MINES Juan Manuel García
email: jmgarcia.engineering@gmail.com

Strength and fatigue strength of a similar Ti-6Al-2Sn-4Zr-2Mo-0.1Si linear friction welded joint

Keywords: Titanium alloy, Linear friction welding, Mechanical properties centred cubic titanium crystal lattice, F , friction axis, P , pressure axis, T , thickness axis, E, Young's modulus, Y , yield strength, UTS, Ultimate Tensile Strength, ε macro , macroscopic engineering strain

Strengths for monotonic and cyclic loadings of similar overmatching Ti6242 Linear Friction Welds (LFW) were studied and compared to the parent material (PM) behaviour. Non destructive synchrotron observations revealed the presence of pores in the weld interface. The Weld Centre Zone (WCZ) showed a higher strength leading to lower macroscopic ductility of the cross-weld samples. Local strain and normalized strain rate have been assessed by stereo Digital Image Correlation (DIC) and revealed an early plastic activity at yielding in the vicinity of the WCZ attributed to residual stresses. For the target life, the fatigue strength was slightly reduced but compromised by a strong scatter. Indeed, an internal fish-eye fatigue crack initiation was found on an unexpected dendritic defect that was very different from the PM microstructure and the known martensitic α ′ in the WCZ. The dendritic defect was linked to surface contamination prior to welding and led to melting.

Introduction

Titanium alloys are widely used in the aerospace industry [START_REF] Boyer | Attributes, characteristics, and applications of titanium and its alloys[END_REF]. An increasing demand of titanium and composite materials has recently been observed [START_REF]Executive Summary. World titanium industry supply and demand overview[END_REF] due to the progressive growth of air traffic [START_REF]Growing horizons 2017-2036[END_REF] and their high compatibility of working together, such as galvanic and thermal expansion coefficients compatibility and corrosion protection [START_REF] Boyer | Titanium for aerospace: rationale and applications[END_REF]. Titanium's excellent corrosion resistance, mechanical resistance and low density give them increasing importance. Ti6242 highlights a very good creep resistance and it enables working in high temperature environments [START_REF] Chen | Process for preparation of near-alpha titanium alloys[END_REF].

A need to improve the buy-to-fly ratio is raising and it could be satisfied, e.g. by the use of novel joining techniques [START_REF] Boyer | Attributes, characteristics, and applications of titanium and its alloys[END_REF]. Linear Friction Welding (LFW) is solid-state joining process which was first patented by [START_REF] Richter | Herbeifuehrung einer haftverbindung zwischen plaettchen aus werkzeugstahl und deren traegern nach art einer schweissung oder loetung[END_REF] and it works as follows: A cantilever workpiece, also known as stationary workpiece, is in contact with a second piece named the oscillating workpiece which follows a linear oscillatory motion. After a fraction of a second of friction, a forging pressure is applied to achieve a target axial shortening. High levels of plastic deformation and localized heat are generated around the weld interface following four distinct phases. Microstructural changes, unknown mechanical properties and considerable levels of residual stresses are found in four distinct welding zones [START_REF] Vairis | High frequency linear friction welding[END_REF] : the weld centre zone (WCZ), the thermo-mechanically affected zone (TMAZ), the heat affected zone (HAZ) and the parent material (PM). This process is very quick, reduces bulk milling operations, enables the conception of dissimilar welds and, in some cases, enhanced weld mechanical properties.

LFW joints may be subjected to strong mechanical and cyclic loadings [START_REF] Flipo | Linear friction welding of ti-6al-4v for aerostructure applications[END_REF][START_REF] Antonio | Blisk fabrication by linear friction welding[END_REF][START_REF] Mateo | Welding repair by linear friction in titanium alloys[END_REF][START_REF] Kuroki | Application of linear friction welding technique to aircraft engine parts[END_REF]. Understanding their mechanical properties in monotonic and cyclic loadings is fundamental for its industrial application. Several authors studied the tensile properties of similar LFW joints using as parent material comparable alloys to Ti6242, such as TA6V and IMI-834 [START_REF] Flipo | Linear friction welding of ti-6al-4v for aerostructure applications[END_REF][START_REF] Mateo | Welding repair by linear friction in titanium alloys[END_REF][START_REF] Kuroki | Application of linear friction welding technique to aircraft engine parts[END_REF][START_REF] Li | Influence of parent metal microstructure and post-weld heat treatment on microstructure and mechanical properties of linear friction welded ti-6al-4v joint[END_REF][START_REF] Li | Microstructure characterization and mechanical properties of linear friction welded ti-6al-4v alloy[END_REF][START_REF] Debeugny | Contribution a la modelisation et a la comprehension du procede de soudage par friction lineaire[END_REF][START_REF] Dalgaard | Evolution of Microstructure, Microtexture and Mechanical Properties in Linear Friction Welded Titanium Alloys[END_REF][START_REF] Dalgaard | Linear friction welding of a forged near-α titanium alloy[END_REF][START_REF] Gd Wen | Cyclic deformation behavior of linear friction welded ti6al4v joints[END_REF][START_REF] Suresh | A comparative evaluation of friction and electron beam welds of near-α titanium alloy[END_REF][START_REF] Zhao | Strain hardening behavior of linear friction welded joints between tc11 and tc17 dissimilar titanium alloys[END_REF]. Some similar and dissimilar joints failed far from the WCZ [START_REF] Mateo | Welding repair by linear friction in titanium alloys[END_REF][START_REF] Li | Influence of parent metal microstructure and post-weld heat treatment on microstructure and mechanical properties of linear friction welded ti-6al-4v joint[END_REF][START_REF] Debeugny | Contribution a la modelisation et a la comprehension du procede de soudage par friction lineaire[END_REF][START_REF] Dalgaard | Evolution of Microstructure, Microtexture and Mechanical Properties in Linear Friction Welded Titanium Alloys[END_REF][START_REF] Gd Wen | Cyclic deformation behavior of linear friction welded ti6al4v joints[END_REF][START_REF] Suresh | A comparative evaluation of friction and electron beam welds of near-α titanium alloy[END_REF]. For instance, [START_REF] Dalgaard | Evolution of microstructure, microtexture and mechanical properties of linear friction welded imi 834[END_REF] observed that the formation of a fine microstructure in the WCZ of a similar IMI-834 LFW joint led to a weld overmatch. In a similar manner, [START_REF] Li | Microstructure characterization and mechanical properties of linear friction welded ti-6al-4v alloy[END_REF] documented the weld overmatch of a Ti-6Al-4V LFW joint.

During tensile tests, the macroscopic strains are typically measured using standard extensometers. This measurement represents a limited relevance while testing cross-weld specimens due to the heterogeneous material microstructure, associated strain heterogeneity and presence of residual stresses. Advancements on experimental mechanics such as Digital Image Correlation (DIC) shed new light on the strain monitoring. The assessment of the strain fields on cross-weld specimens has already been exploited by several authors [START_REF] Dalgaard | Evolution of Microstructure, Microtexture and Mechanical Properties in Linear Friction Welded Titanium Alloys[END_REF][START_REF] Chamanfar | Mechanical properties and microstructure of laser welded ti-6al-2sn-4zr-2mo (ti6242) titanium alloy[END_REF][START_REF] Jc Stinville | High and low cycle fatigue behavior of linear friction welded ti-6al-4v[END_REF][START_REF] De Strycker | Measuring welding deformations with the digital image correlation technique[END_REF]. For the last 20 years a large number of authors have used spatio temporal graphs to highlight the presence of strain bands due to instabilities of Portevin's Le Chatelier effect and the Lüders bands. Yet, very little attention has been given to the chronological strain evolution and strain rate in the weld zones during tensile test.

Friction Stir Welding (FSW) is one of the most broadcast solid state joining processes and it is known for having different kind of defects. The most common defect is called joint line remnant, "lazy S" or "zig-zag curve" ( [START_REF] Zhou | Effect of root flaws on the fatigue property of friction stir welds in 2024-t3 aluminum alloys[END_REF]) and it consists on a line of oxides that zigzags along the thickness of the weld. Another typical defect is called "kissing bond" or "root flaw" and consists of the final part of the JLR remaining open, due to an insufficient penetration of the tool pin [START_REF] Le | Fatigue lifetime and tearing resistance of aa2198 al-cu-li alloy friction stir welds: effect of defects[END_REF]. The two sheets to be welded by FSW must be closer than a given threshold distance, when this distance is not respected, another kind of defect called the "GAP" takes place leading to the presence of cavities [START_REF] Le | Fatigue lifetime and tearing resistance of aa2198 al-cu-li alloy friction stir welds: effect of defects[END_REF]. Some surface defects related to excessive heat input have also been observed such as flash formation, surface galling and nugget collapse.

