Cécile Berriet
email: cecile.berriet@univ-fcomte.fr

Nadia Bahlouli
email: nadia.bahlouli@unistra.fr

Cécile Rogueda-Berriet

Daniel Pessey

Mechanical behavior of recycled PP composites under tensile, bending and creep loading: experimental and modeling

Keywords: recycling process, PP compound, HiPP, mechanical behavior, EPDM, EPR

may come     Mechanical behavior of recycled PP composites under tensile, bending and creep loading : experimental and modeling

Introduction

Because of their good thermal, mechanical and attractive characteristics, plastics are widely used in the automobile sector. The increasing use of this type of materials results in a large number of publications (Friedrich et al. [1], Maiti et al. [2], Duffo et al. [3], Alonso et al. [4],

Fond et al. [5], Castagnet et al. [START_REF] Castagnet | Structural effect in the creep behavior of thermoplastic pressure pipes at high temperature. Role of geometrical defects[END_REF], leading to a better understanding of their mechanical behavior. Nevertheless, the recycling process of these materials doesn't lead them, in general, to be used again in the same components.

Today, the recycled PP compound market can increase, through, for example, a more efficient pick up of ELV. Before 2015, companies in automotive industry have to use in their new cars 95% of recoverable materials, with 85% of recyclable ones to agree with the 2000/53/CE European directive [7]. PP compounds represent about 35% of plastics in a vehicle. However, the mechanical properties of the recycled materials have to be better known to allow an iso-function use in the new car generation.

Few studies have been undertaken on the influence of the recycling process on the mechanical behavior. Existing studies relates to rheological aspects (Luda et al. [8], Luda et al. [9], Guerrica-Echevarria et al. [10]) more than on the mechanical characteristics evolution (Bahlouli et al. [11], Pessey et al. [12]). However it is necessary to take into account the recycling effect while designing automotive structures allowing an iso-function use of recycled materials.

Materials studied here are polypropylene reinforced by addition of elastomeric particles and/or talc fillers. They are used for the production of bumpers in car industry. These materials are supposed to support multi axial stresses at different loading rates. The aim of the present study is the characterization of the mechanical behavior of polymer based polypropylene before and after recycling process through different loading tests: tensile, bending and creep tests. Due to the well known high sensibility of polymers to the strain rate, a wide range of the strain rates has also been studied. Two different models of the recycled materials are proposed: one to describe the elastic-visco-plastic behavior under tensile tests and another based on a rheological model to describe creep tests. A good description of the recycling effects for both loadings has been obtained.

Experimental study

Materials

Experimental results have been obtained with polypropylene based composites usually chosen for the manufacturing of semi-structures car elements. They will arrive on the recycling market within 10 years. These materials were provided by SABIC®. The first material is a melt of three phases referenced as compound 7510®. It is a high impact modified filled polypropylene used for rear car bumpers. It contains 20% of EPDM (Ethylene-Propylene-Diene monomer) particles of less than 1 µm diameter, 12% of talc particles of 8 µm mean length, embedded in a PP matrix. The second material is a copolymer PP/EPR (Ethylene-Propylene-Rubber) referenced as 108MF97® obtained by direct synthesis. The elastomeric phase (22%) is made of nodules of less than 1µm diameter.

In order to simulate the recycling process, 6 extrusions/crushing cycles were performed since Guerrica-Echevarria et al. [10], Aurrekoetxea et al. [13] have shown that the recycling degradation was less important during the first 5 cycles. Samples were machined in 3 mm thick molding sheets obtained by injection process. In the following, 108MF97 (respectively 7510), virgin and 6-time recycled materials, will be referenced as 108MF97 0P and 108MF97 6P (respectively 7510 0P and 7510 6P).

Experimental procedure

Mechanical behavior of PP based polymers; talc filled or not, as well as the recycling effect on the mechanical behavior is characterized for different loading cases in quasi-static conditions. All the specimens were kept at room temperature at least 72h before mechanical testing.

Uni-axial tensile tests were performed on an INSTRON servo-hydraulic test system at room temperature (25°C). An Instron strain gage extensometer (referenced as 2360-102) was used to measure the uni-axial tensile strain. Tests were carried out under constant displacement rates of 10 -4 , 10 -3 and 10 -2 mm.s -1 . The dog bone specimen dimensions were 59 mm in gage length; the calculated corresponding strain rates are therefore assumed to be: = ε& 0.17 10 -4 , 0.17 10 -3 and 0.17 10 -2 s -1 . All tests have been performed until 15% of strain.

For this value, conventional and true strain-stress curves are assumed to be equivalent. Each curve and property represented is an average of five specimens tested.

Three points bending tests at room temperature have been carried out using a set-up specially developed for a tensile INSTRON 6025 device: the beam has been set on two base supports and loaded by a concentrated force providing from the tensile axis. Technical device parameters as supports and awl diameters are in accordance with the EN ISO 178 standard.

An LVDT sensor with a maximal range of 10 mm and 1µm precision is located in the middle of the sample, on the strip side down. Bending specimens were 120 mm by 20 mm rectangular samples. The control of the deflection was allowed with two distinct rates: 0.2mm s -1 and 2 mm s -1 . According with bending classical assumptions and with beam dimensions, it corresponds to strain rates of, respectively, 2.5 10 -4 s -1 and 2.5 10 -3 s -1 . An average of three curves is presented for each type of specimen.

Creep tensile tests were performed, at room controlled temperature, with halter-shaped specimens (effective area: 3 x 10 x 50 mm 3 ) loaded at 4 MPa. This stress, obtained with standard masses, corresponds to the up-limit of the linear creep behavior. Strains have been measured with a ± 10% extensometer on a 35 mm length basis during 3 days of loading. Then masses have been taken out and, without any loading, the remaining strain had decreased showing a visco-elasto-plastic behavior for virgin and recycled materials. From three tests, a representative curves have been chosen for each material.

Results

Tensile stress-strain curves obtained for virgin and recycled materials (Fig. 1 and Fig. 2) show classical finite strain behavior for thermoplastic polymers. A first elastic linear and reversible phase is observed until a yield stress. The yield point is followed by a light strain softening only for the 7510followed by a plastic strain. Initial elastic modulus, yield stress and yield strain were determined from these curves. Three properties were evaluated from each stress-strain curve: elastic modulus (E), yield stress (σ y ) and yield strain (ε y ). Elastic modulus is assumed as the initial slope of the stress-strain curve. Yield strength (σ y ) is assumed to be the maximum stress observed in each stress-strain curve and the corresponding strain is defined as the yield strain.

Curves obtained for recycled materials differ from one material to the other one (Fig. 1 and Fig. 2). Noticeable degradation of the mechanical behavior characterized by a decrease of elastic properties was observed for the 108MF97 recycled material with respect to the virgin one. For the 7510, another remark has to be made. Indeed, as the strain rate increases, the discrepancy between virgin and recycled stress strain curve increases too.

Three points bending tests were performed until a 9.5 mm maximum deflection. Viscoelastic behavior is observed and confirmed during the unloading phase (Fig. 3 and Fig. 4). This visco-elastic behavior remains for recycled materials since only one loop is shown on the Figure 4. On Fig. 3 a slightly weaker slope is observed for the recycled 7510 than for the virgin material. The recycling effect is significantly less important on the 108MF97 behavior since recycled material seems to have a stronger modulus. When the strain rate is increasing from 2.5 10 -4 s -1 to 2.5 10 -3 s -1 , slopes are increasing about 15%. Initial Young modulus for each curve is calculated basing on the elastic model, which is conventionally used to describe stress-strain behavior from flexural measurements. They are presented on Tab.1, showing good agreement with tensile results: recycling impact is greater with 7510 than with 108MF97 and values, even if they are higher, have the same order strain rate dependence.

The Figure 5 shows that creep effect is more important for 108MF97 materials than for 7510 ones. Recycling process is more influent on the 7510 materials creep. The Figure 6 presents the total test, including unloading phase. During the unloading process creep strains are not recoverable, overall for recycled materials: viscoplastic behaviour seems to be observed, with a quicker response for virgin materials.

Discussion

The two materials, despite a great similarity in the mechanical behavior, demonstrate a significant difference with the presence of a "knee" for the 7510, due to the addition of a third phase of talc (Pessey et al. [14]). Indeed, one of the effects of the elastomeric phase is a softening of the mechanical behavior while increasing the ductility of the material and reducing the peak at the threshold are observed (Denac et al. [15], Liang et al. [16]). The elastic modulus and the yield stress thus decrease with the addition of the elastomeric phase, while the deformation at break is slightly modified by the presence of two phases (Denac et al. [15]. Both recycled and virgin high impact PP seems to have the same deformation mechanisms.

