H Rolland

N Saintier
email: nicolas.saintier@ensam.eu

I Raphael

N Lenoir

A King

G Robert

Fatigue damage mechanisms of short fiber reinforced PA66 as observed by in-situ synchrotron X-ray microtomography

Keywords:

The understanding of fatigue damage mechanisms of short fiber reinforced thermoplastics are a key issue in order to optimize material processing and propose physically based multiscale fatigue damage models. The presented work aims at a fine description of 3D damage development as observed by synchrotron X-ray microtomography. Damage processes at the micro and mesoscale are fully described in order to extract the elementary damage mechanisms, their sequence and kinetics. The effects of local fiber configuration and orientation are particularly detailed. From observations it is clearly evidenced that cavitation plays a major role in the fatigue damage process as it triggers all elementary damage mechanisms observed at the microscale. It is also shown that a characteristic length appears in the fatigue damage development. This internal length is in the order of magnitude of the spherulite size, suggesting a strong impact of the spherulite size on the fatigue damage development. Finally the effect of local fiber orientation on the micro and meso crack orientation is presented.

Introduction

Short glass fiber reinforced (SGFR) thermoplastics are materials with a good ratio between density and mechanical performances. For this reason they represent an interest to be used in the automotive field, for instance, where the reduction of the vehicles weight is one priority. In order to optimize the design of parts, the fatigue behaviour of the materials has to be understood and modelled. SGFR thermoplastics are mainly moulded by injection which is a well-suited process for industrial production. Indeed, it allows short process cycles, high dimensional precision and complex shapes. However, during the injection step, the matrix flow field leads to heterogeneous orientations of fibers. The resulting microstructure is generally characterized by distinguishable layers; resulting in a so called core-shell-skin structure.

The effect of fiber orientation on the fatigue behaviour of SGFR thermoplastics has been studied at the specimen scale [START_REF] Zhou | Fatigue performance of an injection-molded short E-glass fiberreinforced polyamide 6,6. I. Effects of orientation, holes, and weld line[END_REF][START_REF] Bernasconi | Effect of fibre orientation on the fatigue behaviour of a short glass fibre reinforced polyamide-6[END_REF] and at a microscopic scale. For instance, Bernasconi [START_REF] Bernasconi | Local anisotropy analysis of injection moulded fibre reinforced polymer composites[END_REF] determined the anisotropy of the material at the local scale, from the analysis of local orientation of fibers. The effect of fiber orientation on damage mechanism has also been investigated in the literature. Lang et al. [START_REF] Lang | Mechanisms of fatigue fracture in short glass fibre-reinforced polymers[END_REF] observed failure surfaces of specimens and deduced fatigue failure mechanisms from them, as Horst and Spoormaker [START_REF] Horst | Mechanisms of fatigue in short glass fiber reinforced polyamide 6[END_REF][START_REF] Horst | Fatigue fracture mechanisms and fractography of shortglassfibre-reinforced polyamide 6[END_REF]. The authors took into account the fiber orientation in their scenario, but could not consider the damage kinetics during the fatigue test nor the damage distribution in the bulk of the material. Tanaka et al. [START_REF] Tanaka | Effect of fiber orientation on fatigue crack propagation in short-fiber reinforced plastics[END_REF] investigated the effect of fiber orientation on the crack propagation, form fractography analysis and scanning electron microscopy (SEM) observations. In a receent study Belmonte et al. [START_REF] Belmonte | Fiber reinforced plastics (SFRPs), fatigue, electron microscopy, injection molding, damage mechanisms, polyamide, fiber volume fraction[END_REF] presented a description of the crack paths of fatigue cracks initiated from sharp notches and associated mechanisms higlighting the role of fiber failure or damage at fiber end from surface SEM observations. However none of these works were able to clearly observe the progressive evolution of damage.

To study the behaviour and the damage mechanisms of these materials with a complex microstructure, 3D observation tools are more and more employed. The development of X-ray microtomography, in particular, allows to reach high resolution observation of the bulk material. This technique is more and more used to evaluate bulk damage in composite materials under diffreent kind of loadings (see for example Tan et al. [START_REF] Tan | X-ray radiography and micro-computed tomography examination of damage characteristics in stitched composites subjected to impact loading[END_REF] for dynamic loadings or Sola et al. [START_REF] Sola | Bearing fatigue of composite laminates: damage monitoring and fatigue life prediction[END_REF] for fatigue damage on laminate composite). In the case of SGFR thermoplastics, Cosmi and Bernasconi [START_REF] Cosmi | Micro-ct investigation on fatigue damage evolution in short fibre reinforced polymers[END_REF] evaluate the volume of damage in specimens tested at different percentages of their expected lifetime. In similar materials, Arif et al. [START_REF] Arif | In situ damage mechanisms investigation of pa66gf30 composite: effect of relative humidity[END_REF][START_REF] Arif | Multiscale fatigue damage characterization in short glass fiber reinforced polyamide-66[END_REF], to characterize the damage mechanisms in this type of material.

Previous works of the authors [START_REF] Rolland | Damage mechanisms in short glass fibre reinforced thermoplastic during in situ microtomography tensile tests[END_REF][START_REF] Rolland | In situ x-ray tomography investigation on damage mechanisms in short glass fibre reinforced thermoplastics: effects of fibre orientation and relative humidity[END_REF] showed that in situ microtomography testing allowed the high resolution 3D monitoring of damage evolution in the bulk of the material under quasi-static loadings. Based on this approach, in situ microtomography fatigue tests were performed to identify the damage mechanisms of short glass fiber reinforced polyamide 6,6. In order to study the effect of fiber orientation on damage mechanisms, specimens have been extracted following different orientations compared to the main flow direction. To the authors knowledge, this paper presents the firsts 3D in situ observations of bulk damage evolution in SGFR polyamide under fatigue loading.

Experimental procedure

X-ray microtomography

Experiments presented in this work were performed on Psyche beam-line at the Soleil Synchrotron (Saclay, France). The set-up parameters used for the experiments are described below. The filtered X-ray beam (2 mrad mirror, 0.5 mm aluminum and 0.25 mm silver) had an energy of about 26 keV. The CMOS detector with 6.5 μm pixels, was associated to a ×10 objective, leading to a voxel edge size of μm 0.65 , on the acquired image. Specimen-sensor distance was 35 mm. 1500 projections were recorded per scan during a 180°rotation of around 5 min, with 31 references pictures before and after scanning.

In-situ microtomogrpahy compact fatigue machine

A machine was developed to test specimens by fatigue loading and to enable X-ray microtomography measurements. The machine has been designed to be compact, in order to minimize the distance between the specimen and the sensor. To maximize the X-ray beam signal, the machine had to present an homogeneous path around the specimen with a minimum attenuation of the X-ray beam. This function is ensured by a 2 mm thickness PMMA tube at the level of the specimen gage length (cf. Fig. 1(b)). The machine was directly mounted on the rotating stage of the beam line, as shown on Fig. 1. A load sensor measures the load applied to the specimen. All tests were performed under load control, with a maximal capacity of kN 1.5 .

