructure and contains all three alloying elements. The vacancy line consists of two rows of missing atoms as the result of surface self-organization to minimize the mechanical stress. The (1×1) structure of the underlying plane is exposed in the vacancy lines. To the best of our knowledge, this is the first direct observation of the surface structure of stainless steel at the atomic scale and the first to reveal a periodic distribution of vacancy lines on a surface.

Figure 3 shows the terrace-step structure in more details and the modifications induced by initial oxidation. On the oxide-free surface (Figure 3(a)), another structure is present in the terrace regions adjacent to the lower and upper edges of the multi-steps. This edge structure (delimited in Figure 3(a)) is continuous along the multi-steps and has a width about of 1.0-1.2 † F. Wiame, V. Ruffine, L. Ma, V. Maurice, P. Marcus, Self-ordering of vacancy rows at the surface of stainless steel, to be published.

nm. It appears lower than the rest of the terrace with a relative height difference depending on the tunneling conditions. As pointed by arrows in Figure 3(a), it contains vacancies that can locally follow the step edges and are no more aligned along the [001] direction. This modified terrace structure near the step edges is attributed to the presence of two-dimensional (2D) chromium nitride surface species resulting from co-segregation of chromium and nitrogen and systematically occurring during the annealing stage of surface preparation, as evidenced by in situ XPS upon annealing under UHV [START_REF] Ma | New insight on early oxidation stages of austenitic stainless steel from in situ XPS analysis on single-crystalline Fe-18Cr-13Ni[END_REF] and verified after preparing tens of surface samples in the same equipment. Indeed, the chemical contrast indicates a different composition of this edge structure and the very low sub-monolayer amount of chromium nitride estimated by XPS is consistent with this interpretation. It is thought that this edge structure contributes to relieve the stress at the origin of the self-organization of the vacancy lines, precluding their alignment to reach the step edge.

Figure 3(b) shows the surface after dosing 1 L of O2 at 250°C. According to XPS [START_REF] Ma | New insight on early oxidation stages of austenitic stainless steel from in situ XPS analysis on single-crystalline Fe-18Cr-13Ni[END_REF], Cr(III) oxide is the main oxide component formed in this very early reaction stage and 2D chromium nitride is partially converted into chromium oxide. The terraces and multi-steps are still visible, as well as the reconstruction of the topmost lattice and the vacancy lines on the terraces. However, new square structures are formed on the multi-steps (one is marked) with sides aligned along the <011> directions. The height of these new structures is 0.19 ± 0.01 nm which corresponds to one atomic step of the alloy substrate, indicating that each atomic step edge of the multi-steps has reacted. These square structures are assigned to nuclei of Cr(III) oxide observed to predominantly formed by XPS. Fe 2+/3+ cations, also observed by XPS, may be incorporated in the nuclei. CrN nitride is excluded since converted after initial oxidation.

The <011> directions correspond to the close-packed directions of the unreconstructed (100) surface, indicating an epitaxial relationship between the oxide nuclei and the metallic surface.

On the terraces (Figure 3(c)), one notices that more vacancies are present and form new patterns adjacent to the initial vacancy lines. New vacancies also appear and accumulate in the terrace borders adjacent to the step edges, in agreement with the conversion of 2D chromium nitride into chromium oxide. This injection of vacancies in the terraces can be thus seen as the evidence of Cr atoms being "pumped" in the topmost plane, both in the regions near the step edges because of their vicinity and at more remote distances, to feed the formation of the chromium oxide nuclei after migration to the step edges.

This study unravels the surface structure of austenitic stainless steel at nanometric and atomic scales and shows a rather complex structure even on the model (100)-oriented Fe-18Cr-13Ni single crystalline surface. The slight misorientation causes the topography to alternate terraces with atomic multi-steps (step bunching) after annealing. On the terraces, the topmost plane is reconstructed with an atomic density half that of the planes below, contains all three alloying elements and adopts a (√2×√2)R45° superstructure. A novel finding for metal and alloy surfaces is the presence, after annealing, of self-organized nanostructures consisting of vacancy lines formed by two adjacent rows of missing atoms, aligned along the close-packed <001> directions of the reconstructed surface lattice. The measured average period of selforganization, related to relaxation of the surface stress, is 7.6 nm. Early reactivity is observed at the defect sites of reduced atomic coordination (steps) and affect the adjacent terrace regions. Cr(III) oxide nucleates at step edges and consumes the Cr atoms locally present but also "pumps" more remote Cr atoms from the topmost plane. The Cr vacancies injected in the terraces cause a local depletion of chromium.