On the contrary, it is reported that the talc particles rigidify the mechanical behavior and decrease the yield stress and the deformation at break (Oksuz et al. [17], Hadal et al. [18]). But in these multi-component materials, several deformation mechanisms at different scales of observation exist: the elastic deformation of the composite, the cavitation of rubber particles, the debonding between matrix and particles and the shear deformation of the matrix (Collyer [19]). As explained in a previous paper (Bahlouli et al. [11]), cavitation was observed by SEM on all the virgin specimens and occurs at very low level of stress and strain before yield stress (whitening of the reference length during tensile testing). The deformation mechanisms of such materials include multi micro cracking of the matrix, shear flow, microvoids and cavitation (G'Sell et al. [START_REF] Sell | [END_REF]). For the 7510, as the strain rate increases, the discrepancy between virgin and recycled material increases.

A comparison between tensile and bending tests is possible. Using the hypothesis of Strength of Materials (SOM), it is possible to link deflection, load and Young modulus whose values once calculated are in agreement with those of tensile tests. It has been noted (Trantina [21]) that SOM tends to over predict the bending modulus in relation to those obtained by tensile test. It is due to the fundamental hypothesis used on SOM: the formula needed to calculate Young modulus from load displacement and geometry of the specimen is true if mechanical behavior is assumed to be linear. But figures 3 and 4 show the behavior is non linear. Thus the young modulus is always over estimated when it is measured from flexural tests.

Recycling has altered various mechanisms involved during the tensile test cited above. Thus, the Young modulus and the threshold stress decrease after recycling (Fig. 1 and Fig. 2) An explanation of these effects is found in the recycling process. Several degradation mechanisms are involved: thermal, mechanical and chemical degradation (Aurrekoetxea et al. [13]). The different extrusion runs have modified the structure of polymers by cutting chains during successive grindings. The degraded chains are mainly part of the amorphous matrix of polypropylene. But this phase plays a role in the deformation mechanisms solicited after the yield point (Addiego et al. [22]. In this study, we show that the elastic properties are degraded by the recycling process. These degradations are not followed by a modification of the initial morphology as explained in Pessey et al, Icrach. In the open literature, it is reported that the recycling increases the elastic properties of the PP (Aurrekoetxea et al. [13]) Indeed, only the effects of strain rates are clearly identified by observation under scanning electron microscope (Bahlouli et al. [11]. In the same way, the effects of time, highlighted during the creep tests, are different depending on whether the material is virgin or recycled. Thus, the relaxation time of the recycled material, determined by a conventional "four parameters" modeling, is approximately equal to 1.3 times that of virgin material in the case of 7510 and 4 times in the case of 108MF97. The chains cut during the successive extrusion runs would be much more movable than in the virgin materials and even more so in the absence of talc fillers. After unloading, some structural modifications still permit the samples to be strained and they are more important for recycled materials. The total recoverable can be hopped for virgin materials but it had not been, already, measured.

In this part, a first modeling of the macroscopic mechanical behavior for tensile tests and for creep tests of our materials is proposed. Tensile tests are modeled using a non-linear law originally developed for particulate reinforced PP talc and proposed by Zhou et al [23]. Creep tests are modeled using a conventional "four parameters" modeling, since a visco-elastoplastic behavior has been observed.

An elastic-visco-plastic model has been proposed by Zhou et al. in order to describe the stress strain curves obtained experimentally. This model describes the strain rate effects.

A modification of this model is proposed to include recycling effect by the way of elastic modulus and yield stress, properties more affected by the reprocessed effects.

The constitutive relation is described by the following equation:

( ) ( ) ( ) m E E ε ε β ε ε ε σ ⋅ ⋅ + ⋅ = & & & 1 (1)
Where E is the elastic modulus of the material, and σ is the stress. Both depend on strain rate as mentioned before and as represented in Figures 7 to 10. β represents a compliance parameter and m is a strain exponent. β and m are calculated from the equation (2) and from its partial derivative. We obtain the expressions given by:

         - = - = m y y y y E m E E m ε β σ ε ε ) 1 ( 1 (2) (3)
The degradation of the mechanical properties (E, y σ ) of the unfilled and talc-filled high impact modified polypropylene for the recycling passes under different strain rates has been described in Figures 7 to 10. It is obvious that a simple linear law can give a good description of the recycling effects. We showed that for virgin materials, the Young modulus and the yield stress are calculated respectively by equation (4) and equation ( 5) :

( )         ⋅ + = 0 1 0 ln 1 ε ε λ ε & & & E E ( )         ⋅ + = 0 2 ln 1 0 ε ε λ σ ε σ & & & Y Y (4) (5)
These equations have two materials parameters based on experimental results: a mechanical reference parameter and a strain rate strengthening coefficient. Figures 7 and8 showed the evolution of the reference Young Modulus and the reference yield stress with the number of recycling passes at this strain rate. From these figures, a linear evolution of these parameters with the number of recycling passes is assumed. Therefore the mechanical reference parameters can be written as follows:

( ) REF E n n E 0 1 0 + = κ (6) ( ) REF Y Y n n 0 0 2 σ κ σ + = (7)
where n is the number of recycling passes, These are rather encouraging preliminary results for the modeling. However, the simulation under finite strain is in progress as well as a description of the degradation due to cavitation during tensile testing. It is also well known that at large strains, molecular orientation plays an important role in the material response and needs to be accounted for the capture the hardening effects.

The chosen model to describe creep tests is a set composed with a Maxwell set and three Kelvin-Voigt sets (Fig. 13)

The equation of the compliance for this model is a sum of 3 parts, the elastic compliance, the visco-plastic compliance and the visco-elastic compliance:

          - +           - +           - + + = = - - - 4 4 3 3 2 2 1 1 1 1 1 1 1 ) ( ) ( 4 3 2 1 1 0 η η η η σ ε t E t E t E e E e E e E t E t t J (8)
E 1 is the elastic spring stiffness; η 1 is the plastic viscosity; E 2 , E 3 and E 4 are the spring stiffness of each Kelvin-Voigt set and η 2 , η 3 and η 4 are the viscosities of them. E 1 and η 1 are calculated by a direct method, and E 2 , E 3 , E 4 , η 2 , η 3 , η 4 are calculated by an indirect method, the Gauss-Newton algorithm In addition of these parameters, the creep retardation time τ can be used. τ is the conventional retardation time such as:

( ) ∞ = J J 63 . 0 ) (τ (9)
The comparison of this model with the experimental data is proposed Figure14. The fit is quite good between the experimental data and the model.

Recycling process leads to modify some mechanical parameters as Young modulus, failure strain, yield stress, creep parameters. Comparing tensile and bending tests, some evolution are similar as for example, the Young modulus decreasing, a less influence on the 108MF97 behavior and strain rate sensibility. Creep tests show the impact is less important with the talc filled polymer. All these microscopic and macroscopic observations leads to a good modeling of the recycled 108 and 7510 PP compounds, including strain rate effects.

In this study only the recycling effect has been studied. But in a real industrial recycling process, ELV bumpers are covered in dust, soaked in liquids, specially oils and are modified by every physical and chemical elements met in its use. The influence on rheological and mechanical properties of pollutants, as basic engine oil and ethylene glycol, has been performed (Pessey et al. [14]). The combination of both: recycling and pollution is under progress and will be presented in a future work.

In addition numerical models have to be integrated with finite element methods in order to study the bumper mechanical behavior.

virgins materials and 1 κ , and 2 κ

 12 Figures 11 and 12 report the comparison between the modeling and the experimental

Acknowledgements

Authors would like to thanks the French Department for Research and Innovation for their financial support (ACI "RECYPRO B" n°ECD073). Authors also cordially thanks Claude Raveyre, Professor Jacques Guillet and Roger Schmitt for providing samples and for the time they kindly spent in preparing samples for this study. Our entire acknowledgement goes to the ACI RECYPROA and B participants for helpful discussions.


Ben Ben Difallah

M Kharrat

M Dammak

G Monteil

IMPROVEMENT IN THE TRIBOLOGICAL PERFORMANCE OF POLYCARBONATE VIA THE INCORPORATION OF MOLYBDENUM DISULPHIDE PARTICLES

Keywords: Polymers (solid) < Materials, Solid Lubricants < Polycarbonate, MoS 2 , Composite, Solid lubricant, Friction, Wear

The present study undertakes the assessment of the effect of the incorporation of molybdenum disulphide (MoS 2 ) flakes on the tribological behavior of polycarbonate (PC) matrix. Five weight ratios of the MoS 2 particles in the PC matrix were considered in the range of 0-10 wt%. The composites were developed by direct injection molding. The determination of various tribological parameters after wear testing (the friction coefficient, the wear volume loss and the profilometric traces) and microscopical observations by scanning electron microscopy (SEM) were combined in an attempt to understand the effect of the solid lubricant in the composites' tribological performance. It was found that the tribological properties were improved by the addition of MoS 2 particles. The maximum reductions in the friction coefficient and wear were obtained with MoS 2 mass content about 7 to 10 wt%. It seems that MoS 2 decreases the polymer surface melting by dissipating the generated heat. Under sliding conditions, the incorporation of MoS 2 particles enhances the abrasive component in the wear mechanism which is manifested by the formation of scratches in the two bodies in contact.