Concerning the documented defects in LFW, literature is less abundant. Some of the documented defects are porosity, oxides and the formation of an abnormal microstructure [START_REF] Wanjara | Linear friction welding of ti-6al-4v: processing, microstructure, and mechanicalproperty inter-relationships[END_REF][START_REF] Li | Abnormal microstructure in the weld zone of linear friction welded ti-6.5 al-3.5 mo-1.5 zr-0.3 si titanium alloy joint and its influence on joint properties[END_REF]. [START_REF] Wanjara | Linear friction welding of ti-6al-4v: processing, microstructure, and mechanicalproperty inter-relationships[END_REF] found that either oxides or porosity could appear in the WCZ as a function of the chosen LFW parameters. Some authors studied the effects of FSW welds defects on the tensile properties [START_REF] Lang | Microstructural evolution of a tc11 titanium alloy during linear friction welding[END_REF]. For instance, [START_REF] Le | Microstructural characterization of internal welding defects and their effect on the tensile behavior of fsw joints of aa2198 al-cu-li alloy[END_REF], [START_REF] Elangovan | Developing an empirical relationship to predict tensile strength of friction stir welded aa2219 aluminum alloy[END_REF] and [START_REF] Nakata | Weldability of high strength aluminum alloys by friction stir welding[END_REF] documented the effect of defects on the tensile strength of FSW joints. The weld properties of sound welds and welds containing defects were similar even if surface defects such as kissing bond acted as crack initiation site during tensile tests. Despite the existence of pores and oxides, some resistance to a monotonic loading can be obtained. [START_REF] Wanjara | Linear friction welding of ti-6al-4v: processing, microstructure, and mechanicalproperty inter-relationships[END_REF] observed the presence of oxides and pores in the WCZ of similar Ti-6Al-4V LFW joints and yet failure always occurred in the TMAZ or the PM. [START_REF] Li | Influence of parent metal microstructure and post-weld heat treatment on microstructure and mechanical properties of linear friction welded ti-6al-4v joint[END_REF] and [START_REF] Li | Abnormal microstructure in the weld zone of linear friction welded ti-6.5 al-3.5 mo-1.5 zr-0.3 si titanium alloy joint and its influence on joint properties[END_REF] reported the presence of abnormal microstructures in the WCZ of similar Ti alloys LFW joints which resulted into failure in the elastic domain with a quasi brittle fracture.

The consequences of FSW defects in terms of fatigue life and fatigue crack propagation have been documented to some extent. [START_REF] Le | Fatigue lifetime and tearing resistance of aa2198 al-cu-li alloy friction stir welds: effect of defects[END_REF] and [START_REF] Lomolino | On the fatigue behaviour and design curves of friction stir buttwelded al alloys[END_REF] found surface defects on a similar FSW joint that may have diminished the fatigue strength. [START_REF] Lombard | Optimising fsw process parameters to minimise defects and maximise fatigue life in 5083-h321 aluminium alloy[END_REF] found that surface defects played a significant role in the crack initiation stage. [START_REF] Di | The influence of zigzag-curve defect on the fatigue properties of friction stir welds in 7075-t6 al alloy[END_REF] and [START_REF] Ceschini | Effect of friction stir welding on microstructure, tensile and fatigue properties of the aa7005/10 vol.% al2o3p composite[END_REF] observed that the zig-zag defect of FSW joints also known as joint line remnant acted as a crack initiation site during fatigue tests diminishing the fatigue life compared to sound welds. [START_REF] James | Weld tool travel speed effects on fatigue life of friction stir welds in 5083 aluminium[END_REF] observed that that the kissing bond defect on a similar aluminium FSW joint shorten the overall fatigue life of the specimen by favouring the the link between two cracks. A considerable understanding of the role of defects on the fatigue crack propagation mechanisms of FSW joints can be found in literature whilst the defects' effects on the fatigue crack initiation and propagation mechanisms of LFW joints seem poorly documented.

A certain agreement about the presence of residual stresses in LFW joints can be found in literature [START_REF] Frankel | Comparison of residual stresses in ti-6al-4v and ti-6al-2sn-4zr-2mo linear friction welds[END_REF][START_REF] Romero | Effect of the forging pressure on the microstructure and residual stress development in ti-6al-4v linear friction welds[END_REF]. Compared to the parent material, LFW joints exhibit a reduced fatigue lifetime due to the presence of tensile residual stresses [START_REF] Webster | Residual stress distributions and their influence on fatigue lifetimes[END_REF]. [START_REF] Romero | Effect of the forging pressure on the microstructure and residual stress development in ti-6al-4v linear friction welds[END_REF] have studied similar Ti6242 and TA6V LFW joints and reported that residual stresses decrease with increasing forging pressure. Despite these evidences, little research has been carried out on the relationship between the fatigue strength and the residual stresses for LFW welds.

In this paper, strength and fatigue strength of the little studied similar Ti6242 LFW joint are studied. The originality of this work relies on three major highlights. Firstly, the presence of defects at the microscopic scale has been assessed using non-destructive observations techniques such as synchrotron laminography. Secondly, a new analysis of the strain fields obtained by DIC has been proposed. Normalized strain rate spatio-temporal graphs were used to detect an early plastic activity in the surroundings of the WCZ and to foresee the fatigue crack initiation site on the welded structure. Finally, the fatigue life scatter and fatigue crack propagations mechanisms are studied. In particular, the effect of the workpiece surface contamination prior to welding on fatigue life has been assessed. In the experimental part, materials, welds and experimental details will be given. In the following section, results will be given in terms of weld microstructure, defects analysis, tensile tests on smooth specimens with additional DIC analysis. In particular, the normalized DIC strain rate fields are analysed to get insight about the potential fatigue crack initiation site. In the last part, the results of an S-N fatigue approach are presented. Particular attention is drawn to fatigue crack initiation sites and fatigue crack initiation mechanisms and their resulting fatigue scatter. The results and in particular the effect of defects is discussed.

Experimental and materials

Parent material (PM) Ti-6Al-2Sn-4Zr-2Mo-0.1Si titanium alloy was used as PM in this study. Ti6242 is a near-α alloy with a β matrix (b.c.c.) and α grains (h.c.p.). The nominal chemical composition is exhibited in Table 1. Billets of a 250 mm diameter produced by Timet were forged in the α + β domain. Blocks with 80 mm × 70 mm × 15 mm dimensions have been machined using Electrical Discharge Machine (EDM) for LFW. The long and short direction coincided with the rolling direction (RD) and transverse direction (TD) of the billet, respectively. The EDM cutting tool was a brass wire composed of Zinc and Copper. Linear Friction Welds Similar Ti6242 LFW joints were produced by ACB. During joining, friction occurred along the F axis and a forging pressure was applied along the P axis, as shown in Fig. 1. F and P axes were parallel to the long and short directions of the blocks, respectively. The third direction corresponds to the thickness (T ). All specimens were machined by EDM parallel to a P T plane and tested in the as welded condition (See Fig. 2). A burn-off of about 2.76 mm was achieved.

Microscopic observations

The samples were prepared by standard metallographic procedure consisting in mounting, grinding and polishing to a mirror like quality. The parent material and welded joint were observed in a ZEISS DSM982 Gemini Scanning Electron Microscope (SEM) operated at 15 keV using backscattered electrons (BSE) detector. The fractographic analysis was carried out at low and high magnification using secondary electron detector in both LEO 1450VP SEM and ZEISS DSM982 Gemini SEM.

Laminography A 500 µm thick sheet-like specimen parallel to a the P T plane was machined, as shown in Fig. 2.

Laminographic observations were performed at the European Synchrotron Radiation Facility (ESRF) on the beamline ID19. A monochromatic beam of 36 keV x-ray energy was used to observe a volume of 1664 µm × 1664 µm × 500 µm.

Voxel size was 0.65 µm resulting in a final reconstructed volume of size 2560 px × 2560 px × 770 px. The normal to the specimen surface and the axis of rotation held an angle of about 30°to the x-ray beam.

Microhardness Vickers microhardness tests were carried out across the weld with a 100 µm step size, a 500 g load and a dwell period of 15 s. Test were conducted following the ASTM E384-17 standard. Tensile test Nine smooth cross-weld specimens were machined. Four PM specimens and five cross-weld specimens were tested. Tensile tests were conducted following the ASTM-E8 standard with a MTS 250 kN load frame at room temperature. Load frame cross-head speed was 0.032 mm. The specimen geometry is shown in Fig. 2. The tensile test specimens were machined parallel to a P T plane and have been tested having the stationary workpiece on the upper grip of the load frame. Load was applied parallel to the P direction. Elongation was measured with optical extensometers. Gage length was 25 mm and cross section was 3 mm × 6 mm.

Digital image stereo correlation During tensile test, weld zones local strain has been monitored using a standard system of Digital Image Stereo Correlation. A system of two 2048 px × 2048 px Manta G-419B cameras was placed to follow the displacement of an artificial random black and white speckle depicted on the specimen surface (see Fig. 3). The distance between the cameras was a = 26 cm and the camera-object distance was b = 31 cm (see Fig. Uncertainty in displacement measurements turned out to be 0.1 µm. This corresponds to a Hencky strain uncertainty of ∆ε PP = 0.0002 with a standard deviation of σ ε PP = 9.56 × 10 -5 %. As shown is Fig. 3b, the load line, the specimen and the cameras frame were aligned using a laser level (red lines in Fig. 3b). Both cameras were aligned to gravity using a water level. Fatigue test Standard fatigue test using smooth specimens have been carried out following the ASTM 466-07 standard. Two sets of specimens have been tested: fatigue specimens made of parent material and cross-weld specimens. PM samples have been machined in a perpendicular plane to the extrusion axis of the billet having its principal axis tangential to the billet section. Cross-weld specimens were machined parallel to a P T plane of the joint, having its principal axis parallel to the P direction, as shown in Fig. 2. Cross-weld samples have been labelled from 1 to 7, being 1 the one on the centre of welded joint. The uniaxial tension zone had a length of 21 mm and a constant gage section of 3 mm × 7 mm. A sinusoidal waveform was imposed using a MTS 250 kN servo-hydraulic load frame. The stress ratio was R = 0.1 and the test frequency was 20 Hz. Specimens corners were rounded with a lime and their surface were polished to a mirror-like state. Targeted fatigue life was N f = 10 5 cycles.