Specimen preparation, geometry and conditioning

The material is a Technyl ® A218V30, a commercial grade of polyamide 6,6 reinforced by 30 wt% of short glass fiber, supplied by Solvay Engineering Plastics-France. Specimens are obtained from rectangular plates with a mm 3.24 thickness, obtained by injection moulding. The injection moulding process leads to an heterogeneous orientation of fibers in the thickness of the plates. This structure is usually described as a superposition of distinguishable layers: the skin, the shell and the core. In our case the core (resp. shell) has a thickness of 0.3 mm (resp. 1.4 mm), the core layer being located at mid-thikness of the plate. The skin exhibits a pseudo random orientation of fibers while fibers in the shell (resp. in the core) part have an orientation which is, in average, close to the injection flow (resp. orthogonal to the injection flow). See Ref. [START_REF] Rolland | In situ x-ray tomography investigation on damage mechanisms in short glass fibre reinforced thermoplastics: effects of fibre orientation and relative humidity[END_REF] for further details.

In order to describe the effect of fiber orientation on the damage mechanisms and the effect of the anisotropy of the identified core-shellskin structure on its development, samples were extracted following three different orientations with respect to the main injection direction: 0°, 45°and 90°.

The geometry of the specimen was designed to accommodate the constrains of the experimental set-up. Indeed, 3D X-ray microtomography only allows to observe relatively small volumes, depending on resolution and sensor size. The synchrotron experimental set-up described in the previous section allows to obtain a cylindrical observed zone of mm 1.33 diameter and mm 1.33 height (2048 pixels x μm 0.65 voxel edge size). The gage length was designed so that the stress state in the observed volume was homogeneous. A square section was chosen to improve microtomography quality (compared to a rectangular section). Taking into account these elements, the geometry of the specimen was chosen as presented in Fig. 2. This geometry allows to obtain similar tensile tests results as on full scale normalized tensile specimens obtained by the same process.

The polyamide matrix is known to be sensitive to the conditioning [START_REF] Arif | In situ damage mechanisms investigation of pa66gf30 composite: effect of relative humidity[END_REF][START_REF] Bretz | Influence of absorbed moisture on fatigue crack propagation behaviour in polyamides. part 1 macroscopic response[END_REF][START_REF] Bretz | Influence of absorbed moisture on fatigue crack propagation behaviour in polyamides. part 2 fractography[END_REF][START_REF] Selvum | Effects of moisture and uv exposure on liquid molded carbon fabric reinforced nylon 6 composite laminates[END_REF][START_REF] Ferreno | Characterisation by means of a finite element model of the influence of moisture content on the mechanical and fracture properties of the polyamide 6 reinforced with short glass fibre[END_REF][START_REF] Launay | Modelling the influence of temperature and relative humidity on the time-dependent mechanical behaviour of a short glass fibre reinforced polyamide[END_REF][START_REF] Benaarbia | Influence of relative humidity and loading frequency on the pa6.6 cyclic thermomechanical behavior: Part i. mechanical and thermal aspects[END_REF]. The water uptake can lead to a larger ductility of the polymer. Therefore, ensuring the material RH stability before and during testing is important. Prior testing, the specimens were put in an environmental chamber at 70°C, RH = 62% of humidity until their water uptake stabilization. Then, they passed 15 days at 23°C, RH = 50% to led to the desired equilibrium humidity content of 50% of relative humidity (RH50 specimens). After conditioning, specimens are sealed in individual packets to prevent any change in RH and opened just before testing. Due to the short duration of each experiment, the water content was considered as constant between the beginning and the end of the tensile tests.

Testing procedure

The in situ X-ray microtomography fatigue tests consist in a succession of scans and loading blocks, until total failure of the specimen. Fatigue tests are performed under load control, at a loading ratio of 0.1 and a frequency of 3Hz. During each microtomographic scan, the specimen load is maintained at a small load (one third of the maximal load applied in fatigue). This load allows to evidence more easily damage mechanisms, thanks to a clear distinction between elements, for instance to distinguish two parts of a broken fiber in the bulk of the material. The scan time was of 3-5 min. This procedure helped to identify damage while the applied load was sufficiently small not to induce damage. For short lifetime ranges (around 2500 cycles), a scan is made after 500 cycles.

For the in situ observations combined with fatigue testing, 5 scans have been obtained for each specimen, as indicated in Table 1.

Results

Fractography

After fatigue failure, specimen fracture surfaces have been observed by SEM. The entire fracture surface for short lifetime (2500 cycles) is presented in Fig. 3 for different orientations. The core layer clearly appears, vertically at the center of each specimen. At this scale, it can be noticed that when fibers are oriented perpendicularly to the loading direction (core layer of 0°oriented specimen and shell layers of 90°o riented specimen), the fracture surface is flatter than when fibers are parallel to the loading direction (shell layers of 0°oriented specimen and core layer of 90°oriented specimen). Due to the core-shell-skin structure, it should be noticed that the core and the shell parts of the specimen exhibit different roughness. In the case of 45°oriented fibers (cf. 3(b)), the fracture surface presents an important roughness. The roughness is directly related to the respective orientation of the crack propagation direction and fiber orientation. The fracture surface roughness is high (resp. low) when the crack propagates perpendicularly to the fiber orientation (resp. parallel to the fiber orientation). These fracture surfaces present mechanisms usually described in the literature [START_REF] Horst | Mechanisms of fatigue in short glass fiber reinforced polyamide 6[END_REF][START_REF] Horst | Fatigue fracture mechanisms and fractography of shortglassfibre-reinforced polyamide 6[END_REF][START_REF] Noda | Fatigue failure mechanisms of short glass-fiber reinforced nylon 66 based on nonlinear dynamic viscoelastic measurement[END_REF][START_REF] Sato | Mechanism of fracture of short glass fibrereinforced polyamide thermoplastic[END_REF][START_REF] Sato | Microfailure behaviour of randomly dispersed short fibre reinforced thermoplastic composites obtained by direct sem observation[END_REF] such as fiber failure and fiber-matrix decohesion. Such post mortem analyses do not allow to explain which mechanisms lead to the final failure of the specimen neither their evolution during the fatigue lifetime. These two aspects can be evaluated with in situ Xray microtomographic observations, as presented in the following paragraphs.

Elementary fatigue mechanisms description

Six damage mechanisms have been observed in the bulk of the specimen: fiber failure, damage at fibre ends, debonding, cavitation, crazing and microcracks. A description of these mechanisms is proposed, focusing on their initiation, growth and interactions.