(13)). Bahadur and Gong (9) performed friction and wear tests on polyimide (PI), polyamide 6-6 (PA 66) and polytetrafluoethylene (PTFE) with MoS 2 as a filler. On the one hand, they found that wear was considerably reduced, and on the other hand, they revealed that the wear resistance of composites was affected by the filler content. The wear rate of PA was minimum improves its abrasive wear and sliding performance with a content of MoS 2 for minimum wear rate around 10 wt%. They also reported that, under sliding conditions, the main wear mechanism of HMW-HDPE was changed from severe melting wear to mild adhesive wear.

As for Zhu, et al. (12), they reported that MoS 2 improved dry and water sliding wear rate of PI for an optimum content of MoS 2 around 10-15 wt%. In the same vein, we have published a previous work (13) dealing with the tribological behavior of two polymers composites filled with different weight fractions of MoS 2 . Conclusive results were found in order to improve the knowledge about the impact of the development methodology on the interfacial adhesion between the filler and the matrix. We concluded that the lubricating ability of MoS 2 depends on the nature of the polymer, the development methodology and the interaction between the filler and the matrix.

EXPERIMENTAL DETAILS

Materials and specimen preparation

A commercial PC thermoplastic polymer was used as the matrix material. The PC pellets (with a diameter of approximately 2-3.5 mm) were provided from Altech, (1.20 g/cm 3 density, 14 g/10 min IF). A flaky-shaped MoS 2 powder (6 µm average size, 5.06 g/cm 3 density) with 95% purity was purchased from Aldrich Chemistry (Sigma-Aldrich) (Fig. 1). The considered weight fractions (wt %) of MoS 2 were 2%, 4%, 7% and 10%. After being dried in a vacuum oven at 110 °C for 4 h, PC was injection molded with MoS 2 using DEMAG ERGOTECH 125/475 injection molding machine. Table 1 gives the injection parameters.

Friction and wear testing

A specific home-made microtribometer was employed for friction and wear tests of the PC/MoS 2 composites. The apparatus is in a reciprocating ball on flat configuration. The composite flat specimens were rubbed against a 19-mm-diameter high chromium steel ball under a constant applied normal load of 5 N. The tests were carried out for 10,000 cycles with the ball oscillating at a frequency of 1 Hz over a displacement magnitude of 2 mm. At least, three friction and wear tests were conducted for each composite. Figure 3 shows the used microtribometer which can be divided into three functional sub-systems. Concerning the first one, it is the mechanical arrangement (measuring head) generating the required contact load (normal load) between the high chromium steel ball and the flat composite sample and allowing the tangential load to be monitored using a piezoelectric sensor. The measuring head is equilibrated by a counterbalancing arm allowing the magnitude of the dead load to be adjusted to very low values. As for the second sub-system, it is the micro-displacement arrangement based upon a translation table with a precise linear ball bearing. This table is coupled to a step-by-step motor using a ball screw. With regard to the third sub-system, it is a control and data acquisition unit used for driving the microtribometer and for data acquisition and processing. The treatment of the measurements and the display of the results are performed by PC-based software.

The volume of each wear scar was measured using the optical 3D surface metrology software program provided by an Infinitefocus Alicona® laboratory system. To eliminate the influence of debris on wear volume measurements, the samples were ultrasonically cleaned. Optical The variations of the friction coefficient with MoS 2 content after 10,000 sliding cycles are better shown in Figure 5. The mean friction coefficient decreases with the increase in the filler content. In fact, it falls from about 0.70 to 0.61 when the MoS 2 mass content increases from 0 wt% to only 2 wt%, whereas, it drops to 0.54 at 10 wt% of MoS 2 . In this case, the reduction in the friction coefficient is about 0.16 over the range of 0-10 wt % of the MoS 2 inclusions. The

RESULTS AND DISCUSSION

Friction testing results

Wear test results

We have measured the wear on different composites after 10,000 sliding cycles by using the 3D metrology device Infinitefocus. Table 2 contains the 2D transversal profiles recorded at the middle of the wear track and the typical 3D datasets registered on the wear areas. The 3D projections have been reconstructed by a precision optic allowing a complete detection of the surface with a vertical resolution of 500 nm. The goal is to trace microgeometry changes on composite surfaces after wear sliding tests. Table 2. Typical transversal profiles and three dimensional images recorded on the worn surfaces of the PC composites with different amounts of MoS 2 fillers after 10,000 sliding cycles.

For the neat PC, positive reliefs were observed over the whole sliding track. Interestingly, adding 2 wt% of MoS 2 changed the surface morphology. Topographic scans of the composite show material removal inside the wear scar and the formation of plough areas. The same trends can be seen with the other filler fractions. Wear peaks seem to be much shallower and less abundant as the fillers content increases. Thus, a finer pattern is generated with the addition of MoS 2 flakes. This was further confirmed by the 2D transversal wear profile of PC and its composites. The plot of the PC 2D profile shows evident positive reliefs along the Figure 7 illustrates the evolutions of the measured grooved volume (V -), the measured pile-up volume (V + ) (Fig. 7-a) and the difference between them representing the wear volume loss (Fig. 7-b) as function of the filler content. It can be seen that both of the grooved and the pileup volumes were reduced when MoS 2 wt% is increased. However, the pile-up volume was immediately affected by the incorporation of 2 wt% of MoS 2 . It falls from 0.0072mm 3 to 0.0056mm 3 when the content of MoS 2 is 2 wt%. Molybdenum disulphide inclusions proved beneficial in reducing the severe adhesive component of the PC wear. On the other hand, the grooved volume (V -) of the different composites shows lower values than the pure PC. It falls from 0.0112 mm 3 with pure PC to 0.0068mm 3 with PC composite at 10 wt% of MoS 2 .

Therefore, with the rise of MoS 2 content, the wear volume loss of the composites increased from about 0.0040 mm 3 for pure PC to 0.0051 mm 3 for 2 wt% MoS 2 flakes-filled PC composites. From this point, the wear volume of the composites rapidly falls with the increase of the filler content. A minimum value of 0.0022 mm 3 is reached with 10 wt% of MoS 2 . It is In order to enhance the analysis of the composites worn surfaces, three-dimensional wear track profiles were developed under an Optical Scanning Microscope (OSM). Figure 8 gives typical profiles obtained on specimens tested for 10,000 sliding cycles for the neat PC and the PC with 10 wt% MoS 2 . The wear track of the unfilled PC is obviously not uniform, showing severe plastic deformation of the neat polymer (Fig. 8-a). Nevertheless, with filling 10 wt% of MoS 2 to the matrix polymer (Fig. 8-b), the wear track of the composite seems to be smoother and more uniform with the presence of light scratches. These results satisfy, with a larger set of observations, the information obtained in Table 2. For a further understanding of the wear mechanisms, SEM micrographs were also recorded in order to manifest the final worn conditions. Figure 10 shows SEM micrographs of the PC worn surface and its counterpart. As expected, PC surface is rough (Fig. 10-a) and covered by wear particles, thus forming adherent agglomerate (Scott (21)). At higher magnifications (Fig. 10-b), the SEM micrograph clearly shows accumulated wear particles under the repeated sliding cycles. As per Arribas et al. ( 22), the generated wear debris gets entrapped in the contact region and forms an adherent layer with the production of severely plastically deformed material at the tip of the wear scar. Figures 10-c andd The micrograph presented in Figure 11 shows the worn surface of PC composite with 10 wt% of MoS 2 and its counterpart. The wear scar of the composite specimen appears smooth and relatively uniform with the presence of fine scratches (Fig. 11-a). At higher magnifications, the micrograph reveals the existence of large debris patches attached at the extremity of the wear track. The formed layer of plastically deformed material seems to be thinner and less adherent compared with that of PC sample (Fig. 11-b). The SEM micrographs of the corresponding pin counterpart are shown in Figure 11-c and11-d, respectively. The worn surface of the steel counterpart shows a large amount of transferred wear debris (Fig. 11-c). It can also be seen that a thick and not uniform film was clearly formed showing slight abrasive scratches (Fig. 11-d). This non-coherent film is controlled by softening and solid lubricant supply. Softening mechanisms result in discontinuous transfer particles (Samyn,et al. (23)).

Analysis of wear mechanisms

According to Lancaster [START_REF] Lancaster | Geometrical effects on wear of polymers and carbons[END_REF], this mechanism is attributed to reducing interaction between counterface roughness and polymer sample (Lancaster (24)). It can be established that the

CONCLUSIONS

In this study, the tribological characteristics of PC/MoS 2 composites were investigated using a ball on flat microtribometer. The experimental results indicated that the unfilled PC has a poor tribological performance characterized by the formation of layered particle debris in some parts of the polymer wear track. In this case, the sheared bodies in contact are put down again while the strength of wear particles is much poorer. Opportunities provided by visual display revealed that severe adhesive/abrasive wear mechanism coupled with serious plastic deformations occurred in the unfilled polymer. The incorporation of MoS 2 flakes improved (4) Wang, Q., Zhang, X. and Pei, X. (2010), "Study on the synergistic effect of carbon fiber and graphite and nanoparticle on the friction and wear behavior of polyimide composites," Mater. Des. 31, 8, pp. 3761-3768.

