Olivier De Almeida
email: olivier.dealmeida@mines-albi.fr

Lisa Feuillerat

Jean-Charles Fontanier

Fabrice Schmidt

Determination of a degradation-induced limit for the consolidation of CF/PEEK composites using a thermo-kinetic viscosity model

In order to assess the impact of the thermal degradation of PEEK on the consolidation of composite preforms, an impregnation model taking into account degradation is proposed. It includes a viscosity model based on a double Arrhenius law describing the viscosity increase due to degradation. The implementation of this viscosity model into an impregnation model allowed to define an intrinsic processing window for the manufacturing of CF/PEEK composites based on a criterion of irrecoverable viscosity level. The simulation shows a good correlation with the experimentally measured porosity rates of commingled preforms. It predicts the absence of impregnation when increasing the consolidation time or the processing temperature from 380 to 410 • C. Above 410 • C or when increasing the pressure, however, a discrepancy is observed between the model and the simulation. This discrepancy is attributed to a change in the degradation kinetics resulting from a change in oxygen access.

Introduction

Because of its melting temperature of 343 • C, the molten state represents a severe condition for Polyether-ether-ketone (PEEK). Therefore, degradation inevitably occurs during processing of long fiber reinforced PEEK matrix composites since PEEK composites are typically processed in the temperature range of 380 to 400 • C.

PEEK degradation mechanisms consist simultaneously in chain cleavage and formation of crosslinks between adjacent aryl groups of polymer chains, and are activated from the rubbery state and above the melting temperature [START_REF] Jonas | Thermal stability and crystallization of poly(aryl ether ether ketone)[END_REF][START_REF] Day | Thermal degradation of poly(aryl-etherether-ketone) : Experimental evaluation of crosslinking reactions[END_REF][START_REF] Courvoisier | Multi-scale and multi-technique analysis of the thermal degradation of poly(ether ether ketone)[END_REF]. As a consequence of chemical modifications, degradation affects PEEK physical and mechanical properties like the crystallization behavior and the glass transition. It also results in a rapid increase of PEEK viscosity with time due to the dominating effect of crosslinking over chain scission in an oxidant environment [START_REF] Phillips | Thermal stability of PEEK/carbon fiber in air and its influence on consolidation[END_REF][START_REF] Feuillerat | Effect of poly(ether ether ketone) degradation on commingled fabrics consolidation[END_REF]. Day et al. indeed demonstrated that the atmosphere strongly influences the degradation kinetics. They showed that PEEK was relatively stable in a non-oxidative environment at 400 • C for periods up to 6 h, but that the glass transition temperature and crystallization behavior were rapidly affected under air conditions [START_REF] Day | Thermal degradation of poly( aryl-ether-ether-ketone) (PEEK): A differential scanning calorimetry study[END_REF].

As a consequence of the fast degradation kinetics at the molten state, the processability of CF/PEEK composite preforms can be significantly affected. Actually, evidence of degradation due to manufacturing operations of carbon reinforced PEEK composites was already reported [START_REF] Dolo | Model for thermal degradation of carbon fiber filled poly(ether ether ketone)[END_REF]. This effect of degradation was for instance observed in a previous study on the consolidation of commingled CF/PEEK preforms [START_REF] Almeida | Influence of composite preform fabrication on the integrity of poly-aryl-ether-ketone matrices[END_REF]. The rapid increase in viscosity of PEEK due to degradation could be correlated with the low level of consolidation obtained under all processing conditions [START_REF] Feuillerat | Effect of poly(ether ether ketone) degradation on commingled fabrics consolidation[END_REF]. Phillips et al. also highlighted the impact of degradation on the processability of CF/PEEK composites by analyzing the influence of a preliminary thermal exposure to air of CF/PEEK AS4/APC-2 preimpregnated tapes on the consolidation behavior [START_REF] Phillips | Thermal stability of PEEK/carbon fiber in air and its influence on consolidation[END_REF]. All studies finally conclude that the optimization of CF/PEEK processing conditions consists in finding a compromise between degradation and impregnation kinetics.