Cavitation

The cavitation mechanism relates to the creation of small spherical damage markers. Cavities may pre-exist in the polymer due to the injection process and due to heterogeneous density at the spherulite scale. Depending on their sizes, those cavities may ( > d μm 1 ) or may not ( < d μm 1 ) be detected on the tomographic image. When detected, they appear in the shape of spheres of 1-5 μm diameter.

These damage markers were found to appear from the first 10 % on the fatigue life and to continuously initiate up to the final failure. The detected void size is quite stable from one scan to another, meaning that void do not grow significantly during the fatigue lifetime. However, it should be noticed that their number significantly increase with fatigue lifetime. This increase, driven by the applied cyclic loading, might be due to two main reasons: first voids may nucleate in defect free zones and second void may growth from pre-existing defects of a size lower than the minimum detectable one.

It should be noticed that this mechanism was not observed in such extent during monotonic tensile loading at the same load level [START_REF] Rolland | Damage mechanisms in short glass fibre reinforced thermoplastic during in situ microtomography tensile tests[END_REF] and such constitute a significant difference between quasi-static and fatigue damage mechanisms. From our observations, cavitation occurs either in fibre free zones or very close to the fiber-matrix interface, as shown in Fig. 4.

• In zones of low densities of fibers, the matrix is free to deform compared to the matrix that is confined and close to fibers. Due to the viscoelastic behavior of the material together with the applied loading ratio (R = 0.1) the mean strain evolves continuously as a function of the fatigue life. Lower fiber density zones, soft zones as compared to high fiber density zones, are more propitious to localized this mean strain component at the microscale. Work of Selles et al. [START_REF] Selles | Voiding mechanisms in semi-crystalline polyamide 6 during creep tests assessed by damage based constitutive relationships and finite elements calculations[END_REF] clearly indicates that under creep loading, cavitation is a privileged mode of damage development in the PA66. The mean strain evaluation under load control fatigue tests, that shows strong similarities with the long term evolution of the axial strain during creep tests together with the observed cavitation development correlate the results of Selles et al. [START_REF] Selles | Voiding mechanisms in semi-crystalline polyamide 6 during creep tests assessed by damage based constitutive relationships and finite elements calculations[END_REF].

• In the vicinity of fibers, the matrix is in a high local hydrostatic stress with a lower amorphous mobility. In semi-crystalline thermoplastics, these conditions are found to promote cavitation mechanism, as shown in the literature [START_REF] Xiong | In-situ saxs study and modeling of the cavitation/crystal-shear competition in semi-crystalline polymers: influence of temperature and microstructure in polyethylene[END_REF][START_REF] Castagnet | Relative influence of microstructure and macroscopic triaxiality on cavitation damage in a semi-crystalline polymer[END_REF].

Thus, under fatigue loading, the cavitation process can be activated in short fiber reinforced thermoplastics by two main parameters: the cyclic mean strain increase and/or high triaxiality level in the vicinity of fiber/matrix interface and confined matrix area (local high fiber density) at the microscale. A schematic view is proposed Fig. 5.

It should be noticed that those voids are also visible on fracture surfaces in both ductile and fragile fracture surface zones. Since the voids are visible on both, it is consistent with the fact that their population progressively evolves during fatigue loading and not only on localized zone corresponding to the final fracture.

Damage at fiber ends

The occurence of decohesion at fiber ends (also called fiber tips) has frequently been observed in our observations. This damage mechanism has also been observed for monotonic tensile testing [START_REF] Rolland | Damage mechanisms in short glass fibre reinforced thermoplastic during in situ microtomography tensile tests[END_REF][START_REF] Rolland | In situ x-ray tomography investigation on damage mechanisms in short glass fibre reinforced thermoplastics: effects of fibre orientation and relative humidity[END_REF] and is explained by the lack of bounding between fiber ends and matrix (due to the process) and the geometry of fibers, turning ends of fiber to stress concentrators. If these damage markers initiate at the first cycle in the same way as in quasi-static solicitation, they evolve very differently during the fatigue lifetime. Indeed, instead of growing in the matrix as for tensile loading by ductile damage growth [START_REF] Rolland | Damage mechanisms in short glass fibre reinforced thermoplastic during in situ microtomography tensile tests[END_REF], each damaged zone tends to initiate a microcrack in the matrix, transversely to the macroscopic tensile direction (as shown in Fig. 6). These damage zones can then be propitious to neighbouring microcracks propagation, depending on the sharpness of their geometry and the orientation of the edge. It should be noticed that the damage to microcrack transition is strongly dependent on the local configuration but starts at approximately 20% of the fatigue life. As observed in Fig. 6, damage progresses by coalescence of adjacent damaged zones. This coalescence is triggered by cavitation that initiates a microcrack in between two fiber ends (see Fig. 6(c)).

Fiber failure

Fiber failure was found to develop all along the fatigue life of the specimens and to a large extent for all fiber orientations. A typical sequence is given Fig. 7. Since fiber failure develops all along the fatigue life, it is reasonable to consider that fibers fail by fatigue and not by a quasi-static failure process (ie fibers do not fail at the very first cycle). Even though fibers are relatively short ( μm 150 350 ), their fragmen- tation in multiple parts was clearly observed.

Failure of individual fibre leads to local stress redistribution and successively foster the failure of neighbouring fibers and of the surrounding matrix. It is worth noting that when a fiber breaks, contrary to observations made for monotonic testing, the damage does not grow spherically but grows in the form of a microcrack transversely to the macroscopic loading as illustrated in Fig. 9, or by debonding and coalescence as in Fig. 7(e). These microcracks can also be found on the fracture surface as illustrated by SEM fractography given Fig. 10. Microcracks generated by the fiber failure appear as a disk around fibers, whether it is in ductile zone (see Fig. 10(a)) or in brittle zone (see Fig. 10(b)). These microcracks are due to high stress and strain concentration in the fiber failure zone. The higher criticity of fiber failure compared to fiber ends damage is illustrated in Fig. 11, where the microcracks are developing at the level of the fiber failure instead of fiber ends. An important aspect of fiber failure is its link with the crossing of adjacent fibers, called "fiber crossing" in the following. Fiber crossing has systematically been observed around broken fibers zones suggesting that local disorientation of close fibers represent a critical microstructural configuration. Two main reasons can explain the fact that fiber crossing promotes fiber failure:

• the presence of fibers with strong disorientation induces local over- stress that triggers the failure of the fiber (this local over-stress is confirmed by numerical computations but not shown here). In that case fiber failure is due to cyclic high local stresses that induce fatigue failure of the fiber,

• it was often observed that the distance between crossing fibers is in the order of magnitude of the resolution of the tomographic image. Thus it is very probable that contact occurs between fibers, creating a local fretting-fatigue situation that could trigger the failure process. The existence of such a fretting like fatigue damage mechanism at the micro scale is confirmed by SEM observations (see Fig. 8) that clearly evidence damage in the contact zone in between two fibers.

