A Shanwan

S Allaoui
email: samir.allaoui@univ-orleans.fr

Different experimental ways to minimize the preforming defects of multilayered interlock dry fabric

Keywords: Fabrics/textiles, Lamina/ply, Preform, Defects

Different experimental ways to minimize the preforming defects of multi-layered interlock dry fabric

Anwar Shanwan, Samir Allaoui

INTRODUCTION

Long fiber-reinforced composites are widely used in various industries, especially in transportation, because it gives the possibility to reach a light final product. Liquid Composite Molding (LCM) processes are among the most interesting manufacturing processes to produce composite parts with complex geometry, because they offer a very interesting compromise in terms of repeatability. The first stage of this process (preforming) is delicate because there are several deformation mechanisms, which are very different from those of steel sheets stamping [START_REF] Allaoui | Experimental tool of woven reinforcement forming International Journal of Material Forming[END_REF].

The quality of preforms of double curved geometries depends on several parameters, such as: punch geometry, relative orientation of punch/fabric-layers and blank-holders pressure. These parameters play a major role on the quality of the final shape in term of defects appearance [START_REF] Allaoui | Experimental preforming of highly double curved shapes with a case corner using an interlock reinforcement[END_REF].

Predicting of preforms quality, for a given shape with a given fabric, and subsequently, the defects that may appear, can be verified by using of finite element simulations [START_REF] Boisse | Modelling the development of defects during composite reinforcements and prepreg forming[END_REF][START_REF] Ten Thije | Large deformation simulation of anisotropic material using an updated lagrangian finite element method[END_REF][START_REF] Nosrat Nezami | Analyses of interaction mechanisms during forming of multilayer carbon woven fabrics for composite applications[END_REF][START_REF] Nosrat Nezami | Active forming manipulation of composite reinforcements for the suppression of forming defects[END_REF][START_REF] Hamila | A meso macro three node finite element for draping of textile composite performs[END_REF][START_REF] Allaoui | Experimental and numerical analyses of textile reinforcement forming of a tetrahedral shape[END_REF] or experimental studies [START_REF] Allaoui | Experimental preforming of highly double curved shapes with a case corner using an interlock reinforcement[END_REF][START_REF] Allaoui | Experimental and numerical analyses of textile reinforcement forming of a tetrahedral shape[END_REF][START_REF] Soulat | Experimental device for the performing step of the RTM process[END_REF][START_REF] Vanclooster | Experimental validation of forming simulations of fabric reinforced polymers using an unsymmetrical mould configuration[END_REF][START_REF] Chen | Defect formation during preforming of a bi-axial non-crimp fabric with a pillar stitch pattern[END_REF][START_REF] Lightfoot | Defects in woven preforms: Formation mechanisms and the effects of laminate design and layup protocol[END_REF][START_REF] Shan Liu | Investigation of mechanical properties of tufted composites: Influence of tuft length through the thickness reinforcement[END_REF]. In addition, during the manufacturing of composite parts, several layers of fabric are stacked together. As these layers (sheets) are not being interdependent, they have different behaviors and can relatively slide, each to other. By this way, an inter-ply friction is generated between them. Several studies showed that the preform quality depends highly on the inter-ply friction, which takes place between the superposed layers during forming [START_REF] Bel | Finite element model for NCF composite reinforcement preforming: Importance of inter-ply sliding[END_REF][START_REF] Allaoui | Effect of inter-ply sliding on the quality of multilayer interlock dry fabric preforms[END_REF][START_REF] Ten Thije | A multi-layer triangular membrane finite element for the forming simulation of laminated composites[END_REF][START_REF] Vanclooster | Simulation of multi-layered composites forming[END_REF][START_REF] Chen | Intra/inter-ply shear behaviors of continuous fiber reinforced thermoplastic composites in thermoforming processes[END_REF][START_REF] Hamila | Simulations of textile composite reinforcement draping using a new semi-discrete three node finite element[END_REF]. Moreover, the friction effect is more severe in case of dry woven fabrics, due to shocks between the overhanging yarns of the superposed layers [START_REF] Allaoui | Influence of the dry woven fabrics meso-structure on fabric/fabric contact behavior[END_REF]. A recent study highlighted the influence and criticality of interply friction according to sequence of layers stacking, especially when the inter-ply sliding is greater than the unit cell length of the fabric [START_REF] Allaoui | Effect of inter-ply sliding on the quality of multilayer interlock dry fabric preforms[END_REF].

The aim of this study is to improve the quality of preforms of dry woven fabrics, by reducing or eliminating the defects via two criteria: the definition of the best process parameters and the second one is the reduction of inter-ply friction by improving the interface between the layers.

MATERIAL AND METHODS

Tests presented in this paper are performed on a commercial composite woven reinforcement, which is a powdered interlock fabric, denoted Hexcel G1151®, with a surface weight of 630 g /m². This fabric is composed of around 7.5 yarns / cm in warp and weft directions.

The unit cell of G1151® consists of 6 warp yarns and 15 weft yarns distributed on three levels. In situ, the average yarn width is about 2mm for warp and 3mm for weft. A specific forming device, developed at LaMé laboratory was used to perform the shaping tests [START_REF] Allaoui | Experimental tool of woven reinforcement forming International Journal of Material Forming[END_REF][START_REF] Soulat | Experimental device for the performing step of the RTM process[END_REF]. This device is equipped with two CCD cameras to track the yarns position and measure the plane shear of the reinforcement.

During preforming process, there is a complex relationship between three parameters: fabric mechanical properties, forming process parameters and punch (part) shape. This paper aims to improve the preforming quality of dry interlock fabric and to avoid, as possible as, the appearance of defects during preforming process on a given shape. To study a wide range of defects with a maximum of amplitudes, our tests were carried-out by means of a highly non-expandable and double curved form (prismatic punch) having a triple point and small curvature radii (10mm). The punch dimensions are shown in Figure 1 [START_REF] Allaoui | Experimental preforming of highly double curved shapes with a case corner using an interlock reinforcement[END_REF][START_REF] Allaoui | Effect of inter-ply sliding on the quality of multilayer interlock dry fabric preforms[END_REF].

The different preforming configurations, presented in this study, are illustrated in Figure 2 [START_REF] Allaoui | Experimental preforming of highly double curved shapes with a case corner using an interlock reinforcement[END_REF][START_REF] Allaoui | Effect of inter-ply sliding on the quality of multilayer interlock dry fabric preforms[END_REF], where eight blank-holders are used around the preform to apply a pressure of 0.15 bar on the fabric (Figure 2, a). The tests were done with a punch speed of 30 mm/min.

For both monolayer and two-layers preforming tests, the same experimental conditions are used.

In case of mono-layer preforming, several orientations of ply/punch are also used (α° : 0°, 30°, 45°, 60° and 90°). The 0° orientation, which is considered as reference configuration (Figure 2.a), means that the weft and warp directions of the stacked layers are parallels to the lateral edges of the punch faces. In case of two-layers performing, the tests are conducted by stacking one of layers at 0° and the other-one at α° (Figure 2.b), with several configurations such as : 0°/0°, 0°/90°, 0°/45°, 45°/0°, etc. Herein, α°/0° means that the upper layer is oriented at α° and the lower one at 0°.

RESULTS AND DISCUSSIONS

For monolayer preforming configuration, the first tests were carried-out with a monolayer oriented at 0° (reference configuration) and at the same optimal conditions, found in a previous study [START_REF] Allaoui | Experimental preforming of highly double curved shapes with a case corner using an interlock reinforcement[END_REF] for the same type of fabric. Preforming tests showed a good preforms quality at macroscopic level (Figure 3.a) since the preform useful area does not have wrinkles defect.

Nevertheless, at mesoscopic level, ''buckle'' defects occur on the faces and the edges of prismatic preform where yarns are subjected to in plane bending. Subsequently, these yarns undergo an outof-plane buckling, so that the weaving pattern is not respected for a long time. In terms of shear angles, the maximal values are reached at the bottom corners of the preforms (50° and 55°). These values are close to the interlock fabric-locking angle. On the other hand, no wrinkles defects occurred in the preform useful area due to the coupling between shear and tension, which can delay the onset of wrinkles when the tension applied on fabric increases [START_REF] Allaoui | Experimental preforming of highly double curved shapes with a case corner using an interlock reinforcement[END_REF][START_REF] Launay | Experimental analysis of the influence of tensions on in plane shear behaviour of woven composite reinforcements[END_REF][START_REF] Harrison | Characterising the shear-tension coupling and wrinkling behaviour of woven engineering fabrics[END_REF].

A comparison between the 0° configuration and the others of 90°, 0°/0°, 0°/90°, 90°/0° and 90°/90°

shows the same results with the same defects (Figure 3.b). In fact, in all of these cases, the relative orientation between yarn networks and the punch remains unchangeable, which confirm the effect of the relative position of punch/fabric. The only difference between the 0° and 90° preforms is the inverting of the position of weft and warp networks.

Oriented monolayer preforming tests

The preforms obtained by oriented monolayers (α ≠0° and α ≠90°) show more extensive defects than the above-mentioned case (0° and 90°) although the shear angle values remain in the same scope obtained in the case of reference configurations.

Despite the small shear angles, wrinkles occur at the useful area, as illustrated at zone 1 of the Figure 4 (case of monolayer oriented at 30°). As shown in this figure, wrinkles appear on two opposite corners of the preform where the observed shear angles are low (22°). Moreover, there are no wrinkles defects on the frontal face (area 3), where high shear angles are observed (49°).

In addition, "buckle" defects are also observed in this preform (areas 2) and are located at different emplacements by comparison with those obtained at 0° monolayer orientation. These "buckle" defects are almost due to bending stresses applied on yarns during preforming. These observations correspond to those obtained in previous studies [START_REF] Allaoui | Experimental preforming of highly double curved shapes with a case corner using an interlock reinforcement[END_REF][START_REF] Allaoui | Effect of inter-ply sliding on the quality of multilayer interlock dry fabric preforms[END_REF] and confirm the significant effect of the relative orientation of punch/ply on the preform quality for complex geometries. Subsequently, in the case of oriented configurations (0° < α <90°), the preforms quality is not acceptable. In fact, a bad preforms quality leads to aesthetic problems and non-respect of the dimensional specifications. In addition, these defects may have an effect on the mechanical performances of the final part [START_REF] Hörrmann | The effect of fiber waviness on the fatigue life of CFRP materials[END_REF][START_REF] Cruanes | Effect of mesoscopic out-of-plane defect on the fatigue behavior of a GFRP[END_REF]. Therefore, the preforms quality needs to be improved.

