J Pellier
email: pellier@emse.fr

J Geringer
email: geringer@emse.fr

B Forest
email: forest@emse.fr

Fretting-corrosion between 316L SS and PMMA: influence of ionic strength, protein and electrochemical conditions on material wear. Application to orthopedic implants

Keywords: Fretting-corrosion, 316L SS, PMMA, Ionic strength, Albumin

In biomedical field, fretting-corrosion between 316L SS femoral stem and bone cement is one of the significant causes of the hip prosthesis loosening. This article investigates wear by fretting-corrosion at the contact between 316L and PMMA . The influences of the ionic strength (NaCl solutions from 10 -3 to 1 mol.L -1 ), a model protein (albumin) and electrochemical conditions on contact behaviour are studied. At OCP (Open Circuit Potential) conditions, the chlorides concentration, i.e. the ionic strength, increases the 316L wear; and albumin, concentration of 1g.L -1 , does not play a significant role in total 316L

wear. At cathodic applied potential E = -400 mV(SCE), a threshold concentration of 10 -1 mol.L -1 (NaCl solution), C th , indicates two behaviours: a protective effect below C th , and an additional anodic dissolution above C th . One might suggest that, beyond C th , the passive layer is not efficient for protecting against the corrosion. At this potential, albumin reduces wear due to corrosion and amplifies mechanical wear induced by corrosion. Albumin seems to act as an anodic inhibitor. To determine the mechanisms of synergism, a "more cathodic" potential is applied, E = -800 mV(SCE), during fretting-corrosion experiments.

Consequently, the corrosive wear can be neglected and the mechanical wear can be only measured.

Introduction

In Europe, each year, there are about 1 million hip replacements, and approximately the same number in USA. Nevertheless, after 10-15 years, approximately 10% of Total Hip Arthroplasties (THA) need a reintervention. Nowadays, the ageing of the population, injuries or diseases like arthrosis are public health issues.

To avoid additional surgical reoperation and improve lifetime duration of implants, studies on orthopedic implants 2 are needed. Three different metal alloys can be used for femoral stem: cobalt-chromium alloy, titanium alloy or austenitic stainless steel. We focus our attention on cemented hip prostheses. In 1960, in order to decrease the number of femoral stem debonding, Sir John Charnley decided to insert hip prostheses with poly(methyl methacrylate) called bone cement [START_REF] Charnley | The long-term results of low-friction arthroplasty of the hip performed as a primary intervention, The Journal of bone and joint surgery[END_REF]. For a cemented prosthesis (Fig. 1), the austenitic stainless steel (316L SS alloy) is usually used for femoral stem thanks to its biocompatibility and high resistance against corrosion in biological environment without friction.

Because of the daily human gait and significant difference of mechanical properties (particularly, Young's moduli) between 316L SS and bone cement, stress shielding phenomenon appears. The metallic material and the polymer do not have the same strain properties, thereby leading to debonding between the femoral stem and the cement. It involves fretting (friction under small displacements, term precisely defined later) and friction. Finally, the upper part of femoral bone is unloaded and then becomes more susceptible to fracture; on the other hand, if bone around femoral stem tip is overloaded, it becomes stronger [START_REF] Joshi | Analysis of a femoral hip prosthesis designed to reduce stress shielding[END_REF]. However, the bone cement acts as a "bumper" between femoral stem and bone, leveling peak forces acting around the prosthesis during the human gait. Femoral stem debonding and consequently friction between femoral stem and bone cement leads to cement degradation and cracking (Fig. 1). Debris from bone cement and femoral stem (metal oxides and ions) go through cement up to bone tissues [START_REF] Langlais | Prothèses totales de hanche. Facteurs biologiques et mécanismes de tolérance[END_REF]. Thus, the disturbance of osteoblasts cell activity and the tissue inflammation, respectively caused by bone cement particles and metallic oxides and ions, involve implant reoperation. It is the reason why fretting-corrosion between femoral stem and bone cement, particles generation, is one of the most 3 important causes of reintervention [START_REF] Kovacs | Correlation between the metal ion concentration and the fretting wear volume of orthopaedic implant metals, Particulate debris from medical implants: mechanisms of formation and biological consequences[END_REF][START_REF] Waterhouse | Occurrence of fretting in practice and its simulation in the laboratory, Materials evaluation under fretting conditions[END_REF]. Consequently, fretting-corrosion experiments were carried out for understanding corrosion and mechanical influences, and improving the lifetime of implants.

Fretting means friction under small reciprocal displacements, and the amplitude of displacement is lower than contact width. Rubin et al. found out, by numerical modeling, the amplitude of displacement is about 50 µm (depending on the location) between bone and stem under applied stresses during human gait [START_REF] Rubin | Intérêt de la modélisation numérique dans l'évaluation pré-clinique d'une prothèse fémorale de la hanche[END_REF]. Nonetheless, the displacement amplitude between bone cement and femoral stem is supposed identical [START_REF] Zhang | Understanding initiation and propagation of fretting wear on the femoral stem in total hip replacement[END_REF].

Wear of a metallic material under the conjugated effects of a mechanical solicitation (friction or fretting in this case) and of corrosion by a medium (physiological liquid) is named tribocorrosion [START_REF] Ponthiaux | Tribocorrosion, Techniques de l'ingénieur[END_REF]. Thus, frettingcorrosion is fretting in a corrosive environment for a metal alloy. This phenomenon leads to passive layer destruction and debris generation, principally metal oxides (Fig. 2) and polymer particles [START_REF] Geringer | Fretting-corrosion of materials used as orthopaedic implants[END_REF][START_REF] Geringer | Wear analysis of materials used as orthopaedic implants[END_REF][START_REF] Geringer | Wear of poly (methyl methacrylate) against a metallic surface in dry conditions[END_REF].

The fretting-corrosion phenomenon between femoral stem and bone cement is modelized by frettingcorrosion between a 316L SS sample (the same material as that of femoral stem) and PMMA which has the same mechanical properties as bone cement. This polymer was chosen because of its optical transparency. In that way, a direct observation of the contact zone and the debris evolution between materials at contact are investigated. during a fretting-corrosion test. To compare corrosion and mechanical behaviours in these solutions, this study aims at investigating the influence of ionic strength I:

  i i i C z I 2 2 1 (1)
where z i : ion charge; C i : ion concentration. Indeed, the ionic strength can interfere in the double layer constitution by the solution content and in the "attraction-repulsion" phenomenon betweenthe contact between two materials [START_REF] Geringer | Friction-corrosion of AISI 316L/bone cement and AISI 316L/PMMA contacts: Ionic strength effect on tribological behaviour[END_REF].

The role of proteins is also investigated. This work focuses on albumin, which is the main protein of blood plasma. Afonso et al. [START_REF] Afonso | The influence of albumin on the anodic dissolution of chromium present in UNS S31254 stainless steel in chloride environment[END_REF] have shown that bovine serum albumin, in NaCl 0.15 M at 37 °C, on UNS S31254 stainless steel, stops anodic dissolution of chromium and decreases iron dissolution. Valero Vidal et al. [START_REF] Valero | Electrochemical characterisation of biomedical alloys for surgical implants in simulated body fluids[END_REF] worked with 316L and CoCrMo alloy in NaCl 0.14 M at 37 °C, with or without albumin (0.5 g.L -1 ). They showed that for 316L, albumin does not modify open circuit potential (OCP) but it acts as an anodic inhibitor at applied potential, i.e. it increases cathodic reaction rate. Albumin also tends to decrease the polarization resistance, removing oxides from a protective layer and then exhibiting a material surface from corrosion. For CoCrMo alloy, albumin acts as a cathodic inhibitor and also increases anodic reaction rate, i.e. it accelerates corrosion. During a fretting-corrosion test between a Ti-6Al-4V alloy and alumina in pH buffered saline solutions at 37 °C, Hiromoto et al. [START_REF] Hiromoto | The influence of proteins on the fretting-corrosion behaviour of a Ti6Al4V alloy[END_REF] showed that albumin (1 g.L -1 bovine serum albumin) mostly modifies cathodic behaviour and acts as a cathodic inhibitor, i.e. it reduces cathodic reaction rate. From a mechanical point of view, albumin does not affect friction coefficient µ and wear volume.

During a fretting-corrosion test, material wear is a combination of mechanical wear (fretting) and corrosion.

However, the total material loss(W) is not only determined as the sum of two different material losses: (i) material loss due to mechanical wear obtained without the influence of corrosion(W m ) and (ii) the material loss due to corrosion obtained without fretting action(W c ). There is a synergistic effect between corrosion wear and mechanical wear. The synergy term(W) means that corrosion increases wear due to fretting(W cm ) and friction increases wear due to corrosion(W mc ) [START_REF] Watson | Methods of measuring wear-corrosion synergism[END_REF][START_REF] Jiang | Modelling sliding wear: from dry to wet environments[END_REF].

W = W m + W c + W = W m +W c + (W cm + W mc ) (2)
This work aims at understanding the role of mechanical action and corrosion on a synergy term, and also calculating each of these terms for a fretting-corrosion test. In a first place, we focus on the percentage of wear due to corrosion obtained from the wear volume due to corrosion V corr (cm 3 ), and the percentage can be found out with Faraday's law:

t i n M F V with W V wear corrosive corr corr * * * 1 100 * %    (3)
where F is Faraday constant (F = 96500 C.mol -1 ), M is the molecular weight (M = 56.39 g.mol -1 ), n is the number of electrons involved in the anodic process (n = 2, hypothesis), t is the total duration of the fretting-corrosion test (t = 14,400 s),  is density ( = 8 g.cm -3 ) and i (A) is the difference between the average current during fretting and the current after fretting. Three electrochemical conditions were investigated for this study. First, the Open Circuit Potential (OCP) condition allows being as close as possible to the in vivo conditions. However, no information on current is available at OCP. Thus, fretting-corrosion tests are also carried out at cathodic applied potentials. -400 mV(SCE) is a threshold potential for anodic and cathodic transition of current. To remove (or to neglect) corrosion and to only obtain mechanical wear (W m ), the cathodic potential of -800 mV(SCE) is chosen. For each electrochemical condition, the role and the influence of albumin are investigated.

Materials and methods

Materials

The 316L femoral stem is modeled by a plane 316L SS sample: 9 mm x 9 mm x 20 mm parallelepiped. One of the flat parts (9 mm x 20 mm) was polished with diamond paste down to 1 µm. This frictional surface exhibits 3D roughness(S a ) of about 10 ± 2 nm (area of 1 x 2 mm, Veeco TM optic profilometer).

The bone cement, involved in THA, is modeled by a cylindrical PMMA, a polymer which has the same mechanical properties as those of bone cement. A sample maintains the length of 15 mm and the radius of curvature of 10 mm. The cylindrical face was polished with 3 µm diamond solution, Altuglass Polish 1 and 2 ® and colloidal solution of silica (particles size of 0.06 µm). The 3D roughness (S a ) is about 35 ± 5 nm.