(5) Bijwe, J., John Rajesh, J., Jeyakumar, A., Ghosh, A. and Tewari, U.S. (2000), "Influence of solid lubricants and fibre reinforcement on wear behaviour of polyethersulphone," Tribol.

Int. 33, 10, pp. 697-706.

INTRODUCTION

  There is a great interest in the development of new polymer composites due to the various advantages, such as cost effectiveness, ease in manufacturing and excellent performance. Polymer composites are recommended in tribo-applications owing to the possibility of producing required material performance with judicious choice of fillers in adequate proportions in the composite. A great deal of research work has been carried out on thermoplastic composites based on layered solid lubricants such as graphite, molybdenum disulphide and boron nitride (Ben Difallah, et al. (1); Zhang, et al. (2); Suresha, et al. (3); Wang, et al. (4); Bijwe, et al. (5)). These studies have not only shown an improvement in the tribological performance of the composites depending on the nature and the amount of the solid lubricant, but also been significant in introducing such fillers to several industrial applications (Mnif, et al. (6); Deng, et al. (7); Cho, et al. (8)). The lubricant ability of the inclusions may provide better functioning by reducing friction and wear values. Particularly, Bahadur and Gong (9) classified molybdenum disulphide (MoS 2 ) as one of the most common solid lubricant used. This material has a crystalline lamellar structure with hexagonal sulphur planes sandwiched between two hexagonal molybdenum layers. The atoms lying on the same crystal layer are strongly covalently bonded to each other. The layers themselves are bonded by weak van der Waals forces. Winer (10) reported that the lubrication capacity of MoS 2 , i.e. low friction characteristics and easy cleavage, is intrinsic to its layered structure. When added to thermoplastic polymers, MoS 2 may enhance friction and wear properties (Bahadur and Gong (9); Pettarin, et al. (11); Zhu, et al. (12); Ben Difallah, et al.

  content of MoS 2 about 15-20 wt%. Pettarin, et al. (11) found that the incorporation of MoS 2 to high molecular weight high density polyethylene (HMW-HDPE)

  Polycarbonate (PC) is an amorphous engineering thermoplastic polymer which combines transparency, good thermal stability, impact resistance and the easiness to be processed on conventional machinery. New PC composites are being developed in order to improve the tribological behavior of the base thermoplastic by using various fillers, such as zinc oxide (ZnO), silicon dioxide (SiO 2 ), short glass fibers, … (Carrión, et al. (14); Carrión, et al. (15); Carrión, et al. (16); Wang, et al. (17); Ho and Jeng (18)). Carrión, et al. studied the wear response of PC when ZnO nanoparticles and organoclays were added to the polymer (14)-(16). By their research work, the authors confirmed the important reduction in the wear rate with respect to neat PC. As for Wang, et al. (17), they investigated the tribological performances of PC film and nano-SiO 2 /PC composite coating, which exhibited lower frictional coefficient. Concerning Ho and Jeng (18), they analyzed the wear behavior of PCreinforced with 20 wt% short glass fibers. The authors reported that the wear volume loss was the fiber orientation according to the sliding direction.Therefore, the fundamental apprehension of the role attributed to different fillers in tribological performance is essential for successful applications. Through this paper, studies are focused on the friction and wear properties of polycarbonate composites containing 2-10% of MoS 2 powder. For this purpose, wear tests of the PC composites were performed using a ball on flat microtribometer. The results obtained could provide evidence to explain the changes in friction and wear mechanisms at various amounts of MoS 2 particles.

Fig. 1 .

 1 Fig.1. SEM image of the flake-shaped MoS 2 particles, as supplied.

Figure 2

 2 Figure 2 gives a typical scanning electron microscopy (SEM) image of the fractured surface

Fig 2 .

 2 Fig 2. SEM picture of the fracture surface of a PC matrix composite containing 10 wt% MoS 2

  OSM) technique was also used to explore the worn surface. PC/MoS 2 composites wear mechanisms were analyzed using SEM, JEOL JSM 6400F. The surface of the sample was coated with gold before SEM observation.

Fig. 3 .

 3 Fig. 3. Schematic representation of the ball on flat microtribometer.

Figure 4

 4 Figure 4 displays typical evolutions of the friction coefficient with the number of sliding

Fig. 4 .

 4 Fig. 4. Typical evolutions of the friction coefficient versus the number of cycles for PC/MoS 2

Fig. 5 .

 5 Fig. 5. Evolution of the mean friction coefficient versus the MoS 2 mass content after 10,000

  wear track. The irregular surface is occupied by molten wear debris which were extracted and re-deposited onto the polycarbonate surface. The wear profile becomes totally different when 2 wt% of MoS 2 is added. In fact, it exhibits almost negative reliefs. Besides, the width and depth of wear tracks are gradually smaller with the increase of MoS 2 amount.Further wear parameters can be specified from the surface topography data. For each PC/MoS 2 composite specimen, the wear volume loss is estimated as the difference between the grooved volume (V -) and the pile-up volume (V + ) which are defined in the schematic representation in Figure6(Cayer-Barrioz, et al. (19)).

Fig. 6 .

 6 Fig. 6. Schematic representation of wear profile groove on a composite surface after the

  wear resistance of PC is greatly enhanced by the addition of MoS 2 fillers. In addition, it can be established that pure PC has a relatively low initial wear associated with large particles adhering to the specimen surface and thus increasing the pile-up volume (V+).

Fig. 7 .

 7 Fig. 7. Evolution of the wear characteristics of PC/MoS 2 composites versus the MoS 2 mass content after 10,000 sliding cycles: (a) grooved volume (V -) and pile-up volume (V + ), (b)

Fig. 8 .

 8 Fig. 8. Three dimensional profiles recorded on the worn surfaces after 10,000 sliding cycles

Figure 9

 9 Figure 9 presents different optical micrographs showing the overall view of typical well-

Fig. 9 .

 9 Fig. 9. Optical observations of the different PC composites after wear tests.

  show representative samplings of the high chromium steel ball tested against neat PC at two different magnifications. The worn surface is almost not damaged and is surrounded by large plate-like debris. Their size is in the order of several tens of micrometers in the in-plane dimensions (Fig.10-d). Consistent with the results reported elsewhere (Carrión, et al. (16)), the unfilled PC is shown to have poor tribological performance characterized by severe damage originally caused by the production of a large amount of wear particles in an adhesive-abrasive wear mechanism.

Fig. 10 .

 10 Fig. 10. SEM micrographs of the worn surface in the unfilled PC (a) and (b); and its

  incorporation of MoS 2 flakes promotes the change of the wear mechanism from adhesion to abrasion since it has been run with other fillers (Carrión, et al. (14); Arribas, et al. (22)). In this case, several previous studies have focused on the great influence of wear particles during Zum Gahr (25); Bourithis, et al. (26)). Depending on their physicochemical properties, their size and shape, third body wear particles may lead to abrasive wear mechanism. In the case of the unfilled polycarbonate, severe surface damages characterized by wear debris detachment in a massive quantity were developed (Carrión; et al. (16); Lee, et al. (27)). Under the repeated sliding cycles, serious plastic deformations and subsequent energy dissipation lead to the adhesion of wear particles and thus to a severe wear mechanism. On the contrary, the incorporation of MoS 2 flakes to the PC matrix seems to change the wear mode into a predominant abrasive one. In fact, it was clearly seen that fine rays were developed in the composite worn surface, furthermore, the number of adherent wear particles decreased significantly. Pettarin, et al. (11) reported that the addition of commercial MoS 2 to HMW-HDPE matrix contribute to enhance the generated heat dissipation, thus it inhibits the surface melting of the polymer (Pettarin, et al. (11)). Consequently, the wear resistance performance of HMW-HDPE was improved by the incorporation of MoS 2 .

Fig. 11 .

 11 Fig. 11. SEM micrographs of the worn surface in the PC composite with 10 wt% MoS 2 (a)

  performances by reduction of friction and wear. The abrasive component of wear took a dominant place by the addition of MoS 2 particles. It was reported in a previous research work that the weak bonds between the filler and the matrix cause the polymer fracture and the detachment of MoS 2 particles in the sliding trace (Ben Difallah et al., (13)). By this way, polymer heating under sliding cycles could be restrained. This result has confirmed the hypothesis that the MoS 2 filler was responsible of decreasing thermal conductivity in various thermoplastic polymers by the increase in heat dissipation during the sliding tests.

  of glass-epoxy composites with and without graphite Particulate Filler," J. Appl. Polym. Sci. 103, 4, pp. 2472-2480.