The improvements can be achieved by different strategies like : substitution of fabric by another one with a better formability, changing of manufacturing process, applying of best manufacturing process parameters, and/or modifying of ply orientations and parts geometry, etc. From an industrial point of view, certain strategies could be costly and/or time-consuming (change of process, change of reinforcement).

However, some parameters are often set by the technical specifications of the part (such as: ply orientations, geometry, type of reinforcement, etc…). Furthermore, the modifying of such parameters can affect the entire project of system in which the part would evolve. Thus, the most interesting strategy to adopt is to modify the parameters that do not affect the specifications of the part. It will be possible, for example, to improve the preforms quality by optimizing of the process parameters.

Hence, a new strategy depending on modifying of some process parameters, such as the blank holder's pressure and their geometry, was adopted. On the other hand, the other parameters like the orientation of layers, the punch geometry and the type of fabric, remain fixed. Preforming tests are held on oriented layers, a change was applied on two parameters: blank holder's pressure and blank holder's geometry. This change was applied separately in order to analyze the results and define which parameter is more important than the others on the preforms quality.

The tests showed that the increasing of tensile force applied on the yarn's networks, which is obtained by increasing of blank holder pressure, leads to a delay on the onset of wrinkles or to avoid them [START_REF] Allaoui | Experimental preforming of highly double curved shapes with a case corner using an interlock reinforcement[END_REF][START_REF] Launay | Experimental analysis of the influence of tensions on in plane shear behaviour of woven composite reinforcements[END_REF][START_REF] Harrison | Characterising the shear-tension coupling and wrinkling behaviour of woven engineering fabrics[END_REF]. Therefore, the pressure was firstly increased up to 0.2 bars only on the two square blank holders located on the opposite corners B&D, where wrinkles defect appear (Figure 4). The maximal value of the pressure was defined by the capacity of the compressed air system.

The obtained results show that the wrinkles remain on the preform but their amplitude is slightly decreased (Figure 5). In addition, the shear angles did not change on the preform areas compared to the case where the pressure applied on fabric is 0.15 bar (figure 4).

The tests showed that the increase in the blank holders' pressure did not allow avoiding of wrinkles completely. Hence, an adapted blank holder's geometry was suggested to improve the preforms quality [START_REF] Capelle | Complex shape forming of flax woven fabrics: Design of specific blank-holder shapes to prevent defects[END_REF]. A single blank holder surrounding the preform, which eliminates the gaps present in the initial configuration, has been used to replace the eight individual ones. Thus, new tests were performed by using of this geometry with a pressure of 0.15 bars. As shown in Figure 6, the obtained preform has a better quality because there is a higher decrease in wrinkles amplitude than the one obtained by pressure increasing. It means that the effect of blank holder geometry on the preform quality is more significant than the effect of pressure because the blank holder controls the force application and its distribution on the yarns. However, the change of blank-holders geometry did not allow the elimination of wrinkles completely.

For this reason, a third solution, depending on combining of the two previous strategies was used in order to improve the quality of the preforms (pressure of 0.20 bars + single blank holder). In this case, a good quality was obtained without any wrinkles defect, as shown in Figure 7. Subsequently, the combining of several optimized parameters can leads to the avoiding of wrinkle defects.

On the other hand, buckles defects remain appeared in the useful area in spite of the previous suggested solutions. The extent of the region of these defects and their amplitude are almost identical. Consequently, "buckle" defects can not be avoided completely by the strategy used in this study. In fact, this defect is generated by in plane bending of yarns that leads to their out of plane buckling promoted by the fact that the fibers are continuous and not bonded together. To avoid this defect completely, it may be possible to change the nature of yarns and/or their geometry. This solution is sometimes possible with natural yarns [START_REF] Capelle | Complex shape forming of flax woven fabrics: Design of specific blank-holder shapes to prevent defects[END_REF], which are close to a homogeneous material because the fibers are bonded between them, but it is difficult or impossible to be achieved in the case of carbon and glass yarns.

As a conclusion of this part, the relative orientation of punch/layer has a significant influence on the preform quality whereas the optimizing of process parameters (blank holder geometry and/or applied pressure) can lead to further improvements in preforms quality. In addition, it is highlighted that the blank holder geometry has more significant effect than the tensile applied on the yarn networks. Finally, the combination of these two solutions led to better results. Moreover, the two improvements do not have an important influence on the mesoscopic defects (buckles) because they have no act on the mechanisms involved in the appearance of these defects.

Multilayers preforming tests

The same approach used in monolayer tests was applied for two-layers preforming tests. In this paragraph, we present the results of 45°/0° preforms (45°/0° means that the oriented layer is the external one in the stacking order). The 45°/0° stacking sequence was chosen for two reasons: firstly, because it is more prone to have defects than the 0°/45° configuration [START_REF] Allaoui | Effect of inter-ply sliding on the quality of multilayer interlock dry fabric preforms[END_REF] and secondly, it enables to observe and make the required measurements on the outer layer (45°), in order to be compared with a monolayer, preformed at 45°. The preforming results of 45°/0° stacking sequence, obtained with the same initial process parameters, show more numerous defects than 45° monolayer preform, and thus, a bad quality is obtained as shown in Figure 8. The type and location of these defects remain the same of those of 45° monolayer configuration but their amplitude and their quantities are significantly higher, whereas the shear angle values remain unchanged relatively (Figure 8). In fact, the bad quality is attributed to inter-ply friction as it has been highlighted and demonstrated in previous study [START_REF] Allaoui | Effect of inter-ply sliding on the quality of multilayer interlock dry fabric preforms[END_REF].

The inter-ply friction lead to the appearance of additional wrinkles in the center of the frontal face of two-layer preforms, where there are highest shear angles. Moreover, when compared with 30° and 30°/0° preforms, the configurations of 45° and 45/0° show more numerous defects and other additional types of defects also, like the weave pattern heterogeneity (Figure 4 and Figure 8). The increase in type and amplitude of defects is induced by the effect of the punch/layer relative orientation.

To improve the quality of 45°/0° preforms, the same strategy, used for oriented monolayers, was applied. Thus, draping tests were conducted firstly with an increasing in the blank holder's pressure, then by using the new blank holder geometry and finally by combining of the two solutions together. The obtained results show an improvement in the two-ply preforms quality with the same trend observed for monolayer preforms, i.e., the use of the new blank holder geometry gives better results than the increase in pressure (Figure 9). When the two solutions are used together, their effect was combined and thus a greater improvement was obtained (Figure 10).

However, defects remain always on the preform in spite of these improvements. Subsequently, the combination of these two solutions did not enable to avoid wrinkles completely.

In fact, in the 45°/0° configuration, there is an interface between the two stacked layers, which plays a major role on the preform quality. It has been showed in a previous study that the amount and the amplitude of defects increase because of inter-ply friction, caused by the relative sliding between layers [START_REF] Allaoui | Effect of inter-ply sliding on the quality of multilayer interlock dry fabric preforms[END_REF]. The fabric/fabric friction behavior is governed by shock phenomenon occurring between transverse overhanging yarns of each ply, which leads to signal variation with high amplitudes due to the high tangential forces generated by shocks (Figure 11). The tangential forces hampers the sliding of the plies locally and lead to an increase in defects appearance and amplitude. The inter-ply friction effect is significant when inter-ply sliding is larger than the fabric's unit cell length. In the case of 45°/0°, the measured sliding distance can reach more than 70 mm while the unit cell length is about 8 mm.

To avoid the overhanging yarns shocks, it is necessary to reduce the inter-ply sliding or to decrease the inter-ply friction. The reduction of sliding distance remains difficult to be achieved because it depends on both relative positions of ply/ply and punch/ply. However, it is possible to reduce the global ply/ply friction behavior by making the dynamic friction smoother. For this aim, avoiding or reduction of shock phenomenon, occurring between yarns, is necessary. This can be achieved by several solutions that require modifying of: crimp, fabric meso-architecture, yarns shape and/or their material, surface treatment, etc. These improvements will therefore induce a change of reinforcement or its characteristics, whereas it is sometimes not possible to change them according to technical specifications.

To overcome this problem, we proposed the inserting of an intermediate mat reinforcement layer between the two performed plies. This solution does not need to change the fabric or change its characteristics (crimp, meso-architecture, ...). As the mat is not a woven fabric, there is no shocks, which take place between the different plies of fabric. Indeed, it is evident that the mat insertion induces a modification of the stack, and therefore, a modification of the mechanical performances and of stage following stage of LCM processes (resin injection/infusion), which have to be considered.

To verify this assumption, friction tests were conducted on fabric/mat in order to compare their results with those of fabric/fabric. Commercial glass mat, with an areal weight of 300 gr/m², was used for this study. These tests were done by means of experimental test bench, which was developed at LaMé laboratory of Orleans University [START_REF] Hivet | Design and potentiality of an apparatus for measuring yarn/yarn and fabric/fabric friction[END_REF]. The bench working principle depends on the sliding of two plans surfaces (Figure 12). A normal force FN is applied on the upper sample, which is fixe and connected to a tensile force sensor. The lower sample could be moved horizontally so that it generates a tangential force, which can be measured by the sensor. Fabric/mat friction tests were carried-out in warp and weft directions according to the experimental conditions illustrated on table 1.

The obtained fabric/mat friction behaviors are presented on Figure 13, where we observe smoother dynamic friction behaviors in comparison with behavior of interlock/interlock (Figure 11 and Figure 13). This means that there are no yarn's shocks during the relative sliding of plies. In addition, the average values of the dynamic friction coefficient for fabric/mat are 0.25 in wrap direction and 0.35 in weft direction. These values are reduced at least to the half in comparison with fabric/fabric case, where the friction coefficient is around 0.61.

Theses results confirm our hypothesis and, therefore, could leads to an improvement of the preform quality of two stacked layers. To verify this fact, preforming tests were carried out after inserting of glass mat between the two layers of 45°/0° configuration with 0.15 bars pressure applied by the single blank holder, which surrounds the preform (Erreur ! Source du renvoi introuvable.). The Figure 15 shows the positive effect of this strategy because the wrinkles defects have decreased significantly in comparison with the case illustrated in Figure 10. The remaining defects have a low amplitude, which could be negligible with comparison to the initial configuration.