The geometry of the contact, cylinder/plane, allows a better control of contact pressure and width. Before the fretting-corrosion test, 316L SS and PMMA samples were stored at least 24 hours in a desiccator. The 316L sample is electrically insulated with Zircalloy alloy sheets and some varnish.

The composition of the 316L austenitic stainless steel (X2CrNiMo17-12, improved cleanliness and very low carbon content) is in accordance with ISO standard 5832-1 (Table 1). Mechanical properties of both materials are shown in Table 2.

Solutions

Two types of solution are used: Ringer solution (composition in Table 3) and NaCl solution, with concentrations of 10 -3 , 10 -2 , 10 -1 and 1 mol.L -1 . Room temperature was of 22 ± 1 °C. To understand influence of proteins on fretting behaviour, albumin of 1 g.L -1 was added in each saline solution.

Test device

To reproduce fretting-corrosion phenomenon, micro-displacements measured in vivo (about 50 µm) and stresses applied in vivo (between 7 and 30 MPa) [START_REF] Rubin | Intérêt de la modélisation numérique dans l'évaluation pré-clinique d'une prothèse fémorale de la hanche[END_REF] must be replicated. A specific device (Fig. 3), conceived and developed in collaboration between ENSM-SE and Böse, was used for fretting-corrosion tests. An electromagnetic motor, first tried for fretting-corrosion, let us obtain the same results as those delivered by the device used previously [START_REF] Geringer | Fretting-corrosion of materials used as orthopaedic implants[END_REF][START_REF] Geringer | Wear analysis of materials used as orthopaedic implants[END_REF][START_REF] Geringer | Wear of poly (methyl methacrylate) against a metallic surface in dry conditions[END_REF]. The load cell is a piezoelectric transducer and the displacement measurer is a capacitive sensor.

The mechanical parameters of fretting-corrosion tests are realistic:  the applied normal load (P) was 127.5 N, i.e. a pressure of about 22 MPa, which is spread from 7 to 30 MPa, range of pressure applied in vivo [START_REF] Rubin | Intérêt de la modélisation numérique dans l'évaluation pré-clinique d'une prothèse fémorale de la hanche[END_REF];  the amplitude of displacement was ± 40 µm, close to the in vivo displacement [START_REF] Rubin | Intérêt de la modélisation numérique dans l'évaluation pré-clinique d'une prothèse fémorale de la hanche[END_REF]. Moreover, the displacement is sinusoidal and the frequency is 1 Hz, i.e. one cycle equals one second, corresponding to the frequency of the gait cycle.

For these mechanical values, the gross slip condition was checked.

To identify actual displacement  between both materials, the accommodation of the device must be considered. Based on the hypothesis that there is an elastic behaviour with compliance C s , the actual displacement conditions, EIS measurements should not be performed for actual values, but only the evolution of electrical parameters was considered [START_REF] Geringer | Assessing the tribocorrosion behaviour of Cu and Al by electrochemical impedance spectroscopy[END_REF]. One may notice that regular EIS measurements, during the fretting phase, have no influence on OCP or on current values after the EIS measurements.

 is:  =  r - acc =  r -C s * Q,
For each electrochemical condition, OCP or cathodic applied potential (-400 and -800 mV(SCE)), two experiments (steps defined in Table 4) were carried out for all solutions with or without albumin. P Step 5 without fretting: 14 h OCP measurement and 1 EIS after 14 h

Wear profiles

Thanks to Veeco TM WYKO NT9100 optic profilometer, the measurements of the total wear volumes for 316L and PMMA were performed. Three measurements were carried out on 316L and PMMA surfaces. The total wear volume was thus extrapolated for the total wear track length (15 mm). This value was compared with the total wear made on the whole length of the track. The wear volume error is about 10 %. Raw data were filtered by an automatic cylindrical shape.

Results

Open Circuit Potential conditions

OCP evolution

After cathodic polarization of 5 min at -1 V(SCE), the open circuit potential (OCP) is recorded without fretting during 1 hour (steps described in Table 4, OCP evolution on Fig. 4). From the beginning of fretting, OCP is significantly decreased and then slightly stabilized. Instantly after the end of fretting, OCP nearly recovers the value before fretting. At regular intervals (every 20 minutes), the polarization resistance (R p ) is determined with Electrochemical Impedance Spectroscopy (EIS) in order to investigate the behaviour of the metal surface. R p is extracted from the simple electrical circuit: R sol (CPE//R p ), R sol is the solution resistance, CPE is a Constant Phase Element and R p is the polarization resistance (resistances of the passive layer and the double layer at high frequencies).

Mechanical behaviour

From a mechanical point of view, the dissipated energy (E d ) during one cycle, which corresponds to the mechanical work of the tangential force, was monitored. For the total duration of the test, the cumulated dissipated energy (E dc ), i.e. the sum of E d for each cycle (1 cycle = 1 second), was calculated. The cumulated dissipated energy during fretting increases with ionic strength (Fig. 6). One may notice that experiments were investigated at two compliances. This fact substantiates that, the dissipated energy variation is controlled by the composition of the solution, not the mechanical device. Total wear volume of 316L (10 6 µm 3 )

L -1 )
Polarization resistance R p x 0.1 (k) Fig. 7 Influence of albumin (1g.L -1 ) at OCP conditions on average OCP during fretting, the total wear volume of 316L SS and polarization resistance for NaCl 1 mol.L -1

Albumin influence

In order to satisfy in vivo conditions and to understand the role of proteins, experiments were carried out in the same electrochemical conditions and the same solutions with the presence of a protein: albumin with a concentration of 1 g.L -1 . As shown on Fig. 7, albumin has no influence (ANOVA test,  = 0.05) on the average value of OCP during fretting and the total material loss for NaCl 1 mol.L -1 . E dc , OCP and R p are not significantly different in cases with and without albumin in NaCl 1 mol.L -1 . The same conclusion is highlighted in other solutions. Nevertheless, albumin has influence on wear volume of PMMA: this one is slightly lower with albumin.

SEM images

Worn surfaces of 316L SS were observed with a Scanning Electron Microscope (SEM) 6400 JEOL combined with an Energy Dispersive X-Ray (EDX) probe. Fig. 8 presents surfaces of 316L samples submitted to frettingcorrosion tests. Corrosion crevices (Fig. 8 a) are mostly localized at the border of the wear track (Fig. 8 b). At 1 mol.L -1 , corrosion seems more localized than that at 10 -3 mol.L -1 . With albumin, grooves are compacter and corrosion crevices follow friction direction (Fig. 8 c).

Cathodic applied potential conditions (E = -400 mV(SCE))

At OCP conditions, although we are close to the in vivo conditions, no information on current is available.

That's why the second part of this work focuses on cathodic applied potential, and more specifically E = -400 mV(SCE). This value was chosen because the influence of ionic strength on current during fretting can be highlighted.

Evolution of the current

Significant values, as the average current during the last 3 hours of fretting (I mf ),I, the difference between the current at the end of fretting (I ff ) and the current after fretting (I af ), were investigated in accordance with ionic strength. As shown on Fig. 9, fretting involves a higher impact on current values for NaCl solution of 1 mol.L -1 (I ~ 11 µA) than that for NaCl solution of 10 -3 mol.L -1 (I ~ 1 µA): the applied potential is enough to protect a surface during friction phase for NaCl 10 -3 mol.L -1 . In the same way, I mf is close to zero and is even positive, i.e. I mf I Fig. 9 Average current during fretting-corrosion, I mf , and difference between current at the end of fretting (I ff ) and that after fretting (I af ), I versus ionic strength I

Wear volume evolution

As described in §2.5, wear volumes were measured on PMMA and 316L samples with the Veeco TM 3D optic profilometer (Fig. 10). Wear volume of PMMA is constant whatever the ionic strength (ANOVA test,  = 0.05) at

OCP and E = -400 mV(SCE) is, but the wear volume of PMMA is slightly higher at OCP conditions. As illustrated on Fig. 11, for 316L samples, total material loss increases with ionic strength for both electrochemical conditions. A threshold concentration is then highlighted, about 10 -1 mol.L -1 . For 10 -3 and 10 -2 mol.L -1 , wear volume measured in OCP conditions is higher than that for E = -400 mV(SCE). Moreover, for concentrations above 10 -1 mol.L -1 , wear volume measured in OCP conditions is lower than that at E = -400 mV(SCE).

Albumin influence

Contrary to OCP conditions, albumin plays a significant role at the cathodic applied potential of E = -400 mV(SCE). Mainly, two values are analyzed: the average current during fretting and the percentage of corrosive wear. In NaCl 1 mol.L -1 (Fig. 12), albumin largely (ANOVA test,  = 0.05) reduces the current during fretting (from ~ -0.5 µA without albumin to ~ -10 µA with albumin) and the percentage of corrosive wear (from ~ 80 % without albumin to ~ 50 % with albumin). One may suggest that albumin acts as an anodic inhibitor, as shown by

Valero Vidal et al. [START_REF] Valero | Electrochemical characterisation of biomedical alloys for surgical implants in simulated body fluids[END_REF].

SEM images

At E = -400 mV(SCE), the main difference between Fig. To neglect wear due to corrosion and to obtain wear due to mechanical wear (W m ), the cathodic potential of -800 mV(SCE) was chosen. To validate this potential value, only extreme ionic strengths (10 -3 and 1 mol.L -1 ) were tested. As shown on Table 5, the average of current during fretting varies in a function of ionic strength and is modified by the presence or not of albumin. However, the total wear volume is same without regard to the condition (ionic strength and albumin). One may assume that the total wear volume equals the mechanical wear volume W m , i.e. W m = 0.3 ± 0.1 10 6 µm 3 .

Discussion

Open Circuit Potential conditions

The evolution of OCP before, during and after fretting is shown on Fig. 4. One may notice that E bf logarithmically decreases with the ionic strength in accordance with [START_REF] Zhang | Passivity breakdown on AISI type 403 stainless steel in chloride-containing borate buffer solution[END_REF]. Chloride ions, Cl -, accelerate anodic dissolution with the formation of an unstable compound MCl n (or M(H 2 O) y Cl x ) [START_REF] Hoar | Breakdown of passivity of stainless steel by halide ions[END_REF]. At high concentration of chloride ions, one may suggest that metallic dissolution is higher and leads to OCP decrease.

The drastic drop of OCP occurs as soon as fretting starts (Fig. 4), expressing the surface degradation. The passive layer on 316L surface is partly destroyed and metal dissolution, i.e. anodic reaction, occurs. In addition, breakdown of the passive layer is highlighted by the polarization resistance (R p ) fall. R p is indeed inversely proportional to corrosion rate (Stern-Geary equation): the R p fall involves acceleration of corrosion.

One may notice that these falls, OCP and R p , decrease with the ionic strength (Fig. 5). According to Macdonald [START_REF] Macdonald | Passivity-the key to our metals-based civilization[END_REF], when the concentration of Cl -increases, the passive layer reconstruction becomes more and more difficult. The result highlighted on Fig. 5 translates the difficulty of passive layer reconstruction during fretting when chlorides concentration increases.