However, degradation kinetics are never taken into account when considering the numerical optimization of processing conditions. Numerical approaches, which are usually based on Darcy's law [START_REF] Bernet | Commingled yam composites for rapid processing of complex shapes[END_REF] or on the degree of intimate contact [START_REF] Phillips | Thermal stability of PEEK/carbon fiber in air and its influence on consolidation[END_REF][START_REF] Lee | A model of the manufacturing process of thermoplastic matrix composites ifacture[END_REF], generally consider a constant Newtonian viscosity that varies with temperature according to an Arrhenius law. As a result, they systematically lead to the definition of processing windows consisting of time and temperature graphs with reciprocal curve shapes of iso-porosity levels [START_REF] Hou | Manufacture of a carbon-fabricreinforced polyetherimide (CF / PEI) composite material[END_REF][START_REF] Ye | Consolidation of unidirectional CF/PEEK composites from commingled yarn prepreg[END_REF].

Therefore, in order to consider the effect of degradation on the processability of CF/PEEK composites, this study proposes to take degradation into account by means of a thermokinetic model representing the evolution of PEEK viscosity with time. The viscosity model is first described and identified from the experimental shear rheology results. This model is then implemented in the impregnation model proposed by Bernet et al. based on Darcy's law to assess the influence of time, temperature and pressure on the consolidation of commingled CF/PEEK composite preforms [START_REF] Bernet | An impregnation model for the consolidation of thermoplastic composites made from commingled yarns[END_REF]. The numerical results are finally compared with experimental consolidation data from a previous article [START_REF] Feuillerat | Effect of poly(ether ether ketone) degradation on commingled fabrics consolidation[END_REF] in order to analyze the degradation process during consolidation as a function of processing conditions.

Materials

The PEEK polymer used as a reference in this study is a Victrex grade 150 provided as a coarse powder (150P). This polymer is characterized by a glass transition of 143 • C and a melting temperature of 343 • C as mentioned in the material's technical data sheet and confirmed by DSC measurements. The composite preform under study is a commingled quadriaxial Non Crimp Fabric (NCF) with a carbon weight fraction of 65%wt. prepared using the same PEEK 150 grade. This NCF preform is composed of four unidirectional layers of an areal weight of 145 g m -2 stitched together with a PEEK yarn of 5 g m -2 . This corresponds to areal weights 𝐴𝑤 𝑓 and 𝐴𝑤 𝑚 of 377 g m -2 and 208 g m -2 for carbon and PEEK phases respectively. This tailored material was provided by Saertex for the purpose of the INMAT2 project and was manufactured by combining together aligned HTS 3k carbon tows and PEEK yarns so as to obtain a global commingled structure. Because of the alignment of yarns, the commingling level in this material remained poor: no reorganization of PEEK and carbon filaments was performed before the weaving operation. Details about this composite material are given in a previous article [START_REF] Feuillerat | Effect of poly(ether ether ketone) degradation on commingled fabrics consolidation[END_REF].

Experimental

Rheological characterization of the matrix

Rheological measurements were performed on PEEK coarse powder and yarns with a Mars Haake rheometer using a plate-plate geometry in oscillatory mode with disposable aluminum plates of a diameter of 35 mm (gap of 1 mm). During the experiments, the shear and shear rates were set to 0.01 and 6.28 s -1 respectively. In order to guarantee the linear viscoelastic domain, strain sweep tests were previously performed so that the complex viscosity could be simply determined from the elastic and viscous moduli 𝐺 ′ and 𝐺 ′′ . The applied shear rate is in agreement with the order of magnitude given in the literature in the case of compression molding processes [START_REF] Seo | A model of the resin impregnation in thermoplastic composites[END_REF][START_REF] Jespersen | Film stacking impregnation model for a novel net shape thermoplastic composite preforming process[END_REF][START_REF] Gebart | Permeability of unidirectional reinforcements for RTM[END_REF][START_REF] Choupin | Macromolecular modifications of poly(etherketoneketone) (PEKK) copolymer at the melting state[END_REF].