3 Results

Microstructure

Fig. 4a shows a micrograph obtained using BSE detector for the PM. One can see that the microstructure consists of equiaxed α grains and lamellar α situated in a β matrix. The Average Grain Intercept method was performed using BSE images of the PM microstructure (not shown here) to compute the average grain size of the α grains.

The resulting average grain size was about 10.7 µm. Fig. 4b shows the microstructure observed in the cross section of the welded joint on a P T plane. The presence of the WCZ is observed within the horizontal ∼100 µm thick band. Microstructure in the surroundings of the WCZ shows indications of strong levels of plastic deformation and the fragmentation of former α grains. The level of plastic deformation is higher close the WCZ. Fig. 4c shows a high magnification view of the WCZ. A very fine recrystallization is observed. Needle shape like grains of ∼150 nm thickness are observed. An acicular entangled α ′ martensite is formed within prior-β RX grains [START_REF] Ballat-Durand | Through analysis of the microstructure changes during linear friction welding of the near-α titanium alloy ti-6al-2sn-4zr-2mo (ti6242) towards microstructure optimization[END_REF]. This microstructure is comparable to the one observed in TA6V and IMI-834 similar LFW joints found in literature [START_REF] Dalgaard | Evolution of microstructure, microtexture and mechanical properties of linear friction welded imi 834[END_REF][START_REF] Anthony R Mcandrew | Energy and force analysis of ti-6al-4v linear friction welds for computational modeling input and validation data[END_REF]. Enhanced UTS is expected to be found in the WCZ.

Defects observation

Fig. 5a shows a 2D section parallel to a P T plane taken from the 3D laminographic volume. In absoption laminography, contrast is mainly based on the mean atomic number of the observed object. Increasing mean atomic number leads to brighter gray levels. Ti6242 is two-phase titanium alloy. Aluminium content stabilizes the α phase increasing the β-transus temperature while molybdenum content stabilizes the β phase decreasing the β-transus temperature. Tin and Zirconium are neutral elements and they can be found in solid solution in both phases. The equiaxed dark features represent the lighter aluminium rich α grains and the brighter features the heavier molybdenum rich β matrix. The parent material microstructure is observed in Fig. 5b. The absence of the brighter features in Fig. 5c reveals the WCZ and thermo-mechanically affected zone. Fig. 5d shows a very low atomic number object with a circular shape surrounded by a very bright white line in its border. This edge enhancement is known to be evidence of a strong phase contrast revealing interfaces between different microstructural entities [START_REF] Shen | Threedimensional quantitative in situ study of crack initiation and propagation in aa6061 aluminum alloy sheets via synchrotron laminography and finite-element simulations[END_REF][START_REF] Helfen | Laminographic imaging using synchrotron radiation -challenges and opportunities[END_REF]. These findings suggests the presence of voids. Using image processing through Python scripts based on the pymicro library (http://github.com/heprom/pymicro), a 3D visualization of the voids population has been performed. A colour has been given to the cavities in the weld interface and all other features have been set in absolute transparency (see Fig. 5). Voids typical diameter was 4 µm and they were located at the blocks interface following lines perpendicular to the friction direction. Fig. 6 shows the average microhardness profile over three lines perpendicular to the WCZ. The measurement standard deviation for the three indentation lines is represented with vertical error bars. Microhardness showed a maximum of 420 HV 0.5 at the WCZ centre. Indentations further than 2.5 mm to the WCZ presented an average microhardness of 330 HV 0.5 . Compared to the PM, microhardness on the WCZ is about 27 % higher.

Microhardness evolution

Standard deviation in microhardness measurement (see Fig. 6) is strongly decreased in the WCZ which is consistent with a reduced grain size in this area. The increased microhardness at the WCZ is consistent with the formation of a meta-stable martensitic phases (see Section 3.1). The affected zone by the welding process can be estimated to be 5 mm wide. Increased microhardness on the WCZ suggests enhanced UTS. During tensile test, failure should thus take place on the PM.

Tensile properties

The macroscopic engineering stress-strain curves for the PM and cross-weld specimens are plotted in Fig. 7a. Tensile test curves are plotted in gray for the PM specimens and in colours for the cross-weld specimens. The position on the welded joint of every cross-weld specimen is indicated in the overlaid schematic drawing of the welded block. Failure location for the cross-weld specimens is shown in Fig. 7b. Average total strain measured over a 25 mm basis was 9.2 % for the cross-weld specimens and 14.0 % for the PM specimens. Young's modulus and UTS were respectively E = 118 GPa and U T S = 960 MPa for both sets of specimens with a very limited scatter. The mechanical resistance of the LFW joint showed a weld efficiency of 100 %.

All cross-weld specimens failed far from the WCZ in the oscillating work-piece side suggesting that the WCZ has a higher UTS (see Fig. 7). These findings are in agreement with the increased microhardness measured in section 3.3, revealing a weld overmatch. 3.5 DIC analysis 3.5.1 Cumulated strain Fig. 8a shows the specimen and its black and white speckle to perform the local strain monitoring. The overlaid green rectangle in transparency depicts the region of interest (ROI for DIC). Fig. 8b shows nine steps of the cumulated strain map within the ROI. The colour bar is shared with Fig. 8c. To illustrate the temporal strain cumulation, the strain history of a generatrix line (vertical white line in Fig. 8a is plotted in the so called spatiotemporal graph [START_REF] Besnard | A space-time approach in digital image correlation: Movie-dic[END_REF][START_REF] Sicong Ren | A constitutive model accounting for strain ageing effects on work-hardening. application to a c-mn steel[END_REF][START_REF] Chmelík | Investigating the portevin-le chatelier effect in strain rate and stress rate controlled tests by the acoustic emission and laser extensometry techniques[END_REF] of Fig. 8c. Macroscopic strain and P coordinates are given in the horizontal and vertical axis, respectively. The mapped variable is the strain field following the load direction (ε PP ). The maximum strain level in the colour bar is set to the maximum local strain found during the test. The WCZ is placed at 0 mm of the P coordinate. The oscillating workpiece side of the weld is placed in the negative values of the P axis. The macroscopic engineering stress-strain curve is plotted in white. The nine strain maps of Fig. 8b are taken in the nine characteristic instants (white squares) of the macroscopic engineering stress-strain curve of Fig. 8c. Tensile tests give information about the macroscopic engineering stress and uniform strain for an uniaxial stress state up to necking. Given the heterogeneity of the welded structure, local information is required. The surface 3D displacement and 2D strain fields are obtained by Stereo Digital Image Correlation. Plastic strain for the PM is higher and slightly asymmetrical. Macroscopic engineering stress reaches the UTS at a macroscopic engineering strain of 0.08. Afterwards, localization takes place at a distance of 10 mm in the oscillating workpiece side reaching a local strain of 0.36.

Strain profiles

To investigate further the heterogeneous strain distribution, Fig. 9 shows the strain profiles for three cross-weld and one PM tensile test specimens at three different characteristic instants of the macroscopic tensile test curve: at yielding (dashed lines), at UTS (thin lines) and at failure (thick lines). Strain profiles at yielding show heterogeneous levels along the ROI. The strain profile at UTS for the PM sample is shown. The Failure strain profile for the PM sample shows the strain localization with a maximum local strain of 0.4 and a neck that affects 10 mm of the gage length. The PM in the cross-weld specimen showed a higher local strain than the WCZ for the strain profile at UTS. WCZ mean strain at UTS is 0.018. Localization takes place at PM on the oscillating workpiece side of the specimen at a distance of 10 ± 2 mm.

The homogeneity of the strain profiles at the yielding strength suggests that the WCZ Young's modulus is the comparable to the PM. Maximum local ε PP strain at fracture was comparable between PM and the PM in the cross-weld specimens. No significant strain increment was observed for the WCZ between UTS and failure. First, it should be pointed out that the WCZ strain contribution to the cross-weld total macroscopic strain is lower that that of PM. Thus PM samples show a higher ductility, as pointed out in Section 3.4. Secondly, it would be interesting to determinate whether the WCZ has reached plasticity or not. Using Hooke's law and the values of E and UTS presented in Section 3.4, it could be calculated that the WCZ elastic strain was 0.008, which was smaller than the measured total strain. Hence, the WCZ had deformed plastically. Since the minimum strain was found at the WCZ, it could be concluded that plasticity takes places in the entire gage length. Understanding the chronological order of the plastic activity at the welding zones can be particularly relevant for the early stages of plasticity that govern low cycle fatigue behaviour.

Incremental strain

Whilst in previous sections the total cumulated strain was investigated, here the instantaneous strain activity will be assessed. Fig. 10a shows a view of the specimen surface showing its black and white speckle for DIC strain monitoring. In Fig. 10b, the same nine instants as analyzed in Fig. 8b-c are now analyzed in terms of incremental strain. This incremental strain ∆ε(t i ) for a given time interval ∆t i is an approximate measure of the local strain rate for a given time ε(t i ). Given that the ε(t i ) signal was weaker for the initial correlation steps, the measurement noise became comparable to the ∆ε(t i ) signal. Different time steps were taken to ensure the same signal-noise ratio: ∆t i = 2000 ms for the elastic domain and ∆t i = 500 ms for the plastic domain. Notice that the strain rate over the generatrix line has been normalized by the maximum strain rate found on the line for a given t i . Consequently, the colour bar has been scaled from 0 to 1. This information permits the instantaneous maximum strain rate to be followed. Fig. 10b and Fig. 10c share the colour bar.