The OCP and R p upturn, directly after cessation of fretting (Fig. 4), confirms corrosion activation during fretting test. However, the OCP value after fretting is lower than E bf . The electrochemical behaviour of 316L surface can indeed be modified by the less protective worn zone and the PMMA and oxides debris deposed on the 316L surface.

From a mechanical point of view, it is worth noting that the cumulated dissipated energy (E dc ) during the fretting test increases with the ionic strength (Fig. 6). One may suggest that when the ionic strength increases, attraction between surfaces is reinforced [START_REF] Brigham | Crevice corrosion initiation and the potential of zero charge[END_REF].

As shown on Fig. 7, albumin has no influence on the average OCP during fretting and on total wear volume of 316L. Without friction, Valero Vidal et al. [START_REF] Valero | Electrochemical characterisation of biomedical alloys for surgical implants in simulated body fluids[END_REF] showed that albumin does not modify OCP values. At this concentration, 1 g.L -1 , albumin does not modify electrochemical behaviour: it has no influence on OCP during fretting and R p values; nor on total wear volume.

Cathodic applied potential conditions (E = -400 mV(SCE))

The applied potential E = -400 mV(SCE) is a cathodic potential, i.e. the current is negative, thus the surface is protected against corrosion. However, this protection is not effective for all solutions. For example, in NaCl 10 -3 mol.L -1 , this protection is effective: I ~ 1 µA while it is not effective in NaCl 10 -1 or NaCl 1 mol.L -1 , respectively I ~ 7 µA and I ~ 11 µA (Fig. 9). During the fretting-corrosion test, the current even becomes positive, i.e.

anodic, for NaCl 1 mol.L -1 . In fact, a threshold concentration and two surface behaviours can be determined (Fig. 11). For concentrations below 10 -1 mol.L -1 , wear volumes at OCP condition are higher than those at E = -400 mV(SCE): the applied potential protects surface. For concentrations above 10 -1 mol.L -1 , wear volumes at OCP condition are lower than those at E = -400 mV(SCE): the metal dissolution is higher and the passive layer is less protective against fretting. without albumin. One may notice that, in presence of albumin, the percentage of wear due to corrosion decreases:

~ 50 % in NaCl solutions of 1 mol.L -1 and 10 -1 mol.L -1 , instead of 80 % without albumin. Especially, in the presence of albumin and for lower ionic strength, standard deviation values are large and the coefficient of variation is in the range from 10 to 100. The preponderant phenomenon is mechanical wear and in this case, the dispersion of corrosive and total wear values is larger. The main mechanical degradation, under albumin and NaCl solutions, should involve hazardous wrenching that should be related to the high standard deviation.

Cathodic applied potential conditions (E = -800 mV(SCE))

As explained in §1, the total wear volume of 316L SS is the sum of wear due to corrosion, W c. and mechanical wear, W m . The total wear volume, W, follows the equation [START_REF] Joshi | Analysis of a femoral hip prosthesis designed to reduce stress shielding[END_REF]. At E = -800 mV(SCE), no anodic current is measured during a fretting-corrosion test. In this electrochemical condition, anodic dissolution, i.e. metallic dissolution, is neglected without regard to ionic strength and the presence of albumin. The mechanical wear W m is also determined: W m = 0.3 ± 0.1 10 6 µm 3 . At E = -400 mV(SCE), thanks to Faraday's law, the wear due to corrosion V corr can be calculated (equation ( 3)). In fact, in comparison with the total wear volume (equation ( 2)), V corr = W c + W mc . By deduction, the term W cm can be determined, as a function of ionic strength at E = -400 mV(SCE). To set apart the synergy term W = W mc + W cm , the term W c must be measured. From polarization resistance values, the dissolution current of the material, i, can be calculated: i = B/R p , with B = 24 mV (hypothesis coming from investigations in the COST 533 round robin). In that way, W c is ~ 100 or 500 µm 3 depending on the ionic strength. W c represents only 0.01% of V corr and this can be neglected. Iwabuchi et al.

found the same ratio: W c /W of ~ 0.01% [START_REF] Iwabuchi | Synergistic effect of fretting wear and sliding wear of Co-alloy and Ti-alloy in Hanks' solution[END_REF].

Fig. 15 a illustrates the contribution of W mc , i.e. the increase of corrosive wear due to fretting. Levels can be defined from NaCl solution of 10 -1 mol.L -1 without albumin: above this concentration, the contribution of corrosive wear is about 80%. Albumin at a concentration of 1 g.L -1 shifts the transition and the percentage of corrosive wear: above 10 -2 mol.L -1 , the contribution of corrosive wear is constant and about 50%. Thus, albumin decreases the percentage of corrosive wear. One may notice that material behaviour in Ringer solution is different from that in NaCl solutions. Because of the presence of other ions (Table 3), the contribution of corrosive wear decreases. For example, the role of carbonates could be determined in future work. Fig. 15 b illustrates the contribution of W cm , the increase of mechanical wear due to corrosion. No trend can be defined: mechanical wear is not a function of ionic strength, and this term matches with an arbitrary wrenching in the surface material. In future work, the influence of albumin concentration on metal behaviour will be studied. To be closer than in vivo conditions, experiments will be realized at 10 and 20 g.L -1 . For example, the ISO standard indicates a concentration of proteins equal to 17.5 g.L -1 for improving the lifetime of hip implants [27,28].

As seen on Fig. 10 a, the characteristic shape of 316L wear track, 'W' wear shape as mentioned in [START_REF] Geringer | Fretting-corrosion of materials used as orthopaedic implants[END_REF][START_REF] Geringer | Wear analysis of materials used as orthopaedic implants[END_REF], is the consequence of crevice corrosion. The evolution of local pH might lead to this particular shape. The influence of pH solution could give some information on the crevice corrosion effect. The crevice corrosion effect will be investigated in further investigations.

Conclusions

Under OCP conditions, the increase of chlorides concentration leads to higher corrosion and a more difficult passive layer reconstruction during the friction phase. From a mechanical point of view, the E dc increases according to the ionic strength; consequently one might suggest attraction between surfaces is reinforced.

At E = -400 mV(SCE), a threshold concentration, around 10 -1 mol.L -1 , highlights that a surface protective phenomenon occurs below this concentration, while more metal dissolution appears above this value.

At E = -800 mV(SCE), only the mechanical wear is determined: W m = 0.3 ± 0.1 10 6 µm 3 . This value is needed to calculate the term of synergy between corrosive and mechanical wear.

Albumin, at 1 g.L -1 , has no influence at OCP conditions. However, at E = -400 mV(SCE), the percentage of corrosive wear is lower in presence of albumin. Albumin seems to play the role of an anodic inhibitor.

When the chlorides concentration, i.e. the ionic strength in this study, increases, the 316L wear increases too.

The most interesting result is: albumin promotes the mechanical degradation compared with the corrosive wear, under cathodic polarization. This assertion includes the pure mechanical degradation and the synergism mechanical wear assisted by the corrosion. One might suggest this synergistic term should be the key-point of the 316L wear, under cathodic polarization.

Fig. 1

 1 Fig. 1 Total hip joint cemented prosthesis components

Fig. 2 (

 2 Fig.2(a) Fretting-corrosion between femoral stem (Exeter V40 TM ) and bone cement[START_REF] Zhang | Understanding initiation and propagation of fretting wear on the femoral stem in total hip replacement[END_REF]; (b) fretting-corrosion between a head (316L) and a femoral neck (Ti-6Al-4V)

  where  r and  acc are respectively the monitored and accommodated displacements, and Q is the tangential load[START_REF] Fouvry | Quantification of fretting damage[END_REF].

7 2. 4

 74 Electrochemical measurementsFor electrochemical measurements (OCP), current density and Electrochemical Impedance Spectroscopy (EIS), a PARSTAT 2263 potentiostat with a three-electrode set up was used: the working electrode was the stainless steel sample,  the counter electrode was a circular wire of Pt having the diameter of about 60 mm,  the reference electrode was a Saturated Calomel Electrode (SCE, E = +246 mV(SHE) at T = 22 °C).

Fig. 3

 3 Fig. 3 Fretting-corrosion device: ENSM-SE and Böse prototype

Fig. 4

 4 Fig. 4 Detail of experiment: OCP measurement before, during and after fretting and R p measurements from EIS. R p : difference between R p before and R p after 2400 cycles of fretting; OCP: difference between OCP before fretting (E bf ) and OCP at the end of fretting (E ff ). Solution is constituted by NaCl 10 -3 mol.L -1 , displacement amplitude is of ± 40 µm, 1 cycle is equal to 1 second Fig. 4 exhibits OCP and R p values in a NaCl solution of 10 -3 mol.L -1 . It is worth noting OCP and R p evolutions are the same as those of other solutions, only OCP and R p vary in accordance with the different solutions (Fig. 5).

Fig. 5

 5 Fig. 5 exhibits the decrease of OCP and R p according to the ionic strength. Both electrical values are consistent and they are related to the evolution of the contact submitted to fretting, i.e. less passive behaviour of the AISI 316L SS.

Fig. 5 Fig. 6

 56 Fig.5R p : difference between R p before fretting and 2400 cycles after fretting start; and OCP: difference between OCP before fretting (E bf ) and that at the end of fretting test (E ff ) versus ionic strength I

Fig. 8

 8 Fig. 8 SEM images of 316L SS in NaCl 1 mol.L -1 (a), (b) without albumin (c) with albumin, arrows show the direction of sliding

  anodic for one experiment at NaCl 1 mol.L -1 even though it is cathodic (~ -15 µA) for NaCl 10 -3 mol.L -1 .

14 Fig. 10 3D

 1410 Fig. 10 3D wear profiles of (a) 316L and (b) PMMA, in NaCl 1 mol.L -1 at OCP conditions, image size of 1x1 mm 2

Fig. 11

 11 Fig. 11 Total wear volume of 316L versus ionic strength for OCP conditions and E = -400 mV(SCE)

Fig. 12

 12 Fig. 12 Influence of albumin (1g.L -1 ) at E = -400 mV(SCE) on average current during fretting and the percentage of corrosive wear of 316L SS for NaCl solution of 1 mol.L -1

  13 a and Fig. 13 b, i.e. NaCl 1 mol.L -1 with or without albumin, concerns the grooves inside crevices. Without albumin, grooves indicate that pulled out particles are enough hard to damage surfaces. With albumin, no groove is observed into crevices: particles are probably softer or are ejected more rapidly. At NaCl 10 -3 mol.L -1 (Fig. 13 c), the central zone of the contact is not damaged and localized corrosion is not observed.