Thus, the fiber failure mechanism plays a key role in the initiation and propagation of microcracks during fatigue loading.

Debonding

Debonding occurs at the fiber-matrix interface, as illustrated in Fig. 12. It mainly happens along fibers oriented transversely to the macroscopic loading. This mechanism was observed to initiate from damage at fiber ends but, mostly by damage localization along the fiber at the fiber-matrix interface, promoted by a confinement effect between neighbouring fibers. Debonding mostly appears at an advanced stage of the fatigue lifetime (approximately 90 %) and contributes significantly to the meso-crack propagation process. As usually considered, debonding may appear as an adhesive or cohesive process (illustrated in Fig. 13). The nature of debonding appear to be linked to the orientation of the fibers, on the neighbouring fibers (confinement effect) and on the quality of the interface (e.g. regularity of the sizing). In the case of adhesive failure, debonding was clearly initiated by the development of multiple cavitation at the fiber matrix interface. Damage then develops in the form of penny-shape voids (micro-crack similar to the crazes described in the next section) of a typical size of five to ten micron that quickly connect to form an interfacial debonding. It should be noticed that debonding was found to be triggered by cavitation along the fibermatrix interface. In our case, debonding was mostly a cohesive failure process, promoted by proper chemical fiber-matrix treatments.

Crazing -fibrillation

Crazes are damaged zones of the matrix, where fibrils are still present between the two sides of the damage marker and of a typical size of 10-30 μm and appear in the last stage of the fatigue life. Once again cavitation plays a major role in this process. Indeed crazes were found to initiated by cavitation of the matrix and observed close to the fiber-matrix interface (see Fig. 14) or between pre-damaged zones of the matrix (see Fig. 15(a)), often in shear-band like localized zones. All the crazes are oriented transversely to the macroscopic loading, whatever they are close to a fiber-matrix interface or in the matrix. In the case of near fiber-matrix interface crazes there are strong similarities with the decohesion process. In both cases cavitation initiates the process and penny-shape voids can be observed in the first stage. The only difference is the fiber orientation with respect to the loading direction. In the case of fibers near perpendicular to the loading direction, voids grow on the same plane and connect to form a cohesive debonding. For lower angles (80°-30°) voids do not grow on the same plane so that a full population of voids might be observed as observed Fig. 16. The growth of each damage marker seems limited in size, with a characteristic length between a few microns and μm 20 . Remarkably, this length range is equivalent to spherulites diameter obtained by optical microscopy (see Fig. 16). This correlation is further confirmed by the three-dimensional segmentation of craze inside the thermoplastic matrix given Fig. 17 (near a fiber matrix interface). These structures are flat, penny shape like volumes of about μm 20 in diameter. These observations strongly suggest that each craze correspond to the damage of one spherulite and is initiated by cavitation in the core of the spherulite. This observation is of particular importance since it directly links the development of fatigue damage with the spherulite size.

Microcracks

Microcracks have only been observed in advanced steps of the fatigue lifetime, as illustrated in Figs. 18 and19. Microcracks larger than a few hundred microns result from the growth and coalescence of damage markers in highly damaged zones. The propagation rate and the crack path are highly dependent on the local microstructure, and especially on the disposition of damage markers and fiber orientation. If microcracks rely on the junction of elementary damage markers, their local orientation is not systematically transverse to the macroscopic loading, each individual fiber representing a microstructural barrier to overcome. In the case of 0°specimens, the propagation process is mostly driven by localization of damage in the form of 45°bands in between pre-existing damage zones, as observed in Fig. 20. For 90°s pecimens, the damage coalescence is promoted by the favourable orientation of the fiber-matrix interface that provides an easy crack propagation path. It has to be noticed that, at the specimen scale, 0°specimens provide a more important density of microcracks than 90°s pecimens where the transition from microcracks to a critical mesocracks appears more sudden. 0°specimens appear far more damage tolerant than 90°specimens.

As for damage initiation, microcracks seem to progress by steps with a size that corresponds to the spherulite size, as illustrated in Fig. 19. This observation is confirmed by the three-dimensional segmentation of microcracks (Fig. 21) as they form in the thermoplastic matrix. Microcracks are also penny shape like volumes, with a diameter close to the spherulite size.

From microcracks to mesocracks

During fatigue tests, the maximum strain per cycle was monitored. As soon as a deviation of this parameter was observed, the test was stopped in order to check if a particular event happened in the specimen. In each case, a thin line was visible to the naked eye (mesocrack) in the gage length o the specimen. In order to observe this region at the microstructural level, the subsequent microtomography scans were recentered on it.

The mesocrack appears in a region of the specimen where microcracks were well developed and where numerous elementary damage markers were present, as shown on a slice of a microtomographic picture of a fatigued 0°specimen on Fig. 22.

The path of the mesocrack from a specimen to another are significantly influenced by the local fiber orientation.

• 0°specimen

In 0°oriented specimen, the mesocrack appeared centered on the core zone layer, as illustrated in Fig. 23. In the core, where most of fibers are oriented at 90°, the mesocrack consists of fiber-matrix debonding and fiber failure of fibers transverse to the macroscopic loading (see Fig. 24(a)). In the matrix, microcracks are also clearly transverse to the macroscopic loading. These elements lead to a relatively straight path of the mesocrack in the core of 0°oriented specimen (see Fig. 24(b)).

On the contrary, the path is really tortuous in the shell, where fibers are oriented at 0°, as presented in Fig. 24(c) and (d). The tortuosity results from the presence of fibers perpendicular to the mesoscopic direction that represent microstructural barriers to overcome and induce crack deviation by shear localization at the micro scale as discussed previously. The mesocrack propagation process is mostly based on damage initiation and coalescence at fiber ends of fibers parallel to the macroscopic loading and of shear at the interface of fibers between highly deformed local zones leading to their debonding and contributing to the connection of microcracks. At the macroscopic scale the crack propagates perpendicularly to the loading direction but is found to be very tortuous at the mesoscopic scale. The tortuosity results from the presence of fibers perpendicular to the mesoscopic direction that represent microstructural barriers to overcome and induce crack deviation by shear localization at the micro scale. The high density of shear localization and the resulting tortuosity of the meso crack suggests a highly dissipative process compared to 90°specimens.

• 90°specimen

In 90°oriented specimen, the mesocrack appeared in a corner of the specimen, as illustrated in Fig. 25, where fibers are oriented transversely to the macroscopic loading direction. The mesocrack path is similar to the part of the mesocrack in the core of the 0°specimen: it is mainly based on debonding at the interface and forms a relatively straight path (see Fig. 26). This propagation is a far less dissipative process than the one acting on 0°specimens, since the density of damage markers, shear localization zones and the developed surface of the crack is of several order of magnitude lower than in the 0°specimens.