The macroscopic engineering stress-strain curve was linear and the normalized strain rate map was homogeneous until ε macro PP ∼ 0.0065. The second map has been taken at the beginning of the non-linearity of the macroscopic engineering stress-strain indicating the onset of plasticity. Some localized plastic activity is observed in the vicinity of the WCZ (P = 1.5 mm). The strain rate maps 3 to 9 shows that plastic activity shifted from the WCZ to the oscillating workpiece side. Fig. 10c shows that the maximum strain rate shifted from the WCZ to the PM where final localization took place, leading to failure. The most astonishing fact is that, even if failure takes place far from the WCZ, plastic activity initiates at its vicinity despite the weld overmatch. This behaviour could be linked to the presence of residual stresses [START_REF] Frankel | Comparison of residual stresses in ti-6al-4v and ti-6al-2sn-4zr-2mo linear friction welds[END_REF][START_REF] Romero | Effect of the forging pressure on the microstructure and residual stress development in ti-6al-4v linear friction welds[END_REF][START_REF] Kim | Residual stress and plastic strain in ai51 304l stainless steel/titanium friction welds[END_REF]. Fatigue failure is known to initiate where the first stages of plastic activity take place. Therefore, fatigue crack initiation should take place in the vicinity of the WCZ. Fig. 11 shows the S-N curve for the PM fatigue specimens (white triangles) and the cross-weld fatigue specimens (yellow triangles) specimens. For the sake of simplicity, only the LFW-1 and LFW-3 fatigue specimens have their label next to its marker on the S-N curve. For the target fatigue life of 10 5 cycles, fatigue strength of PM and LFW joint are ∼ 600 MPa and ∼625 MPa, respectively. The LFW-1 and LFW-3 fatigue specimens were both tested at a maximum stress of 500 MPa. Compared to the PM samples, fatigue resistance of cross-weld specimens is slightly reduced. However, cross-weld specimens present significant fatigue life scatter.

Crack initiation site

The specimen surface parallel to the P T plane has been observed post-mortem using BSE detector for five cross-weld fatigue specimens. Fig. 12 shows the distance between the crack initiation site and the WCZ for five cross-weld fatigue specimens. The WCZ of every specimen has been aligned to the vertical green dashed line on the right. Red crosses indicate the crack initiation site for every specimen. The LFW-1 fatigue specimen presented its crack initiation site at the WCZ. The distance from the WCZ to the crack initiation site for the cross-weld fatigue specimens (i = 2, 3, 4, 5) specimens occurred at a mean distance of 1.5 mm. The LFW-6 fatigue specimen failed at a distance of 2.8 mm. As anticipated in Section 3.5.3, all cross-weld specimens had its fatigue crack initiation in the vicinity of the weld possibly due to the presence of residual stresses [START_REF] Romero | Effect of the forging pressure on the microstructure and residual stress development in ti-6al-4v linear friction welds[END_REF][START_REF] Frankel | Comparison of residual stresses in ti-6al-4v and ti-6al-2sn-4zr-2mo linear friction welds[END_REF].

Fractographic observations

The fatigue crack propagation mechanisms of the PM and LFW cross-weld fatigue specimens are studied through SEM and BSE fractographic observations of the PM-1, LFW-1 and LFW-3 fatigue specimens fracture surfaces. Surface crack initiation site of the PM-1 fatigue specimen is shown in Fig. 13a-b. Long fatigue crack propagation ridges converge to a point at the specimen surface. Fig. 13c and Fig. 13d show respectively a SEM and BSE high magnification view of the crack initiation site. Features of a comparable size to the PM underlying microstructure, i.e. α grains, are seen. The orientation of the crack propagation plane seems to change at the boundaries of α grains. The crystallographic facets indicate a stage I fatigue initiation mechanism for the PM.

Figs. 14a-b show the surface crack initiation site of the LFW-3 fatigue specimen. The fracture surface is located at a distance of ∼1.5 mm from the WCZ as shown in Fig. 12. Several fatigue ridges converge to a region at the specimen surface. Following the zoom of Fig. 14b, it seems that the crack initiated at several closely spaced sites. Figs. 14c-d show a SEM and BSE high magnification micrograph of the central crack initiation site, respectively. Three features resembling to PM α grains are seen. A stage I fatigue crack propagation similar to the PM is observed. This is consistent with the fact that microstructure similar to the PM is found this location. However, it seems that the residual stresses in this location, as registered by [START_REF] Frankel | Comparison of residual stresses in ti-6al-4v and ti-6al-2sn-4zr-2mo linear friction welds[END_REF][START_REF] Romero | Effect of the forging pressure on the microstructure and residual stress development in ti-6al-4v linear friction welds[END_REF][START_REF] Kim | Residual stress and plastic strain in ai51 304l stainless steel/titanium friction welds[END_REF], were sufficient to trigger the onset of plastic activity in several sites of this area.

Defect induced internal crack initiation

Fig. 15a shows the fracture surface of the short fatigue life LFW-1 fatigue specimen. Fatigue ridges converge to a line in the centre. Up to the dashed green line, the surface roughness around the fatigue ridges was smooth; afterwards, surface became rougher. It seems that fatigue crack propagation happened in vacuum up to the point it reached the specimen surface allowing the air to enter. The entering air may have changed the surface roughness during fatigue crack growth, due to the influence of oxidation layers in the crack tip (see Fig. 16e). This phenomena is known as 'fish-eye' and has already been documented for martensitic steel by ([48, 49, 50]). A high magnification image at the centre of the central line is shown in Fig. 15b. Three main features are observed: gray round-cornered features resembling to dendrites (see Figs. 16a-c), a population of nanometric black voids and flat surfaces reminding cleavage facets (see Fig. 16b). It should be recalled that the LFW-1 fatigue specimen had its fatigue crack initiation site in the WCZ (see Fig. 12) and that the microstructure in this location is typically an acicular entangled α ′ martensite (see Fig. 4). In constrast, the round-cornered features seen in Figs. 16a-c are very different from the underlying microstructure in this location. These features resemble to dendrites as e.g. described by [START_REF] Polmear | Light alloys: from traditional alloys to nanocrystals[END_REF] and [START_REF] Hayakawa | Solidification structure and segregation in cast ingots of titanium alloy produced by vacuum arc consumable electrode method[END_REF] and hence imply local melting of the material as will be discussed in Section 4. It seems that an internal crack was provoked during the first tensile cycle, due to a brittle fracture at the surroundings of dendritic defects. At the frontier of the internal cleavage crack, the failure surface convey the impression of the martensitic lath of the underlying microstructure (see Figs. 4c and16d). Seemingly, a crystallographic fatigue crack propagation occurred corresponding to stage I-like fatigue crack propagation at low levels of stress intensity factor and small plastic zones sizes. This phenomena has been approached elsewhere ( [START_REF] Abdesselam | On the crystallographic, stage i-like, character of fine granular area formation in internal fish-eye fatigue cracks[END_REF][START_REF] Petit | Some critical aspects of low rate fatigue crack propagation in metallic materials[END_REF]). The final ductile rupture mechanisms are put in evidence by the dimples of Fig. 16f. A better understanding about the origin of these dendritic defects and the internal cleavage crack is required. A chemical analysis was performed over the fracture surface of the LFW-1 fatigue specimen to get a better understanding on the origin of fatigue crack initiation site. A view of the internal fatigue crack initiation site is shown in Fig. 17b. The red line shows the curvilinear path on which a EDX analysis has been performed. It should be noted that at the coordinate ∼400 µm of the analyzed path, the dendritic defect shown of Fig. 16a is located. In this analysis, all elements on Table 1 plus two extra elements not present in the PM composition have been indexed: Cu and Zn. These elements are present in the cutting tool as described in Section 2. Fig. 17b shows the weight percentage of Cu and Zn over the red line of Fig. 17a. A maximum of 5 % wt. Cu is found for the coordinate 388 µm. A maximum of 3 %wt. Zn is find for the coordinate 913 µm.

Chemical Analysis

Discussion

The microstructure observed at the WCZ and the monotonic mechanical properties of the studied joint have shown a strong agreement with available research in literature on similar LFW joints made of comparable Ti alloys [START_REF] Dalgaard | Evolution of microstructure, microtexture and mechanical properties of linear friction welded imi 834[END_REF][START_REF] Anthony R Mcandrew | Energy and force analysis of ti-6al-4v linear friction welds for computational modeling input and validation data[END_REF]. The quality of the studied weld in terms of UTS, ductility and burn-off is satisfactory. In terms of presence of defects and cyclic properties, it is more compromising.

Origin of defects. In Section 3.8, the presence of Cu-Zn hot spots has been highlighted. From the present study the following scenario can be suggested. It is very likely that the observed brass contaminants were spread by the EDM cutting tool during the machining of the blocks prior to welding. [START_REF] Dalgaard | Linear friction welding of a forged near-α titanium alloy[END_REF] registered local temperature measurements during LFW of similar joint made of IMI-834 titanium alloy which is material comparable to the Ti6242 used in this study. The registered temperatures overreached ∼1000 • C which is comparable to the melting point of a vast range of Cu-Zn alloys [START_REF] Predel | Cu-zn (copper-zinc): Datasheet from landolt-börnstein -group iv physical chemistry[END_REF]. These brass smeared hot spots may have melted and then further solidified favouring the apparition of dendrites and shrinkage voids (see Fig. 16a-c). These kind of voids have already documented for casting alloys [START_REF] Hayakawa | Solidification structure and segregation in cast ingots of titanium alloy produced by vacuum arc consumable electrode method[END_REF]. It may reasonably be assumed that the power input was enough to produce a weld overmatch but slightly insufficient to properly auto-clean the smeared weld interface leaving contaminants as suggested by [START_REF] Anthony R Mcandrew | Modelling the influence of the process inputs on the removal of surface contaminants from ti-6al-4v linear friction welds[END_REF]. A less likely hypothesis for the apparition of these voids may be related to the vaporisation of low melting point elements present in the weld interface. The presence of a Cu-Zn hot spots leads to localized melting of the bulk. In such conditions, the welding technique is no longer a solid-state joining process. To the author's knowledge, this phenomena has not been studied yet.