Fig. 13 SEM 16 3. 3

 13163 Fig. 13 SEM images of 316L SS in NaCl 1 mol.L -1 (a) without albumin (b) with albumin (c) in NaCl 10 -3 mol.L -1 without albumin, arrows show direction of sliding

Fig. 14

 14 Fig.14The total wear volume of 316L SS, W, as a function of wear due to corrosion, V corr , in the logarithmic scale. The dashed straight line: case where wear is only due to corrosion  W = V corr . Ionic strength decreases from the right to the left

1 ) 1 )

 11 Fig.[START_REF] Hiromoto | The influence of proteins on the fretting-corrosion behaviour of a Ti6Al4V alloy[END_REF] The contribution of the different synergy terms with albumin (empty symbols) or without albumin (full symbols) :(a) W mc /W is the increase of corrosive wear due to fretting and (b) W cm /W is the increase of mechanical wear due to corrosion

Table 1

 1 Chemical composition of 316 L stainless steel

	Elements	Cr	Ni	Mo Mn	Si	Co	C	Cu	S	Fe
	Composition (% w/w) 17.4 13.0 2.6 1.73 0.66 0.20 0.0165 0.097 < 0.001 Balance

Table 2

 2 Mechanical properties of tested materials: 316L stainless steel and PMMA, *: obtained by ultrasonic measurements;

		**: manufacturer data
	Mechanical	Young's modulus	Poisson's	Yield stress	Ultimate tensile
	properties	E (GPa)*	ratio *	(MPa)**	strength (MPa)**
	316L	197	0.30	280	635
	PMMA	2.5	0.39	65	75

Table 3

 3 Ringer solution composition

		NaCl	KCl	CaCl 2	NaHCO 3
	Concentration (g.L -1 )	8.50	0.25	0.22	0.15

Table 4

 4 Electrochemical measurements steps for each electrochemical conditions, OCP or cathodic applied potentials (E = -

		400 or -800 mV(SCE))
	Electrochemical conditions	OCP	Potential applied: -400 or -800 mV(SCE)
	Step 1	Cathodic polarization: -1 V(SCE), 5 min
	Step 2	without fretting: 1 h + EIS	without fretting: 10 min + EIS
	Step 3	with fretting: 4 h + 10 EIS regular distribution
	Step 4	without fretting: 14 h + 2 EIS after fretting stop and 1 EIS after 14 h	without fretting: 10 min + 2 EIS after fretting stop

Table 5

 5 Average current during fretting I mf and total wear volume W measured at E = -800 mV(SCE), with or without albumin.

		Influence of albumin and ionic strength is determined by an one-way ANOVA test ( = 0.05)
		I mf (µA)	Albumin	W (10 6 µm 3 )	Albumin
		without albumin	with albumin	influence?	without albumin	with albumin	influence?
	10 -3 mol.L -1	-17.60 ± 0.30	-14.93 ± 0.32	YES	0.25 ± 0.07	0.19 ± 0.03	NO
	1 mol.L -1	-27.96 ± 9.31	-45.57 ± 3.11	YES	0.38 ± 0.14	0.35 ± 0.08	NO
	Ionic strength influence?	NO	YES		NO	NO

Acknowledgements

The authors wish to acknowledge Saint-Etienne Métropole and Conseil Général de la Loire for the financial support. Moreover the authors thank Pr. D.D Macdonald for fruitful discussions and Dr. Kim about reviewing of the English language.


Jean Geringer
email: geringer@emse.fr

Witold Tatkiewicz

G Rouchouse
email: gilles.rouchouse@cetim.fr

WEAR BEHAVIOR OF PAEK, POLY(ARYL-ETHER-KETONE), UNDER PHYSIOLOGICAL CONDITIONS, OUTLOOKS FOR PERFORMING THESE MATERIALS IN THE FIELD OF HIP PROSTHESIS

Keywords: PAEK, UHMWPE, metallic alloys, wear rate, hip implants

This study is focused on performing tribological tests on new materials for orthopaedic implants applications, PAEK (Poly Aryl Ether Ketone) polymer group. The experiments were performed in physiological liquid, at 37 °C, for simulating the human body fluid. PAEK's tribological properties that are wear rate of polymers and wear mechanisms on common metallic alloys used as orthopaedic implants: Co-Cr, 316L SS and Ti-6Al-4V are compared to the gold standard used for hip joint prosthesis, the UHMWPE (Ultra High Molecular Weight PolyEthylene) on the same metal alloys. PEEK (Poly Ether Ether Ketone) and PEKK (Poly Ether Ketone Ketone)/CF (Carbon Fibers) show the lowest wear rate on every counter metallic material; the system UHMWPE on any metal alloys exhibit the highest wear rate although having the lowest friction coefficient. From microscopic images and the evolution of the friction coefficient, a wear mechanism was suggested for each polymeric material.

Introduction

About 800,000 hip prostheses are implanted in Europe, each year. With ageing of population, the implants durability is becoming a health problem and it will be a key point of health issues in the next 10 years. Nowadays the lifetime of hip implants is approximately 15 years. The challenge is to increase their lifetime to avoid an additional surgical operation, involving risks for patients and costs for health organism.

Different materials systems are investigated for the artificial hip joint: hard-hard assembly for head-cup joint, metal-metal or ceramic-ceramic; hard-soft assembly, metalpolymer or ceramic-polymer. This study will focus on the hard-soft artificial joint. Usually, for the acetabular cup, the polymer used is UHMWPE (Ultra High Molecular Weight PolyEthylene) since it gives satisfactory lifetime. However, taking into account the debris generation, the main reason for the failure of implants is the aseptic loosening [START_REF] Blunt | The role of tribology and metrology in the latest development of bio-materials[END_REF].

Nowadays, so as to replace UHMWPE as a bearing surface, other polymers such as PAEK and their carbon fibers composites are investigated.. These materials are promising in the biomedical field in terms of biocompatibility, low wear rate in comparison with UHWMPE, and machining for artificial cup, hip joint prosthesis [START_REF] Kurtz | PEEK biomaterials in trauma, orthopedic, and spinal implants[END_REF][START_REF] Sagomonyants | The in vitro response of human osteoblasts to polyetheretherketone (PEEK) substrates compared to commercially pure titanium[END_REF][START_REF] Utzschneider | Inflammatory response against different carbon fiber-reinforced PEEK wear particles compared with UHMWPE in vivo[END_REF]. For instance, PEKK and its composites are manufactured for spinal implants. In this paper, the tribological behavior of these PAEK polymers will be evaluated for orthopedic implants.

In this work, it is proposed to investigate the tribology of four polymers: UHMWPE, PEEK, PEKK and PEKK CF 30 % against the most usual biocompatible metallic alloys implanted in human body: AISI 316L stainless steel, Ti-6Al-4V alloy and Co-Cr alloy, i.e. twelve materials systems. The tribological tests will be carried out with respect to a sphere (metals)/plane contact (polymers) in bovine serum which is the closest liquid medium to the human physiological liquid,. The results will be compared to the results of Harsha and Tawari [START_REF] Harsha | Tribo performance of polyaryletherketone composites[END_REF]. A tribometer was specifically equipped to perform pin (metallic alloys)-on-disc (polymers) tests in bovine serum at 37 °C. During tests, the friction coefficient gives information about the wear mechanisms taking place between the materials in contact. The post mortem investigations, i.e. wear volumes and wear zones images, allow classifying the different friction couples. Ultimately, from experimental data and microscopic analyses (optical and SEM images), a wear scenario, for UHMWPE and three different polymeric materials from the PAEK group, will be investigated.

Experimental

Materials

Tables 1-3 describe the chemical composition of 316L stainless steel, Ti-6Al-4V (or TA6V) alloy and the Co-Cr alloy respectively; these metal alloys will be considered as the "pins" for the tribological investigations. The chemical compositions were obtained by spark optical emission spectrometry. The mechanical properties of all the materials used in the study are presented in Table 4. 4: mechanical properties of the investigated materials; *data from the manufacturers datasheet and from internal characterizations.

E / GPa

The polymer materials were supplied either with a disc shape or a rod shape and were machined to the right dimensions, then polished on an automatic machine following the conditions presented in Table 5. As far as the metallic cylinders are concerned, they were machined and polished on a lathe. The cylinder was fixed to a spindle and polishing papers then discs were manually maintained in contact with the sphere rims: the pin. Examples of polished surfaces so-obtained are presented in Figure 2. The top of the cylinders' hemisphere was homogenously smooth over area that exceeded the approximated diameter of contact. Scratches of machining were no longer visible. Analyzes, especially EDX analysis, were carried out to be confirm that, with the polishing protocol, no colloidal silica particles were incrusted in the polymer material.

SEM and 3D profilometry

The polymer and metallic samples were observed with a Scanning Electron Microscope (SEM) JEOL 6400 coupled with an EDS probe. A particular attention was paid on insulating polymer, especially PAEK, for performing the SEM images. It is the reason why , after friction tests, a gold sputtered layer covers the worn surfaces in order to highlight transferred particles between two materials in contact and to understand the wear behavior for all friction couples. The 3D profilometry was investigated thanks to a SOMICRONIC ® profilometer. Data were treated by the Surfascan ® 3D software. It is worth noting that the minimum Ra value corresponds to PEEK. It is the easiest material for the polishing step. On the contrary, the UHMWPE material was not easily polished. The Ra value can be compared to a machined surface.

Tribocorrosion device

Figure 3 presents the friction device (tribometer) in which was described in details in a previous work [START_REF] Geringer | Friction-corrosion of AISI 316L/bone cement and AISI 316L/PMMA contacts: Ionic strength effect on tribological behavior[END_REF]. The Normal load was equal to 30.4 N and was applied by a calibrated rod fixed on the pin support. The alignment and parallelism of the pin support was carefuly verified before each test. The pin, made out of metallic alloy (Co-Cr, 316L SS or Ti-6Al-4V), was firmly pushed in the pin support. The spherical pin allows a perfect sphere/plan contact, i.e. a disk, contact area, according to the contact configuration. The actual tangential load, and so the friction coefficient, were continuously monitored. The tribological conditions are summarized in Table 7. The test last for 8 hours to pass the running-in period. The samples were immersed into the same solution used for the wear tests, that is the bovine serum (PAA Laboratories GmbH, Austria) diluted in proportion 1:4 with distilled water. One part of sodium azide (ultra pure: >99.5%; Fluka Analytical) per 100 parts of resulting solution was added, according to the ISO 14242-1. Sodium azide is used as an antioxidant to avoid proteins alteration. The electrochemical behavior, and consequently the wear behavior, of metal alloys depend on anti-oxidant content in a proteins solution [START_REF] Geringer | Influence de la teneur en protéines de solutions physiologiques sur le comportement électrochimique du Ti-6Al-4V : reproductibilité et représentation tempsfréquence[END_REF].

To summarize, Table 8 highlights all the investigated contacts and the number of experiments that were performed: 3 for each contact type so 36 experiments in total.

CoCr 316L TA6V PEKK CF XXX XXX XXX PEKK XXX XXX XXX PEEK XXX XXX XXX UHMWPE XXX XXX XXX
Table 8: Summarizing of the tests number.

Finally, so as to make sure of the repeatability of the tests, samples were dried and conditioned in bovine serum before pin-on-disc tests. This step was added to the protocol in order to take into consideration the absorption of liquids into polymers.