( 6 )

 6 Mnif, R. Ben Jemaa, M.C. Hadj Kacem, N. and Elleuch, R. (2013), "Impact of Viscoelasticity on the Tribological Behavior of PTFE Composites for Valve Seals Application", Tribol. Trans. 56, 5, pp. 879-886.(7) Deng, J., Song, W., Zhang, H., Yan, P. and Liu, A. (2011), "Friction and wear behaviors of the carbide tools embedded with solid lubricants in sliding wear tests and in dry cutting processes," Wear 270, 9-10, pp. 666-674. (8) Cho, M.H., Ju, J., Kima, S.J. and Jang, H. (2006), "Tribological properties of solid lubricants (graphite, Sb 2 S 3 , MoS 2 ) for automotive brake friction materials," Wear 260, 7-8, pp. 855-860. (9) Bahadur, S. and Gong, D. (1992), "The action of fillers in the modification of the tribological behavior of polymers," Wear 158, 1-2, pp. 41-59. (10) Winer, W.O. (1967), "Molybdenum disulphide as a lubricant: a review of fundamental knowledge," Wear 10, 6, pp. 422-452.

( 11 )

 11 Pettarin, V., Churruca, M. J., Felhös, D., Karger-Kocsis, J. and Frontini, P.M. (2010), "Changes in tribological performance of high molecular weight high density polyethylene induced by the addition of molybdenum disulphide particles," Wear 269, 1-2, pp. 31-45. (12) Zhu, P., Wang, X., Wang, X.D., Huang, P. and Shi, J. (2006), "Tribology performance of thermoplastic polyimide under dry and water lubrication conditions," Ind. Lubr. Tribol. 58, 4, pp. 195-201. (13) B. Ben Difallah, M. Kharrat, M. Dammak and G. Monteil, (2012), "Microstructure, friction and wear analysis of thermoplastic based composites with solid lubricant", Mechanics & Industry 13, 5, pp.337-346. (14) Carrión, F.J., Sanes, J. and Bermúdez, M.D. (2007), "Influence of ZnO nanoparticle filler on the properties and wear resistance of polycarbonate," Wear 262, 11-12, pp. 1504-1510. (15) Carrión, F.J., Sanes, J. and Bermúdez, M.D. (2007), "Effect of ionic liquid on the structure and tribological properties of polycarbonate-zinc oxide nanodispersion," Mater. Lett. 61, 23-24, pp. 4531-4535. (16) Carrión, F.J., Arribas, A., Bermúdez, M.D. and Guillamon, A. (2008), "Physical and tribological properties of a new polycarbonate-organoclay nanocomposite," Euro. Polym. J. 44, 4, pp. 968-977. (17) Wang, Z.Z., Gu, P. and Zhang, Z. (2010), "Indentation and scratch behavior of nano-SiO 2 /polycarbonate composite coating at the micro/nano-scale," Wear 269, 1-2, pp. 21-25. (18) Ho, K.C. and Jeng, M.C. (1997), "Tribological characteristics of short glass fibre reinforced polycarbonate Composites," Wear 206, 1-2, pp. 60-68.

( 19 )

 19 Cayer-Barrioz, J., Mazuyer, D., Tonck, A., Kapsa, Ph. and Chateauminois, A. (2006), "Nano-scratch and friction: An innovative approach to understand the tribological behaviour of poly(amide) fibres," Tribol. Int. 39, 2, pp. 62-69.

( 20 )

 20 Zhang, X., Liao, G., Jin, Q., Feng, X. and Jian, X. (2008), "On dry sliding friction and wear behavior of PPESK filled with PTFE and graphite," Tribol. Int. 41,3, pp. 195-201.

( 21 )

 21 Scott, F.H. (2002), "High-temperature sliding wear of metals," Tribol. Int. 35, 8, pp. 489-495. (22) Arribas, A., Bermúdez, M.D., Brostow, W., Carrión-Vilches, F.J. and Olea-Mejía, O.

Figure captions Fig. 1 .

 captions1 Figure captions

Fig 2 .

 2 Fig 2. SEM picture of the fracture surface of a PC matrix composite containing 10 wt% MoS 2

Fig. 3 .

 3 Fig. 3. Schematic representation of the ball on disk microtribometer.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Typical evolutions of the friction coefficient versus the number of cycles for PC/MoS 2

Fig. 6 .

 6 Fig. 6. Schematic representation of wear profile groove on a composite surface after the

Fig. 7 .

 7 Fig. 7. Evolution of the wear characteristics of PC/MoS 2 composites versus the MoS 2 mass content after 10,000 sliding cycles: (a) grooved volume (V -) and pile-up volume (V + ), (b)

Fig. 8 .

 8 Fig. 8. Three dimensional profiles recorded on the worn surfaces after 10,000 sliding cycles

Fig. 9 .

 9 Fig. 9. Optical observations of the different PC composites after wear tests.

Fig. 10 .

 10 Fig. 10. SEM micrographs of the worn surface in the unfilled PC (a) and (b); and its

Fig. 11 .

 11 Fig. 11. SEM micrographs of the worn surface in the PC composite with 10 wt% MoS 2 (a)

  Fig. 1

  mc.manuscriptcentral.com/tandf/tribtrans, E-mail: FSadeghi@stle.org Submitted Manuscript for Tribology Transactions for Peer Review Only

Table 1 .

 1 Injection molding parameters of PC composites.

Table captions Table 1 .

 captions1 Injection molding parameters of PC composites.

Table 2 .

 2 Typical transversal profiles and three dimensional images recorded on the worn surfaces of the PC composites with different amounts of MoS 2 filler after 10,000 sliding cycles.

	F o
	r
	P
	e e r
	R e v i e w
	O n
	l y
	-19-

Table 1

 1 Injection pressure (bar) 724

	Page 31 of 33
	Injection temperature (°C)	290
	Cycle time (s)	31
	Holding pressure (bar)	310
	Screw rotation speed (mm/s)	220

http://mc.manuscriptcentral.com/tandf/tribtrans, E-mail: FSadeghi@stle.

org Submitted Manuscript for Tribology Transactions for Peer Review Only

	F o
	r
	P
	e e r
	R e v i e w
	O n
	l y

Table 2

 2

	Composite specimens	2D wear profile	3D micrograph
	PC

http://mc.manuscriptcentral.com/tandf/tribtrans, E-mail: FSadeghi@stle.org Submitted Manuscript for Tribology Transactions for Peer Review Only

ACKNOWLEDGEMENTS

The authors would gratefully acknowledge the financial assistance of the Electro-Mechanical Systems Laboratory in the National Engineering School of Sfax funded by the Ministry of Higher Education and Scientific Research of TUNISIA as well as the assistance provided by the Department of Applied Mechanics in the FEMTO-ST Institute at Besançon-FRANCE.

Thanks should also be extended to the members of the Polymer Processing Center of Sousse-TUNISIA for their help in samples preparation.


E Falconnet

H Makich

J Chambert
email: jerome.chambert@univ-fcomte.fr

G Monteil

P Picart

Numerical and experimental analyses of punch wear in the blanking of copper alloy thin sheet

Keywords: Wear testing, Blanking, Copper alloy, Wear modelling, Finite element modelling

This research on punch wear resulting from the blanking of copper alloy thin sheet has been conducted by means of experimental and numerical analyses. Firstly, the experimental method has consisted in measuring punch worn profiles from replicas, and secondly in obtaining the wear coefficient by using a specific tribometer. The numerical modelling of blanking process has been developed with the finite element method to compute the mechanical fields necessary to calculate wear. Thus, the Archard formulation for abrasive wear has been programmed to compute the wear depth and the resulting punch geometry.

Finally the simulation results of wear prediction have been compared to experimental ones.

Introduction

Among the shearing processes, blanking is one of the most frequently used due to its reliability and capability of mass production. The process is also very economical because it allows to easily obtain the appropriate size and shape of a large parts number. As in every production process, tools life time is of major concern for multiple reasons: the part quality mainly depends on tool wear, frequent tool changes slow down production time and increase maintenance costs. Therefore, predicting tool wear can be a key feature to improve the process efficiency.