Consequently, defects amplitude is highly reduced thanks to the mat using. The observed improvements were specially been observed at B and D corners (Figure 15). In this case, the global amelioration is due to two reasons:  The mat prevents any direct contact between overhanging yarns of G1151® preformed layers, i.e., there are no shocks between the yarns of the two layers, even if the sliding between layers is higher than the fabric's unit cell length. Subsequently, the using of an intermediate layer (glass mat) has an important role on the stabilization of friction coefficient. In addition, stress is also reduced during the sliding between performed layers.

 The mat allows a smooth friction during the inter-ply sliding, and so, the friction coefficient is reduced. Hence, wrinkles and buckles amplitudes are enormously reduced.

These results highlight the importance of the intermediate mat layer in the reduction of friction coefficient and consequently in the reduction of the amplitude of defects. In addition, the using of an intermediate mat layer ensures a stabilization in friction coefficient variation during the sliding, i.e. the variation amplitude of friction coefficient in the case of mat/fabric fiction was reduced to a quart comparing to the case of fabric/fabric friction.

Finally, it can be concluded that the combining of the three previous solutions (new blank-holders geometry, pressure increasing and mat using) allows an enormous reduction in the defects appearance and in their amplitude. Thanks to combining of these solutions, it was practically possible to avoid the defects appearance in the preform useful area, especially, wrinkles defects.

Nevertheless, whichever the improvement level, the defects remain even with small amplitude. For this reason, we decided to combine all previous improvements solutions with the last improvement, which is the use of compaction effect between layers. Indeed, it has been shown that if the layer subjected to defects was at the inner position, relatively to the punch, the outer ply applies a compaction effect that leads to decrease in defects [START_REF] Allaoui | Effect of inter-ply sliding on the quality of multilayer interlock dry fabric preforms[END_REF] (case of configuration 0°/45°). This configuration is more interesting because in conventional laminates, a ply oriented at 0 ° or 90 ° is often placed outside the stacking, which make this improvement viable industrially. Subsequently,  Laying the oriented ply below the non-oriented one, i.e., using the 0°/45° stacking sequence. Indeed, as shown in Figure 16, wrinkles defects were completely disappeared, thanks to combining of the four mentioned solutions. Only the buckles defect still on the preform, as shown at the central face of the preform (Figure 16).

Finally, each one of these four improvement solutions was applied alone, in this experimental study, in order to classify them according to their influence on the defects appearance. The defects and the preform quality obtained after applying of each solution were compared quantitatively and qualitatively. The results are summarized on table 2. The sign (+) means that the solution has a positive effect to avoid the considered defect while the (-) sign means a bad effect.

According to these results, the improvement solutions can be classified according to their importance, from the more significant to the smallest one, as follows:

1) Reduction and stabilization of dynamic friction coefficient (by introducing of intermediate mat between the layers);

2) Adapted blank-holders' geometry and number;

3) Laying the oriented layer below the non-oriented one; 4) Applying a tensile, through the blank holder pressure, on the yarns' networks.

CONCLUSION

This study presents a strategy to improve the quality of dry complex preforms. The results showed that the inter-ply friction and the relative orientation between layers and the punch influence the preforms quality significantly by inducing numerous defects with large amplitudes and extent. The modifying of the blank holder geometry and the increase of their pressure enabled to improve the quality of the monolayer preforms. The changes in these parameters allowed avoiding wrinkles in the monolayer preforms. On the other hand, they did not show significant improvements in the two-layer preforms quality since the inter-ply friction, occurring during the preforming of multi-layers, affects the defects appearance hugely.

The reduction of the inter-ply friction can be achieved by several solutions; the majority of them induces a change of the reinforcement or its characteristics, which is sometimes not possible, according to technical specifications of a composite part. The better solution to be proposed is to insert a mat fabric between the preformed layers. This one allow the decreasing of the number and amplitude of wrinkles significantly. However, this modification in the stack has to be considered, as it will induce a modification in the mechanical performance of the material and also of stage following stage of LCM processes (resin injection/infusion).

The obtained results showed that the inter-ply friction is the first and the most important parameter, which influences the defects appearance. Then, the blank-holders geometry is considered as the second parameter according to its importance. Next, the compaction between layers and finally the tensile applied on the yarns networks. In conclusion, suitable technical solutions should be applied to improve the friction during the shaping of dry reinforcements, in order to improve the preforms quality, which is hugely affected by the friction between layers.

  preforming tests were done by combining of the four following solutions together:  Use of a new blanks-holders geometry;  Use of the optimal pressure value (0,15 bars);  Use of intermediate mat layer between the preformed fabric's layers;

Figure 1 Figure 2 :Figure 3 :Figure 4 :Figure 5 :Figure 6 :Figure 7 :Figure 8 :

 12345678 Figure 1 : Punch dimensions

57°± 4 48°± 2 (

 2 a ) External layer, oriented at 45° ( b ) Internal layer at 0°  ******** Wrinkles zone at B&D corners and in interne layer  ******** Buckles zones  ******** Zone of an important shear without wrinkles

Figure 9 :

 9 Figure 9 : 45°/0° defects after using of new blank holder geometry

Figure 10 :Figure 11 :

 1011 Figure 10 : 45°/0° defects after combining of new blank holder geometry and pressure increasing

Figure 12 :

 12 Figure 12 : Friction bench principle

Figure 13 :

 13 Figure 13 : Fabric/mat friction behaviors according to wrap and weft directions

Figure 14 :

 14 Figure 14 : Configuration of two layer preforming (45°/0°) with mat inserting.

Figure 16 :

 16 Figure 16 : Complete disappearance of wrinkles defect when combining the four solutions: new blanks-holders geometry, optimal pressure value, using of mat layer and laying of the oriented layer below the non-oriented one.

Table 1 :

 1 Experimental condition of friction tests

	Improvement solution	Wrinkles Buckles Global quality
	Two layers in initial configuration 45°/0°	---	-	-4
	Pressure increasing	--	-	-3
	New blanks-holders geometry (rectangular form)	-	-	-2
	Intermediate Mat insertion	++	+	+3
	Pressure decreasing and new blanks-holder geometry	+++	+	+4
	Pressure decreasing, new blanks-holders geometry and intermediate mat	++++	+	+5
	Pressure decreasing, new blanks-holders geometry, intermediate mat and 0°/45° stacking sequence	++++	++	+6

Table 2 :

 2 Classification of the process parameters effect and their influence on the preform quality.


L Montero

S Allaoui
email: samir.allaoui@univ-orleans.fr

G Hivet

Characterisation of the mesoscopic and macroscopic friction behaviours of glass plain weave reinforcement

Keywords: A. Fabrics/textiles, A. Yarn, B. Mechanical properties, E. Preforming

Friction at different levels of the multi-scale structure of textile reinforcements is one of the most significant phenomena in the forming of dry fabric composites. This paper investigates the effect of the test conditions on fabric/fabric and yarn/yarn friction. Friction tests were performed on a glass plain weave and its constitutive yarns, varying the pressure and velocity.

The results showed that the friction behaviours at the two scales were highly sensitive to these two parameters. An increase in pressure led to a decrease in the friction coefficients until steady values were reached, while an increase in velocity led to an increase in the friction coefficients.

At each scale, the frictional behaviour of the material was significantly influenced by the structural reorganisation of the lower scale.

Introduction

Fibre-reinforced composite materials are gaining in popularity in industry because of their high performances, lightweight and design flexibility. In addition, textile composites offer sustainable solutions concerning environmental issues, for instance in transport sectors where decreasing the weight of the different structures can reduce fuel consumption and hence polluting emissions. However, even if fibrous composites appear to be a good solution, many issues remain, especially as regards mastering processes such as the predictability of the quality of the part, cycle time, cost price, etc.

Liquid Composite Moulding (LCM) processes are among the most attractive candidates to manufacture complex composite shapes with a high degree of efficiency (cost/time/quality).

The first step in LCM processes consists in forming the fibrous reinforcement. The mechanical behaviour of dry reinforcement with respect to the shape geometry is a key point in order to ensure both a correct final shape and good mechanical properties of the final part. In addition, during a multi-layer forming process, friction between the reinforcement layers and between tools and external layers has a significant effect on the quality of the preform obtained (appearance of defects) [START_REF] Allaoui | Effect of inter-ply sliding on the quality of multilayer interlock dry fabric preforms[END_REF][START_REF] Thije | A multi-layer triangular membrane finite element for the forming simulation of laminated composites[END_REF]. However, the mechanisms governing the preforming of dry reinforcements are far from being fully understood [START_REF] Hivet | Analysis of woven reinforcement preforming using an experimental approach[END_REF]. During preforming, the reinforcements are subjected to different loadings such as tension, shear, compression, bending, and friction at different levels of the multi-scale structure of the textile reinforcement. Friction can cause local defects such as wrinkling or yarn breakage, significantly altering the quality of the final product, and can modify the final orientation of the fibres, which is crucial for the mechanical behaviour of the composite part. Friction also plays a significant role in the cohesion and the deformation mechanism of a dry fibrous network. Consequently, understanding the friction behaviour between reinforcements is necessary so as to understand, master and optimize the first forming step in LCM processes. A growing number of studies have therefore been conducted on the friction behaviour between fibrous reinforcements or on the relationship between friction and formability [START_REF] Allaoui | Effect of inter-ply sliding on the quality of multilayer interlock dry fabric preforms[END_REF][START_REF] Thije | A multi-layer triangular membrane finite element for the forming simulation of laminated composites[END_REF][START_REF] Hamila | Simulations of textile composite reinforcement draping using a new semi-discrete three node finite element[END_REF][START_REF] Gorczyca-Cole | A friction model for thermostamping commingled glass-polypropylene woven fabrics[END_REF][START_REF] Sachs | Characterization of the dynamic friction of woven fabrics: Experimental methods and Benchmark results[END_REF][START_REF] Allaoui | Influence of the dry woven fabrics meso-structure on fabric/fabric contact behaviour[END_REF][START_REF] Thije | Design of an experimental setup to measure tool-ply and plyply friction in thermoplastic laminates[END_REF]. However, since it is a complex issue due to the multi-scale fibrous nature of the reinforcements, considerable research remains to be done in order to fully understand e this phenomenon.

Different kinds of studies on the frictional behaviours of textile and technical reinforcements have been conducted over the past years. These materials are in general defined in terms of their multi-scale character: macroscopic (fabric), mesoscopic (tow or yarn) and microscopic (fibre). Studies carried out at each scale, using different devices, show that depending on the scale considered, the behaviour obtained appears to be different.