Another possible explanation to this phenomenon is the so called strain induced porosity. [START_REF] Sl Semiatin | The thermomechanical processing of alpha/beta titanium alloys[END_REF] and [START_REF] Tamirisakandala | Strain-induced porosity during cogging of extra-low interstitial grade ti-6al-4v[END_REF] have documented the apparition of void nucleation in microstructural phases boundary when loading two-phase titanium alloys under high temperature for certain levels of strain rates. The computation of the maximum strain rate using the weld parameters and the theoretical formula proposed by [START_REF] Vairis | High frequency linear friction welding[END_REF] turned out to be εmax = a f L = 1.25 s -1 . If this value, the temperature measured by [START_REF] Dalgaard | Linear friction welding of a forged near-α titanium alloy[END_REF] and the grain-boundary microcracking map proposed by [START_REF] Sl Semiatin | The thermomechanical processing of alpha/beta titanium alloys[END_REF] were taken into account, it appears that the strain induced porosity phenomenon might have occurred.

Two populations of nanometric and micrometric cavities have been observed in the non destructive observations and fractographs of Sections 3.2 and 3.6, respectively. Similar voids have already been observed elsewhere [START_REF] Wanjara | Linear friction welding of ti-6al-4v: processing, microstructure, and mechanicalproperty inter-relationships[END_REF]. Nonetheless, their origin remains unexplained.

Fatigue crack initiation site and early plastic activity. Microhardness profiles and tensile test revealed that the WCZ and its vicinity have higher strength than the PM. An early plastic activity was however observed in the vicinity of the WCZ. The origin of this activity is of particular interest since it allowed the fatigue crack initiation site location to be predicted (see Section 3.5.3). Several authors have reported high levels of tensile residual stresses following the P axis [START_REF] Frankel | Comparison of residual stresses in ti-6al-4v and ti-6al-2sn-4zr-2mo linear friction welds[END_REF][START_REF] Romero | Effect of the forging pressure on the microstructure and residual stress development in ti-6al-4v linear friction welds[END_REF][START_REF] Kim | Residual stress and plastic strain in ai51 304l stainless steel/titanium friction welds[END_REF] which are likely to have caused to the first states of plasticity in the vicinity of the WCZ. According to [START_REF] Romero | Effect of the forging pressure on the microstructure and residual stress development in ti-6al-4v linear friction welds[END_REF], a maximum tensile residual stress peak is located a few millimetres away from the WCZ on the oscillating workpiece side of the weld. These results are consistent with the fact that localized plastic activity initiates on the oscillating workpiece side, as shown in Fig. 10. Defects and fatigue life scatter. The LFW-1 and LFW-3 fatigue specimens were tested at a maximum stress level of 500 MPa. Fatigue life for both specimens were 0.3 and 2 × 10 5 cycles, respectively. An important fatigue life scatter was found. If the graph of Fig. 11 were used as a reference for the design of a workpiece under cycling loading, the fatigue life of the LFW-1 specimen would be very limiting. Hence, it is worthy to better understand the underlying cause of this fatigue life scatter. Both fatigue specimens were pre-polished to a mirror-like state. Thus, it could be stated that the surface roughness of both samples led to similar surface stress concentrations. In Section 3.7.1, a fish-eye crack and the creation of a ∼40 µm wide internal crack from a dendritic defect on the LFW-1 fatigue specimen during the first fatigue cycles is shown. Consequently, the fatigue crack propagation for the LFW-1 sample occurred with a significant initial stress intensity factor caused by the defect. The threshold of the stage II for the fatigue crack propagation is known to take place when the plastic zone size at the crack tip is in the order of several grains. By considering the internal crack as crack in a infinite plate, an approximative and conservative estimation of the stress intensity factor can be made using ∆K = ∆σ × √ π a ≈ 5.16MPa √ m [START_REF] Murakami | Metal fatigue: effects of small defects and nonmetallic inclusions[END_REF]. Crack size, associated small plastic zone size and the vacuum environment (internal crack) seem to favour a stage I-like propagation [START_REF] Abdesselam | On the crystallographic, stage i-like, character of fine granular area formation in internal fish-eye fatigue cracks[END_REF].

The stress intensity factor continued to increase until reaching stage II. Crack propagation took place at first in vacuum and then in air for the LFW-1 fatigue specimen. [START_REF] Sarrazin-Baudoux | Atmospheric influence on fatigue crack propagation in titanium alloys at elevated temperature[END_REF] have shown that fatigue crack propagation speed is lower for a propagation in vacuum, in particular for stage I-like propagation. Therefore, compared to the LFW-3 fatigue specimen, more cycles should be needed in propagation. Despite the slower fatigue crack propagation, the fatigue life was strongly reduced by the internal crack. The initial stress intensity factor was finally decisive in the trade-off between fatigue crack growth speed and number of cycles for fatigue crack initiation. The fatigue failure scenario for the internal defect is summarized in the schematic graph of Fig. 18 and as following: during the first cycles of tensile cyclic loading an internal crack was created in the surroundings of brass contaminants hot spots due to a brittle fracture; the stress intensity factor induced by this internal crack favoured a stage I-like fatigue propagation revealing the underlying α ′ acicular martensite microstructure; the growth of the internal fatigue crack continued until the stress intensity factor was enough to favour a stage II fatigue propagation in vacuum; the internal crack reached the specimen surface enabling the air entry and changing the crack propagation environments conditions; oxides layers on the crack tip changed the roughness around the fatigue ridges and increased the fatigue propagation speed; finally, ductile mechanisms are found.

Weld auto-cleaning Certainly, brass contamination should receive special attention. However, It could be argued that EDM cutting is not a commonly used technique in the industry and that industrial cutting techniques could probably less contaminate the surface of the blocks prior to welding. In such case, joints of better quality in terms of defects and fatigue life scatter may have been produced. Furthermore, the choice of welding parameters could be questioned. Increasing power input could favour the extrusion of impurities but conversely increase temperature, promoting further melting in the weld interface. It is worthy to highlight that only the fatigue specimen coming from the centre of the welded joint was affected by this contamination and that the fatigue life scatter would be significantly lower, if this single internal crack initiation had not occurred.

Conclusions

Similar Ti6242 LFW joints in the as welded state were investigated and compared to the PM. The following conclusions can be drawn:

• The PM microstructure, consisting in equiaxed α grains situated in a β matrix, was recrystallized into an entangled acicular α ′ martensite in the WCZ.

• Two populations of nanometric and micrometric voids were observed in the WCZ.

• Microhardness of the PM and the WCZ were 330HV 0.5 and 420HV 0.5 , respectively. Microhardness showed an increase of 27 %. The zone exhibiting modified microhardness was less than 5 mm wide.

• The weld showed an overmatch. LFW cross-weld samples have shown a strength of 960 MPa such as the PM and a total strain of 9.2 % measured over a 25 mm basis compared to 14.0 % for the PM.

• Under monotonic loading, failure occurred at the oscillating workpiece, 10 mm away from the WCZ in the PM.

• An original DIC measurement of the normalized strain rate fields showed an early strain activity close to the WCZ, despite the weld overmatch.

• The fatigue strength for 10 5 cycles of the PM and the LFW cross-weld sample was ∼625 MPa and ∼600 MPa, respectively. LFW fatigue strength was compromised by significant scatter. The fatigue crack initiation site for all samples was located in the vicinity of the TMAZ at a distance of 1.5 mm away from the WCZ consistent with the early strain activity measured by DIC and probably linked to residual stresses.

• An unexpected internal dendritic defect in the centre of the WCZ caused the reduced fatigue life for a welded joint and led to a fish-eye crack.

• A contamination of Cu and Zn was observed in the WCZ in the dendritic defect. It was attributed to EDM cutting of the blocks before welding and associated local melting/solidification of the brass contaminants during welding.

Figure 1 :

 1 Figure 1: A schematic view of the welded joint showing the friction direction (F), the forging pressure direction (P) and the thickness direction (T).

Figure 2 :

 2 Figure 2: a) Geometry of the fatigue specimen; b) geometry of the tensile specimen; c) schematic view of the specimen location in the welded joint and d) laminography specimens. All measures are given in mm.

  3a), leading to a field of view of 40 mm × 40 mm. Images were exploited with Vic-3D™ from Correlated Solutions, Inc. (version 7.2.4, 2014). Acquisition was carried out taking 2 frames per second. Subset size was 35 px ≈ 175 µm, step size was 9 px and filter size was 15 px. Before tensile testing, the displacement and the Hencky ε PP measurements uncertainty were determined by correlating two consecutive images of the static specimen.

Figure 3 :

 3 Figure 3: a) Schematic top view of the experimental setup for performing stereo correlation with a standard DIC system. b) Specimen, camera frame and load line aligned to gravity using a laser level (red laser lines).