For the last decades, wear in blanking has been the subject of several experimental researches, mainly to understand its impact on the product quality (burr height). Maeda et al. [START_REF] Maeda | Wear on shearing tools[END_REF][START_REF] Maeda | The study on wear of blanking tool for 18-8 stainless steel and bainite hardened steel strips[END_REF] have investigated blanking tool wear distribution and its influence on the process parameters (blanking force, energy, burr height). Hernandez et al. [START_REF] Hernandez | Modelling and experimental analysis of the effects of tool wear on form errors in stainless steel blanking[END_REF] have studied the effects of tool wear on the shearing mechanism and resulting form errors. Monteil et al. [START_REF] Monteil | In situ punch wear measurement in a blanking tool by means of thin layer activation[END_REF] have developed a direct method for measuring punch wear, based on selective activation technique, which allows to quantify in real time the influence of blanked material or lubrication. However, compared to other forming processes such as deep drawing [START_REF] Ersoy-Nürnberg | Simulation of wear on sheet metal forming tools -An energy approach[END_REF][START_REF] Jensen | Applying the finite-element method for determination of tool wear in conventional deep-drawing[END_REF] and hot forging [START_REF] Behrens | Prediction of wear in hot forging tools by mean of finiteelement-analysis[END_REF], the combination of experimental and numerical methods to predict tools wear has been less investigated in blanking. Hambli [START_REF] Hambli | Blanking tool wear modelling using finite element method[END_REF] has developed a finite element (FE) model and has implemented an algorithm to predict punch wear during steel metal sheet blanking. The Archard formulation [START_REF] Archard | Contact and rubbing of flat surfaces[END_REF] for adhesive wear was considered to calculate wear depth on the punch, and a comparison with experimental results was performed. Hambli [START_REF] Hambli | BLANKSOFT : a code for sheet metal blanking processes optimization[END_REF] has also proposed a theoretical approach to predict tool wear based on the evolution of the punch edge radius within Blanksoft, an industrial software dedicated to the optimization of sheet metal blanking processes. It is worth noting that the mentioned studies have been conducted with steel and stainless steel materials; less interest has been accorded to copper alloys.

In the present paper, punch wear profile has been determined experimentally by a doublereplication method, and the wear coefficient of Archard formulation has been obtained by a specific tribometer. Then, FE simulation results have been used within a wear algorithm based on an Archard formulation applied to abrasive wear in order to predict the worn punch profile.

The final section of this paper presents a comparison between experimental and numerical results of wear prediction.

Experimental method

The main objective of the experimental study conducted by Makich [START_REF] Makich | Etude théorique et expérimentale de l'usure des outils de découpe; Influence sur la qualité des pièces découpées[END_REF] has been to determine the influence of punch wear on the part quality during copper alloy thin-sheets blanking. A double-molding procedure has been developed to observe wear profiles, and a specific tribometer has been designed to determine the wear behaviour of several material couples.

Blanking test description

As shown in Fig. 1a, the blanking process consists in a metal sheet positioned over a die in which a punch passes through to plastically deform the metal until a crack propagates and leads to complete separation of the cut part. A sheet-holder is added to maintain the sheet during the travel of the punch to avoid elastic springback and movement of the sheet, thus increasing the quality of the cut edge profile. The blanking tests have been performed on a BRUDERER 50 tons press with a speed of 500 strokes/min. The principal geometrical data of the model is illustrated in Fig. 1a andlisted in Table 1. In this study, the blanked material is a copper-iron alloy strip of 15 mm width and 0.254 mm nominal thickness. The mechanical properties of the blanked material have been obtained by a conventional tensile test. The true-stress -true-strain curve (Fig. 1b) has been approximated by the following equation:

n kε σ σ + = 0 (1)
The rational (true stress and strain) tensile test curve (Fig. 1b) has been linearly extrapolated to take account of large deformation plasticity within FE modelling. The chemical composition and mechanical properties are respectively provided in

Determination of the punch wear profile

A double-print method has been developed in order to obtain the punch wear profile at different production stages without removing the punch from the mechanical press, and then not modifying the operating conditions. This in situ procedure of wear measurement by profilometry was divided into three major steps :

Obtaining the imprint of the punch (without dismantling)

Making a replica of the punch

Measuring the edges of the replica by profilometry.

Observation of the punch by microscopy has revealed that the wear mechanism involved was purely abrasive.

Imprint of the punch

To carry out the imprint of the punch, a mold has been milled in a wedge block (Fig. 2a and2b) to be filled with a volume of silicone resin (designated Coltène® President plus jet Light Body). The extremity of the punch has been immerged in this mold for a couple of minutes, according to the resin drying time. Impressions have been taken every 12,500 strokes of the punch. Fig. 3 gives a detailed representation of a punch replica after 787,500 punch strokes. Besides the presence of abrasive wear streaks, the precision of this method allows to observe regrinding streaks.

Extraction of wear profiles

When the replica of the punch has been carried out, a variable focus optical microscope (InfiniteFocus®) has been used to extract 3D surfaces of the punch at four diametrically opposed locations. For each surface, an average profile has been determined and a representative state of wear for a given punch strokes number has been obtained by calculating an average profile from the four previous ones. Finally, a mathematical equation has been employed to fit this profile (Fig. 4), thus allowing to integrate the punch geometry in a numerical simulation. As already mentioned by Hernandez et al. [START_REF] Hernandez | Modelling and experimental analysis of the effects of tool wear on form errors in stainless steel blanking[END_REF], the worn punch profile may be decomposed in three zones: face wear, cutting edge wear and flank wear (Fig. 4). In addition, the initial profile obtained after regrinding is shown on Fig. 4. The initial and worn profiles have been positioned according to reference planes determined outside worn areas.

Determination of the wear coefficient

The Archard wear formulation [START_REF] Archard | Contact and rubbing of flat surfaces[END_REF] describes the wear volume as dependent on the load N F , the sliding distance s , and the wear coefficient K . This coefficient depends on the material couple and is originally defined as the probability of contacts resulting in the removal of a particle. The wear coefficient has been measured experimentally in this study by means of a tribometer placed before the opening of the mechanical press, where the sheet coil is unrolled.

Principle and description of the specific tribometer

The tribometer developed by Makich [START_REF] Makich | Etude théorique et expérimentale de l'usure des outils de découpe; Influence sur la qualité des pièces découpées[END_REF] has been intended to measure a wear coefficient with specified parameters, and has been designed specially to be integrated on a production line (Fig. 5). Thus, it allows to directly test different operating conditions during the blanking tests on the mechanical press.

As illustrated in Fig. 5, the configuration of the tribometer consists in a spherical pin (5 mm diameter; same material as the punch) lying on a flat sheet of the studied metal grade. A normal load (7 N) is applied on the pin, as the sheet translates in a continuous motion toward the mechanical press (37 mm/s; imposed by the stroke rate).

Contrary to most of conventional tribometers such as pin-on-disc or ring-on-ring where the wear track remains the same during the tribological experiment, the open tribometer permits the rubbing surface to be constantly renewed. Therefore, the friction conditions with this tribometer get closer to the ones met during the blanking operation. Greban [START_REF] Gréban | Découpabilité du cuivre et des alliages cuivreux[END_REF] has performed friction tests on a conventional pin-on-disc tribometer and noticed that, despite the ease of implementation of this method, the operating conditions were very different from those found during blanking. Contrary to the pin-on-disc tribometer, the punch always rubs into a renewed material at each stroke, allowing to better evacuate wear particles for example.

Fig. 5 : Tribometer location on the production line

After a prescribed sliding distance of metal sheet, the spherical pin has been taken apart from the tribometer and the volume loss has been measured. This procedure has been repeated two times to obtain a mean value of the volume loss.

Evaluation of the wear coefficient

After a sufficient sliding distance, the material loss of the spherical pin has appeared to be comparable to a regular spherical cap. Then, the first approach for determining the volume loss has consisted in measuring the radius of the base of the cap and using the expression of a hemisphere volume (Fig. 6a and6b). However, a closer look at the worn pin has revealed cavities and asperities contributing significantly to the volume loss. Therefore, a second approach has been considered by employing a 3D topographic acquisition method with a confocal microscope (Alicona®). The acquired image has been postprocessed with Gwyddion® software in order to create a reference plan, corresponding to the non-worn shape of the sphere. The wear volume has then been determined by integrating the volume under the reference plane with Surfcom® software (Fig. 7).

Wear modelling

Wear is a phenomenon widely investigated due to its economical concerns. Mechanical wear can be sorted in several classes, the most commons in metal forming being the abrasive wear and adhesive wear. In the literature, several authors [13 -15] have reviewed numerous models to predict wear phenomena. Hegadekatte et al. [START_REF] Hegadekatte | A predictive modeling scheme for wear in tribometers[END_REF] have classified wear models into two main categories: mechanistic models based on material failure mechanisms, and phenomenological models which are using principles of contact mechanics. In the first category, Suh [START_REF] Suh | The delamination theory of wear[END_REF] has developed the delamination theory of wear which involves dislocation mechanics. Kapoor [START_REF] Kapoor | Wear by plastic ratchetting[END_REF] has studied wear under repeated loading where the material accumulates unidirectional plastic strain until a critical value, which leads to a failure termed ratchetting. In the second category, Archard [START_REF] Archard | Contact and rubbing of flat surfaces[END_REF] has proposed a simple linear model in terms of material volume loss, contact pressure and sliding distance of contacting parts. Over the past, Archard's equation has been modified to meet particular case studies. Rhee [START_REF] Rhee | Wear equation for polymers sliding against metal surfaces[END_REF] has proposed a wear equation with separate exponents on the contact pressure and the sliding distance. Sarkar [START_REF] Sarkar | Friction and wear[END_REF] has included the friction coefficient to take account of the asperity junction growth in wear phenomenon. Ersoy-Nürnberg et al. [START_REF] Ersoy-Nürnberg | Simulation of wear on sheet metal forming tools -An energy approach[END_REF] have presented a wear coefficient to be variable with the accumulated wear work, which depends on dissipated energy.