• 45°specimen

In the case of 45°specimen, fibers of both shell and core form an angle of 45°with the macroscopic loading direction. This orientation leads to differences of crack propagation. The mesocrack is mainly based on damage at the interface: debonding and damage at fiber ends, as presented in Fig. 27. From the interface of one fiber to another, the propagation through the matrix is mainly transverse to the macroscopic loading.

Globally, the mesocrack path is an in between configuration form the one of 0°and 90°specimens, driven by both fiber-matrix debonding and matrix damage coalescence. Thus, the propagation process in a 45°s pecimen is slightly more dissipative than in the case of 90°specimen.

Concluding remarks

This study presents the first results by in situ microtomographic fatigue tests on reinforced thermoplastics, with low voxel edge size μm 0.65 . The elementary mechanisms that occur during the fatigue lifetime of the short glass fiber reinforced polyamide 6,6 have been evidenced: fiber failure, debonding or damage at fiber ends and matrix damages (cavitation, fibrillation and cracks formation). From observations it is clearly evidenced that cavitation plays a major role in the fatigue damage process as it triggers all microscale elementary damage mechanisms observed. The cavitation process is promoted by local fiber configuration: low fiber density leads to cavitation through high deformation of the matrix whereas high fiber density leads to cavitation through matrix confinement between close fibers. The presented observations will be compared to full field microstructure computation in a fore-coming paper. It can then be conclude that controlling the cavitation behavior of the polymer may lead to significantly enhanced fatigue properties of the composite material.

It was also shown that a characteristic length appears in the fatigue damage development. The crazing development during fatigue tests show a characteristic size of 10-20 μm and a specific orientation, which can respectively be linked to the spherulite size and spherulitic failure in the equatorial region, as observed in another polyamide material [START_REF] Selles | Voiding mechanisms in semi-crystalline polyamide 6 during creep tests assessed by damage based constitutive relationships and finite elements calculations[END_REF]. This internal length is in the order of magnitude of the spehrulite size, suggesting a strong impact of the spherulite size on the fatigue damage development.

A comparison between fatigue and monotonic damage mechanisms shows some similarities (dependency on zones of fiber confinement) but some major differences, particularly concerning matrix damage and damage evolution. Indeed, fatigue testing induced important cavitation and fibrillation development compared to monotonic loadings. It also has to be noticed that damaged zones did not grow as during tensile tests with large local deformation, but propagates in the form of mesocrack by damage coalescence and micro-shear.

Finally the damage evolution during fatigue testing was found to be strongly dependant on local fiber orientation. Propagation is an oriented phenomenon and, according to the local fiber orientation, can be limited (perpendicular orientation of fibers) or favoured (fibers parallel to the microcrack). The propagation process in 0°is a far much dissipative process than the one acting on 90°and 45°specimens since, in that case, fiber orientation promotes damage development in the full gage length of the specimen and meso-crack deviation and branching.

Acknowledgement

The authors gratefully acknowledge Solvay Engineering Plastics for supporting this work and for providing specimens. This work was

Fig. 1 .

 1 Fig. 1. Compact fatigue machine set up for in situ testing on the Psyche beam-line.

Fig. 2 .

 2 Fig. 2. Specimen geometry for in situ fatigue tests.

Table 1 Fig. 3 .

 13 Fig. 3. Fracture surface observed by SEM -RH50 specimens -short lifetime range.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Cavitation -RH50 45°specimen = N 1537 R

Fig. 6 .Fig. 7 .

 67 Fig. 6. Damage at fiber ends -RH50 0°specimen = N 2468 R

Fig. 8 .Fig. 9 .

 89 Fig. 8. SEM observation of fiber failure initiated by fretting-fatigue on the fracture surface -RH50 45°specimen.

Fig. 10 .

 10 Fig. 10. SEM observations of fiber failures by fatigue on the fracture surface -RH50 0°specimen = N 2468 R

Fig. 11 .

 11 Fig. 11. Microcracks more developed around the fiber failure than at the fiber ends.

Fig. 12 .

 12 Fig. 12. Debonding -RH50 0°specimen = N 2468 R

Fig. 13 .

 13 Fig. 13. Different debonding -RH50 0°specimen.

Fig. 14 .

 14 Fig. 14. Crazing -RH50 0°specimen = N 2468 R

Fig. 15 .

 15 Fig. 15. Crazing -RH50 0°specimen, cavitation evidenced by arrows.

Fig. 16 .

 16 Fig. 16. RH50 0°specimen observed by optical microscopy in cross polarization.

Fig. 17 .

 17 Fig. 17. Crazing segmented in a RH50 45°specimen.

Fig. 18 .

 18 Fig. 18. Microcracks -RH50 0°specimen = N 2468 R

Fig. 19 .Fig. 20 .

 1920 Fig. 19. Microcracks mechanism as a function of spherulite organization. Microcracks are represented in red. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 21 .

 21 Fig. 21. Advance of the crack tip, segmented in a RH50 0°specimen and viewed in the plane orthogonal to the loading direction, revealing the relationship between microcrack geometry and spherulitic structure.

Fig. 22 .

 22 Fig. 22. X-ray microtomography observation in the bulk of fatigued ( = N N / 98.2% R

Fig. 23 .

 23 Fig. 23. Microcracks localization -RH50 0°specimen.

Fig. 24 .

 24 Fig. 24. Side view of mesocracks -RH50 0°specimen.

Fig. 25 .

 25 Fig. 25. Microcracks localization -RH50 90°specimen.

Fig. 26 .

 26 Fig. 26. Side view of mesocracks -RH50 90°specimen.

Fig. 27 .

 27 Fig. 27. Side view of mesocracks -RH50 45°specimen.

performed in the framework of the DURAFIP project (FUI project supported by Oseo). The tomography experiments performed at SOLEIL Synchrotron were financially supported by the synchrotron proposal n°20150398.


Marie Dumont

Céline Cataye

Arnaud Lehner

Eric Maréchal

Patrice Lerouge

Denis Falconet
email: denis.falconet@cea.fr

Jean-Claude Mollet
email: jean-claude.mollet@univ-rouen.fr

A Simple Protocol for the Immunolabelling of Arabidopsis Pollen Tube Membranes and Cell Wall Polymers

The pollen tube, a fast tip-growing cell, is an excellent model to study membrane and cell wall biosynthesis. Here, we describe a simple protocol using an easy to use device to perform immunofluorescence labelling of pollen tube membrane and cell wall. The use of the NucleoSpin column to perform all the steps of the immunolabelling procedure results in obtaining more intact pollen tubes.