The local nanostructures formed at the stainless steel surface, directly observed in this work, are rich and complex. As precursors of the surface reactivity, they are foreseen to play a significant role in the subsequent evolution of the surface interacting with its environment, impacting the mechanism of chromium enrichment essential to the stability of the surface oxide film that protects the surface in a chemically aggressive environment. surface preparation included mechanical polishing followed by electrochemical polishing to remove the cold-work layer and was then annealed at 900°C in a flow of ultra-pure hydrogen at atmospheric pressure, as described elsewhere [START_REF] Maurice | X-ray photoelectron spectroscopy and scanning tunneling microscopy study of passive films formed on (100) Fe-18Cr-13Ni single-crystal surfaces[END_REF]. After introduction in the UHV system, the sample surface was cleaned in situ by repeated cycles of Ar + ion sputtering (1 kV, 10 µA, 10 minutes) and annealing (700°C, 10 minutes) in the preparation chamber. Surface cleanness, including the absence of oxide, and structure, reconstructed on the as-prepared oxide-free surface, were controlled by XPS and LEED, respectively. LEED was used to ascertain the crystallographic directions of the crystal. Oxygen gas (O2) dosing was controlled at a pressure below 10 -8 mbar in order to achieve high precision low exposure. Early oxidation was studied for 1 L exposure (1 L = 1.33×10 -6 mbar•s) at 250°C, achieved by exposing the sample in the range 1-3×10 -9 mbar for 10 minutes.

Figure captions

STM experiments were performed with a VT STM XA. STM was calibrated from atomic resolution images on a clean Cu(111) reference surface and the tungsten tips were treated by annealing, voltage pulses and high voltage scanning. The STM measurements were carried out at room temperature. Topography leveling was performed to enhance contrast in the terraces, first by correcting the terraces from their average slope and then by subtracting the height differences between them

Figure 1 (

 1 Figure 1(d) shows an atomic resolution STM image on a terrace between the periodic lines.

Figure 1 (

 1 Figure 1(f) shows an atomic resolution image of the structure in the area marked in Figure

Figure 1

 1 Figure 1 Surface structure at the nanometric and atomic scales of the (100)-oriented oxide-free Fe-18Cr-13Ni surface: (a) STM image of the terrace-step topography (50 nm × 50 nm, I = 3.5 nA, V = -0.5 V); (b) height profile of terraces and multi-steps along the line in (a); (c) typical height variation on the terraces across periodic parallel lines (perpendicular to [001] direction); (d) atomic resolution STM image on a terrace (the unit cell is highlighted) (3.6 nm×3.6 nm, I = 4.0 nA, V = -0.4 V); (e) height profile along the line in (d); (f) atomic resolution STM image of the highlighted region in (a) (8 nm × 8 nm, I = 4.0 nA, V = 0.5 V).

Figure 2

 2 Figure 2 Atomic structure of the (100)-oriented Fe-18Cr-13Ni surface with a reconstructed topmost plane including a double vacancy row: (a) STM image (4.3 nm × 1.8 nm, I = 4.0 nA, V = -0.5 V) ; (b) top view atomic model of (a) with unit cells of reconstructed and bulk-terminated planes marked; (c) average height profile of region (a); (d) side view of atomic model.