The Archard model has been considered in this study to be a suitable solution in connection with a finite-element model, since each variable can be calculated within the blanking simulation. Moreover, the proposed experimental method for punch wear measurement favoured a phenomenological approach, as it was based on observing and fitting a punch shape resulting from prescribed working conditions.

The Archard model

The Archard wear model is widely used to predict the wear behaviour of surfaces. This model is based on a phenomenological approximation of the adhesive wear mechanism that takes into account the load and the sliding distance in the interface of two contacting bodies.

The formulation has been adapted to other wear mechanisms and can be expressed as follows:

s F K V N ⋅ ⋅ = ( 2
)
where V is the worn volume, N F is the applied load and s is the sliding distance. The wear coefficient K is originally defined as the probability that an asperity contact produces a wear particle. It is also interpreted as "the fraction of asperities yielding wear particles, as the ratio of the volume worn to the volume deformed, as a factor inversely proportional to a critical number of wear cycles, and as a factor reflecting the inefficiencies associated with the various processes involved in generating wear particles" [START_REF] Rigney | The roles of hardness in the sliding behaviour of materials[END_REF]. This coefficient is established for a material couple, and can be measured experimentally by means of a tribological test (see section 2.3).

Numerical implementation of the model

By considering a representative elementary volume of material, Eq. ( 2) can be written:

ds dF K dV N ⋅ ⋅ = (3)
Introducing the elementary contact area Ω d allows to express the wear depth dW from the

relations Ω ⋅ = d dW dV and Ω ⋅ = d p dF N
, where p is the contact pressure:

ds p K dW ⋅ ⋅ = (4)
For numerical applications, Eq. ( 4) is calculated over a time interval [t n , t n+1 ] corresponding to the n and ) 1 ( + n increments of the simulation. The incremental expression is then implemented following an Euler scheme:

i i i i P n n n P n P n P s p K W W ) ( 1 1 1 + + + ⋅ ⋅ + = with n P n P P n n i i i s s s - = + + 1 1 ) ( ( 5
)
where n P i W is the wear depth at increment n calculated for a given punch node i P of coordinates i x , and However, as the punch is modelled by rigid elements, no calculation of mechanical variables is performed on this tool. Thus, the contact pressure and sliding distance values calculated on the sheet are used to determine wear on the punch. Wear depth on the punch P W is then obtained by integration of the calculated wear depth from the sheet T W along the corresponding punch profile l:

       - = - = ∫ ∫ y y x x y y x y x x d ) ( ) ( d ) ( ) ( ) ( 1 ) ( l l T P W W ϕ φ ϕ φ (6)
where x and y are respectively the coordinate vector of the punch nodes and the sheet surface nodes.

According to the non-local modelling developed by Pijaudier-Cabot and Bazant [START_REF] Pijaudier-Cabot | Nonlocal damage theory[END_REF], the product + ⋅ obtained from the sheet nodes j T (coordinates j y ) and located near the considered punch node. Eq. ( 5) can then be expressed by using Eq. ( 6) as a discrete integral corresponding to the calculation of the wear depth at node i P :

[ ]

2 2 1 1 1 1 1 exp ) ( and ) ( ) ( with ) ( ) ( ) ( c j i j i N j j i i N j j i T n n n T i P n P n P L s p K N W W j j i i y x y x y x x y x x - - = - - =       - ⋅ ⋅ ⋅ + = ∑ ∑ = = + + + ϕ ϕ φ ϕ φ (7)
where c L is the parameter which determines the number of sheet nodes N considered for the weighting operation (

P c t L 2
= in this study) and P N is the number of punch strokes. This distribution allows to take account of the relative distance separating a given punch node from a sheet node, thus traducing a more realistic wear behaviour.

The wear prediction is performed during the steady-state wear stage. Therefore, a multiplication of the wear depth from one punch stroke is appropriate to approximate the wear occurring after several punch strokes. However, this number of strokes should not be too high for two main reasons. The first one is that one must avoid reaching the accelerated wear state.

The second reason is that according to the shape variation of the wear profile during the process, stress and contact pressure fields are expected to vary, thus modifying wear distribution along the punch profile. Choosing an elevated number of punch strokes will not take into account this wear distribution variation and will lead to a significantly different wear profile.

The wear algorithm based on these equations has been programmed under Matlab® environment. Data including contact pressure, relative tangential motion, coordinates of the sheet and punch nodes, have been collected from the FE simulation. After processing, punch worn profiles have been built by normal projection of wear depth values.

Numerical simulation

4.1 Modelling of the blanking process

Model main characteristics

The process modelling has been performed with the FE code Abaqus/CAE 6.9®, using the large deformation theory. The solution has been obtained by the included implicit solver Abaqus/Standard® [START_REF]ABAQUS/Standard-HKS, Abaqus Analysis User's Manual -Version 6[END_REF], following a quasi-static approach of the process simulation. The Newton iteration method has been employed to solve the nonlinear equilibrium equations.

Due to the revolution geometry of the problem, axisymmetry has been considered for the whole setup, so only one meridian plane of the problem has been modelled.

The blanking tools have been modelled using 1D rigid elements. The sheet has been mainly meshed with quadrangular first order axisymmetric elements. The real worn punch geometry has been fitted by an exponential formula in order to improve the accuracy of the numerical modelling (Fig. 4).

In the blanking process, deformations are concentrated in the shear band located between the punch and die cutting edges. Thus, the sheet mesh has been divided in three zones to obtain a fine mesh in the zone of large deformation, and a coarse mesh elsewhere to minimize simulation computational cost. Moreover, fine mesh has been required on the sheet surface to obtain accurate contact pressure and sliding distance data necessary for wear calculation (Fig. 8b).

The sheet material behaviour has been described by an elasto-plastic Von Mises constitutive model with isotropic hardening, and the stress-strain data necessary for the non-linear behaviour of the sheet has been obtained by Makich [START_REF] Makich | Etude théorique et expérimentale de l'usure des outils de découpe; Influence sur la qualité des pièces découpées[END_REF] using tensile tests.

Contact formulation

Contact between the die, the sheet and the sheet-holder has been modelled by Coulomb law with a value of 0.1 for the friction coefficient. Due to the lubrication applied during the blanking process, no friction has been considered between the punch and the sheet.

For the contact formulation, the penalty contact algorithm has been used by defining a master surface (punch profile) and a slave surface (on sheet boundary).

Failure

Examination of the experimental blanked edge generally reveals two main zones traducing the material behaviour during the process. The first one is the sheared zone, formed by the punch before failure occurs. The second one is the fracture zone and corresponds to the ductile fracture of the material as the punch continues to penetrate the sheet. Failure was not taken into account in the numerical model because it is supposed that only wear on the punch lateral face is involved after the onset of material failure. This hypothesis is suggested by the observations made by Maeda [START_REF] Maeda | The study on wear of blanking tool for 18-8 stainless steel and bainite hardened steel strips[END_REF] and Faura [START_REF] Faura | Criterion for tool wear limitation on blanking 18-8 stainless steel strips[END_REF] concerning the face wear of punch, which is less developed than flank wear. Indeed, blanking vertical force drops off when failure is initiated, reducing the contact pressure on the punch face; contact between the punch face and the sheet is also lost when the part or scrap is separated from the sheet. However, failure mechanism will decrease the stresses within the material and will create new contact surface, thus influencing wear results especially on punch flank.

The maximum punch penetration (relative percentage of the sheet thickness) has been defined according to the experimental data of the shear zone height and fracture zone height of the sheet, which remained rather constant during the steady-state wear stage.

As mentioned in Eq. ( 5), the computation of pressure and sliding distance has been required to calculate wear. Contact pressure in Abaqus® is defined as the normal stress between two faces at a point, and depends on the interpenetration of the surfaces. The sliding distance is provided by the relative tangential motion, which is defined as the scalar product of the slip direction and the incremental relative nodal displacement vector. This vector measures the motion of a sheet node relative to the motion of the punch. The sliding distance computed is thus direction-dependent and cumulated at each increment.

Remeshing

In metal forming processes, one of the major problems to deal with is the non linearities due to the large displacements and deformations. Some finite elements of the mesh can become severely distorted and no longer provide a good discretization of the problem. The remeshing solution retained in this work has consisted in creating a new mesh before the distortion of some elements became too important, and to transfer the mechanical variables field from the old deformed mesh to the new one. After the remeshing operation, a loss of structure equilibrium has been obtained so that several increments have been necessary to reach a new equilibrium state.

Results and discussion

Firstly, the punch has been modelled according to the experimental punch dimensions except for the punch cutting edge which has been approximated by a constant quarter circle.

Secondly, experimental wear profiles from the method presented in section 2.2.3 have been employed to improve the cutting edge wear modelling and trying to predict worn profiles.