Materials and Reagents

1. Arabidopsis day-0 flowers according to [START_REF] Boavida | TECHNICAL ADVANCE: Temperature as a determinant factor for increased and reproducible in vitro pollen germination in Arabidopsis thaliana[END_REF] Note: Choose the last inflorescence buds opened at the top of the inflorescence stem. The stamen must not be higher than the stigma. b. Submerge in 1 ml of PGM in a 1.5 ml Eppendorf tube.

c. Shake the tube vigorously manually and with a vortex for 5 min to release the pollen grains from the anthers.

d. Check the pollen number density with an inverted microscope.

e. Remove all the flower debris with a pair of tweezers.

f. Spin-down the pollen suspension using the microcentrifuge at 3,200 x g for 7 min (a yellowish pellet should be visible).

g. Remove the supernatant by pipetting.

h. Add 250 µl of PGM and resuspend the pellet.

i. Place the tube horizontally in the incubator at 22 °C in the dark for 6 h. j. After 6 h, check for pollen germination and pollen tube growth with the inverted microscope (Figure 1). 3. Remove the medium by aspiration or centrifugation and wash three times with 100 µl TBS buffer (or CMF-DPBS, both filtered at 0.22 µm using a syringe filter). Pollen tubes are gently resuspended in the buffer by pipetting up and down and the buffer is removed by aspiration/centrifugation.

4. Seal the bottom of the column with parafilm ® and add 100 µl 0.002% saponin in TBS for 15 min for pollen membrane permeabilization (skip this step and the next one for the cell wall immunolabelling).

5. Remove the medium by aspiration/centrifugation.

6. Seal the bottom of the column with parafilm ® and incubate the pollen tubes with 100 µl blocking buffer 1 (or blocking buffer 2), freshly prepared, for 1 h.

7.

Remove the blocking buffer by aspiration/centrifugation.

The cell wall labelling requires three washes with CMF-DPBS as explained in step B3

(Skip this step for the membrane immunolabelling). 9. Seal the bottom of the column and add 50 µl of primary antibody 1:10 dilution DGDG-specific rabbit serum in TBS-1%FBS-0.002% saponin and incubate 1 h at room temperature (or for the cell wall labelling: 1:20 primary antibody in CMF-DPBS overnight at 4 °C). Negative controls are prepared by omitting the primary antibody.

10. Wash three times with TBS-1% FBS-0.002% saponin (or CMF-DPBS) as explained in step B3.

11. Seal the bottom of the column and add 50 µl 1:500 dilution Alexa secondary antibody in TBS-1%FBS-0.002% saponin and incubate 1 h at room temperature (or for the cell wall labelling: FITC-coupled secondary antibody 1:50 dilution in CMF-DPBS for 2 h at 30 °C).

Note: From this step, keep the tubes in the dark in aluminum foil.

12. Wash four times in TBS-1% FBS-0.002% saponin and a final wash with TBS (or five times with CMF-DPBS) as explained in step B3.

http://www.bio-protocol.org/e1502 Vol 5, Iss 12, Jun 20, 2015 5 13. In order to recover the pollen tubes, resuspend them by adding at the top of the column 100 µl of TBS (or water) and by pipetting up and down several times with an enlarged tip and transfer the solution which contains the pollen tubes on a microscope slide with a cover slip. Figure 3 shows the confocal images showing the results of immunofluorescence labelling of Arabidopsis pollen tubes with anti-DGDG. Figure 4 gives an overview of the method for the membrane or cell wall immunolabelling of pollen tubes.

2 .

 2 Fetal Bovine Serum (FBS) (Sigma-Aldrich, catalog number: F0804) 3. Goat serum (Sigma-Aldrich, catalog number: G9023) 4. Saponin (Sigma-Aldrich, catalog number: S4521) 5. Primary antibody against plant cell wall polysaccharides/glycoproteins (http://www.

Figure 1 .

 1 Figure 1. 6 h-old Arabidopsis pollen tubes. Note that the pollen grain density is important to obtain good pollen germination rates.

Figure 2 .

 2 Figure 2. NucleoSpin ® Plasmid Binding Columns connected to a hose for aspiration

Figure 3 .

 3 Figure 3. Arabidopsis pollen grains were germinated for 6 h, pollen tubes were fixed and the pollen tube membrane immunolabelled with anti-DGDG antibodies. Alexa 488 was excited using the 488 nm line of an argon laser and fluorescence was collected between 500-539 nm. Superposition of control red autofluorescence induced by excitation at 543 nm laser is also shown.

Figure 4 .Recipes 1 .

 41 Figure 4. Schematic representation of the sample preparation for Arabidopsis pollen tubes plasma membrane and cell wall immunolabelling. Green dashed box indicates special step or buffer for plasma membrane labelling whereas blue dashed box points out the steps for the cell wall labelling. The picture at the bottom of the image shows a pollen tube labelled with an anti-rhamnogalacturonan-II (a pectic motif) antibody developed by Matoh et al. (1998) using a microscope Leica DMI6000B equipped with a DFC450 C camera (FITC filter: absorption, 485-520 nm; emission, 520-560 nm wavelengths).

  4. Calcium-and magnesium-free Dulbecco's phosphate-buffered saline (CMF-DPBS)

	137 mM NaCl
	2.7 mM KCl
	7 mM Na 2 HPO 4 7H 2 O
	1.5 mM KH 2 PO 4
	pH 7.2
	5. Blocking buffer 1
	1x TBS
	5% (w/v) FBS
	5% (w/v) goat serum
	0.002% Saponin
	6. Blocking buffer 2
	137 mM NaCl
	2.7 mM KCl
	7 mM Na 2 HPO 4 . 7H 2 O
	1.5 mM KH 2 PO 4
	pH 7.2
	3% fat-free milk

Note: It is better to filter at 0.22 µm using a syringe filter all the washing solutions.

Acknowledgments

Original versions of the protocols were described in Dardelle et al. (2010), Botté et al. (2011) and Dumont et al. (2014). This work was supported by the University of Rouen, the region Haute Normandie, and the "Trans Channel Wallnet" project that was selected by the INTERREG IVA program France (Channel) -England European cross-border cooperation program, which is co-financed by the European Regional Development Funds (ERDF). The work performed at LPCV (Grenoble) was supported by the Agence Nationale de la Recherche (ANR-10-BLAN-1524, ReGal; ANR BioAdapt Reglisse). http://www.bio-protocol.org/e1502 Vol 5, Iss 12, Jun 20, 2015


Z Sun

D Retraint

B Guelorget

L Waltz

Micro-pillar compression tests to characterize the mechanical behavior of a nanocrystalline layer induced by SMAT in a 316L stainless steel

Keywords: nanocrystalline material, compression tests, micro-pillars SMAT, nanocristallisation superficielle, matériau nanocristallin, essais de compression, micro-piliers

Micro-pillar compression tests were used to study the mechanical behavior of a stainless steel treated by SMAT (Surface Mechanical Attrition Treatment), particularly the induced nanocrystalline surface layer. Micro-pillars were first machined using a Focused Ion Beam (FIB) on the cross-section of the SMATed specimen. They were then deformed with a flat head mounted on a nanoindenter. Stress-strain curves were obtained for various micro-pillars machined at different distances from the SMATed surface. Deformed micro-pillars after compression tests were examined using FEG SEM to analyze deformation mechanisms. According to the obtained stress-strain curves, the mechanical strength of the stainless steel is significantly improved after SMAT, and the deformation mechanisms of the material appear to be different according to the distance from the treated surface.