Figure 3

 3 Figure 3 STM images of the terrace-step topography of the (100)-oriented Fe-18Cr-13Ni surface before (a) and after (b,c) early gaseous oxidation at 250°C: (a) terrace structures adjacent to the lower and upper edges of the multi-steps are delimited by dotted and plain lines, respectively, and vacancies therein pointed (levelled image, I = 0.5 nA, V = -0.5 V); (b) Cr(III) oxide nuclei formed at each edge of the multi-steps are pointed (I = 0.2 nA, V = -0.7 V); (c) new vacancies injected in the terraces and forming new lines or patterns are pointed and circled, respectively (levelled image, I = 0.2 nA, V = -0.7 V).

Figure 1 13 Figure 2 14

 1132 Figure 1

Figure 3

 3 Figure 3

Acknowledgments

This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (ERC Advanced Grant No.

741123, Corrosion Initiation Mechanisms at the Nanometric and Atomic Scales : CIMNAS).

Région Île-de-France is acknowledged for partial funding of the STM equipment. China Scholarship Council (CSC) is acknowledged for the scholarship to the first author (No.

201606380129).

Acknowledgments

This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (ERC Advanced Grant No.

741123, Corrosion Initiation Mechanisms at the Nanometric and Atomic Scales : CIMNAS).

Région Île-de-France is acknowledged for partial funding of the STM equipment. China

Material and methods

The experiments were performed in a multi-chamber UHV system from Scienta Omicron including a preparation chamber and two analysis chambers for XPS (X-ray Photoelectron Spectroscopy) and STM, maintained at a base pressure below 10 -10 mbar. The preparation chamber is equipped with cold cathode ion gun for sputtering, resistive heating filaments for annealing and LEED (Low Energy Electron Diffraction) for surface periodicity characterization.

The sample was heated from back side and the temperature was controlled through a thermocouple attached on the manipulator in contact with the sample. A (100)-oriented Fe-18Cr-13Ni single crystal with 99.9999% purity was used. The sample was mechanically and electrochemically polished before introduction in the UHV system. The initial ‡ Corresponding authors: F.W. (email: frederic.wiame@chimie-paristech.fr); V.M. (email: vincent.maurice@chimieparistech.fr); P.M. (email: philippe.marcus@chimie-paristech.fr).

Scholarship Council (CSC) is acknowledged for the scholarship to the first author (No. 201606380129).


Benaïssa Malek

Catherine Mabru

Michel Chaussumier

Fatigue behavior of 2618-T851 aluminum alloy under uniaxial and multiaxial loadings

Keywords:

AA2618 aeronautical aluminum alloy has been largely used in the past, especially in well-known Concorde aircraft, developed during sixties decade. In more recent aircraft, this alloy has been largely replaced by others such as 7075 which present greater fatigue resistance. Forgotten for a time, AA2618 comes back in new aircrafts for structural parts submitted to fatigue loading at high temperature because of only a slight decrease of fatigue resistance of this alloy compared to room temperature fatigue resistance. In this paper, a complete fatigue characterization of 2618-T851 aluminum alloy is presented: fatigue tests under uniaxial tensile or torsion cyclic loadings, with mean tensile or shear stress have been realized; fatigue tests under combined tensile-torsion, in or out-of-phase have also been conducted as well as some combined tensile-torsion-internal pressure fatigue tests. All these tests covered 10 4 -10 7 cycles range. At last, Crossland multiaxial fatigue criterion has been used and extended to median fatigue life domain to analyze these results.