Figure 4 :

 4 Figure 4: SEM Backscattered electron micrograph of the a) PM , b) affected zone containing the WCZ and the TMAZ and c) the very fine entangled acicular α ′ martensite on the WCZ.

Figure 5 :

 5 Figure 5: a) A 2D view of a P T section of the reconstructed laminographic volume. b) PM microstructure, α grains and the β matrix are observed in the darker and brighter phases, recpectively. c) TMAZ. d) Cavities in the weld. e) 3D visualisation of the micrometric cavities population.

Figure 6 :

 6 Figure 6: Mean Vickers microhardness over 3 profiles along the WCZ, having in vertical error bars the measurements standard deviation.

Figure 7 :

 7 Figure 7: a) Engineering strain-stress curves for the LFW cross-weld (colour) and PM specimens (gray) b) Macroscopic post mortem view of the LFW cross-weld specimens showing failure location.

Figure 8 :

 8 Figure 8: a) LFW cross-weld tensile specimen in the load frame showing the region of interest (ROI) (green rectangle) and a generatrix line (white line); b), nine steps of the strain field in the ROI; and c) a cumulated strain spatio-macroscopic deformation graph and the macroscopic engineering strain-stress curve.

Figure 9 :

 9 Figure 9: Strain profiles obtained by DIC for PM (gray) and LFW cross-weld (colours) tensile specimens at yielding, at UTS and at failure.

Figure 10 :

 10 Figure 10: a) LFW cross-weld tensile specimen in the load frame showing the ROI (green rectangle) and a generatrix line (white line); b) nine steps of the instantaneously normalized strain rate field in the ROI; and c) a normalized strain rate spatio-macroscopic deformation graph with the overlaid macroscopic engineering strain-stress curve.

Figure 11 :

 11 Figure 11: S-N curve for the PM (blue) and LFW cross-weld (yellow) fatigue specimens (R = 0.1).

Figure 12 :

 12 Figure 12: Post mortem backscattered electron view of the specimen surface on a P T plane showing with a red cross the failure location and its distance to the WCZ for five LFW cross-weld fatigue specimens.

Figure 13 :

 13 Figure 13: Fractograph of the PM-1 fatigue specimen, showing a) fracture surface; b) low magnification micrograph of the crack initiation site; c) SEM high magnification observation; and d) BSE observation of the crack initiation site.

Figure 14 :

 14 Figure 14: Fractograph of the LFW-3 fatigue specimen, showing a) fracture surface; b) SEM low magnification micrograph of the crack initiation site; c) SEM high magnification observation; and d) BSE observation of the crack initiation.

Figure 15 :

 15 Figure 15: a) Fractograph of the LFW-1 fatigue specimen showing the internal crack; b) High magnification fractograph of the internal crack showing dendritic defects and first stages of the crystallographic stage I-like fatigue propagation. Region of interests (ROIs) of Fig.16 are indicated by white rectangles.

Figure 16 :

 16 Figure 16: a) Fractographs of the LFW-1 fatigue specimen showing a) dendritic defect; b) brittle facets; c) dendritic defects; d) crystallographic stage I-like crack propagation in α ′ martensite; e) transition of crack propagation in vacuum/air; f) dimples showing the final ductile fracture.

Figure 17 :

 17 Figure 17: a) Zn and Cu profile indexation of an EDX analysis over the red path of Fig.17b and b) fractograph of the LFW-1 fatigue specimen showing the EDX profile of Figure Fig.17a (red line).

Figure 18 :

 18 Figure 18: Schematic fatigue crack propagation describing the fatigue scenario of the LFW-1 fatigue specimen.

Table 1 :

 1 Nominal chemical composition (%wt.) of the Parent Material.

	Al Sn Zr Mo Si
	6	2	4	2	0.1

Acknowledgements

The authors wish to thank UTC, CEMEF, Mines-ParisTech and Airbus Central R&T for the valuable discussions. ACB is thanked for providing the welds for this study. Lukas Helfen at ESRF ID 19 line is gratefully acknowledged for his kind help in non destructive laminographic observations. Henry Proudhon at Centre des Matériaux is thanked for the provided training on the PyMicro library (http://github.com/heprom/pymicro) for the 3D image processing. Vladimir Esin at Centre des Matériaux insight in microstructure analysis is acknowledged. Anne-Françoise Gourgues-Lorenzon at Centre des Matériaux is kindly thanked for the discussions about rupture mechanisms. Steve Dodds at TWI is to be thanked for the discussions about the Strain Induced Porosity phenomenon. The authors acknowledge the financial support from the French National Research Agency (ANR) and FRAE through OPTIMUM ANR-14-CE27-0017 project.


J J Thomas

L Verger

A Bignonnet

E Charkaluk

Thermomechanical design in the automotive industry

Keywords: automotive, constitutive model, engine, fatigue, thermomechanical, viscoplastic

A C T In this paper thermomechanical fatigue assessment in the automotive industry is discussed. The design strategy is based upon a consistent approach of the thermomechanical loading, the mechanical constitutive law of the material, the damage parameters and the fatigue strength criteria. The good understanding of these different steps allows one to perform predictive calculations of automotive parts subjected to thermomechanical loading. The main hypotheses and modelling choices are presented and results are illustrated by a series of computations on real 3D structures. Cracked area and lifetime prediction are described in the case of aluminium alloy cylinder heads subjected to transient thermal loadings.

I N T R O D U C T I O N

Development in numerical simulation over the past 20 years have led to increased performance of numerical tools and the development of new algorithms. Today this enables ever-quicker calculations of loads and displacements in structures. Nevertheless, whilst academic work is quite active few studies have been performed on structures subjected to multiaxial thermomechanical loading. Only a small number of components in automotive technology experience thermomechanical loading cycles of a severity capable of producing low-cycle fatigue. Most of these parts are related to the engine: cylinderheads, exhaust manifolds, crankcases, . . . . It is important to note that the low-cycle fatigue problems in such engine components are related to the start-operate-stop cycles and not to the combustion cycles. Therefore they involve large temperature changes. A previous study was dedicated to cast-iron exhaust manifolds. 1 This work showed an original comprehensive approach, which resulted in a reliable prediction of damage location and of lifetime in spite of basic assumptions like the separation of the damage and the mechanical constitutive behaviour. The paper presents an overview of this approach and the specific details of the applications in the case of the cylinder head in aluminium. The results are illustrated by a series of computations on real 3D structures. The words comprehensive approach shall denote the following series of items:

Correspondence: Jean-Jacques Thomas. E-mail: jeanjacques.thomas@mpsa.com r thermal analysis, r elasto-viscoplastic mechanical analysis and r fatigue analysis.

These three aspects are linked together; the thermal loading and the material behaviour determine the mechanical response of the structure and from that the fatigue strength of the structure can be estimated through a damage indicator and a pertinent fatigue criterion.

For a design strategy, one should not concentrate separately on these four aspects of the problem. It should be a comprehensive approach to obtain an important robustness and to allow its integration in a development process [START_REF] Charkaluk | Dimensionnement en fatigue des structures[END_REF] by the ability to answer the asked question in the appropriate time. That is to say in our case: is the fatigue strength of the component guaranteed or not before the production of tooling for a prototype? The cylinder head is made of an aluminium alloy (in this case an A356 alloy) and locally experiences temperature cycles ranging from 20 to 300 • C. The mechanical behaviour of the aluminium alloy is plastic at low temperatures and highly viscoplastic at the upper temperatures. Moreover, aluminium alloys are also subjected to thermal ageing effects for temperatures over 150 • C.

Therefore different steps had to be defined in order to apply the comprehensive approach in this case: r modelling of the ageing behavior of the material, r modelling of the cyclic viscoplastic behavior of the mate- rial, r calibration of the parameters of the models on the basis of isothermal and non-isothermal uniaxial tests, In order to keep the above methodology at a complexity level compatible with the constraints of the industrial design engineers, several assumptions regarding the uncoupling of the different phenomena have been made: uncoupling between thermal computation and mechanical computation; uncoupling between ageing evolution and mechanical behaviour and uncoupling between the constitutive law and the damage modelling. Another important hypothesis is the existence of a stabilized mechanical response of the structure. The design strategy is based on the assumption that an acceptable component will rapidly reach a stabilized response to the cycling loading. It means that shakedown will occur. Rather than simulating the whole life of a component, it is then possible to focus on the stabilized response of the structure and to extract some damage indicator from this cycle. To save time, one must define an efficient method to rapidly reach this stabilized response. One must also define a relevant damage indicator which will permit prediction of the lifetime. One of the main difficulties exists in the fact that the calibration of the temperature dependant parameters of the constitutive law with non-isothermal tests data could not be simplified. [START_REF] Verger | IUTAM Creep in Structures 2000[END_REF]

R E P R E S E N TAT I O N O F I N S E R V I C E L O A D I N G

In the first step it is important that the thermal loading applied at the validation stage on engine testing and while calculating virtual prototype should be representative of the customer's uses from the point of view of the fatigue damage. An analysis method, which can be used, is the stress-strength interference analysis 4 that is frequently used for high-cycle fatigue studies. The main elements of this method are: a counting method (e.g., rain-flow counting) on the appropriate and accessible variable (e.g., forces, accelerations and temperatures); a cumulative damage law or equivalent damage method (e.g., Miner's rule) and a risk analysis and the description of the fabrication scatter (material and process). The extension of this method to the thermomechanical fatigue is particularly delicate due to the non-linearity (behaviour, loading, . . .) and assumes several simplifying hypothesis. Nevertheless, this can be reasonably done and is used to define bench test to represent the customer's use with the desired severity. Figure 1 schematically represents the different steps of this work for a typical thermal loading of an exhaust pipe. The acceptance criterion is given with regard to an objective customer taking into account the fabrication scatter on a definite risk.