Contact mechanics about the selected couples

Actual pressures and geometry of contact sphere-plan were calculated using Hertz's theory of contact [START_REF] Hertz | Uber die berührung fester elasticher Körper[END_REF][START_REF] Hills | Mechanics of Elastic Contacts[END_REF][START_REF] Johnson | Contact Mechanics[END_REF]:

3 3 E* R F r    (1) 2 r F P    (2)
Where: r: contact radius : average pressure, F: normal force to the surface, E*: effective Young's modulus:

    2 2 1 1 2 1 1 1 * 1 E E E       (3)
R: effective radius:

1 2 1 1 1 R R R   (4)
In these experiments, R 1 is 3 mm and R 2 is infinite (plane sample).

E i , ν i , R i are as follows: Young's modulii, Poisson's ratios and radii of samples respectively.

Indexes 1 and 2 refer to metallic samples and polymer sample respectively.

The calculated contact radii and average contact pressures are presented in Table 9 and Table 10.

Contact radii / µm

Metallic material / sphere It is worth noting that in the experimental conditions of the tests, a high average contact pressure was involved. To correlate the wear behavior to the mechanical parameters, the ratios of the average contact pressure on tensile strength of each polymer material (PEKK CF 30 %, PEKK, PEEK, UHMWPE) were calculated. The ratios are presented in Table 11.

As the polymer materials are brittle, according to the calculated pressures, the debris generation should be promoted in these experimental conditions as confirmed by typical ratios higher than 1. Moreover the higher the ratio is, the higher the wear rate should be. This assumption will be discussed later in details thanks to post mortem analyses. Table 11: Relative pressures, ratio of average contact pressure to tensile strength in contact zone for 4 polymer materials.

Relative pressures

Results and discussion

In this part, a specific attention will be paid to the friction coefficient evolution according to the time, to the wear rate and to the microscopic analyses of the wear track area in order to understand the wear behavior of the tribological systems. Therefore, the effect of the debris generation, between both materials in contact, is significantly different for PEKK composite. Indeed, if the friction coefficient decreases according to the time, it means that the third body might play the role of a lubricant. In the case of PEKK CF 30 %/metal, on the contrary, the friction coefficient increases and, consequently, the third body seems play the role of abrasive particles, probably due to the carbon fibers against a metallic alloy. Sometimes, as could be seen in Figure 5 b) for the PEEK / TA6V couple, a discrepancy is highlighted within the 3 experiments performed for each contact type. It is the reason why, to be able to explain the evolution of the friction coefficient, numerous tests have to be carried out for the same contact type. Finally, the trend obtained from the average friction coefficient could be entrusted. So as to validate or not the hypotheses made on the evolution of the friction coefficient, the wear rate of polymer material will also be investigated.

Friction coefficient

Wear rate analysis

The friction coefficient is not sufficient to describe the wear behavior of materials couple since even if the friction coefficient is weak, the wear rate could be the highest when a material couple series is compared to another. It is the reason why, in this part, we will focus our interest, about the wear rate. It is worth noting that the wear of metallic alloy could not be measured.

Figure 6 a) presents the wear zone of the PEKK CF 30 %, the pin being a 316L ball.

As one can see, the wear track area is heterogeneous. In Figure 6 b) the reference line defines the width, the depth and the wear surface of a wear track zone. These three parameters will be investigated for all contacts type. Figure 7 a) depicts the wear rate, i.e. the wear volume per unit of normal load and per unit of length (wear distance) for all materials couples. Figures 7 b) andc) present respectively the width and the highest depth of the wear track area, obtained from the 3D profilometry scans. First the results obtained for PAEK polymers should be compared with the wear rate measured by Zhang et al [START_REF] Zhang | Study on tribological behavior of plasma-treated PEEK and its composite[END_REF]. From the wear rate values in Figure 7, it is clearly highlighted that the UHMWPE is the most worn material. The UHMWPE wear rate is 10 times higher than the ones of PEKK + CF 30 %, PEKK and PEEK. The PEEK material seems to involve the lowest wear rate against all metallic material. The PEEK / Co-Cr wear rate seems to be the lowest even against PEKK CF / Co-Cr. This result has to be linked to the lowest value of Ra attributed to PEEK samples. From the tribological tests, Co-Cr seems to be the best counter part for PEKK, PEKK CF and PEEK. If we analyze the width and the depth of the wear track area from the polymer discs: one can conclude that the width for UHMWPE samples is 3 times higher than the ones for PAEK samples. Moreover, the depth for UHMWPE is 10 times higher than the ones for PAEK samples. Finally, the wear depth of UHMWPE is definitively the highest. A representative plot in Figure 8 shows the correlation between the friction coefficient and the disc wear rate.

The lowest wear rate corresponds to the couple PEEK vs. Co-Cr so that this materials couple should be investigated for the artificial hip joint: Co-Cr could replace the femoral head and PEEK the acetabular cup. A future work could investigate the wear behavior of the PEEK CF discs against metallic pins. The highest wear rates are assigned to the UHMWPE couples.

Figure 8 highlights that the lowest friction coefficient, for investigated materials, is not related to the lowest wear rate. In fact the trend is the opposite. Finally after tests and comparisons, the volumetric measurements thanks to a mechanical profilometer (or optical) seems to be the best method to determine the wear volume for the polymer material. Indeed, the weight gain of the polymer samples during tests does not allow measuring correctly the weight variations, due to hieratic water absorption.

Concerning hip prosthesis, head-cup joint for instance, some previous investigations [START_REF] Wang | Carbon fiber reinforced polyether ether ketone composite as a bearing surface for total hip replacement[END_REF] were carried out to evaluate the lifetime of a PEEK CF cup against a head made of metal or alumina. PEEK CF highlights the advantage to be not degradable after sterilization, especially  radiation, a requirement for implanting a biomaterial [START_REF] Godara | The influence of sterilization processes on the micromechanical properties of carbon fiber-reinforced PEEK composites for bone implant applications[END_REF]. The biocompatibility, interactions with cells as osteoblasts, was investigated and satisfying results were found [START_REF] Kurtz | PEEK biomaterials in trauma, orthopedic, and spinal implants[END_REF][START_REF] Sagomonyants | The in vitro response of human osteoblasts to polyetheretherketone (PEEK) substrates compared to commercially pure titanium[END_REF].

If PEEK is still now implanted for spinal cages, some investigations are carried out for increasing the cytocompatibility in order to reach the same level than the one of titanium [START_REF] Sagomonyants | The in vitro response of human osteoblasts to polyetheretherketone (PEEK) substrates compared to commercially pure titanium[END_REF]. In an international multicenter clinical study, a cup made of PEEK CF was implanted against an alumina head for replacing a hip joint. . The wear depth in the retrieved cup of PEEK/CF showed a value of 0.057 mm a year [START_REF] Pace | Technical and Histologic Analysis of a Retrieved Carbon Fiber-Reinforced Poly-Ether-Ether-Ketone Composite Alumina-Bearing Liner 28 Months After Implantation[END_REF], to be compared, for example, with 0.174 mm a year for a UHMWPE cup [START_REF] Manning | In Vivo Comparative Wear Study of Traditional and Highly Cross-linked Polyethylene in Total Hip Arthroplasty[END_REF]. Knowing that the UHMWPE wear volume is within the range of 58-140 mm 3 /year [START_REF] Bragdon | Wear of retrieved cemented polyethylene acetabula with alumina femoral heads[END_REF], the PAEK wear volume is expected to be minimum 2 times lower than that of UHMWPE, which is a huge improvement for implant lifetime. It is worth noting that the gap between the linear and volume wears of retrieval implants is drastically different than the ones from the tribological tests presented in this study. However in the current tests, the difference between wear rate of UHMWPE and PAEK is in the range of magnitude about 10 times, which means that the volumetric wear rate of PAEK, should be lower than the one of UHMWPE. Consequently, PAEK polymers, should be considered as promising materials for artificial hip cup. Particular investigations should be carried out for testing PEKK or PEKK CF cups in in vitro conditions. Future investigations will aim at improving the wear rate of PAEK materials taking into account that the actual shape of cup against a metallic or ceramic head and considering the actual loading conditions, that is thanks to a hip walking simulator.

The next part of the paper will be dedicated to the morphological analyses of the wear track area.

Microscopic analyses of wear track areas

The pins and the discs surfaces were observed by optical and scanning electron microscope. For comprehension purpose, the following discussion will be divided in two parts: the first about the polymer discs and the second one about the metallic pins.

Polymer discs

Figure 9 shows pictures of the polymer discs surface after wear tests. The type of counter part, i.e. metallic pin, is indicated in the left column. Different wear mechanisms could be clearly distinguished in Figure 9. Fatigue waves are only seen on the UHMWPE wear track area. This typical tribological behavior of UHMWPE was already mentioned by Wang et al [START_REF] Wang | Lubrication and wear of ultra high molecular weight polyethylene in total joint replacements[END_REF]. On the contrary, debris or scratches are hardly observed for UHMWPE in comparison with other polymer materials, i.e. PAEK. It is worth noting that for PEEK perpendicular scratches are highlighted, especially for PEEK/Co-Cr and PEEK/316L contacts.

These scratches are pretty long, up to few hundred of micrometers, which indicate that delamination is a part of the wear process for PEEK. For instance, this kind of delamination process does not occur for PEKK. The PEKK CF sample exhibits a particular wear track area.

No significant difference is seen when comparing Co-Cr, 316L and Ti-6Al-4V contacts. It can be seen that carbon fibers were broken in the transversal direction and that some fibers were pulled out from the polymer matrix. Such behavior involves that fibers, 100 µm long and approximately 10 µm in diameter could have been ejected from the disc and could have played the role of an abrasive third body. It is worth noting that this third body, that is carbon fibers of different lengths, may be a key point if the biocompatibility is considered. In this study, this key point will not be considered.

Metallic pins

As the contact pressure on the pin is lower than its ultimate tensile strength (see Table 10), the metallic material, Co-Cr, 316L and Ti-6Al-4V, does not undergo any significant degradations. Figure 11 The wear mechanisms will be investigated in the next part.

Wear mechanisms-overview

A summary of the observations made on disc and pins deterioration is presented in As this behavior was observed for all tests, the tribology of the contact could only be due to the composite material. Moreover, the debris layer found on discs results (PEKK discs) from an extensive corrosion of pins and delamination is clearly correlated to variations of the friction coefficient during tests, as seen in Figure 4.

oscillations resulting from the evolution of the friction coefficient. Neither UHMWPE nor PEKK+CF exhibit this behavior due to the "global" wear mechanism from very beginning of experiment. Two mechanisms are possible -delamination and debris production, knowing that both could take place at the same time. None of these mechanisms seems to be dominant.. However, as discussed previously, debris production could explain the extensive corrosion of pins. If the oxides protective layer of pin is constantly damaged then corrosion occurs. One can imagine that the passive layer could be destroyed by presence of hard particles (carbon fiber debris in composite) or wear by high pressures (all PAEK materials).