Key words: SMAT / surface nanocrystallization /

Introduction

Surface treatment processes are very important for many industrial applications in the field of aerospace, automotive or biomedical. Indeed, crack initiation begins very often on the surface of components mechanically loaded in service [1]. The improvement of the surface (mechanical properties and roughness) is an effective way to enhance the overall behavior and increase the lifetime of materials.

1 ICD, LASMIS, University of Technology of Troyes (UTT), UMR 6281, CNRS -Troyes, France delphine.retraint@utt.fr 2 LMGC, Université Montpellier II, UMR 5508, CNRS -Montpellier, France SMAT (Surface Mechanical Attrition Treatment) is a technique that can alter the surface layer of coarse grained materials to obtain nano-sized grains by severe plastic deformation (SPD) [2,3]. With repetitive mechanical impacts at high strain rate, a large number of defects such as dislocations and consequently grain boundaries may be generated by SMAT, which can progressively lead to nano-sized grains at the surface. Nevertheless, the bulk of the material is not affected by SMAT, and the material characteristics such as grain size remain unchanged

Material and experimental procedures

In this work, the studied material is a 316L stainless steel (AISI 316 -ASTM F138) and the chemical composition of this material is presented in Table 1. The grain size in the as-received state is between 10 and 50 µm. SMAT is based on the vibration of spherical shot (3 mm diameter, in this work) boosted by a high frequency (20 kHz) ultrasonic generator. Random shot impacts are generated at the material surface leading to the formation of multidirectional plastic deformation as well as a superficial nanocrystalline layer. In this paper, the SMAT treatment time is equal to 30 min. A more detailed description of the SMAT process can be found in references [2,3].

After SMAT of the sample surface, the technique of focused ion beam (FIB) was used to "machine" micropillars in the cross-section of the SMATed samples in different regions beneath the treated surface including the nanocrystalline layer (see Fig. 1a). The micro-pillars have a truncated cone shape. The upper and the lower diameter are respectively 2 and 4 µm, whereas the height is 10 µm. Figure 1b shows an example of a micro-pillar prepared by FIB in this study.

The compression tests were carried out with a Nanoindenter XP (Nanoinstruments, Knoxville), using a flat circular diamond head with a diameter of 11 µm. The indenter speed was varied in order to ensure a constant ratio ḣ/h equal to 0.05 s -1 , with h being the penetration depth. The force-displacement curves were rectified to obtain the stress-strain curves. To do this, the average diameter of as well as the mechanical properties in this area. Between the nanocrystalline layer and the bulk of the material, a transition layer is present. This transition layer is characterized by a high strain hardening gradient with a grain size which varies from several nanometers (in the nearsurface layer) to several micrometers (in the bulk material). Significant compressive residual stresses can also be present in the region affected by SMAT [4]. These compressive residual stresses coupled with a grain refinement of the microstructure are expected to delay fatigue crack initiation and propagation and thus to enhance fatigue strength of the SMATed alloy [5][6][7].

In order to understand the gradient of the mechanical behavior of SMATed materials, it is important to characterize the mechanical properties of each layer, for example the nanocrystalline layer and the transition layer. The characterization of the mechanical behavior of the nanocrystalline layer is difficult, given its very small thickness (tens of micrometers). The micro-pillar compression technique was originally used to characterize the mechanical response and to understand the deformation mechanisms of pure Ni single crystals [8], Au [9]andMo [10]. It is becoming a new approach to quantify the uniaxial mechanical properties of materials at micrometer scale, thus it offers a new way to characterize the mechanical behavior of the nanocrystalline layers.

To our knowledge, the micro-pillar compression technique has not been widely used to study the mechanical behavior of nanocrystalline materials induced by SMAT. This type of mechanical behavior study can be crucial not only in terms of mechanical properties characterization of materials, but also in terms of numerical simulation. Indeed, individual mechanical behavior of each layer needs to be precisely characterized and can then be incor- the micro-pillar was used to calculate the stresses. In addition, the Sneddon criterion [11] was used to calculate the displacement of the upper surface purely due to micropillar deformation. In this criterion, the elastic deformation of the substrate below micro-pillar and that of the diamond indenter were subtracted from the displacement measured by the instrument [12,13]. With this criterion, the real displacement of the upper surface of micro-pillar d p is given by the equation as follows:

d p = d meas - 1 -v 2 i E i F meas D top - 1 -v 2 b E b F meas D bottom (1
) where d meas and F meas represent the displacement of the micro-pillar surface and the force measured by the nanoindenter respectively. E i , E b , v i and v b are respectively the Young's moduli and Poisson's ratios of the diamond indenter (1141 GPa and 0.07 [START_REF] Simmons | Single crystal elastic constants and calculated aggregate properties, A handbook[END_REF]) and the substrate (base) of the micro-pillars. Finally, D top and D bottom represent the upper and the lower diameter of each micropillar respectively.

Knowing the real displacement of the upper surface of micro-pillar, the strain can be calculated by dividing it by the initial length of each micro-pillar.

The deformed state of all micro-pillars after compression was examined with scanning electron microscopy (SEM).

Results and discussion

Figure 2 shows the nominal stress-strain curves obtained during the compression tests of micro-pillars machined at different distances from the treated surface, including the nanocrystalline layer. It can be seen that for all the stress-strain curves, an initial non-linearity occurs when the head of the diamond indenter begins to get into contact with the upper surface of each micro-pillar, probably because the flat indenter and the micro-pillars are not perfectly parallel. Then, the stress increases linearly with the deformation, which corresponds to the elastic range of the deformation of the material. Then the material enters in the range of plastic deformation.

The micro-pillar strength represented by yield stress is much higher in the nanocrystalline layer which is close to the treated surface. The reached yield stress level for the curve obtained for a micro-pillar located at a distance of 20 µm (#1) beneath the surface is about twice as large as that obtained for a micro-pillar at a distance of 420 µm (#3). It is important to note that the micro-pillar machined in the nanocrystalline layer (#1) is composed of nanograins and submicron grains with an average size of about 20 nm [6].