At the microscopic scale, Nowrouzieh et al. evaluated experimentally and with a microscopic model the inter-fibre friction forces of cotton to study the fibre processing and the effect of these forces on the yarn behaviour [START_REF] Nowrouzieh | The investigation of frictional coefficient for different cotton varieties[END_REF][START_REF] Nowrouzieh | Inter fiber frictional model[END_REF]. They found that the friction behaviour was correlated to the yarn strength and its irregularity (variation in the fibre section). The fibre with the highest friction coefficient produced more regular yarns. Analysis of the variance of the modelling results showed that inter-fibre friction was more sensitive to the normal load than to the velocity.

At the mesoscopic scale, the friction between various couples of materials such as tow/tow, tow/metal and tow/fabric has been studied on reinforcements made from different fibres (aramid, carbon and E-glass). The results demonstrated the significance of the relative orientation between the tows (parallel and perpendicular) on inter-tow friction for technical reinforcements [START_REF] Vidal-Sallé | Friction Measurement on Dry Fabric for Forming Simulation of Composite Reinforcement[END_REF][START_REF] Cornelissen | Frictional behaviour of high performance fibrous tows: Friction experiments[END_REF]. The contact model proposed by Cornelissen provides a physical explanation for the experimentally observed orientation dependence in tow friction (tow/metal or inter-tow) [START_REF] Cornelissen | Frictional behaviour of high performance fibrous tows: Friction experiments[END_REF][START_REF] Cornelissen | Frictional behaviour of high performance fibrous tows: A contact mechanics model of tow-metal friction[END_REF]. The mesoscopic frictional behaviour of carbon tows was explained by the microscopic constitution of the tow assuming a close packing of filaments which leads the normal load in a stationary tow to transfer from one layer of filaments to the layer beneath. Some recent papers deal with fabric/fabric and fabric/metal friction at the macroscopic scale.

Many of them deal with textile materials and focus on the effect of test conditions with the aim of improving the manufacturing process or adapting and functionalizing the final product (clothes). Ajayi studied the effect of the textile structure on its frictional properties by varying the yarn sett (number of yarns/cm) and the crimp while keeping the Tex and thickness constant [START_REF] Ajayi | Effects of fabric structure on frictional properties[END_REF]. The frictional properties increased by increasing the crimp (and thus the density), which was attributed to the knuckle effect of the textile. The term knuckle refers to the cross-over points of the warp and weft yarns making up the fabric. During the weaving process, knuckles generate yarn undulations, i.e. an irregular and rough surface of the fabric, because the two sets of yarns interlace with each other. The yarn undulation is characterised by the yarn knuckle, which is defined as the yarn crown. Furthermore, several studies have been conducted to understand the effect of the test conditions, such as atmospheric conditions which are relevant for textiles used for clothing especially as they are often made of natural materials. Several parameters, such as relative humidity, fabric structure, type of fibre material and direction of motion were found to exhibit an effect on the textile/textile friction while temperature (0-50°C) did not significantly influence the frictional parameters [START_REF] Arshi | Modeling and optimizing the frictional behavior of woven fabrics in climatic conditions using response surface methodology[END_REF]. Here again, the most significant parameter was related to the fabric structure. Das and co-workers [START_REF] Das | A study on frictional characteristics of woven fabrics[END_REF] examined the textile/textile and textile/metal frictional characteristics that simulate interaction between clothing items and fabric movement over a hard surface. They performed frictional tests with different normal pressures on commercial fabrics typically used in clothing industries in which some are composed of 100% of the same material while others are blended (made with two materials such as polyester/cotton). It was concluded that fabric friction is affected by the rubbing direction, type of fibre, type of blend, blend proportion, fabric structure and crimp. Fabric/metal friction is less sensitive to the rubbing direction.

A few studies deal with the macroscopic frictional response of technical reinforcements. These materials have many similarities with the textile family but also differences such as material constitution, unit cell size and some of the mechanisms involved during their frictional behaviour. A recent benchmark compared results obtained with different devices developed by teams working on this topic [START_REF] Sachs | Characterization of the dynamic friction of woven fabrics: Experimental methods and Benchmark results[END_REF]. Experimental tests on fabric/metal friction performed by the different teams on Twintex reinforcement exhibited an effect of pressure and velocity on the dynamic friction coefficient. In another study, the fabric/fabric friction behaviour was characterized using a specific device on different glass and carbon fabric architectures [START_REF] Allaoui | Influence of the dry woven fabrics meso-structure on fabric/fabric contact behaviour[END_REF]. It was shown that the fabric/fabric friction was highly different and more complex than that of textile or homogeneous materials. The measured values varied by up to a factor of two during the friction test under the same conditions. A period and an amplitude that depend strongly on the relative positioning and shift of the two samples characterize the frictional signal. The period of the signal can be directly related to the unit-cell length (periodic geometry). In addition, the specificity of the fabric/fabric contact behaviour was found to be directly related to the shocks taking place between overhanging yarns. However, no studies were found in the literature addressing the interesting question of the effect of test conditions that are representative of the preforming of dry reinforcements on fabric/fabric friction behaviour.

The study carried out by Cornelissen is undoubtedly useful to build a relationship between the micro and the meso scales as regards friction, but extensive experimental work needs to be performed at the meso and macro scales in order to obtain enough data for the correct definition and identification of a future model. It is therefore necessary to study the variation in friction behaviour with respect to the normal pressure and velocity for different fabric architectures to contribute to a better understanding of fabric/fabric friction behaviour. This is the goal of the present paper.

Materials and Methods

Tested dry fabric

The experiments were conducted on a glass plain weave dry fabric (figure 1.a). This balanced fabric has a thickness of 0.75 mm and an areal weight of 504 g/m 2 . The width of the yarn is 3.75mm and the average spacing between neighbouring yarns (for weft and warp directions) is around 5mm comprising 1.25mm of spacing because the yarns are not tightened together. The unit cell length is ~10 mm. For the tow samples, the yarns were extracted from the woven fabric.

Description of the device

When undertaking experimental investigations of dry-fabric friction, the various mesoscopic heterogeneities, the different unit cell sizes and anisotropy should be considered. This requires the use of specific experimental equipment designed to consider these properties. A specific experimental device at the laboratory PRISME, presented in Figure1.b, is dedicated to this task [START_REF] Hivet | Design and potentiality of an apparatus for measuring yarn/yarn and fabric/fabric friction[END_REF]. The device consists of two plane surfaces, on which the two samples are fixed, sliding relative to each other. The bottom sample is fixed on a rigidly and accurately guided steel plate that can be moved horizontally in a fixed direction. The imposed velocity can vary from 0 to 100 mm/s. The top sample is fixed on a steel plate which is linked to a load sensor connected to a data acquisition system used to record tangential forces during the test. A dead weight on the top sample provides a constant normal load F N . To obtain a uniform pressure distribution on the contact area of the samples, a calibration procedure was performed before testing to determine the optimal position of the dead weight [START_REF] Hivet | Design and potentiality of an apparatus for measuring yarn/yarn and fabric/fabric friction[END_REF]. For fabric/fabric experiments, the position of the dead weight was defined by using the mean of the tangential force. This approach gives an average position which limits the effect of specimen misalignment.

Test conditions

Before starting the experiments, the samples were conditioned in standard laboratory conditions (T~23°, RH~50%). To distinguish the different physical phenomena occurring during the friction tests, an acquisition frequency of 50Hz was used. This value was chosen based on tests performed in a previous study on the same material with the same bench. The friction coefficient (µ) was calculated using Coulomb's theory:

𝜇 = 𝐹 𝑇 𝐹 𝑁 = 𝐹 𝑇 𝑀•𝑔 (1)
where F T is the tangential load measured by the sensor, F N is the normal load, M is the total mass of the upper specimen with the dead weight and g is gravitational acceleration.

To investigate the effect of the shaping process conditions on both the macroscopic and mesoscopic behaviours of the fabric, two kinds of friction tests were performed: fabric/fabric and yarn/yarn. Tests were conducted in four relative positions of the samples, varying: pressure and test speed. For the relative positioning of the samples, four different orientations were tested: 0°/0°, 0°/90°, 90°/90° and 0°/45°. These configurations, generally used in laminates, exhibit extreme friction coefficients (maximum and minimum) of two fabric plies [START_REF] Allaoui | Influence of the dry woven fabrics meso-structure on fabric/fabric contact behaviour[END_REF]. The position 0°/0° was the reference one, and consisted in orienting the weft yarns of the two samples in the stroke direction. For 0°/90° and 0°/45°, the lower sample was kept along the same direction as the reference configuration, while the upper sample was rotated. For the 90°/90° configuration, the warp yarns of the two samples were oriented in the sliding direction.

For the yarn samples, the 0° orientation corresponds to the tows oriented in the movement direction, while 90° means that they are perpendicular.

Tests were conducted at five different pressures (3, 5, 10, 20 and 50 kPa) that are in the range of values involved during dry fabric preforming and at a speed of 1 mm/s. This velocity is the one used in a previous study to investigate the effect of pressure on fabric/metal friction behaviour [START_REF] Sachs | Characterization of the dynamic friction of woven fabrics: Experimental methods and Benchmark results[END_REF]. It is in the order of magnitude of inter-ply velocity values during the forming of dry reinforcements [START_REF] Allaoui | Effect of inter-ply sliding on the quality of multilayer interlock dry fabric preforms[END_REF]. The pressure is calculated by dividing the normal force by the areal size of the upper specimen. This definition is even the same for the fabric/fabric and yarn/yarn tests. Indeed, each specimen (upper and lower) of yarn/yarn tests contain several yarns that were placed next to each other. Consequently, the calculated pressure for fabric/fabric tests will be a theoretical one and not a real one because the contact between the two samples will not occur on this whole surface due to crimp and nesting.

The velocity values selected were 0.1, 1, 10 and 50 mm/s. This gives us a factor of 500 between the lowest and highest speed which covers the inter-ply sliding speed range during multi-layer forming whatever the laminate considered [START_REF] Allaoui | Effect of inter-ply sliding on the quality of multilayer interlock dry fabric preforms[END_REF]. The tests with different pressures were analysed to determine the pressure value at which the tests with various velocities were performed. This pressure was determined in order to distinguish the effect of the two parameters and make the comparison reliable.

At least five tests were performed for each test case.