Consolidation by compression molding

Consolidation of the CF/PEEK preform was performed with a compression molding pilot plant equipped with an induction-heated mold developed by Roctool (3iTech ® technology, [START_REF] Ramakrishnan | Optimized manufacturing of thermoplastic biocomposites by fast induction-heated compression moulding: Influence of processing parameters on microstructure development and mechanical behaviour[END_REF]) following the exact same protocole as in [START_REF] Feuillerat | Effect of poly(ether ether ketone) degradation on commingled fabrics consolidation[END_REF]. The laminates were processed with a 200 × 200 mm 2 picture frame at different temperatures comprised between 380 • C and 440 • C during 5 to 30 min and under 25 or 50 bar. All tested experimental conditions are presented in Supplementary data.

A representative processing cycle used for composite consolidation is shown in Fig. 1. The data displayed in Fig. 1 were recorded during the test. It should be noted that the applied force was taken from a load cell in the actuator head of the press and not from the hydraulic pressure, and converted into a pressure by considering the size of the picture frame.

Table 1

Slope of the lines of best fit in Fig. 5 corresponding to factor 𝐵 in Eq. ( 4), for each temperature. Ratio of the second bundle size 0.5

Temperature (

Characterization of the final void content of composite plates

Thanks to the picture frame, the flow of resin was constrained into the cavity and squeeze of resin out of the composite stack was avoided. The average laminate thickness 𝑡 𝑙𝑎𝑚 of the manufactured laminates could therefore be used as a significant indicator of the porosity level in the composites. The void content 𝜙 was calculated using Eq. ( 1), where 𝐴𝑤 𝑓 and 𝐴𝑤 𝑚 are the areal weights of the carbon reinforcement and the PEEK matrix respectively, 𝜌 𝑓 and 𝜌 𝑚 are the density of carbon fibers and PEEK matrix, set to 1.77 g cm -3 and 1.30 g cm -3 respectively according to the manufacturer's data sheets, and 𝑛 𝑝𝑙𝑖𝑒𝑠 corresponds to the number of NCF blankets used to manufacture the composite laminates.

𝜙 = 1 - 𝑛 𝑝𝑙𝑖𝑒𝑠 𝑡 𝑙𝑎𝑚 ( 𝐴𝑤 𝑓 𝜌 𝑓 + 𝐴𝑤 𝑚 𝜌 𝑚 ) (1)

PEEK viscosity modeling including degradation kinetics

Effect of thermo-oxidation on PEEK viscosity

In order to characterize the influence of temperature on PEEK viscosity and to assess the effects of degradation in the compression molding process, the influence of thermal degradation on the viscous behavior of Victrex PEEK 150 (raw PEEK) and NCF matrix (PEEK yarns) was investigated by measuring the viscosity change with time for different temperatures above PEEK melting temperature. The rheological samples were rapidly heated to a temperature just below the desired temperature so as to avoid temperature overshoot. The PEEK samples were considered as non-degraded at the beginning of the trials. Viscosity measurements of PEEK Victrex 150 coarse powder were carried out for different temperatures between 370 and 420 • C in air (Fig. 2). Due to the difficulty of isolate PEEK filaments from the commingled NCF preforms, only two different temperatures were tested for this PEEK reference (Fig. 3). Indeed, due to the stitched assembly of carbon and PEEK yarns in the NCF preform, PEEK strands had to be extracted one by one until the few grams needed to prepare rheological samples were obtained. The two chosen temperatures are 380 and 400 • C as these are usual processing temperatures for CF/PEEK composites. Higher temperatures could not be used to measure the viscous behavior of PEEK yarns because their fast degradation kinetics [START_REF] Feuillerat | Effect of poly(ether ether ketone) degradation on commingled fabrics consolidation[END_REF][START_REF] Almeida | Influence of composite preform fabrication on the integrity of poly-aryl-ether-ketone matrices[END_REF]. Degradation would have rapidly occurred during the heating phase and the test results would not have given accurate information about the actual viscosity.