In addition, the differences observed in terms of wear mechanisms between PEKK and PEEK material could be affected by some intrinsic physical interactions between polymer chains. Indeed, PEKK ketone groups could be in meta and para configurations whereas, for PEEK, only para configuration is possible (see Figure 1) Consequently, configurations of polymer chains are expected to be different between PEEK and PEKK and so the crystalline phases should be different [START_REF] Stephen | Polymorphism and crystal structure identification in poly(aryl ether ketone ketone)s[END_REF].

Conclusion

These tribological investigations showed some interesting insights into the behavior of PAEK materials, including composite polymer PEKK and carbon fibres 30 %. These PAEK materials were potentially used as implants, artificial hip joint for example.

Superior properties of the materials from PAEK group seem incontrovertible in comparison with the usual UHMWPE used for acetabular cup. They are more wear resistant, producing less debris. PAEK wear rates are 10 times lower than the one of UHMWPE. It could be beneficial concerning contaminating living organism, interactions between debris and cells. This assumption will be assessed in a future work taking into account the size and the shape of debris particles. The PAEK materials class also meets basic needs concerning volume wear for the development of new Hard-on-Soft hip prosthesis.

The study of the mechanisms of deterioration also gave satisfying explanations of the wear behavior. One might pay attention to link mechanical properties and the ratio of average contact pressures on tensile strength to the wear behavior of polymer materials. In terms of this ratio defined above on Table 10, UHMWPE and PEKK + CF belong to the same class. It means that the composite polymer material is submitted to high contact pressure. The role of the third body, especially carbon fibres, in the prediction of the wear rate on a long period of time, should be investigated through additional tests,.

The key-point for introducing PEEK or PEKK or composites with carbon fibers in hip prothesis should be biological response of living cells to those materials. Therefore the next stage that consists in introducing PEKK or PEEK-as acetabular cup on orthopedy marketcould be undertaken. Nevertheless, the exact wear mechanism and more data on materials behavior in actual prosthesis have to be examined in order to accomplish this challenge.

About the tribocorrosion tests, this study cast light on the passive layer reconstruction hypothesis. Electrochemical follow-up of metal samples should be very interesting to highlight particular corrosion behavior in presence of carbon fibers as a third body. At the interface of carbon fibers, there is usually greasing and protective specimens that enhance procedure of composite manufacturing. This key-point should change the adhesion of carbon fibers with the polymer matrix. Finally, very long experiments with low pressure could reveal whether other mechanisms of deterioration are dominant when pressure is closer to the real pressure in hip joints. As wear would be very weak, other variable -namely time -should be increased and the experiment could be carried out on hip walking simulators. Anatomic position of components would prevent debris accumulation, and the geometrical set-up would be more similar to clinical case. The tribological behavior could be entirely different with acetabular cup design due to particular sample geometry compared to pin-on-disk samples.

Figure 1 :

 1 Figure 1: PEEK and PEKK monomers formula

Figure 2 :

 2 Figure 2: Surfaces after polishing: a) PEKK+CF 30%, b) UHMWPE (right side of picture), c) Co-Cr cylinder

Figure 3 :

 3 Figure 3: Pin on disc tribometer; a) scheme of pin-disk assembly; b) device image.

Figure 4 :

 4 Figure 4: Friction coefficient vs. duration of friction tests with 316L SS against a) UHMWPE; b) PEEK; c) PEKK; d) PEKK CF 30 %.

Figure 5 Figure 5 :

 55 Figure5presents a summary of the friction coefficient evolution for all materials couple during 60 minutes (Average 1-60) and during the complete test duration (Average 500). First of all, the friction coefficient of UHWMPE/metal (Co-Cr alloy or 316L or Ti-6Al-4V, TA6V) is the lowest, approximately 2 times lower than the ones of PAEK/metal couples in average.As far as PEKK CF 30% / metal couples is concerned, its behavior is different since the friction coefficient increases with time. .

Figure 6 :Figure 7

 67 Figure 6: a) wear track area of a PEKK CF 30 % sample (contact PEKK CF 30 %/316L), the z-scale is in µm; b) Typical 2D view of x-z plane from a wear zone.

Figure 8 :

 8 Figure 8: Friction coefficient vs. disc wear rate for the 9 couples of materials; blue circle, red star and green square are respectively related to Co-Cr, 316L and TA6V (Ti-6Al-4V); the discrepancy is the standard deviation

Figure 10 presentsFigure 9 :Figure 10 :

 10910 Figure10presents pictures of PEKK and PEKK CF samples. A special attention should be paid to these particular polymer materials as they highlight the impact of carbon fibers. Traces on pure PEKK polymer were not clearly defined -scratches became visible only at high magnification and found homogenous and straight. Any other features were visible. The borders of wear track were characterized by big spacing and rough edges of scratches, incrusted particles could also be found inside the wear track area.

Figure 11 :

 11 Figure 11: SEM images of metallic pins, black patchs are corrosion debris and proteins

15 Table 1 :

 151 chemical composition of 316L stainless steel

Table 2 :

 2 chemical composition of Ti-6Al-4V alloy 20

Table 3 :

 3 chemical composition of Co-Cr alloyThe PEEK 450 CA30 was obtained from Victrex ® ), and OXPEKK C, OXPEKK C30C (30 % carbon fibers) were both supplied by Oxford Performance Materials ® , part of the

	Elements	Cr	Ni	Mo	Mn	Si	Cu	C	P	S	Fe
	Composition (% w/w)	17.05	14.55	2.80	1.73	0.40	0.10	0.02	0.02 <0.01 Bal.
	Elements		Al	V	Fe		O	Cr		Ni	C	N	Ti
	Composition (% w/w or ppm)	5.91%	3.87%	1096 ppm	1038 ppm	137 ppm	125 ppm	124 ppm	53 ppm Bal
	Elements		Cr	Mo	Mn	Si	Ni		C	Al	Co
	Composition (% w/w)		28.50%	5.87%	0.78	0.46	0.25	0.037	0.02	Bal

Poisson's ratio ν Density / g.cm -3 UltimateTensile strength / MPa

	PEKK+CF 30%	28.0	0.30	1.36	248  20
	PEKK	3.8  0.4	0.35	1.31	110  10
	PEEK	3.5	0.40	1.30	105  10
	UHMWPE	0.7  0.2	0.46	0.94	40  10
	Co-Cr	200  10	0.30	8.30	2000  200
	316L SS	200  10	0.30	7.96	630  50
	Ti-6Al-4V *	110  4	0.31	4.42	1300  300
	Table

Table 5 :

 5 Polishing protocols for PAEKs (PEEK, PEKK, PEKK+CF), UHMWPE and cylinders made out metallic alloys.

		Abrasive factor	Time / min Force / daN Velocity / RPM
	PAEKs	Abrasive paper 600	5 min	11	150
		Abrasive paper 1200 5 min	11	150
		Abrasive paper 4000 5 min	11	150
		3 µm diamond paste 5 min	5.5	300
		Colloidal silica	5 min	5.5	200
	UHMWPE Abrasive paper 80	1 min	5.5	200
		Abrasive paper 120	1 min	5.5	200
		Abrasive paper 600	1 min	5.5	200
		Abrasive paper 1200 2 min	5.5	200
		Abrasive paper 4000 3 min	5.5	200
		Colloidal alumina	5 min	5.5	200
	Cylinders Abrasive paper 4000 5.5 min	MANUAL
		6 µm diamond paste 5.5 min	MANUAL
		3 µm diamond paste 5.5 min	MANUAL
		1 µm diamond paste 5.5 min	MANUAL

Table 6

 6

	gives the surface

Table 7 :

 7 Tribological conditions: displacement and charge specifications.

	Parameter	Unit	Value
	Rotation radius	mm	10.0
	Frequency	Hz	1.0
	Speed	mm.sec -1 62.8
	Time of experiment	h	8.0
	Total distance	m	1809.6
	Load	N	30.4

Table 9 :

 9 Contact radii, before friction test, in µm, for all investigated contacts

		Co-Cr	316L	Ti-6Al-4V
	Polymer material / disc
	PEKK CF 30 %	136	137	141
	PEKK	254	253	255
	PEEK	261	260	261
	UHMWPE	380	380	380

Table 10 :

 10 Average contact pressure in MPa for all investigated contacts; values were calculated from the average values of tensile strength

Polymer material / disc PEKK CF PEEK PEKK UHMWPE Typical ratio Average pressure/Tensile strength

	~2.3	~1.4	~~1.4	~1.7

  4 presents the evolution of the friction coefficient with respect to the contact time of 316L SS vs. UHMWPE, PEEK, PEKK and PEKK + CF 30 %. After a running-in period, the values of friction coefficient for pure polymers against metallic alloy constantly decreased until they reached a plateau below the initial value. The same trend is observed for each pure polymer/metal couple although the friction behavior depends specifically on the polymer. On the other hand, the behavior of the PEKK composite is different: after 3-5

				316L + UHMWPE			0.16		316L + PEEK
	Friction coefficient	0.08 0.12 0.16				Exp 1 Exp 2 Exp 3	Friction coefficient	0.08 0.12				Exp 1
												Exp 2
												Exp 3
		0.04						0.04
		0	100	200	300	400	500	0	100	200	300	400	500
				Time / min					Time / min
				316L + PEKK CF					316L + PEKK
		0.16
								0.16
	Friction coefficient	0.08 0.12				Exp 1	Friction coefficient	0.08 0.12			Exp 1
						Exp 2					Exp 2
		0.04				Exp 3		0.04			Exp 3
		0	100	200 Time / min 300	400	500	0	100	200 Time / min 300	400	500

minutes of test, the tangential force was drastically increased. After 100 min following this trend, values start to stabilize but still slightly rising. The most unstable values of the friction coefficient are for the contact 316L/PEKK. This particular evolution might be due to debris generation during the tribology test. Such production of a "third body" allows reaching a very low friction coefficient, comparable to that of UHMWPE material. The question raised then is: is the corresponding wear rate high or low? This question will be discussed further in the paper.

Table 12

 12

	exhibits the Anova tests

  presents samples of Co-Cr, 316L and another 316L against PEKK CF, PEKK and PEEK respectively. In figure11left picture, scratches and grooves could be seen on the Co-Cr surface. It is worth mentioning that the Co-Cr sample against PEKK CF is the most damaged one compared to other polymers without carbon fibers,. The wear track area of other metallic pins (friction against PEKK CF) exhibits the same pattern. Obviously, pictures of metallic samples against UHMWPE were not shown because no damages were visible. From these images of Co-Cr surface, one may suggest that femoral head made of Co-Cr against composites polymer as cup, would involve increased wear of metal compared to the standard couple Co-Cr or 316L against UHMWPE. This is the reason why one should recommend investigating materials couples via in vitro tests in conditions as close as possible to a hip joint with head and cup.

	PEKK CF Co-Cr	PEKK 316L	PEEK 316L

Table 13 .