Results and discussion

FABRIC/FABRIC FRICTION BEHAVIOUR

Typical layer/layer friction behaviour for dry fabric is illustrated in figure 2. This curve shows very clearly that the fabric/fabric friction behaviour is very different from the Coulomb/Amonton friction behaviour of a homogeneous material. A previous study showed that this behaviour is due to the superposition of two phenomena [START_REF] Allaoui | Influence of the dry woven fabrics meso-structure on fabric/fabric contact behaviour[END_REF]: yarn/yarn friction between the yarns of the two dry fabric plies, and shocks between the transverse overhanging yarns of each ply. During the weaving process, warp and weft yarns are manipulated in such a way that the two sets of yarns interlace with each other to create the required pattern of the fabric. The sequence in which they interlace with each other is called the woven structure (meso-structure). The yarns of one direction are bent around their crossing neighbour yarns, generating different crimps of the two networks resulting from the asymmetry of the weaving process. As a result, a height difference is obtained between the weft and neighbouring warp which is defined as depth overhanging or knuckle height (see figure 3) which promotes the shock phenomenon (lateral compression of yarns). These shocks occur periodically and generate high tangential reaction forces (F) leading to a substantial increase in the maximum friction values. The periodicity of the shocks is linked to the fabric meso-architecture and the relative position of the plies since it is difficult to control the relative position of the two samples during the tests, especially for reinforcements that have a weak unit cell length. During the positioning of the two samples on each other before testing, one may obtain a configuration in which the two are perfectly superimposed (figure 4.a) or laterally shifted (figure 4.b). When the two plies are perfectly superimposed the peak period is associated to the length of the sample unit cell, which is ~10 mm for the glass plain weave considered here. Figure 2 illustrates this configuration. On the other hand, when the plies are not perfectly superimposed (shifted samples), the peaks appear at periods equal to a portion (half in the case of the plain weave) of the fabric unit cell length.

In order to analyse the variation in the values of the fabric/fabric friction coefficient, the static frictional coefficient (μ s ) was first taken as the highest peak at the beginning of the motion (e.g. around 4 seconds in figure 2). After an area containing the maximum peak (20 seconds on figure 2), the dynamic friction domain can be considered as established. The dynamic friction coefficient (μ k ) can then be associated to the average of all the measured values. Moreover, the maximum values of the dynamic friction (peaks) and minimum values (valleys) were measured in order to assess the effect of the test conditions on the shock phenomenon. Maximum and minimum friction coefficients are noted respectively μ maxi and μ mini . The mean and standard deviation (σ) of each are calculated. These measurements were only considered for friction tests in which the period was close to the length of the unit cell for the configurations 0°/0°, 0°/90° and 90°/90°. For 0°/45°, as it is difficult to distinguish the unit cell length in the signal, all the peaks and valleys were considered to calculate μ maxi and μ mini.

Effect of Normal Pressure

The first test parameter considered in this study was the normal pressure. Fabric/fabric friction experiments were conducted at five pressures: 3, 5, 10, 20 and 50 kPa. The results of the static friction coefficients (µs) and the mean values of the dynamic friction coefficients (µk) are presented in Table 1 and illustrated on figure 5 It can be seen that the fabric/fabric static friction coefficients were higher than the dynamic coefficients in all the test configurations (Table 1) and had slightly higher standard deviations. This is a common observation in friction responses, which has also been noticed on textiles [START_REF] Ajayi | Effects of fabric structure on frictional properties[END_REF][START_REF] Das | A study on frictional characteristics of woven fabrics[END_REF]. Furthermore, the relative orientation of the two specimens has an effect on the frictional behaviour. In all cases, the static and dynamic frictional coefficients were higher for the 0°/0° configuration than for the 90°/90° configuration (Figure 5, Figure 6 and figure 7). The same trend has been observed on other fabric architectures, such as carbon interlock [START_REF] Allaoui | Influence of the dry woven fabrics meso-structure on fabric/fabric contact behaviour[END_REF], and can be attributed to the weaving effect (difference in crimp between the two yarn networks). As already mentioned, the fabric/fabric friction behaviour is governed by yarn/yarn friction and shocks between overhanging transverse yarns. The friction coefficient varied hugely (by up to a factor of two) because of high tangential forces due to the second phenomenon which predominates the global friction behaviour. According to the measures obtained, the tangential reaction forces due to shocks between weft yarns (configuration 0°/0°) are higher than those between warp yarns (configuration 90°/90°). As the reinforcement is assumed to be balanced and networks (weft and warp) are composed of the same yarns, this can be explained by the difference in crimp between the two networks resulting from the asymmetry of the weaving process. To confirm this fact, the crimp of warp and weft yarns was measured according to the ASTM D3883-04 standard [START_REF]and Yarn Take-up in Woven Fabrics[END_REF]. The crimp obtained for warp and weft yarns were respectively 0.35% and 0.43% confirming that higher crimp leads to higher tangential reaction forces due to yarn shocks. The increase in crimp results in a higher overhanging of the more crimped network yarn and thus in an increase of the friction coefficient. This conclusion is in good agreement with the study by Ajayi [START_REF] Cornelissen | Frictional behaviour of high performance fibrous tows: A contact mechanics model of tow-metal friction[END_REF] which showed that an increase in the weft yarn density generated an increase in the frictional resistance of textile.

For the 0°/90° configuration, transverse yarns are warp yarns (with high overhang value) for the bottom sample and weft yarns (with a low overhang value) for the upper sample. The shock phenomenon occurs between warp yarns that have high crimp and weft yarns with low crimp.

As a result, the tangential forces obtained in this configuration and thus the friction coefficients remain in between those obtained in the 0°/0° and 90°/90° configurations (figure 5, figure 6 and figure 7). There are still some points for which this trend was not confirmed (e.g. 3 kPa and 5 kPa), especially for maximum and minimum friction coefficients (figure 7), which may be due to the imperfect superimposition of the two samples.

As expected, the lowest friction coefficients were obtained for the configuration 0°/45° (see figures 5, 6 and tables 1 and2). The measured signal of the tangential force was smoother than the other configurations (figure 8). The amplitude of the signal was very weak (figures 7 and figure 8), which means that shocks between the overhanging yarns were not severe. In fact, Shocks occurred between network of yarns, one of which was oriented at 45°, which led to a very weak instantaneous lateral contact width between yarns. As a result, the yarn/yarn friction in this configuration governed the frictional behaviour and consequently the measured dynamic coefficient was closer to that of the yarn/yarn at 0°/90° (see section 3.2). When the normal pressure increased, the static and dynamic friction coefficients decreased (figure 5 and figure 6). This observation is in agreement with the results obtained for fabric/metal tests [START_REF] Sachs | Characterization of the dynamic friction of woven fabrics: Experimental methods and Benchmark results[END_REF]. For the four configurations (0°/0°, 0°/90°, 90°/90° and 0°/45°), friction coefficients significantly decreased in the pressure range of 3-20 kPa before converging to a steady value whatever the test configuration (figure 5, figure 6 and figure 7). The only singular point is the friction behaviour at 0°/90°, for which the maximum coefficient (μ max ) measured at a pressure of 5 kPa was higher than that measured at 3 kPa. This has an impact on the static and dynamic coefficient values, which show the same trend. This can be attributed to the low pressure. At this level of pressure (3 kPa), the shock phenomenon is not the predominant one and the behaviour is dominated by yarn/yarn friction. Thus, at this level of pressure, the friction behaviour tends closer to that of the 90°/90° configuration. This point will be addressed in future work.

After a pressure of 20 kPa, the fabric/fabric friction behaviours levelled off. Thus, the static (µs) and dynamic (µk) coefficients reached stabilized values with a low standard deviation, which denotes the good reproducibility of these behaviours (Table 1). The maximum decrease was obtained for the 0°/0° configuration (around 30% for the static and dynamic coefficients) while in the 0°/45°configuration only a 7% and 11% decrease was respectively observed for µs and µk.

This decrease in the friction coefficients can be attributed to the effect of fabric compaction and its consequences at the mesoscopic and macroscopic levels. When the pressure increases, the upper sample exerts a greater compaction on the lower. This leads to a high transverse compression strain of the fabric inducing at the mesoscopic level a reduction of the yarn's overhang height and a spreading of the yarns. At the macroscopic level, the reduction in the thickness of the reinforcement can potentially lead to a lateral spreading of the fabric in the inplane directions, and therefore a decrease in crimp. As the crimp at these stress states decreases, the texture ("roughness") of the fabric related to its meso-architecture decreases, and the contact area increases. However, the real contact area between the two samples driving the effective pressure is difficult to quantify for fabric/fabric friction tests (due to nesting, for example) in contrast to fabric/metal [START_REF] Cornelissen | Dry friction characterisation of carbon fibre tow and satin weave fabric for composite applications[END_REF].

The reduction in yarn's overhang height due to compaction leads to the decrease of the tangential reaction forces between the transverse yarns of the samples. As a result, the maximum friction coefficient (µ max ), measured on the peaks of the curves, decreased (figure 7).

In addition, the yarn spreading associated with the decrease in their overhang height generated a lower fabric "roughness". Therefore, the tangential reaction forces' signal, due to this new "roughness", was also smoother as observed for the 50 kPa pressure, while below 20 kPa the rise and fall in forces at each peak were more pronounced and abrupt (figure 9). It can also be seen that the maximum friction coefficient µ max continued to decrease slightly and was not completely stable at 50 kPa (figure 7), except for the configuration 0°/45 where the shocks phenomenon has a weak effect. Stabilization would probably occur at almost no meso roughness, which might be achieved at very high pressure not encountered during the composite shaping process.

The minimum friction coefficient (µ min ) measured in the curve valleys, which is attributed to yarn/yarn friction [START_REF] Allaoui | Influence of the dry woven fabrics meso-structure on fabric/fabric contact behaviour[END_REF], was not affected by this phenomenon and its evolution followed the same trend as the global friction behaviour (figure 7).

Effect of Velocity

In order to evaluate the effect of the sliding velocity on the fabric/fabric frictional behaviour, tests were conducted at four velocities: 0.1, 1, 10 and 50mm/s. These tests were performed at a pressure of 35 kPa as the friction behaviour versus pressure is stabilized at this pressure. It was previously observed that the friction coefficients at 0°/90° were situated between those of the 0°/0° and 90°/90° configurations and generally close to the 0°/0° configuration. For this reason, only the 0°/0°, 0°/45° and 90°/90° configurations were tested here. The static and dynamic friction coefficients obtained are summarized in table 2. The coefficients were measured with a good reproducibility (maximum deviation of 12% for the dynamic coefficient).