For both materials, the initial viscosity at𝑡 = 0 decreases with increasing temperature, which is consistent with the conventional temperature dependence of polymer viscosity. Then, for all temperatures, the viscosity increases rapidly and the viscosity evolution is all the more rapid as the temperature is high above the melting temperature of PEEK. At 420 • C for instance, the increase of raw PEEK viscosity is so rapid that the viscosity is tripled within 18 min. As seen in a previous 4) is given for each temperature by the slopes of the linear regression of experimental data. Fig. 6. Kinetic factor 𝐴(𝑇 ) of the viscosity model (Eq. ( 6)) as a function of temperature for 𝐵 = 2 and comparison with the prediction given by the Arrhenius law of Eq. (5). Fig. 7. Iso-viscosity contours computed with the viscosity model accounting for degradation (Eq. ( 6)) using material parameters identified from viscosity measurements on PEEK yarns (Table 2). The black curve connecting the maximum time of each iso-viscosity level defines a limit of irrecoverable degradation. 10) and ( 12)) for a consolidation pressure of 25 bar using material parameters identified from viscosity measurements on PEEK yarns (Table 2). Dashed gray lines represent the iso-porosity levels considering the temperature dependency of initial viscosity but without considering degradation kinetics (Eq. ( 2)); colored lines are obtained using the viscosity model accounting for degradation (Eq. ( 6)). The red line connecting the minimum time of each iso-porosity contour defines the processing window for impregnation. 2) without degradation, ◊) and when taking into account degradation in addition (Eq. ( 6), ⧫). The blue symbols (◊) correspond to the simulation performed with the parameters identified for the pure matrix, the red symbols (◊) for the PEEK yarns from the preform. Dotted lines are shown to indicate trends.

Raw PEEK viscosity modeling

To further analyze the effect of degradation, a viscous model accounting for degradation kinetics was developed. The aim of this model is to predict the viscosity change over time for any temperature above the melting temperature.

First, as already noticed, the thermal dependency of the initial viscosity at 𝑡 = 0 is in good agreement with the conventional behavior of thermoplastic polymers, and therefore can be modeled using an Arrhenius law. The viscosity at 𝑡 = 0, 𝜂 0 (𝑇 ), was modeled with Eq. ( 2), where 𝑎 𝑇 is the shift factor, 𝐸 𝑎 is the Arrhenius activation energy, 𝑅 is the gas constant and 𝑇 0 is a reference temperature (380 • C in the present study). As shown in Fig. 4, the alignment of the data points in the chart of 𝑙𝑛(𝑎 𝑇 ) vs. 1∕𝑇 confirms the Arrhenius type for the thermal sensitivity of initial viscosity. The identified activation energy is 36372 J mol -1 , which is in agreement with values given in literature 2) without degradation, ◊) and when taking into account degradation in addition (Eq. ( 6), ⧫). The blue symbols (◊) correspond to the simulation performed with the parameters identified for the pure matrix, the red symbols (◊) for the PEEK yarns from the preform. Dotted lines are shown to indicate trends.

for the viscosity of PEEK grade 150 [START_REF] Khan | Identification of some optimal parameters to achieve higher laminate quality through tape placement process[END_REF][START_REF] Shekar | Fibre-fibre hybrid composites for aerospace applications[END_REF].

𝜂 0 (𝑇 ) = 𝜂 0 (𝑇 0 )𝑎 𝑇 = 𝜂 0 (𝑇 0 ) exp ( 𝐸 𝑎 𝑅 ( 1 𝑇 - 1 𝑇 0 )) (2)
As PEEK degradation is a kinetic phenomena, the degradation kinetics is usually described as an exponential function of time 𝑡 in viscosity models. Analytical models predicting an exponential change in viscosity have already been proposed by Phillips et al. and Malkin et al. [START_REF] Phillips | Thermal stability of PEEK/carbon fiber in air and its influence on consolidation[END_REF][START_REF] Malkin | Rheokinetics of curing[END_REF]. In a first approach, the temperature dependence of degradation kinetics was thus described with Eq. ( 3), where 𝐴(𝑇 ) is a parameter that depends only on the temperature.