 13 It was established from optical microscopy observations of both counter parts as well as friction coefficient recording.The UHMWPE disc/metal pin contact involves a common behavior that is the UHMWPE disc surfaces, after tribological tests, exhibit fatigue waves and abrasion. The metallic surfaces do not suffer any degradation and no corrosion insights.On the other hand, insights of abrasion were highlighted on all PAEK disc samples; abrasion is the main wear mechanism. The PEEK samples exhibit delamination and debris, signs of corrosion. Concerning the PEKK discs, two conclusions may be drawn: 316L and Ti-6Al-4V involve continuous delamination and relatively homogeneous debris layer, visible after triboblogical tests. PEKK discs, against Co-Cr, do not exhibit continuous delamination and debris that adhere to the wear track area (PEKK debris do not stuck to the samples). The medium (bovine serum) could play a significant role about the potential of zero charge of this polymer. Additional investigations are required to validate this assumption. Finally, the PEKK CF samples exhibit abrasion and a continuous debris layer. The metallic heads were significantly damaged by corrosion. The carbon fibers, hard particles, could play a significant role for destroying the protective oxides layer of the metallic head.

  In further work, additional investigations on the XRD should get insights on this point. When experiments are maintained long enough, local areas of delamination or debris layer become continuous, which result from the stabilization of the friction coefficient. One originality of this paper lies in the fact that the wear experiments performed were significantly longer in comparison to what is described in bibliography, typically 2 hours [19-21]. Such long experiments give a good insight into the tribological behavior of PAEK and composites materials.As a conclusion of these studies and previous ones, one can say that the carbon fibers play the role of lubricant in the contact at the beginning of tests, low friction coefficient. However, long investigations, up to 5 hours, were already not carried out, this is the main improvement of this study. According to results about the composite with carbon fibers, this work may

suggest that lubricating properties of carbon fibers are only temporal. The significant problem should be, concerning the composite polymer, the wear of metallic counterpart due to abrasive behavior of carbon fibers. After long time of prosthesis usage, unfavorable effects of debris presence, mainly fibers, would be more harmful than beneficial due to questionable lubrication.

µm 20 µm 20 µm

Acknowledgements

The authors want to acknowledge Ms. Prisca Leveque for the polishing assistance. Moreover they are grateful to the Region Rhône-Alpes and Carnot Institute Cetim, Centre Technique des Industries Mécaniques, for the financial and technical support and providing the opportunity to carrying on the research activities between two Carnot Institutes Cetim and M.I.N.E.S.

Polymer

Metallic alloy Fatigue Abrasion Debris Delamination Corrosion of

The Figure 12 presents the summarized wear behavior proposed. In the case of UHMWPE, where pressure exceeds tensile strength of material, disc yields and deforms creating a wide path. As far as degradation is concerned, it is due to low-cycle fatigue mechanism. However the darkening and murking of the medium during experiment suggest that debris were produced and accumulated in bovine serum. Because of the UHMWPE low density, debris of UHMWPE would float onto medium and not stay close to the wear track area. This would diminish the influence of debris on pins' deterioration, whereas more dense PEAK's debris would become "incrusted" into wear track and induce abrasion and corrosion of metallic pins. Moreover the surface charges on the debris should be drastically taken into account for these aggregated particles on the polymer samples. The considered medium, i.e.

pH, proteins and ions concentrations, should play a significant role on this debris adsorption.

So as to conclude with the PEKK CF, after short running-in period, the whole track is covered with carbon fibers debris and the pins surface is homogenously damaged, involving a more severe corrosion of metallic pins than the ones with the UHMWPE/metal contact.

When the average pressure is comparable with the material tensile strength, like for PEEK and PEKK, wear remains local. Typically for PEKK disc, this is materialized by big


Joëlle Forest
email: joelle.forest@insa-lyon.fr

THE CREATIVE RATIONALITY AS A KEY DRIVER FOR ENHANCING INNOVATION CAPABILITY

Keywords: Design, creativity, innovation, ingenium, rationality

Several recent works point out that design is one of the main driver of innovation. Therefore, it is interesting to analyze how design contributes to these last process. The point of view we present in this communication assumes that design is based on a specific rationality we called creative rationality. This paper aims at presenting its theoretical roots. Creative rationality derives from Vico's notion of Ingenium. Creative rationality explains the creation of new artifacts and knowledge by knoting in a ingenious way scattered knowledge. It depends on several cognitive, individual and social variables one can identify, measure, and combine in a unified model. If our hypothesis is relevant, then innovation policies or strategies should improve the effectiveness of such a rationality.

Introduction

The way we conceptualize innovation has dramatic effects. It explains the purpose and the content of the policies implemented by governments. Thus, the dominant innovation model is what one calls the R&D model (Research & Development model) or the big science model. In such a model, innovation is seen as an outcome of the science. It is no more than applied science. There is no innovation without research breakthrough, discovery, serendipity... Researchers produce new ideas which will then be embedded in products by skilled engineers and exploited by opportunistic entrepreneurs. The innovation process is represented as a linear succession of stages. It goes from the world of knowledge creation to the those of technical application and entrepreneurial know-how. Innovation policies improve the innovation process by strengthening the research and the transfer from science to the rest of the society.

Is this last model always relevant? The answer is clearly no [START_REF] Dertouzos | Made in America, traduit de l'américain par P. Chemia[END_REF]. Data from the Innobarometer 2007 survey show that more than 50% of innovative firms innovate without performing R&D. If R&D seems to be an important driver of innovation, it is not sufficient by itself. The comparison between linear model and empirical studies has led theorists to propose a more complex view of innovation process. There is no simple causal relation between the scientific capacities (number of researchers, R&D expenses...) or outcomes (number of articles...) and the rate of innovation [START_REF] Bonnaure | Politique scientifique et technologique[END_REF]. In the mid of the 1980s, the American economist Stanley Kline and the Historian Nathan Rosenberg explained such a paradox by building what they called the "chain-linked model" [START_REF] Kline | An overview of innovation[END_REF]. Innovation is knoting. It involves several activities tha should be closely associated by different loops. Kline and Rosenberg underlined the key role of design. "The central process of innovation is not science but design" [START_REF] Kline | An overview of innovation[END_REF]. Without good designers, no innovation. Many recent studies confirm Kline and Rosenberg's insight. Indeed, a recent survey of Swedish companies shows a very interesting fact. Firms that use their design activity as a strategic driver are five times as likely to develop new products as compared to firms that do not do it (Swedish Industrial Design Foundation, 2008;European Commission, 2009). Moreover, these firms developed radical innovation (Irish Center for Design Innovation, 2007 ;[START_REF] Tether | Design in Innovation Coming out from the Shadow of R&D An Analysis of the UK Innovation Survey of 2005[END_REF]. The practical consequence one can infer from such data is trivial. Innovation policy must not only be focused on research. Design should be one of its targets. Improving European competitiveness requires a shift of focus from exclusive R&D to design, as Finland, Ireland, Spain, Denmark and the United Kingdom have been understood since two decades [START_REF] Hollanders | Design, creativity and innovation: a scoreboard approach[END_REF].

If design contributes to innovation, then we aim, as design theorists, to understand the reason and the level of its contribution. What is the intrinsic characteristic of the design which makes it a main innovation process driver? Our hypothesis is that design involves a specific rationality. We call it creative rationality. It explains the creation of new artefacts and knowledge by knoting in a ingenious way scattered knowledge. It depends on several cognitive, individual and social variables that should be identified and combined in a comprehensive model.

The remainder of this communication is structured as follows. Section I presents where the creativity is nestled in the design process. Section II shows the origin of the creative rationality involved in such a process. Section III presents a first draft of the creative rationality.

Design as a creative process

Defining design per se is a difficult task. However, all researchers and practitioners of the field recognize that design is a non-trivial process. Contemporary design of complex products (planes, buildings, professional software, cars., factories...) involves a large number of stakeholders (Micaëlli, Visser, 2005), skills or firms with varied expertises [START_REF] Micaëlli | Artificialisme, Presses Polytechniques Universitaires Romandes[END_REF]. Design is also a convergent (if not, it impossible to achieve an outcome) and a satisfying process [START_REF] Forest | L'économie de la conception au coeur du processus d'innovation[END_REF]. It is temporally constraint and has its own rhythm, different from those of the sciences [START_REF] Micaëlli | Artificialisme, Presses Polytechniques Universitaires Romandes[END_REF]. Last but not least, design is seen as a creative process. Its outcome consists of an original, astute and unimaginable result. Such a creativity can be explained because the design intrinsic logic. Its purpose is to create alternatives, not to choose amongst well-defined alternatives.

Several authors underline the creative aspect of design. "design involves (…) the presence of a creative step (...)" [START_REF] Archer | Systematic method for designers[END_REF]. "(…) all designing is iterative, using creativity and compromise to move from a field of possibilities to one unique solution" [START_REF] Roy | Product design and technological innovation[END_REF]. "Design is a structured creative process" (UK Department of Trade and Industry, 2005). "Design is a creative activity whose aim is to establish the multi-faceted qualities of objects, processes, services and their systems in whole life cycles" (ICSID, 2009).

Of course, the precedent list of citations can be extended ad infinitum. They can be considered as themselves. However, I believe that they are the symptom of an interesting social phenomenon. They led to substitute the design in the creation, quite as the rational in the inexplicable [START_REF] Faucheux | Expliquer l'inexplicable, science de la conception et créativité[END_REF]. Creation is no longer seen as a mystical affair. It is no longer related to the myth of a divine intervention (Albert, [START_REF] Runco | The concept of creativity : prospects and paradigms[END_REF]. "Plato argued that a poet is able to create only that which the Muse dictates (…), Rudyard Kipling referred to the Daemon that lives in the writer's pen (…). Many people seem to believe, as they do about love (…) that creativity is something that just doesn't lend itself to scientific study, because it s a spiritual process", [START_REF] Sternberg | The Concept of Creativity: Prospects and Paradigms[END_REF] wrote.

If we study the design process, then we will have a clearer vision of creativity. It is not longer a mystical fiat, but an empirical attribute of the design process. Design theorists have been trying to understand it since several decades. "creativity is the synthesis of new ideas and concepts by the radical restructuring and re-association of existing ones whereas innovation is the implementation of the result of creativity" [START_REF] Torrance | The Management of Innovation and Design[END_REF]. "Creativity as the generation of ideas" [START_REF] Gurteen | Knowledge, creativity and innovation[END_REF]McAdam, McClelland, 2002). It is "(...) a cognitive process that generates solutions to a task, which are novel or unconventional and satisfy certain requirements" [START_REF] Kryssanov | Understanding design fundamentals: how synthesis and anlysis drive creativity, resulting in emergence[END_REF].