S I M U L AT I O N O F T H E T H E R M A L L O A D I N G

For engine components, the main element of the loading is the thermal evolution of the components in operating engine conditions defined to be representative of customer use (the mechanical loading is essentially linked to the bolt tightening between the different components and to the press fit of valve seats or valve guides in the case of cylinder head; these different aspects can be represented rather easily). This is a dominant step of the approach, because the accuracy of thermal data conditions governs the accuracy of the mechanical response of the structure and, therefore, the estimated fatigue strength. The input data come from engine combustion simulation using numerical tools (KIVA, FIRE, FLUENT, . . .). In the case of the exhaust manifold, these data are associated with the gas flow in the exhaust ports and pipes to determine the gas temperatures, and therefore, to determine the internal exchange coefficient. For the cylinder head, they are used as thermal flux on the fire deck. A transient thermal calculation done in both cases enables the determination of the thermal loading hich is used for the thermomechanical calculation. [START_REF] Lederer | Numerical lifetime assessment of engine parts submitted to thermomechanical fatigue, application to exhaust manifold design[END_REF] The determination of the thermal loading is still the major difficulty of a thermomechanical fatigue approach in the automotive industry (particularly for thermal exchange between the engine components: cylinder head, crankcase, piston, exhaust pipe, . . .) and will necessitate extensive work in the forthcoming years.

M O D E L L I N G T H E M AT E R I A L B E H AV I O U R

The origins of failures encountered at high temperature in automotive components is linked to thermal loading. Three main aspects can be underlined: r The temperature cycles between ambient and maximum temperature (250 • C in the cylinder head, 800 • C and above on exhaust pipe or 700 • C for brake disk) reach a domain where mechanical strength of material becomes quite low.

r High temperature dwell time enhances creep (that is the case for engine crankcases).

r Steep thermal gradients leads to inelastic deformations in confined zones.

Failure analysis also evidences the cyclic aspects of the loading with high and variable temperatures.

Within these temperature ranges (0.3-0.5T m -melting point) the behaviour of the material is strongly non-linear. We can no longer speak of elasticity.

Material testing is performed on material/process representative specimens (similar microstructure and metallurgical quality as the actual component) at different strain rates with dwell times at imposed strains. The material behaviour shows a strain rate dependence of this threshold and a stress recovery during dwell time. As an example, the mechanical behaviour of a 356 Al alloy is given in Fig. 2.

Experimentations at constant stress reveal creep of the material. These phenomena clearly demonstrate the role of viscosity and therefore a simple plasticity model is not able to represent our problem. We are faced with an elastoviscoplastic behaviour.

For the modelling of high temperature deformation, mechanisms have been described by several authors (Franc ¸ois et al., [START_REF] Francois | Comportement mécanique des matériaux[END_REF] Lemaitre and Chaboche [START_REF] Lemaitre | Mechanics of Solid Materials[END_REF] ). Most of the work on that field started with the growth of the nuclear industry and the aeronautics. Two approaches have been particularly developed at this time: the unified theory characterized by constitutive law with a unique inelastic strain [START_REF] Sehitoglu | Stress strain response of a cast 319-T6 aluminium under thermomechanical loading[END_REF][START_REF] Nicouleau-Bourles | Thermomechanical fatigue of aluminium alloys: experimental study and numerical simulation[END_REF] and the damage mechanics initiated by Kachanov [START_REF] Kachanov | Time on the rupture process under creep conditions[END_REF] and further developed by Chaboche. 11 If these results are often used, in aeronautics for example, they present some disadvantages:

r The constitutive law can rapidly become complex to model all the physical phenomena. The number of characteristic parameters becomes quite important and their eventual coupling makes their calibration difficult.

r These mechanical models are not necessarily representa- tive of the whole physical phenomena, because they are often imperfect to model both creep and stress relaxation (Franc ¸ois et al. [START_REF] Francois | Comportement mécanique des matériaux[END_REF] ).

r Coupling damage and constitutive behaviour lead to diffi- culties in parameters calibration and numerical implementation, and overall leads to lengthy calculation.

Based on these observations, one can conclude that to be appropriate to the automotive context, thermomechanical modelling is subjected to several constraints: r The necessity is to represent the behaviour of the material in the structure by simple constitutive equations. In this context, one should adopt the representation of the mechanical behaviour without coupling with damage (Fig. 3). From experience, most of the times this coupling is not necessary and does not improve the predictivity of the behaviour of the structure. [START_REF] Sermage | Multiaxial creep-fatigue under anisothermal conditions[END_REF] Usually it is not necessary to describe the evolution of the structure cycle by cycle and particularly the early stage of the life of the structure. Therefore the calibration of the parameters of the constitutive equation can be done on steady-state cycles from material testing.

r The implementation in a finite-element code using a numerical integration algorithm for the constitutive law stable and robust enough to enable large integration steps.

The unified model can be described by the following equations:

ε = ε e + ε vp , σ = C : ε e , α = 3 2 1 H X, εvp = 3 2 J 2 (σ -X) -σ y η m s -X J 2 (s -X) = α,
where x denotes the positive part of x, J 2 (a) = The viscoelastic-elastoplastic model can be described by the following equations:

ε = ε elas v + ε v , ε = ε elas p + ε p , α = 3 2 1 H X, ε elas v = 1 + ν K v σ v - ν K v tr (σ v ) I, ε elas p = 1 + ν K p σ p - ν K p tr(σ p )I, εv = 3 2 J 2 (σ v ) η m s v J 2 (σ v ) , εp = γ s p -X J 2 (σ p -X) = α.

Cylinder head

The studied automotive cylinder heads are made of an A356 aluminium alloy composed of 7% silicon and 0.3% magnesium (in mass percentage). In critical areas during the engine processing, the temperature of the material can reach the value of 300 • C. At these temperatures, the material shows two main behaviours: on one hand a considerable thermal ageing resulting in the loss of at most 70% of its mechanical characteristics, on the other hand a highly viscoplastic mechanical behaviour as the temperature approaches 60% of the melting temperature.

Ageing behaviour

In order to optimize the mechanical characteristics of the studied alloy at an upper level despite of the high temperature, the entire cylinder head is submitted to a typical T7 thermal treatment after casting: homogenization at 540 • C to dissolve the precipitates, water quenching, artificial ageing at 200 • C during which the components Mg 2 Si precipitates are formed. The temperature influence on this original T7 alloy has been measured during an appropriate experimental programme of conventional yield stress and hardness measurements on specimens submitted to constant temperature dwells (Fig. 4). A quite simple exponential function has been used to model the temperature and time-dependant ageing of the alloy: This function has proved to be correctly fitting the experimental data on specimens [START_REF] Boussac | Influence du Vieillissement Thermique sur les Caractéristiques Mécaniques à Température Ambiante de l'AS7G03 Y39[END_REF] as well as on processed cylinder heads (Fig. 5).

H B (t, θ) = H BS + (H B0

Mechanical behaviour

Several tests have been performed on specimens in order to show the cyclic mechanical behaviour of A356 aluminium alloy (Fig. 6). These are tension/relaxation/compression (TRC) cyclic tests at different temperatures in the range 20-300 • C, performed at various strain rates: 10 -3 s -1 , 5.10 -4 s -1 and 10 -4 s -1 . A viscous behaviour has been evidenced by exponential stress/time relaxation response. Plastic yield stress and hardening are noticed at each temperature. A classical viscoplastic model with one single inelastic strain variable similar to those developed by Chaboche [START_REF] Lemaitre | Mechanics of Solid Materials[END_REF] has then been used with temperature-dependant parameters (Fig. 3).

Uncoupled damage

As some classical low cycle fatigue (LCF) tests have been performed in the same range of temperatures, it has been shown that the A356 aluminium alloy undergoes a slight cyclic softening during almost the whole life of the specimens (Fig. 7). The coupled modelling of such a cyclic damage with the viscoplastic behaviour would be very expensive in terms of identification tests and computation times. Furthermore, several studies have already shown that this coupling may not be necessary to perform reasonably predictive lifetime calculations. 1,[START_REF] Sermage | Multiaxial creep-fatigue under anisothermal conditions[END_REF] As a result, it has been chosen not to include any damage variable in the constitutive law used to represent the mechanical response of the studied material. The cyclic damage will then be calculated from the mechanical variable results of a 'stabilized cycle' numerical simulation (for more details, see the fatigue design part of the present document).

Constitutive law calibration

The unified viscoplastic model chosen in this case is available over the whole range of temperature provided that its five parameters are computed as temperature-dependant functions. The calibration method is based on an optimal control approach. [START_REF] Bourgeois | Contr ôle Optimal et Problèmes Inverses en Plasticité[END_REF] The parameters as functions of temperature are determined through the minimization of a cost function defined as

J ( p) = 1 2 [σ exp -σ calc ( p, t)] 2 dt, ( 2
)
where the time integral measures the difference between the experimental and the computed stresses (σ exp and σ calc ), respectively, over a complete stabilized cycle. In order to determine parameters from several experiments, the corresponding cost functions can be added using weight factors. The minimization itself is performed by a classical BFGS gradient descent algorithm.