𝜂(𝑡, 𝑇 ) = 𝜂 0 (𝑇 ) exp (𝐴(𝑇 )𝑡)

(3)

As shown in Fig. 5, the plot of ln(ln(𝜂(𝑇 )∕𝜂 0 (𝑇 ))) vs. ln(𝑡) exhibits straight lines which means that degradation kinetics can be modeled by an exponential of the product of two factors respectively depending on time and temperature. However, contrary to previous studies, the linear regression over the ln(𝑡) domain gives slope values different of unity. A power of time is therefore required to accurately model the time dependent behavior of PEEK viscosity. An exponent coefficient B was therefore added to Eq. ( 3) to obtain Eq. ( 4). This time exponent B reflects the sensitivity of the degradation to time and is therefore indirectly related to the kinetic constants of the chemical degradation reactions. However, the degradation mechanisms are governed by about ten reactions and it is therefore not possible to establish a direct relationship between the exponent and the kinetic constants.

𝜂(𝑡, 𝑇

) = 𝜂 0 (𝑇 ) exp ( 𝐴(𝑇 )𝑡 𝐵 ) (4)
Table 1 summarizes the 𝐵(𝑇 ) values for the different temperatures. As it can be seen, they are comprised between 1.81 and 2.22, with no apparent temperature dependency and it was decided in a first approximation to use the mean value of the slopes i.e. 2.00 for coefficient 𝐵 in Eq. (4). To improve the model definition for 𝐴, the 𝐴(𝑇 ) coefficients were recalculated for each temperature considering the mean value of 𝐵, i.e. 𝐵 = 2. This was achieved simply by re-identifying the intercept of the line of best fit with the 𝑦-axis in Fig. 5 specifying the exponent 𝐵 = 2. Fig. 6 shows the temperature dependency of recomputed coefficients 𝐴.

Here again, the variation of 𝐴 with temperature is consistent with an exponential function of the reciprocal of temperature. Considering the chemical crosslinking process that is responsible of this change, a chemical based Arrhenius law is thus proposed to model 𝐴(𝑇 ) according to Eq. ( 5). In the same way as for 𝐴(𝑇 ) and 𝐵 coefficients, the preexponential factor 𝐴 0 and the activation energy 𝐸 𝑐 𝑎 in Eq. ( 5) could be identified by means of a linear regression on the plot of 𝑙𝑜𝑔(𝐴) versus the reciprocal of temperature.

𝐴(𝑇 ) = 𝐴 0 exp ( -𝐸 𝑐 𝑎 𝑅𝑇 ) (5)
As shown in Fig. 6, the Arrhenius law accurately predicts the variation of 𝐴 with temperature. The identified values for the preexponential factor 𝐴 0 and the activation energy 𝐸 𝑐 𝑎 are respectively 1.18 × 10 14 and 267.6 kJ mol -1 . This value of activation energy is in agreement with the literature [START_REF] Khan | Identification of some optimal parameters to achieve higher laminate quality through tape placement process[END_REF].

The proposed model finally allows determining the variation of PEEK viscosity with time and temperature from a reference of initial viscosity 𝜂 0 (𝑇 0 ) with only 4 parameters (Eq. ( 6)): the activation energy of the relaxation process (𝐸 𝑎 ), the activation energy of the thermally activated degradation process (𝐸 𝑐 𝑎 ) and two constants 𝐴 0 and 𝐵. As it can be noticed in Fig. 2, the predicted values of viscosity are in good agreement with the experimental degradation kinetics: the model accurately predicts the initial viscosity as well as the increase in viscosity over time.

𝜂(𝑡, 𝑇

) = 𝜂 0 (𝑇 0 ) exp ( 𝐸 𝑎 𝑅 ( 1 𝑇 - 1 𝑇 0 )) exp ( 𝐴 0 exp ( -𝐸 𝑐 𝑎 𝑅𝑇 ) 𝑡 𝐵 ) (6)

Viscosity of PEEK yarns from NCF

The same procedure was applied for the identification of the model parameters for PEEK yarns in order to predict their viscosity during the consolidation of the semi-finished product. The comparison of the experimental viscosity data with the model is displayed in Fig. 3. Although the model does not agree as well with the experimental data as in the case of raw PEEK, a good correlation is observed up to 40 min of isotherm for PEEK yarns. Since the consolidation of NCF semi-finished products has been studied experimentally up to 30 min of isothermal plateau, the model prediction, nevertheless, remains accurate in a processing window from 0 to 40 min.