Beyond the variety of these definitions, one notes that the creativity is neither considered as non-rational, intuitive, mystical, and inexplicable phenomenon. It is also no longer seen as a state. It is viewed as a process involving the achievement of a set of specific cognitive activities [START_REF] Wallas | The Art of Thought[END_REF][START_REF] Guilford | [END_REF][START_REF] Boden | The creative mind[END_REF]. Such a point of view leads to consider the creative process as an object of thought. Thus, the study of creative outcomes is no longer postulate as the point of departure of any study on the creativity. The study of the processes it achieves is required. I conjecture that it will lead to the rehabilitation of a kind of reason the Occidental tradition has forgotten [START_REF] Faucheux | Expliquer l'inexplicable, science de la conception et créativité[END_REF]. The fierce opponent of Cartesianism Giambattista Vico has called it Ingenium. We can call it creative rationality.

Before presenting creative rationality, let us note an important point. If creativity is a main attribute of the design process, then the relationship between creativity, design and innovation must be studied with a new point of view. We can no longer see design as linking creativity (i.e. new ideas generation) to innovation (i.e. successful exploitation of new ideas) as proposed P. Swann and D.Birke (2005) in their interactive model. Creativity is a core element of design. It is not an outside entity of the design. It does not exist outside or before the design process.

From Ingenium to creative rationality

Creative rationality can be defined as the ability to associate in an effective way scattered items (concepts, things, technologies, knowledge domains...). It is the faculty to bring together different perspectives, to make distinct domains closer, to find and explore relations none have previously made. The fiat or Eurêka effect can be understood as a result of such a knoting [START_REF] Martindale | Biological bases of creativity[END_REF].

In his main book titled Scienza Nuova (1725), Vico stated that the Ingenium explained how the main western inventions of the End of the Middle-Ages and the Renaissance (e.g. Brunelleschi's works) were created. They were not developed following Cartesian methodological principles (i.e. Decomposition), or what we call analytical rationality.

Vico's insight has found an echo in contemporary literature on creativity. It is mainly considered in architectural terms. Creativity seems to be a word one uses to describe the combination of piece of knowledge "To create consists of making new combinations of associative elements which are useful" (Poincaré, 1913in Martindale, 2005:137), "People create new knowledge or ideas by combining and reorganizing existing concepts or categories" [START_REF] Swann | How do creativity enhance business performance ? A framework for interpreting the evidence[END_REF]. This associative and architectural view induces several questions: What are the knowledge attributes ? Where are these knowledge parts? How to manage the knowledge diffusion, that is to say both the accessibility and the appropriation of these knowledge, to improve innovation process? These questions gave place to a great amount of literature in social and engineering sciences. However, the question to know how such a combination leads to innovation remains open.

It is however possible to go further by mobilizing the [START_REF] Hatchuel | La théorie C-K, Fondements et usages d'une théorie unifiée de la conception[END_REF] C-K theory. It stands that the creative reasoning is based on the mapping between two spaces. The space C represents the space of the concepts. The space K represents the space of the knowledge. According to them, the design reasoning begins by a disjunction K-C transforming propositions of K into concepts. It ends with a conjunction C-K. This last one transforms a concept into knowledge. The concept contains then a set of properties which allows it to acquire a logical status in K C-K theory postulates thus that without knowledge, expansion of concepts is impossible. Without concepts, the designer investigates objects the definition of whom never changes.

Hatchuel and Weil's theory depicts the dynamics of the combination. The key aspect with regards to C-K theory is the focus on knowledge production without which novelty cannot appear. The reality and the role of knowledge production has been empirically tested in a study conduct on innovative companies of the French region Rhône Alpes [START_REF] Forest | Production de connaissances et développement territorial, quelles politiques mettre en oeuvre ?[END_REF]. This study leads thus to put in perspective the importance granted to the diffusion of knowledge in innovation policy.

However, a complete theory of creative design reasoning can not occult the limits of the human rationality. Herbert Simon showed in various empirical and theoretical works. These limits have two rationale [START_REF] Simon | A behavioral model of rational choice[END_REF][START_REF] Simon | From substantive to procedural rationality[END_REF]. The first one depends on our limited knowledge of the environment. The second one is the impossibility for a designer to process all the available information and all possible options he can address. His attention and his computational capabilities are indeed limited. The bounded rationality aims not to show that individuals (e.g. designers) are irrational in their decisions. It is to highlight that the entire range of potential options is never practically accessible. Human mind has a limited ability to generate and compare alternatives. The expansion underlined by A. Hatchuel and B. Weil must be then a bounded process.

Nevertheless, extend the C-K theory by integrating the bounded rationality it is not sufficient. Computationalist approach of design remains a "egocephalocentric" theory. This last one minors the question of the social inscription of the knowledge production. We need a model to have further knowledge about the design reasoning. This model should take into account the cultural, historical and social inscription of the design process. This aim is not a pure theoretical stake. It is also a practical one. By fostering creative rationality, one could improve design, and then innovation.

Basis of a creative rationality model

The aim of these last section is to present a draft of a possible model of creative rationality. This model is based on two main hypothesis. Without knowledge, an ingenious combination can not occurs. Without challenging problem, the creative rationality can be effective.

The knowledge production, noted I, resulting from the creative rationality of an actor I (i=1,...n), is a function of the knowledge he owns (Kmi). Let us assume that there exists a relationship between Kmi and, on one hand, the current state of knowledge in society (Ks), on the other hand, his initial knowledge. Such a knowledge can be acquired attending a certain curricula or through working experiences 1 .

The scope of the expansion process depends on the variety of the parts of knowledge bringing together. This characteristic determines the more or less innovative level of the combination. "In recent literature there is increasing consensus that resource heterogeneity provides a clear potential for learning and innovation" (Nooteboom & alii, 2007). If we have access to the same part of knowledge, we will investigate concepts which the definition never changes. "Little progress would be made in a world of clones" [START_REF] Maskell | Knowledge creation and diffusion in geographic clusters[END_REF]. Theoretically, the combination is not based on a collective activity. However, in current design situations, such an activity is required. Our contemporary knowledge is specialized 2 and complex product development requires the cooperation of different actors, skills, knowledge domains, scienes, technologies... Experience shows that it is very difficult for an actor to master several disciplines. I is thus a function of knowledge held by the different design actors implied in the process. The design actors population being noted A={1,…,n} at a given time t, one can have this production function: I=f(Kmit).Kst, with i=1,...,n.

Two points must be underlined. First, each actor is endowed with a vector of knowledge. However, the potential of the interaction is not an addition of the knowledge these vectors contain. One must take into account the complementarity of the knowledge vectors. Some knowledge can indeed be substitutable. Besides, the design project require, for every actor, only a part of his knowledge vector.

Moreover, if the variety offers potentialities and opportunities for interesting expansion, these last one can occur only if the cognitive distance [START_REF] Nooteboom | Learning by interaction: absorptive capacity, cognitive distance and governance[END_REF] is not too important. Nooteboom points out an interesting idea. The "cognitive distance" provides an opportunity to learn from others who, according to their own experience, interpret, understand, and estimate the world differently. If the cognitive distance is increasing, then opportunities of new combinations favourable to innovation will appear. Beyond a certain threshold, the cognitive distance becomes to long and lead directly to a common misunderstanding. The absorption capacity of a design actor is indeed a decreasing function. The more the cognitive distance increases, the more it is difficult to understand each other. The lack of a common language, shared values or shared perception induce a cognitive cost. The interaction can fail.

The innovation depends then a parabolic function of the cognitive distance in the form of an inverted U (Nooteboom & alii, 2007). Fig. 1 represents the graph of this function. The summit of the parabola represents the optimal cognitive distance between the actors. This optimal distance is the distance: (1) which is wide enough to allow the innovation and (2) weak enough to allow effective cooperation. At this point, many efforts would be required to overlap ambiguities and eliminate mutual misunderstandings.

1 One must considers the depreciation of the knowledge acquired through experience. The development of knew knowledge and technologies accelerate the obsolescence of its parts. 2 According to Adam Smith (1723-1790), the knowledge specialization is the logical outcome of the division of labour. It is then a prerequisite for further knowledge creation [START_REF] Maskell | Knowledge creation and diffusion in geographic clusters[END_REF]. The main result we can take into account by applying Nooteblom's model is that creative rationality is drive by the bounded rationality principles and by the cognitive distance between design actors. We can add that their personality, their respective experience or expertise must be integrated in an unified model of creative rationality. Several studies based on creative actors have shown that they master their domain to overcome it. According to J.R. [START_REF] Hayes | Cognitive process in creativity[END_REF], an average period of 10 years is required to master a domain (Fig. 2,A). Then during 15 years a strong creative productivity can occur (Fig. 2,B), followed by a period of stability of 20 years (Fig. 3,C), before declining (Fig. 2,D). The effectiveness of the creative rationality is also conditioned by the environment in which designers realize their working activity. Many works have already stressed the influence of the social environments on individuals' creativity level.

Family environment -It seems that exists a positive correlation between a individual recognized as creative and and the age of his (her) parents, his (her) born order (Simonton, 1992). Other sociologists state that an intense creative life would be incompatible with a family life3 .

Communitarian environments -From the field dynamics point of view, "each variation in a field's characteristics will affect how creativity develops within its confines or how the confines are changed to accommodate new visions of the domain. The field is the source of acceptance or rejection of potentially creative contributions (...)" (Feldman, 2005).

Macro environment -Other macro-social factors drive individual creativity. It is the case of the religious values and context, the type of society (democratic vs. authoritarian), the political context (war vs. peace), the economic situation (penury vs. wealth, monopolistic situations vs. competitive ones...), etc. For example, Richard [START_REF] Florida | The rise of the creative class, And How It's Transforming Work, Leisure, Community and Everyday Life[END_REF] postulates that the attractiveness of the creative class depends on the tolerance index associated with the city and the urban style of life. According to him, members of the "creative class" prefer open-minded and tolerant places.

Conclusion

This short communication aims at showing a first glance to what we call creative rationality. Such a concept is required to understand how design contributes to innovation. Creative rationality explains the creation of new artefacts and knowledge by knoting in a ingenious way scattered knowledge. It depends on several cognitive, individual and social variables.

Of course, the proposed model is just a draft. It should be refined and completed. Indeed, in its current shape, our model does not consider the personality traits of the designers which interact. It neither considers the influence of the geographical and relational proximity between the designers. It does not take into account the cost of knowledge acquisition, sharing, sustaining...

The elaboration of such a model is the prerequisite to identified the main parameters and possible condition to foster creative rationality. By this way, it also raises the question of relevant indicators and metric. A main issue is the definition of I. Patents are usually used as a proxy to measure innovation. The lack of indicators to measure design and creativity has already been stated (DTI, 2005;[START_REF] Hollanders | Design, creativity and innovation: a scoreboard approach[END_REF]. Nevertheless, the way of measuring the impact of design and creativity on countries' innovation performance remains a opened question. More and more researchers recognize that patents is a poor metric of knowledge production.

Fig. 1 .

 1 Fig.1. Cognitive Distance Optimum.

Fig. 2 .

 2 Fig.2. Expertise Maximum.

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Sorr has studied the lives of Kant, Wittgenstein and Newton. He underlined that "they showed a lack of close involvement with other human beings"(Storr, 1988[START_REF] Policastro | From case studies to robust generalizations: an approach to the study of creativity[END_REF].

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