Introduction

Derived from high strength aluminum alloys developed before first world war by Royce Rolls (RR serie 1929), aluminum copper 2618 T851 alloy (Hiduminium RR58; AU2GN) has been further developed by High Duty Alloys Ltd for aircraft gas turbine compressor engines and has been widely used in Concorde aircraft structure (fuselage skin, outer skin of engines, wings) because of its high resistance stress level, its low density and its high resistance at high temperature (130 °C) [START_REF] Doyle | The development of Hiduminium-RR58 aluminium alloy: the background to the choice of the main structural material for Concorde[END_REF][START_REF] Williams | Progress in structural materials for aerospace systems[END_REF]. This aluminum alloy is an Al Cu Mg Fe Ni alloy; Fe and Ni atomic elements addition are responsible of this high temperature re sistance as they form coarse intermetallic particles (Al 9 FeNi) providing microstructural stability at high temperature. Nowadays this alloy has been replaced by aluminum alloys such as 2214 or 7075. However, 2618 aluminum alloy is still used in industrial applications that involve high strength to weight ratio with high temperature exposures such as compressor wheels of exhaust turbochargers or automotive engine cy linder heads or aeronautical applications such as components of aircraft engines. This alloy can be also employed for application where short time exposure to temperature up to 300 °C is involved. Some research works have been recurrently realized in the four last decades con cerning this particular alloy; most of these research studies concern microstructural characterization and deal with the condition of for mation of intermetallic particles during heat treatment [3 8]. AA2618 T6 microstructure generally consists of mixed recrystallized and non recrystallized solid solution Al α Cu Mg grains, a slight proportion of stable S phase Al 2 CuMg fine coherent plate like intermetallic pre cipitates homogeneously distributed in the matrix, and, in larger pro portion (99%), of stable Al 9 FeNi intermetallic particles distributed in homogeneously in Al α grains as wells as in grains boundaries. S phase coarse particles can rarely appear in grain boundaries; in that case precipitates free zone (PFZ) are observed along grain boundaries. S phase particles are identified to mainly contribute to strengthening; it has been also shown that metastable S phase needles size was sensitive to deformation before ageing treatment; S phase needles are smaller in deformation ageing state, and consequently, dispersion strengthening is more efficient. Otherwise, hardness peak during ageing treatment is reached faster in DAT state than in T6 state. Moreover, Al 9 FeNi are identified to contribute to grain size control at elevated temperature and dispersion hardening as effective barrier for dislocation movement. Other type of intermetallic particles (Al 2 Cu, Mg 2 Si, AlCuNi, Al 7 Cu 2 Fe) can be found also. As well as for all 2xxx, 6xxx or 7xxx aluminum al loys, monotonic mechanical properties (yield stress, ultimate strength and elongation) clearly depend on heat treatment conditions, especially on aging conditions even if the conditions of solution treatment have also unneglectable influence as it controls the dissolution of most of intermetallic particles in the matrix, except Al 9 FeNi particles.

Since the first mechanical behavior investigation [9 11], AA2618

⁎ Corresponding author.

E-mail address: michel.chaussumier@insa-toulouse.fr (M. Chaussumier).

https://doi.org/10.1016/j.ijfatigue.2019.105322

analysis pointed out the nature of such particles: Al 9 FeNi (Fig. 6).

Whatever the stress level is and the surface roughness is, fatigue crack initiate systematically on such kind of particles (Fig. 7). These particles act as stress concentrators because of their me chanical properties. This phenomenon is well known for aluminium alloys [START_REF] Shahzad | Effect of sealed anodic film on fatigue performance of 2214-T6 aluminium alloy[END_REF][START_REF] Chaussumier | A predictive fatigue life model for anodized 7050 aluminium alloy[END_REF].

In the case of stress ratio Rσ = -2 (Fig. 8), no more sensitivity can be considered: at 10 6 cycles, the stress decrease is only of 10 MPa, which is lower than observed scatter of the data, which is however greater than the dispersion observed for stress ratio of 0.1. Crack in itiation mechanisms are similar to those observed for a load ratio of 0.1 with Al 9 FeNi intermetallic particles as initiation site.

Under uniaxial torsion loadings, no surface roughness sensitivity is observed (Fig. 9); this can be explained by the fact that surface shear stress is aligned with machining (turning) grooves.