The friction coefficients changed slightly regardless of the configuration tested. The static friction coefficient increased from 0.427 to 0.503 when the velocity increased from 0.1 to 50 mm/s in the 0°/0° orientation, an increase of approximatively 17 % (figure 10). On the other hand, the 90°/90° configuration was less sensitive to the velocity with a maximum decrease of 9% at 50 mm/s compared to 0.1mm/s, which remains in the order of magnitude of experimental deviations. Once again, the 0°/0° configuration was more sensitive to the test parameters, which is likely due to its high crimp and therefore the predominance of the shock phenomenon.

The same trend was observed for the dynamic friction coefficients but to a lesser extent. The coefficients increases between 9 % and 14 % for all the configurations (figure 10). This slight increase in the dynamic friction is essentially due to the contribution of the minimum friction (µ min ) coefficient while the maximum (µ max ) decreased as can be observed on figure 11.

Consequently, increasing the speed has more influence on the amplitude variation than on the average value. Increasing the speed leads to an increase in the frequency of shocks which has two consequences:  The kinetic energy of the yarns (of the lower sample) enables them to pass over the overhanging transverse yarns in a shorter time with a lower force. The maximum friction coefficient therefore decreases. This also causes an up and down movement of the upper sample that can be described as stick-slip phenomenon.

 Between two shocks, a steady sliding between yarns does not exist, consequently the tangential force does not reach the stabilized value tending towards the friction coefficient of the yarns. Accordingly, the minimum coefficient increases.

For the configuration 0°/45°, both coefficients (µ max and µ mini ) increased. As, it has been discussed previously, these values are given in this configuration for information only and are not related to the meso-architecture in which case the values would have been different. Therefore, they cannot be used for comparison with other configurations.

To summarize, as the velocity increases, the upper sample does not follow strictly the irregularities of the lower sample which leads to a decrease in the signal variation just as if the irregularities were lower. It can be concluded that at low velocities (0.1 to 1mm/s) the dynamic frictional coefficient can be considered as almost constant whatever the orientation while beyond a velocity of 1 mm/s, its evolution as a function of the velocity should be considered.

YARN/YARN FRICTION BEHAVIOUR

The second aim of this study was to determine the effect of the test parameters on the friction behaviour at the mesoscopic level. Yarn/yarn friction tests were therefore conducted, varying the pressure and the velocity. Only the 0°/0° (parallel case) and 0°/90° (perpendicular case) configurations were performed. Recall that the 0° orientation means that the yarns are oriented in the direction of the stroke and 90° in the transverse direction.

Effect of Normal Pressure

As in the fabric tests, yarn/yarn friction tests were conducted by varying the normal pressure at 1mm/s. The results of the static (μs) and dynamic (μk) friction coefficients are summarized in table 3 and illustrated on figure 12 and figure 13. As expected, the static friction coefficients and their standard deviations were higher than for the dynamic coefficients. Moreover, the friction values were greater at 0°/0° than at 0°/90° which is in good agreement with previous studies carried out on carbon, aramid and glass yarns [START_REF] Vidal-Sallé | Friction Measurement on Dry Fabric for Forming Simulation of Composite Reinforcement[END_REF][START_REF] Cornelissen | Frictional behaviour of high performance fibrous tows: Friction experiments[END_REF].

The friction behaviour for the perpendicular configuration is mainly controlled by inter-fibre friction while for the parallel case, other phenomena are involved, among which: fibre bending, fibre reorganisation in the yarns, transverse compression, fibre damage, intermingling of fibres between yarns, etc. These phenomena are promoted by the spinning process, because fibres do not remain straight and some of them are damaged like it can be seen on figure 14. This generates reaction forces during tests that lead to the increase in friction forces. When the pressure increased, the static and dynamic coefficients decreased before reaching a plateau beyond 10 kPa. The decrease was larger in the parallel case (0°/0° configuration) with respect to the perpendicular one (0°/90°). For high pressure (50kPa), the friction increase because the higher compression rate generates more fibre damage. This fact is illustrated on Figure 15 showing the results where the friction coefficient increases after stabilization (beyond 40 s).

Observations performed using a microscope on this sample after the test showed a large number of broken fibres.

Effect of Velocity

The friction tests according to velocity were performed under 35 kPa as for the fabric/fabric tests. The results are summarized in table 4 and illustrated in figure 16. Once again, it was observed that the static friction coefficient was higher than the dynamic one.

As for fabric/fabric, the tow/tow friction behaviour remained unchanged in the range 0.1-1 mm/s velocities whatever the relative position of the samples. The friction was still constant for the parallel yarns (0°/0°) while for the perpendicular (0°/90°) case, an increase of more than 43% in the friction coefficient values was observed with the increasing velocity. It can be concluded that while the velocity does not affect the phenomena (intermingling of fibres between yarns, fibre reorganisation in the yarns, bending, etc.) controlling inter-tow friction in parallel yarns, it significantly affects the response for the 0°/90° configuration which is mainly controlled by interfibre friction. This trend is very different from the one observed on natural cotton fibres, which are more sensitive to pressure than to speed [START_REF] Nowrouzieh | The investigation of frictional coefficient for different cotton varieties[END_REF][START_REF] Nowrouzieh | Inter fiber frictional model[END_REF]. The differences between these fibres and those used in the present study (glass) are mainly related to their mechanical behaviour (brittle vs ductile), their compressibility and roughness. These characteristics are highly correlated with the friction coefficient [START_REF] Nowrouzieh | The investigation of frictional coefficient for different cotton varieties[END_REF]. As a conclusion, the fibre material significantly influences the effect of the test conditions on the microscopic friction behaviour (fibre/fibre) which results in the same effect at the mesoscopic level (yarn/yarn).

CONCLUSIONS

This study has highlighted the influence of test conditions on the frictional behaviour of dry reinforcements at mesocopic and macroscopic scales. It was found that the friction behaviour depends strongly on the relative orientation of the samples. Furthermore, experimental tests performed at the macroscopic level (fabric/fabric) showed that, for a given yarn, the friction coefficient is highly related to the yarn crimp because of the shock phenomenon occurring between transverse overhanging yarns. Friction coefficients decrease when the normal pressure increases until reaching steady values, which are almost identical whatever the relative orientation of the specimens. The greater decrease observed for the 0°/0° configuration can be attributed to the effect of the fabric compaction and its consequences on the yarn and fabric structure, i.e. a decrease in the yarn's overhang height and yarn spreading leading to the decrease in crimp.

Velocity has the opposite effect on fabric/fabric friction since the coefficients increase with the velocity. The static friction coefficient and the 0°/0° configuration are more sensitive to this parameter. The dynamic friction coefficient remains almost unchanged at low velocities whatever the relative orientation of the two samples while it increases slightly for high speeds.

This increase is due to the contribution of the minimum friction coefficient (µ min ) that increases because the high frequency between two shocks does not permit a stabilization of the tangential force at values tending towards the friction coefficient between yarns. However, the main effect of high speeds is a finite decrease in the amplitude variation of the friction response.

At the mesoscopic level, the results show the same trend as for macroscopic friction as a function of the test parameters. The parallel configuration 0°/0° is more sensitive to pressure while the 0°/90° is more influenced by velocity. This is due to the fact that friction behaviour in the perpendicular configuration is mainly controlled by inter-fibre friction while for the parallel case, other phenomena promoted by the spinning process are involved. It has been shown that the material constituting the fibres mainly influences the effect of the test conditions on the microscopic friction behaviour (fibre/fibre) which results in the same effect at the mesoscopic level (yarn/yarn).

We can conclude that at each scale, the frictional behaviour of the material studied here, which is heterogeneous and multiscale (micro-meso-macro), is governed by friction but is also significantly influenced by the structure of the lower scale. These structures (meso, micro) reorganise when test conditions such as pressure are varied, which leads to a variation in the friction behaviour. Thus, even if the same trends of the effect of test conditions are observed at different scales (meso, macro), they are caused by different mechanisms which are due to the structural reorganization at the lower scale.

  and figure 6. The results of the maximum values of the dynamic friction (measured at the peaks of the signal) and minimum values (measured at the valleys) are illustrated on figure 7. The error bars represent the standard deviations (σ).

Figure 1 .Figure 2 .Figure 3 :

 123 Figure 1.Material and equipment of the study

Figure 4 :Figure 5 .Figure 6 .Figure 7 .Figure 8 .Figure 9 .Figure 10 .Figure 11 .Figure 12 .Figure 13 .Figure 14 .Figure 15 .

 456789101112131415 Figure 4: Relative positioning of the samples

Figure 16 .

 16 Figure 16. Evolution of yarn/yarn friction coefficients according to testing velocity at pressure of 35kPa. The error bars represent the standard deviations

Table 1 .

 1 Fabric/fabric frictional characteristics function of the normal pressure at 1mm/s.

	Orienta tion	Normal pressure (kPa)	µs	Standard deviation [σ]	[σ/µs]*100 (%)	µk	Standard deviation [σ]	[σ/µk]*100 (%)
		3	0.5590	0.1461	26.13	0.4074	0.0155	3.80
		5	0.5224	0.0690	13.21	0.3499	0.0148	4.22
	0°/0°	10	0.4543	0.0442	9.72	0.3092	0.0131	4.23
		20	0.3911	0.0276	7.06	0.2810	0.0162	5.78
		50	0.3915	0.0339	8.65	0.2698	0.0120	4.45
		3	0.4041	0.0467	11.55	0.3315	0.0198	5.98
		5	0.5012	0.0878	17.51	0.3401	0.0461	13.54
	0°/90°	10	0.4327	0.0375	8.66	0.2931	0.0067	2.30
		20	0.3566	0.0142	3.97	0.2789	0.0396	14.20
		50	0.3558	0.0320	9.00	0.2656	0.0107	4.02
		3	0.3950	0.0210	5.33	0.3123	0.0223	7.12
		5	0.3928	0.0705	17.94	0.2982	0.0030	1.02
	90°/90°	10	0.3479	0.0287	8.25	0.2635	0.0167	6.34
		20	0.3504	0.0158	4.51	0.2678	0.0042	1.58
		50	0.3661	0.0354	9.67	0.2625	0.0062	2.35
		3	0.2256	0.0320	14.18	0.1799	0.0070	3.90
		5	0.2093	0.0133	6.35	0.1818	0.0159	8.75
	0°/45°	10	0.1985	0.0162	8.14	0.1737	0.0039	2.27
		20	0.2014	0.0040	1.99	0.1602	0.0019	1.17
		50	0.2102	0.0073	3.49	0.1605	0.0012	0.75

Table 2 .