Thirdly, a global discussion is presented at the end of this section.

Setup test of the wear algorithm

Since the value of the punch edge radius is closely related to the tool wear status [START_REF] Hambli | Etude expérimentale, numérique et théorique du découpage des tôles en vue de l'optimisation du procédé[END_REF], a first approach for testing the wear algorithm has consisted in varying the edge radius in the FE simulation and observing the effects on the punch wear distribution. In a first attempt, the size chosen for the radii has been sufficiently large to allow a significant penetration of the punch without remeshing the sheet. Indeed, a small radius requires small enough elements to avoid interpenetration of the sheet into the punch surface, but small elements will also degenerate more rapidly compared to larger elements for a given punch displacement. According to the dimension of each punch edge radius, the punch elements size has been adapted to always keep 10 elements within the quarter circle for accuracy purpose.

Thus, the setup test has been performed with respect to the geometrical dimensions listed in Table 1 and by varying the radius of curvature at the punch cutting edge from a range of values (25 µm, 50 µm and 65 µm). Die wear has not been taken into account during the experimental study, so the hypothesis has been made that it worn the same manner as the punch.

The wear coefficient for this study has been fixed to 2.10 -3 mm²/N in order to get a significant quantitative wear depth for one punch stroke.

The results of wear depth provided by the algorithm have been originally expressed along the curvilinear abscissa of the punch profile (Fig. 9). This representation gives a global view of wear but is not appropriate for comparing profiles. Thus, a nondimensionalized curvilinear abscissa based on the extremities of the edge radius has been introduced. As shown in Fig. 10, the middle of the quarter circle corresponds to the zero abscissa (point O ), and the left and right extremities respectively represent the "-1" (point A ) and "+1" (point B ) abscissa. The nondimensionalized curvilinear abscissa of point M is then calculated by dividing the arc

⋅ =

). Fig. 13a represents the evolution of wear depth at each punch node from the first worn profile (766,500 strokes), during one punch penetration. Extrapolated values of wear depth at each punch node have then been reported on the corresponding normal vectors to generate worn profiles. The value P N from Eq. ( 7) has been set to 37,500 punch strokes in order to compare the numerical results with the experimental corresponding profile (see Fig. 15). For the numerically predicted worn profile at 804,000 punch strokes (Fig. 15), a magnification factor of 50 has been applied to the computed wear values. This has been performed to clearly display the computed profile despite the low values of wear depth.

Discussion

Numerically predicted worn profiles show most wear on the punch flank. Wear depth values in the cutting edge radius are less significant due to the presence of a neutral zone. However, wear is globally less important than the one observed experimentally.

Different causes of the non-correspondence between experimental and theoretical results may be identified.

The Archard phenomenological wear formulation neglects the tribological aspect of wear (surface roughness, third-body, …) by focusing mainly on the sliding distance and contact pressure effect. It can be appropriate to determine wear for simple interactions as in a tribometer system (constant load and sliding speed) but shows some limitations when applied in situations with varying parameters.

The wear coefficient determined by the specific tribometer shows lower values compared to bibliography. According to [START_REF] Kalpakjian | Manufacturing processes for engineering materials[END_REF], the wear coefficient K varies over the range 10 -2 -10 - 6 mm²/N under unlubricated conditions for different material couples. This difference can be partly explained by the configuration of the tribometer which differs from conventional ones where wear particles are not evacuated and contribute to the wear mechanism.

The fitted punch profile based on experimental data allows to obtain a smooth FE mesh of the punch, but in counterpart it neglects the surface roughness of the tool, which can take an important role in the wear mechanism. Indeed, the surface asperities create local stress concentrations which deform the metal plastically and lead to the formation of wear particles.

The fitting curve used to model the experimental wear profile is more accurate than a constant curvature radius. However, the formulation can locally misrepresent the punch cutting edge.

One simulation of blanking is performed and then the wear results are multiplied by the number of punch strokes. A too important value may have favoured the neutral face wear and misrepresent the real evolution of wear.

Only the down travel of the punch has been modelled. It has been observed

experimentally that after the separating of the cut part, the sheet tends to pinch the punch due to remaining elastic stress. This contributes significantly to the flank wear during the up travel of the punch.

Conclusion

The experimental study carried out by Makich [START_REF] Makich | Etude théorique et expérimentale de l'usure des outils de découpe; Influence sur la qualité des pièces découpées[END_REF] has provided sufficient data to establish and adjust a punch wear algorithm for blanking of copper alloy thin sheet. First, a specific tribometer has allowed to test the material couple in a configuration closer to the conditions met during the blanking process. Second, an original double-print method for wear profiles extraction has shown interest in accurately modelling the punch geometry. The Archard formulation used to model the abrasive wear mechanism in blanking process has given a qualitative description of punch wear compared to the experimental observations. Third, an original method has been developed to transfer the wear calculation from the sheet nodes to the punch geometry. Finally, the combination of experiments with FE simulations of the process allows to explain the wear distribution along the punch profile, and to exhibit a minimal wear zone in the cutting edge radius. To improve the wear modelling especially on the punch flank, ductile fracture and crack propagation should be covered by further research.

Fig 1 :

 1 Fig 1: a) Configuration of the studied blanking process b) Tensile test curve of the blanked material

Fig. 2 :

 2 Fig. 2 : Experimental device used for producing an imprint of the punch : (a) global view on the mechanical press (b) detailed view of the wedge block

Fig. 3 :

 3 Fig. 3 : Replica of a punch after 787,500 strokes

Fig. 4 :

 4 Fig. 4 : Initial profile, worn profile and corresponding fitting curve (766,500 punch strokes) from a punch replica with zoom on the cutting edge

Fig. 6 :Fig. 7 :

 67 Fig. 6 : a) Wear aspect of spherical pin (2025 m sliding distance); b) corresponding wear profile at center line

Fig. 8 .

 8 Fig. 8. a) Axisymmetric blanking scheme b) Deformed mesh at 50% of punch penetration

Fig. 9 .Fig. 10 .

 910 Fig. 9. Wear distribution for three punch edge radii at different punch penetrations

Fig. 12 .

 12 Fig. 12. Blanking force versus punch penetration for two punch profiles

Fig. 13 .

 13 Fig. 13. (a) Wear evolution from worn profile at 766,500 strokes (b) Corresponding punch profile with node numberingAgain, it can be noticed that the location of the three different types of wear remains the same

Fig. 14 .

 14 Fig. 14. Wear evolution for punch nodes n°30 and n°67 from 766,500 strokes profile

Fig. 15 .

 15 Fig. 15. Worn profiles at 766,500 and 804,000 punch strokes

Table 1 . Main geometrical characteristics of the blanking process

 1

	Value	1.85 mm	254 µm	10 µm

Parameter Punch radius R p

Sheet thickness e Punch -die clearance j pm

  Table 2 and 3.

	Element	Cu	Fe	P	Others
	wt.%	>99.61	0.05 -0.15 0.025 -0.04 < 0.2

Table 2 . Chemical composition of the blanked material

 2

	Parameter	Symbol	Value
	Young's modulus	E		121 GPa
	Poisson's ratio	ν		0.34
	Yield strength	σ	0	332 MPa
	Material constant	k		221 MPa
	Strain hardening exponent	n		0.52

Table 3 . Mechanical properties of the blanked material

 3

  increment n provided by the FE solution. This value can be negative due to the non unidirectional movement of the nodes.

	n n s ) ( 1 +	i P	is the sliding distance between increments n and	( + n	) 1	and n P i s is the cumulated
	sliding distance at
			1 + P i n p is the contact pressure at increment	( + n	) 1	expressed at the same
	node.

Acknowledgements

The authors wish to thank the industrial partners Alstom, Diehl Augé Découpage, Cryla, CETIM, and financial partners Région Franche-Comté, FEDER, Conseil Général du Doubs and Communauté d'Agglomération du Grand Besançon, which have made this research work possible.

Fig. 11. Wear kinetics at three representative locations of the punch

The region of minimal wear (point b in Fig. 11 and abscissa value of -0.4 in Fig. 10) has been identified as a "neutral" zone where the punch and the sheet surfaces move similarly, thus conducting to a small relative displacement. Contact pressure at this location tends to reach a local maximal value but this value keeps lower than the pressures under the punch.

The resulting wear is then less important at this place than elsewhere. Moreover, this "neutral zone" is located at the same nondimensionalized abscissa for every punch cutting edge radius.

Wear prediction from real punches

Once the algorithm has been tested on setup test, two worn punch profiles obtained during the experimental study have been integrated into the FE modelling. The aim has been to predict the shape of the worn geometry by calculating wear depth and multiplying the results by a determined punch strokes number. Thus, the mesh has been applied on the punch geometry defined by the fitting curve presented on Fig. 4. The first one corresponds to 766,500 punch strokes and the second one 1,266,500. For numerical concerns, these profiles have been chosen sufficiently worn (i.e. with a large curvature radius) and still in a steady-state wear to