Previous studies on aeronautical aluminium alloys pointed out some influence of surface roughness [START_REF] Shahzad | Influence of surface treatments on fatigue life of Al 7010 alloy[END_REF][START_REF] Shahzad | Effect of sealed anodic film on fatigue performance of 2214-T6 aluminium alloy[END_REF] so that fatigue life prediction under uniaxial tensile loading based on stress concentration coefficient induced by surface roughness gave good results [START_REF] Chaussumier | A predictive fatigue life model for anodized 7050 aluminium alloy[END_REF]. These alloys were characterized by an homogeneous repartition of fine strengthening in termetallic particles which were also the initiation site of fatigue cracks. For these alloys, the influence of surface roughness was explained by stress concentration whose intensity was considered of same level than stress concentration due to intermetallic particles so that these two sources could interact. At high stress level, influence of surface roughness disappears because of the larger plastic zone around initia tion site so that stress concentration due to surface roughness does not interact with particles any longer. For the present alloy, such fine mi crostructure is not observed; on the contrary, as it can be seen on Fig. 1, intermetallic particles are so coarse that it becomes obvious that, whatever the stress level is, stress concentration due to these particles is predominant compared to stress concentration due to surface rough ness.

Influence of stress ratio

Influence of tensile and torsion stress ratio on fatigue lifetime has been investigated for a given surface roughness of 0.8 µm. Concerning stress ratio effect for uniaxial tensile cyclic loadings (Fig. 10); the re sults are in agreement with expected results in this fatigue regime: the deleterious influence of positive tensile stress on fatigue resistance can be observed. This experimental result has been largely presented through literature and most fatigue criteria take into account some mechanical quantity in order to reproduce this influence.

Under torsion cyclic loadings, sensitivity to shear mean stress is also observed even if maximum shear stress is less than shear yield stress (Fig. 11). Same influence has been observed by Zhang [START_REF] Zhang | Effect of mean shear stress on torsion fatigue failure behavior of 2A12-T4 aluminium alloy[END_REF] for Al2A12 T4 and Gates for Al 2024 T3 [START_REF] Gates | On the consideration of normal and shear stress interaction in multiaxial fatigue damage analysis[END_REF]. It clearly appears that this influence decreases for low shear stress amplitude. This is why most of the multiaxial fatigue criteria, developed for fatigue limit, do not take into account this influence. This obviously must be considered carefully experimental value corresponding to the same number of cycles to failure, or an another way, the corresponding fatigue life prediction is higher than experimental one so that prediction is not conservative. One can observe a large scatter of predictions around the mean β curve. In particular, Crossland criterion is not able to reproduce the effect of shear mean stress (red triangular plots in Fig. 15). However, one can remark that some results for combined tensile torsion loadings are above the mean β curve, which means conservative fatigue life predictions. For combined tensile and/or torsion and internal pressure, results are quite all below the underlying dashed β curve which cor responds to thirds of the mean lifetime (Fig. 16); for such loadings, Crossland criterion is not able to give any good fatigue life predictions.

Conclusions

An exhaustive fatigue study of 2618 T851 aluminum alloy has been realized; 66 fatigue tests have been conducted under various kinds of loading: uniaxial tensile loading for 2 stress ratio (-2 and 0.1); tor sional loading under two shear stress ratio ( 1 and 0.1); combined tensile torsion loadings under in or out of phase conditions and dif ferent stress ratio (-1 and 0.1); combined tensile torsion internal pressure on tubular specimens. Effect of surface roughness induced by machining on uniaxial fatigue behavior has also been investigated. It has been observed that:

No significant influence of machined surface roughness on fatigue resistance has been clearly observed for tensile loadings regardless of the stress ratio; for torsion loadings, it is obvious that there is no influence. Fatigue behavior resistance is sensitive to mean tensile stress as well introduced.

It seems obvious that the specific microstructure of 2618 aluminum alloy, characterized by a very high density of Al 9 FeNi coarse particles disseminated in grains highly influence the fatigue behavior. Compared to 2214 or 7050 aluminium alloys, such microstructure annihilates surface roughness effect. Perhaps 2618 microstructure could also ex plain the great influence of mean shear stress on fatigue resistance; this must be investigated more precisely by looking carefully at the me chanisms involved in the fatigue damage. Because of this particular sensitivity, any multiaxial fatigue criteria which does not include some mechanical terms relative to mean shear stress, such as Crossland used in this paper, will not be able to provide good fatigue life predictions for loading conditions including mean shear stress. Research work on a new criterion, based on Macha Lagoda bi axial fatigue criterion, in cluding shear mean stress, is currently in progress.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Geometry of specimens for uniaxial and tension-torsion fatigue test.