According to the ageing of the alloy, both measured and calculated on the structure (Fig. 5), it has been chosen to calibrate the material parameters under two stable states: on one hand the original T7 state which makes up the 'cool' part of the cylinder head, and on the other hand the fully aged state found in the 'hot' part of the structure, which undergoes the thermomechanical fatigue phenomena. By means of a set of calculations on structure, the consequences of the lack of realistic ageing modelling of the second order in the transitional area on the fatigue predictions have been shown. A particular effort had to be made on the determination of the experimental database to be used for the identification analysis. [START_REF] Verger | IUTAM Creep in Structures 2000[END_REF] Indeed the viscosity parameters η and m show an important coupling behaviour on the TRC tests simulation at constant temperature (Fig. 8). Then, the use of non-isothermal experimental data provide us with a useful additional information. Furthermore, the loading conditions applied on specimens for non-isothermal tests can be defined using the typical thermal and strain history recorded on the engine component (Fig. 9). As a result, the parameters identified from both isothermal TRC and non-isothermal 'structure-like' measurements are likely to perform realistic behaviour simulations on structure calculations.

F AT I G U E A N A LY S I S

The final objective is to evaluate the fatigue strength, or the lifetime of the structure, from the stabilized response of this structure. A criterion must then be defined upon the mechanical variables linked to the stress and strain fields. The first studies on the LCF criteria give some useful parametric laws. Nevertheless, all the classical approaches like Manson-Coffin, [START_REF] Coffin | A study of the effects of cyclic thermal stresses on a ductile material[END_REF][START_REF] Manson | Behaviour of materials under conditions of thermal stresses[END_REF] strain range partitioning [START_REF] Halford | Life prediction of thermal-mechanical fatigue using strainrange partitioning[END_REF] (SRP) or the function defined by Smith-Watson-Topper 18 (SWT) initially expressed from uniaxial isothermal tests were not really adaptable to the thermomechanical fatigue of the complex structures. The difficulties came from the multiaxial character of the loading of such structures as well as the large temperature range seen under operation. Actually the usual interpretation of low cycle isothermal fatigue tests with the Manson-Coffin law shows a large differences in fatigue life for test with the same strain amplitude but at different temperature (as shown on Fig. 10 for cast iron), and it is not clear how it can be generalized to the multiaxial case. Furthermore, the predictions by means of cumulative plastic strain as proposed by the strain range partitioning method on a stress-strain isothermal curve is somewhat hazardous. An analysis of an anisothermal test using the SWT function (SWT = √ Eσ max ε) is difficult because the choice or the definition of σ max had no real sense and is in fact impossible in the anisothermal case. Therefore the major criticism for all these criteria is the impossibility of their generalization to complex loadings. This situation is also the case for the creep fatigue laws developed by Chaboche. [START_REF] Chaboche | Une loi différentielle d'endommagement de fatigue avec cumulation non linéaire[END_REF] These laws have been generalized to anisothermal cases using a reduced stress σ /σ u , where σ u is the ultimate strength at the considered temperature, used to define the maximal stress or the mean stress independently of the temperature. This reduced variable is not justified from mechanical and physical point of view. For that reason Chaboche [START_REF] Chaboche | Une loi différentielle d'endommagement de fatigue avec cumulation non linéaire[END_REF] proposed to redefine the damage law in the anisothermal context. A possible way to overcome these difficulties is the energetic approach. Skelton [START_REF] Skelton | Energy criteria for high temperature low cycle fatigue[END_REF] describes the damaging process by the growth of crack through a process zone of constant size ρ at the crack tip. He considered the growth of the crack when a sufficient quantity of energy has been cumulated in this process zone. From that Charkaluk and Constantinescu 1 observed that the dissipated energy per cycle, at a steady-state W S , can be representative of the fatigue behaviour of a material:

W S = t+T t σ dε p .
The advantage of the dissipated energy per cycle comes from three main points: r this energetic quantity can be generalized to multiaxial sit- uation, r its determination is independant of the temperature, be- cause it integrates the whole loading path and therefore allows calculations with anisothermal loading and r W S is representative of the cyclic behaviour of materials.

The fatigue criterion can be simply expressed by a relationship:

Ws • N β = C. ( 3
)
The dissipated energy is calculated over the stabilized cycle obtained from the mechanical analysis. It is a good damage indicator to be associated with a macroscopic crack initiation.

Cylinder head

The thermomechanical loading cycles considered for a cylinder head correspond to a start/stop cycle of the engine. This implies to calculate the whole assembly of cylinder block, gasket and cylinder head in order to perform the thermal and mechanical analysis. The heating conditions consist of an inflow of hot gases through the fire deck and the exhaust pipes of the cylinder head. Then a dwell time at maximum temperature is performed, followed by a cooling down due to engine shutting down and circulating pressurized cold water. Therefore three computations will determine the global behaviour of the structure:

Numerical simulation and fatigue strength prediction

For such complex models, the submodelling technique is recommended. It consists of a global elastic calculation of the structure. For the area where the behaviour is strongly non-linear a sub model is extracted. The displacements at the boundary of the submodel and the temperature are then applied to this submodel to perform the viscoplastic calculation. This technique allows to limit the viscoplastic calculation only where it is necessary. This helps to minimize the calculation time, which can be typically 2 × 10 5 s CPU. Once the mechanical fields of a stabilized cycle are obtained, the fatigue analysis consists of applying the dissipated energy LCF criterion.

Fatigue assessment

In the case of the A356 alloy, the fatigue criterion has been established using classical isothermal LCF tests on fully artificially aged specimens at different temperatures between 20 and 300 • C under strain control. A series of TMF (thermo mechanical fatigue) tests on clamped specimens were also conducted to assess the fatigue criterion. Figure 12 represents the comparison between experimental lifetime and calculated results for these different tests, as well as for two real structure calculations. All the lifetime results stay within an acceptable ±2.5 error margin on lifetimes. The prediction of the crack location (Fig. 13) as well as the lifetime has been proved to be fully satisfactory on complete structure calculations. It should be noticed that these results have been achieved on large FEM models of more than 800 000 degrees of freedom in computing times compatible with the constraints of the industrial design engineers.

C O N C L U S I O N

A complete design approach has been proposed for structures undergoing thermomechanical fatigue. Formerly applied to cast iron exhaust manifolds, the method is developed here for the design of aluminium alloy cylinder heads. Based on the use of a simple elasto-viscoplastic law and an energetic failure criterion both suitable under multiaxial and non-isothermal loading conditions, the design approach also calls for some important assumptions regarding the uncoupling of modelled phenomena which permit the computations of large structures. This design approach has been successfully applied on several industrial structures. It has shown a good correlation between prediction and experiment for the crack initiation location as well as for the durability, which demonstrates the robustness of the approach. Moreover this method is compatible with an engine development schedule and permits to decrease the number of validating thermal shock tests on real components.

Fig. 1

 1 Fig. 1 Transformation of in service temperature analysis to an equivalent loading, with a known severity for tests or calculation, and decision strategy.

Fig. 2

 2 Fig. 2 Influence of the temperature and evidence of the stress relaxation for a 356 Al alloy.

Fig. 3

 3 Fig. 3 Unified model and viscoelastic-elastoplastic model.

3 2

 3 dev (a) : dev (a), s = dev (σ) and X is the hardening.

Fig. 4

 4 Fig.4 Temperature ageing evaluation of a T7 A356 aluminium alloy[START_REF] Boussac | Influence du Vieillissement Thermique sur les Caractéristiques Mécaniques à Température Ambiante de l'AS7G03 Y39[END_REF] by the evolution of the hardness (a) and conventional yield stress (b).

  -H BS )exp(0.95 ln(θ ) + 15.7 ln(t) -86.4) 1 + exp(0.95 ln(θ ) + 15.7 ln(t) -86.4) ,(1)with H B0 the original hardness in Brinell scale, and H BS the hardness of the fully aged material.

Fig. 5

 5 Fig. 5 Comparison of hardness measurements (a) and calculations (b) on a section of intervalve space of a tested cylinder head.

Fig. 6

 6 Fig. 6 Response of T7 (a) and fully aged (b) specimens to a cyclic TRC test at several temperatures.

Fig. 7

 7 Fig. 7 Maximum stress during LCF strain controlled tests at constant temperature.

Fig. 8

 8 Fig. 8 Isovalue of the cost functional showing the (η, m) coupling in the length of its minimum valley.

Fig. 9

 9 Fig. 9 Strain and temperature conditions of the non-isothermal test (a) and the stress/strain response of the viscoplastic model (b).

Fig. 10

 10 Fig. 10 Manson Coffin curve for cast iron at 200, 350, 400, 600 and 700 • C.

Fig. 11

 11 Fig. 11 Maximum temperature field (a) and hardness distribution after 10 000 cycles (b) computed on a cylinder head subjected to thermomechanical cycles.

r

  a combustion and fluid flow simulation supplying the heat exchange coefficients and the thermal fluxes, r a transient thermal computation simulating heating and cooling down and supplying the temperature distribution (and consequently the ageing state distribution, see Fig. 11) and r a mechanical computation with the temperature field as the main load parameters.

Fig. 12

 12 Fig. 12 Comparison of the estimate lifetime (in cycles) and experimental lifetime for A356 alloy LCF and TMF tests and several structures.

Fig. 13

 13 Fig.13 Crack initiation on a cylinder head prototype and distribution of the fatigue criterion on the FE model.

Charkaluk, E. and Constantinescu, A. (2000) Energetic approach in thermomechanical fatigue for silicon molybdenum cast-iron. Mater. High Temp. 17, 373-380.