 2 Experimental friction coefficients of fabric/fabric at 35 kPa according to velocity

	Orientation	Velocity (mm/s)	Log [velocity]	µs	Standard deviation [σ]	[σ/µs]*100 (%)	µk	Standard deviation [σ]	[σ/µk]*100 (%)
		0.1	-1.0	0.4274	0.0541	12.65	0.2846	0.0269	9.46
		1.0	0.0	0.4275	0.0484	11.31	0.2760	0.0032	1.17
	0°/0°
		10.0	1.0	0.4338	0.0424	9.78	0.2928	0.0031	1.07
		50.0	1.7	0.5031	0.0289	5.75	0.3098	0.0149	4.82
		0.1	-1.0	0.3993	0.0130	3.25	0.2623	0.0136	5.20
		1.0	0.0	0.4186	0.0358	8.55	0.2746	0.0084	3.06
	90°/90°
		10.0	1.0	0.3809	0.0394	10.33	0.2802	0.0057	2.03
		50.0	1.7	0.3652	0.0089	2.42	0.2950	0.0185	6.26
		0.1	-1.0	0.2072	0.0095	4.57	0.1687	0.0082	4.8858
	0°/45°	1.0	0.0	0.2034	0.0009	0.43	0.1593	0.0074	4.6386
		10.0	1.0	0.2267	0.0245	10.79	0.1640	0.0042	2.5559
		50.0	1.7	0.2383	0.0146	6.12	0.1925	0.0025	1.2873

Table 3 .

 3 Yarn/yarn frictional characteristics function of normal pressure at 1 mm/s

	Orientation	Normal pressure (kPa)	µs	Standard deviation [σ]	[σ/µs]*100 (%)	µk	Standard deviation [σ]	[σ/µk]*100 (%)
		3	0.4037	0.1766	43.74	0.3188	0.0126	3.96
		5	0.3478	0.0751	21.59	0.2831	0.0084	2.96
	0°/0°	10	0.2670	0.0058	2.16	0.2584	0.0068	2.64
		20	0.3336	0.0442	13.26	0.2822	0.0090	3.18
		50	0.3332	0.0122	3.67	0.3055	0.0059	1.93
		3	0.2165	0.0164	7.57	0.1867	0.0091	4.88
	0°/90°
		5	0.2186	0.0059	2.71	0.1913	0.0051	2.65

Table 4 .

 4 Experimental friction coefficients of yarn/yarn at 35 kPa according to velocity

	Orientation	Velocity (mm/s)	Log [velocity]	µs	Standard deviation [σ]	[σ/µs]*100 (%)	µk	Standard deviation [σ]	[σ/µk]*100 (%)
		0.10	-1.0	0.3471	0.0017	0.49	0.2963	0.0412	13.89
	0°/0°	1.00	0.0	0.3406	0.0500	14.67	0.2914	0.0224	7.69
		10.00	1.0	0.3448	0.0320	9.28	0.2947	0.0104	3.53
		50.00	1.7	0.3664	0.0564	15.39	0.2997	0.0063	2.10
		0.1	-1.0	0.1757	0.0002	0.13	0.1563	0.0068	4.37
	0°/90°	1.0	0.0	0.1825	0.0068	3.71	0.1739	0.0048	2.76
		10.0	1.0	0.2163	0.0075	3.45	0.1829	0.0026	1.43
		50.0	1.7	0.2458	0.0143	5.82	0.2243	0.0214	9.52

Acknowledgments

The research leading to these results received funding from the Mexican National Council of Science and Technology (CONACyT) under grant no I0010-2014-01.


D Haering

C Pontonnier

G Nicolas

N Bideau

G Dumont

3D Analysis of Human Movement Science 2018

Introduction

In industrialized countries, musculoskeletal disorders (MSD) represent 80% to 90% of work related disorders. Ulnar nerve entrapment (UNE) and epicondylitis are the most common elbow MSDs within manual workers (1,2). UNE and epicondylitis are associated with maintained elbow flexion, or near-maximal elbow extension coupled with large loads (3). Awkward shoulder postures while using elbow increase MSD risk (4). Articular mechanical load can be estimated in regards of its maximal isometric torque from dynamometric measurements [START_REF] Haering | Proc XXVI Congress ISB[END_REF]. Most studies focusing on elbow ergonomics considered tasks executed in oneusually naturalshoulder configuration. A comparison between elbow isometric torque characteristics in natural and awkward shoulder configurations could help reduce the risk of elbow MSDs.

Research Question

The study highlights differences in elbow isometric torque characteristics when varying shoulder configurations and implications for ergonomics.

Methods

Dynamometric measurements and personalized torque-angle modelling were performed on a worker population to define elbow isometric torque characteristics during natural or awkward manual tasks.

Twenty-five middle-aged workers (33±6 years, 1.80±.07 m, 79±8 kg) participated in our study. One classical and five awkward shoulder configurations were tested: flexion 0° with external rotation (F0ER), 90° flexion with external rotation (F90ER), 180° flexion with external rotation (F180ER), 90° abduction with external rotation (A90ER), 90° abduction with internal rotation (A90IR), and 90° flexion with internal rotation (F90IR) (Fig. 1). Dynamometric measurements consisted in static calibration, submaximal concentric and eccentric warm-up, and isometric trials. Trials included 5 isometric contractions maintained for 5 s in flexion and extension evenly distributed through the angular range of movement of the participants.

A quadratic torque-angle model ( 6) was used to fit isometric torque measurements, where model parameters: peak isometric torque Γ 𝑚𝑎𝑥 , maximal range of motion Γ 𝑚𝑎𝑥 , and optimal angle Γ 𝑚𝑎𝑥 , were optimized. Optimal isometric torque for awkward shoulder configurations were compared to natural configuration in terms of: optimal model parameters (one-way repeated measures Anova), torque magnitude 𝑀 and angle phase 𝑃 (7).

Results

Significant effects of shoulder configuration on elbow peak isometric torque are shown (p<.01). In flexion, F0ER displays larger than F90ER and F180ER. In extension, F90ER shares highest with F0ER larger than F180ER (table 1). Magnitude analysis also reveals that maximal isometric torque over the full range of motion is overall the largest for A90IR in flexion or F0ER in extension.

No significant differences are found for maximal range of motion 𝑅𝑜𝑀.

Effect of shoulder configuration on elbow optimal angle 𝜃 𝑜𝑝𝑡 is found (p<.01). F0ER, F90ER and F180ER display smallest optimal angles (closest to anatomical reference) in flexion. Inversely, F0ER and A90IR show largest 𝜃 𝑜𝑝𝑡 in extension. Phase analysis show similar correspondences. Table 1. Awkward versus natural shoulder configuration in terms of average isometric torque parameters, torque magnitude and angle phase.

Torque direction

Shoulder configuration

Γ 𝑚𝑎𝑥 [N. m] 𝑅𝑜𝑀 [°] 𝜃 𝑜𝑝𝑡 [°] 𝑀 [%] 𝑃 [%] FLEXION F0ER (

Discussion

Peak isometric torque and magnitude results give a clear idea of elbow torque available for all shoulder configurations. Results confirm that natural position (F0ER) allows good compromise between peak torque and torque magnitude. For flexion, F90ER and F180ER appear as weakest configurations. Except for F90ER in elbow extension tasks, shoulder flexion should be minimized in strenuous working tasks. Those results agree with common ergonomic recommendations in terms of posture [START_REF] Mcatamney | [END_REF]9).

In flexion, F0ER with smaller optimal angle could also help reduce UNE occurrence by favoring tasks with less flexed elbow. Similarly in extension, F0ER and A90IR could help reduce epicondylitis by favoring less extended elbow work.

While A90IR appears as good alternate on torque and angle criterion, visibility issue might interfere.

Figure 1 .

 1 Figure 1. Natural and awkward shoulder configurations tested for elbow torque on dynamometer.


R Moulart

R Rotinat

Elasto-plastic strain field measurement at micro-scale on 316L stainless steel

Keywords: méthode de grille, échelle micrométrique, élasto-plasticité, acier 316L grid method, micrometric scale, elasto-plastic behavior, stainless steel

Cette étude traite de la caractérisation du comportement mécanique d'un acier inoxydable austénitique (316L) à l'échelle micrométrique. Pour cela, la méthode de grille a été adaptée à cette échelle. Les grilles de pas d'environ 5 µm sont obtenues par photolithographie interférentielle sur une résine photosensible préalablement déposée à la surface de l'échantillon. L'éprouvette est soumise à une traction par paliers de chargement permettant ainsi la numérisation des grilles à l'aide d'un microscope interférométrique en lumière blanche pour chaque pas de chargement. Ces images ont ensuite été traitées pour en extraire le champ de déformations plan (résolution inférieure à 2×10 -3 pour une résolution spatiale de 20 µm). Ces déformations ont alors rendu compte de localisations des déformations compatibles avec les frontières des grains. Une tentative de détection de l'initiation de la plasticité locale a ensuite été mise en oeuvre : à partir des courbes contraintes-déformations moyennes par grain, il est possible de définir une valeur de limite élastique σ Y (à 0,02 % par exemple) locale. Il a alors été constaté que ces valeurs de σ Y locales ainsi déterminées peuvent varier de +/-20 MPa autour de la valeur macroscopique (180 MPa).

Introduction

To be able to precisely predict the global mechanical behaviour of a material, it is necessary to understand the physical phenomena taking place at the scale of its heterogeneities. Indeed, once the local mechanical behaviour is known, it is possible to deduce the overall properties via homogenisation schemes [START_REF] Qu | Fundamentals of Micromechanics of Solids[END_REF]. However, the experimental determination of the local behaviour still remains challenging as the classical experimental procedures are not robust anymore at a reduced scale. Consequently, the development of quantitative displacement and strain field measurement techniques at this scale is an important field that very much remains an open problem. Only a few papers can be found in the literature. Some works studied the plastic behaviour of an aluminium alloy under tensile test from moiré interferometry [START_REF] Nicoletto | On the visualization of heterogeneous plastic strains by Moiré interferometry[END_REF][START_REF] Guo | Study on deformation of polycrystalline aluminum alloy using moiré interferometry[END_REF] with a region of interest ranging from a few square millimetres to centimetres. The author managed to put in evidence the heterogeneous nature of the plastic strains due to the microstructure of the sample. More recently the digital image correlation (DIC) technique is also applied to study titanium alloy [START_REF] Lagattu | In-plane strain measurements on a microscopic scale by coupling digital image correlation and an in situ SEM technique[END_REF] with SEM images. Another interesting studies couple full-field strain measurements (using DIC with a scanning electronic microscope) with grain orientations through EBSD [START_REF] Héripré | Coupling between experimental measurements and polycrystal finite element calculations for micromechanical study of metallic materials[END_REF][START_REF] Padilla | Relating inhomogeneous deformation to local texture in zirconium through grain-scale digital image correlation strain mapping experiments[END_REF].