According to the micro-hardness curves presented in reference [START_REF] Sun | [END_REF], the total depth affected by SMAT is about 400 µm. The micro-pillar #3 is therefore located in an area that is not affected by SMAT where grains have an initial size between 10 and 50 µm. Given the small dimension of the micro-pillars compared to the grain size of material, the micro-pillar #3 is probably composed of a single crystal. This point of view seems to be confirmed by SEM observations of the deformed state of this micropillar (see Fig. 3). For the micro-pillar #3, slip bands are clearly visible on the surface, which represent the concentration of plastic slip (Fig. 3). This phenomenon is not present for the micro-pillar #1 which is in the nanocrystalline layer (Fig. 4). This means that micropillars machined in the nanocrystalline layer are more isotropic since they contain a great number of grains as the grain size (nanoscale) is very small compared to the dimension of the micro-pillars. For the stress-strain curve obtained with a micro-pillar located in the transition layer (#2, with a distance from the SMATed surface equal to 70 µm), the reached stress level is intermediate (Fig. 2). In grain boundary sliding and /or rotation of the grains tend to be dominant [START_REF] Ramesh | Nanomaterials -Mechanics and Mechanisms[END_REF]. As for the transition layer, the strain hardening phenomenon is intermediate. In this zone, the material is mechanically reinforced by strain hardening and a high dislocation density is expected to be present, which makes the strain hardening effect higher than in a non-hardened material (in the SMAT non affected area, for example see micro-pillar #3).

Conclusions

The micro-pillar compression technique was used to study the mechanical behavior of a 316L stainless steel treated by SMAT. The following conclusions can be obtained:

-The strength of material represented by yield stress is significantly enhanced by the nanocrystallization phenomenon induced by SMAT. -Deformation mechanisms are different according to the location of the micro-pillars beneath the SMATed surface.

As an outlook, several elements could be considered and studied in more details. In terms of experimental tests, the reproducibility will be studied by performing compression tests in other zones with the same distances to the SMATed surface. In addition, the effect of micro-pillars size will be studied to see the effect of this parameter on the stress-strain curves as a function of the grain size gradient. In terms of numerical simulations, the mechanical properties of each layer can be incorporated into finite element models to predict the global mechanical behavior of materials processed by SMAT. addition, the plastic slip present on the surface of micropillar is much less remarkable than for the micro-pillar #3 which is thought to be composed of a single crystal (Fig. 5).

The second element that can be seen on the curves is the strain hardening phenomenon, represented by the slope of the stress-strain curve in the plastic deformation range. First of all, a strong level of strain hardening can be observed for the micro-pillars machined in the nanocrystalline layer. It seems that in the literature, for nano-materials elaborated by different processes such as accumulative rolling and annealing, ECAP (equal-channel angular pressing), the strain hardening capacity is very limited or absent [16,17]. However, these elaboration processes are different from SMAT, and to the authors' knowledge, the mechanical behavior of the nanostructured layer induced by SMAT has never been directly characterized. Another possible reason for this strong strain hardening could be due to the fact that the shape of micro-pillars used in this study is not cylindrical but is a truncated cone. Further work is under progress in this way.

According to the curves, qualitatively the strain hardening level is dependent on the areas where the micropillars are machined. It is much greater in the nanocrystalline layer (#1) than in the regions where the grain size is in the micrometer scale (#3) (Fig. 2). This means that the deformation mechanisms may be different according to the location where the micro-pillars are machined and more precisely to the distance from the treated surface. In a single crystal, the deformation is essentially accommodated by plastic slip, while in the case of a material with nanograins, the deformation mechanism can be fundamentally different. Indeed, when the grain size is reduced to ultrafine and/or nanocrystalline regime, there is a significant effect of grain size on the mechanical behavior and the mode of microscopic deformation. For example, when the grain size decreases to nanometer scale, the

Fig. 1 .

 1 Fig. 1. (a) Cross-section of the SMATed steel: locations of the micro-pillars machined at different distances from the treated surface, (b) example of a micro-pillar prepared by FIB.Fig. 1. (a) Section transversale de l'acier SMATé : localisation des micro-piliers usinés à différentes distances de la surface traitée, (b) exemple d'un micro-pilier préparé par FIB.

Fig. 1 .

 1 Fig. 1. (a) Cross-section of the SMATed steel: locations of the micro-pillars machined at different distances from the treated surface, (b) example of a micro-pillar prepared by FIB.Fig. 1. (a) Section transversale de l'acier SMATé : localisation des micro-piliers usinés à différentes distances de la surface traitée, (b) exemple d'un micro-pilier préparé par FIB.

Fig. 2 .

 2 Fig. 2. Nominal stress-strain curves obtained by compression tests of micro-pillars machined at different distances from the SMATed surface. Fig. 2. Courbes contrainte-déformation nominale obtenues par essais de compression de micro-piliers situés à différentes distances de la surface SMATée.

Fig. 2 .

 2 Fig. 2. Nominal stress-strain curves obtained by compression tests of micro-pillars machined at different distances from the SMATed surface. Fig. 2. Courbes contrainte-déformation nominale obtenues par essais de compression de micro-piliers situés à différentes distances de la surface SMATée.

Fig. 3 .

 3 Fig. 3. Example of a deformed micro-pillar located at a distance of 420 μm beneath the treated surface (in the SMAT non-affected area), after a compression test (ε ∼ 0.22). Fig. 3. Exemple d'état déformé d'un micro-pilier situé à une distance de 420 μm sous la surface traitée (dans la zone non affectée par le SMAT), après un essai de compression (ε ∼ 0.22).

Fig. 5 .

 5 Fig. 5. Example of a deformed micro-pillar located at a distance of 70 μm beneath the SMATed surface (in the transition area), after a compression test of ε ∼ 0.13. Fig. 5. Exemple de l'état déformé d'un micro-pilier situé à une distance de 70 μm sous la surface traitée (dans la zone de transition), après un essai de compression avec ε ∼ 0.13.

Fig. 4 .

 4 Fig. 4. Example of a deformed micro-pillar machined at a distance of 20 μm below the SMATed surface (in the nanocrystalline layer), after a compression test with ε ∼ 0.15.

Fig. 4 .

 4 Fig. 4. Exemple d'état déformé d'un micro-pilier situéàune distance de 20 μm (dans la couche nanocristalline), après un essai de compression avec ε ∼ 0.15.

Table 1 .

 1 Chemical composition of the studied steel (in wt%). .013 1.7 0.26 0.017 0.003 17.37 14.52 2.80 0.08 0.088 <0.005 0.07

	Fe	C	Mn	Si	P	S	Cr	Ni	Mo	Cu	N	Ti	V
	48.4 0

Acknowledgements. Financial support for this research from the Champagne-Ardenne Research Council through Nanosurf and Nanotribo projects is greatly appreciated. This work was also partly supported by the French RENATECH network and the authors acknowledge the scientific and technical assistance of D. Troadec.