Fig. 4 .

 4 Fig. 4. Cylindrical coordinates system used to express internal pressure loading.

Fig. 9 .

 9 Fig. 9. Fatigue results in torsion cyclic loading -Stress ratio Rτ = 1 -Effect of surface roughness.

Fig. 10 .

 10 Fig. 10. Fatigue results in tensile cyclic loading -Ra = 0.8 µm -Effect of stress ratio Rs.

Fig. 11 .

 11 Fig. 11. Fatigue results in torsion cyclic loading -Ra = 0.8 µm -Effect of stress ratio Rs.

Fig. 12 .

 12 Fig. 12. Fatigue results for tensile-torsion cyclic loading -Effect of in or out of phase for two values of biaxial stress ratio λ.

Fig. 13 .

 13 Fig.[START_REF] Khalil | Influence of microstructure on the quasistatic and low cycle fatigue behavior of an AA2618 aluminium alloy[END_REF]. Fatigue results in tensile-torsion cyclic loading -Effect of in or out of phase with mean normal stress or mean shear stress.

Fig. 14 .

 14 Fig. 14. Crossland criterion characterization for 2618-T851 aluminum alloy.

Fig. 15 .

 15 Fig. 15. Results for combined tensile-torsion loadings (in and out of phase) for Al-2618-T851 in Crossland′s diagram.

Fig. 16 .

 16 Fig. 16. Results for combined tensile-torsion-internal pressure loadings for Al-2618-T851 in Crossland diagram.

Table 2

 2 Monotonic characteristics of 2618-T851 aluminum alloy.

	Young modulus E (GPa) Ultimate tensile stress	Tensile yield strength (0,	Compressive yield strength (MPa) Shear modulus G (GPa) Shear yield strength	Ratio
		(MPa)	2%)			(0.2%) (MPa)	σ y /τ y
			(MPa)
	72	464	438	400	27	260	1.79

Table 3

 3 Fatigue tests results under bi-axial tension-torsion.

		Tension	Torsion
	σ zz	alt	Rσ	σ zθ alt	Rτ	Phase shift (°)	λ	Nf
	40	1	110	1	0	2.75	1.243 × 10 6
	40	1	110	1	90	2.75	1.17 × 10 6
	150	1	7 0	1	0	0.47	2.64 × 10 5
	150	1	7 0	1	90	0.47	2.81 × 10 5
	150	1	100	0.1	90	0.67	7.425 × 10 4
	150	1	70	0.1	0	0.47	9.948 × 10 4
	150	0,1	70	1	90	0.47	3.356 × 10 4
	137	1	9 7	1	0	0.7	1.364 × 10 6
	95	1	193	1	0	2.03	2.05 × 10 4

Table 4

 4 Fatigue tests results under combined tensile-torsion-internal pressure.

	Tensile	Torsion	Internal pressure	Nf
	σ zz	alt	σ zθ alt	σ θθ alt	cycles
	100	0	20.83	1.33 × 10 5
	90	0	18.75	2.58 × 10 5
	0	90	18.75	1.95 × 10 5
	0	69	14.4	1.467 × 10 6
	100	100	20.83	1.94 × 10 4
	69	69	14.4	1.14 × 10 5
	50	50	10.4	> 10 6

as mean shear stress. Under combined tensile torsion loadings, the influence of phase shift is negligible. For all loadings, fatigue cracks initiate systematically on Al 9 FeNi coarse intermetallic particles Crossland generalized fatigue criterion is not able to reproduce correctly the experimental results obtained with multiaxial fatigue loadings, especially when mean shear stress and internal pressure is

Acknowledgements

Special thanks are given to Université Paul Sabatier (Toulouse) for financial support of this research study and to IRT M2P, in particular Joffrey Tardelli (IRT M2P), Benjamin Mouls (IRT M2P), Cédric Marchetto (IRT M2P) and Aimé Ramakistin (INEOSURF).

Declaration of Competing Interest

The authors declared that there is no conflict of interest.