The present paper uses an original alternative to the above technique, with the hope to reach the right compromise between resolution and spatial resolution to study the transition between elastic and local microplastic behaviour. In this context, this work is aimed at characterising an austenitic stainless steel sample (FCC crystal system) under tensile loading at the scale of its grains in its elasto-plastic domain. This is done by applying the experimental procedure initially developed in the study of a ferritic steel [START_REF] Moulart | On the realization of microscopic grids for local strain measurement by direct interferometric photolithography[END_REF][START_REF] Moulart | Full-field evaluation of the onset of microplasticity in a steel specimen[END_REF]. This methodology is shortly recalled before introducing the results on the stainless steel sample.

Methodology

The micro-extensometric method used here has been previously developed [START_REF] Moulart | On the realization of microscopic grids for local strain measurement by direct interferometric photolithography[END_REF][START_REF] Moulart | Full-field evaluation of the onset of microplasticity in a steel specimen[END_REF]. It is based on the so-called "grid method" [START_REF] Surrel | Moiré and grid methods: a signal-processing approach[END_REF] which consists in analyzing the deformation of a periodic pattern deposited onto the surface to study by a spatial phase stepping algorithm here fitted to a micrometric scale. The overall procedure is schematically summarized in figure 1 and recalled hereafter.

FIG. 1 -Schematic summary of the experimental micro-scale full-field strain measurement procedure First of all, the samples are prepared: they are cut from a laminated plate of the studied stainless steel, then submitted to a recrystallization tempering heat treatment (to get bigger and equiaxed grains) and finally polished.

Cross-gratings (pitch: 5 µm) are then produced at the surface of the specimen by direct interferometric photolithography. This technique consists in recording the parallel interference fringes of two collimated laser beams on a photoresist layer spread onto the surface to study. Thus, the pitch can easily be adjusted depending only on the wavelength of the light and the angle between the two incident beams interfering on the sample. In order to obtain cross gratings (so as to have access to both components of the in-plane displacement), the process is simply repeated after rotating the sample by 90° (first step on figure 1). The deformation of the photoresist is assumed to follow exactly the one of the underlying substrate.

Then, the samples can be submitted to a tensile test thanks to a small home-made mini tensile machine. Its kinematic chain has been designed to be symmetrical with two mobile cross-heads in order to avoid as much The gratings on the region of interest are digitized in-situ at every step of the loading with a white-light interferometric microscope. Based on short length coherence interferences concepts, it allows to digitize the 3D profile of a sample with a subnanometric resolution in the vertical direction and with a spatial resolution limited by the diffraction limit (second step on figure 1). In practice, pitches down to 2 µm can be used. It is important to note that the surface must also be reasonably reflective to use such a microscope. Another important feature is the fact that the measured profile depends solely on the internal distance in the lens between a semi-transparent lens and the imaging plane. Therefore, not only will the out-of-plane displacements be recorded at the same time as the in-plane ones, but the latter will be independent from the former. This is one of the main advantages of this procedure compared to optical microscopy where the very low depth of field is clearly a problem [START_REF] Bartali | Fatigue damage analysis in a duplex stainless steel by digital image correlation technique[END_REF].

The profile images of the grating are then computed by the "grid method", based on a windowed spatial phase shifting algorithm [START_REF] Surrel | Moiré and grid methods: a signal-processing approach[END_REF]. Indeed, considering the sample grating as a periodic signal, it is possible to compute the phase value of this signal for each period, leading to the displacement maps [START_REF] Moulart | On the realization of microscopic grids for local strain measurement by direct interferometric photolithography[END_REF]. In this way, the spatial resolution of displacement is equal to the pitch of the grating These maps undergo a 2×2 "stitching" operation in order to enlarge the field of view (finally equal to 450×340 µm²).

From these fields and to get access to mechanical parameters, strain fields have to be calculated. For that, and considering that experimental data are noisy, it is necessary to use an appropriate smoothing procedure.

Here, it has been chosen to use a diffuse approximation (DA) scheme [START_REF] Devlin | Locally weighted regression: An approach to regression analysis by local fitting[END_REF][START_REF] Nayroles | La méthode des éléments diffus[END_REF]. DA is based on local weighted least-squares minimization using a polynomial diffuse approximation. It has shown that concerning the choice of the polynomial degree, the best compromise is 2 [START_REF] Feissel | Comparison of two approaches for differentiating full-field data in solid mechanics[END_REF].The DA approach is powerful technique which provides stable results but is also a time consuming technique. The strain resolution is deduced from the displacement resolution. For a full-field measurement method, the latter is often considered to be the standard deviation of the noise. By applying a smoothing/differentiation algorithm to the noise maps, it is possible to determine the strain resolution as the standard deviation of the generated ''noisy-strain" maps [START_REF] Pierron | Full-field assessment of the damage process of laminated composite open-hole tensile specimens. Part I: methodology[END_REF].

Finally, the observed microstructure of the region of interest is plotted on the strain maps to allow a comparison between it and the localizations of strain components. With this approach, it has been shown that the local strain resolution is inferior to 2×10 -3 for a spatial resolution of 20 µm [START_REF] Moulart | Full-field evaluation of the onset of microplasticity in a steel specimen[END_REF]. It has to be compared to the average size of a grain (≈ 100×100 µm²).

Results and discussion

The mechanical test performed on the stainless steel sample has consisted in a 52 load steps tensile test. Fig. 2 shows the stress-strain curves obtained from both a gauge glued onto the back side of the sample and an averaging of the ε xx maps on the whole surface of the region of interest. It also shows the three in-plane strain maps for the last stage of loading, once the material has reached its overall elasto-plastic domain.

FIG. 2 -Micro-extensometric results for the last step of loading

From this figure, two main remarks can be made:

The two stress-strain curves are quite different. This can be due to two main causes. The first possible cause is that there was some bending moment superimposed to the tensile load during the test leading to different longitudinal strain components on the two sides of the sample. The second possible cause is that the size of the observed region is inferior to the one of the representative Stress-strain curve

ε xx (x10 -3 ) ε yy (x10 -3 ) ε xy (x10 -3 )
volume (which is possible considering the total number of grains).

The different strain maps for the last step of loading show localizations that are in accordance with the positions of the grain and twin boundaries. It has to be noted that on the micrograph made after the test on the sample, some slip lines can be seen on some of the regions where ε xx is maximal. This reinforces the confidence and relevancy of the obtained strain maps.

One way to exploit these full-field data in order to characterize the onset of micro-plasticity is to perform an averaging of the strain values over the surface of a single grain or a single twin (considered here as the same kind of "unitary cell" of the microstructure). The averaging has two main advantages:

it gives access to a single representative value for the whole grain;

on a metrological point of view, the averaging increases the signal to noise ratio.

This allows plotting a stress-strain curve per grain. figure 3 shows such curves (grains 1 and 2 are grains that are submitted to large plastic deformation, showing slip lines on the micrograph whereas grains 3 and 4 are grains that are less deformed; see figure 2 ) to be compared to the one obtained for an averaging on the whole surface of the region of interest.

These curves show that, for this stainless steel sample, the local strain can vary of a 2.5 factor from a little solicited grain to a hugely solicited one. From this observation, it can be asserted that the proposed technique should be able to give information about the local onset of micro-plasticity.

To this purpose, two semi-automatic procedures of determination of a local yield point have been implemented.

The first one is simply based on the transposition of the normalized value calculation of the yield point to this scale: a value of the "0.02% yield stress" is thus proposed for the considered local regions. For that, a linear regression is made on the first value of strain/stress (up to a stress value equal to 100 MPa, to be sure to stay in the elastic domain while having enough experimental value to get a relevant regression law). Then, the deduced straight line, shifted by a value of 0.02 % in strain, is plotted. The intersection point between this line the experimental curve gives the σ Y 0.02% value (figure 4(a)). Thus, two values characterizing the onset of micro-plasticity are available. They, and the difference between them and the reference value obtained for the whole surface of the region of interest, are given in table 1.

Whole

Conclusion

The exposed study, based on a full-filed micro-extensometric methodology, has been applied to a austenitic stainless steel sample submitted to a tensile test.

The proposed experimental procedure has confirmed its robustness and relevancy to measure local small strains (strain resolution ≈ 2×10 -3 for a spatial resolution about 20 µm). Moreover, it has allowed showing that the plastic domain starts earlier than the macroscopic yield point (which can be considered only as an average value of all the local yield points). This was known for a long time (especially, once studying fatigue behaviour, the permanent deformations appearing before to reach the macroscopic yield stress are decisive) but has hardly been experimentally measured.

Equipped with this method, a possible continuation to this work could be to combine it with thermographic observation to link the local measured plastic strains to the heat dissipation of a studied material and, thus, develop a tool to better characterize the endurance limit.

  rigid body motion in the middle part of the sample.

FIG. 3 -

 3 FIG. 3 -Average stress-strain curves for several grains or twins of the sampleThe second one consists in finding the intersection between the regression line previously obtained from the first sets of values, and a 4 th order polynomial curve computed by regression on the last stages of loading. This allows getting rid off the possible influence of the noise affecting the experimental data on the determination of σ Y 0.02% by the previous method and to get a closer value to the local loss of linearity (figure 4(b)).

FIG. 4 -

 4 FIG. 4 -The two ways to determine the local yield point

  Values of local yield points for different grains of the sampleOne can conclude from this table that grains 1 and 2, which are more solicited, are entering in their plastic domain earlier that the whole observed region (for a nominal tensile stress ≈ 20 MPa lower). On the contrary, grains 3 and 4, less solicited, are entering in their plastic domain later (for a nominal tensile stress ≈ 30 MPa higher). The difference of values for grain 2 and grain 3 between the two values of σ Y 0.02% and σ Y can be explained by the noisier experimental data for these grains.

		surface	Grain 1 Grain 2 Grain 3 Grain 4	Average / 4 grains
	σ Y 0.02%	180 MPa	164 MPa 164 MPa 211 MPa 204 MPa	185 MPa
	Difference from
		-	-16 MPa -16 MPa 31 MPa 24 MPa	5 MPa
	the whole surface
	σ Y	145 MPa	122 MPa 105 MPa 195 MPa 171 MPa	148 MPa
	Difference from
		-	-23 MPa -40 MPa 50 MPa 26 MPa	3 MPa
	the whole surface
		TAB. 1 -