All identified model parameters, i.e. 𝐸 𝑎 , 𝐸 𝑐 𝑎 , 𝐴 0 and 𝐵, and reference data 𝜂 0 (𝑇 0 ) for PEEK yarns and raw PEEK are summarized in Table 2. The same reference temperature of 𝑇 0 = 380 • 𝐶 was chosen in the Arrhenius law of initial viscosity for both materials (Eq. ( 2)). The activation energy identified for the initial viscosity 𝐸 𝑎 is significantly higher in the case of PEEK yarns than for raw PEEK. This can be explained by the presence of sizing on the surface of the extruded yarns which has relatively low thermal stability [START_REF] Almeida | Influence of composite preform fabrication on the integrity of poly-aryl-ether-ketone matrices[END_REF]. At low temperatures, the yarn sizing provides a lubricating effect that lowers the initial viscosity, but this effect vanishes at higher temperatures due to sizing degradation. The other parameters that are involved in the description of the degradation kinetics (Eqs. ( 4) and ( 5)) are also significantly different between the two PEEK references. The identification of the exponent B for the PEEK yarns led to a value of B=1. The model formulation used for PEEK yarns is therefore similar to the model previously proposed in literature [START_REF] Phillips | Thermal stability of PEEK/carbon fiber in air and its influence on consolidation[END_REF][START_REF] Malkin | Rheokinetics of curing[END_REF]. Nevertheless, the activation energy 𝐸 𝑐 𝑎 related to crosslinking kinetics is lower for the PEEK filaments than for raw PEEK, which indicates that less energy is required to degrade PEEK yarns than the raw PEEK. This is consistent with the experimental rheology measurements showing that the temperature has a stronger effect on the viscosity increase for PEEK yarns than for raw PEEK. Here again, this can be attributed to the presence of the sizing solution on the surface of the extruded PEEK yarns. The high temperature sensitivity of the sizing accelerates degradation kinetics as the temperature increases.

Impregnation model accounting for PEEK degradation

In order to predict the advancement of commingled preform consolidation, the viscosity model taking degradation into account was implemented in the impregnation model proposed by Bernet et al. [START_REF] Bernet | An impregnation model for the consolidation of thermoplastic composites made from commingled yarns[END_REF].

In this way, it was possible to predict the final porosity content of the composite plates manufactured with the studied commingled preform.

Bernet's impregnation model for commingled yarns

The impregnation model developed by Bernet et al. [START_REF] Bernet | An impregnation model for the consolidation of thermoplastic composites made from commingled yarns[END_REF] is a twodimensional model specifically proposed for modeling the consolidation of commingled preforms. This section summarizes the main assumptions and equations of this approach. For further information on this model, the reader is invited to refer to the corresponding article detailing the approach developed by these authors.

The main assumption of Bernet's model is that all commingled yarns in a preform are geometrically equivalent and undergo impregnation simultaneously. The model is therefore based on a description of a commingled preform by means of a representative unit element, which is the commingled yarn. Once the matrix is melted, the commingled yarn is assumed to be constituted of dry fibers surrounded by the matrix bed under pressure. In order to account for the size distribution of the dry fiber bundles, different populations of fiber bundles are considered in the description of the commingled preform.

The initial state of a dry fiber bundles from a population 𝑖 is defined by its radius 𝑟 𝑖 0 that is defined with Eq. ( 7) in which 𝑅 𝑓 corresponds to the radius of an elementary fiber (𝑅 𝑓 = 3.5 μm is considered in this study for carbon fibers), 𝜈 𝑓 is the fiber volume fraction in dry fiber bundles and 𝑁 𝑖 𝑓 is the number of fibers in the fiber bundle.

𝑟 𝑖 0 = √ √ √ √ 𝑁 𝑖 𝑓 𝑅 2 𝑓 𝜈 𝑓 ( 7
)
The molten matrix is considered as a fluid of constant viscosity and impregnation is described using Darcy's Law (Eq. ( 8)), where 𝑢 𝑙 and 𝑢 𝑠 are respectively the local velocities of matrix and fibers, 𝐾 𝑃 is the permeability tensor within fiber bundles which depends on 𝜈 𝑓 , 𝜂 the viscosity and 𝑃 the local pressure.

(1 -𝜈 𝑓 )(𝑢 𝑙 -𝑢 𝑠 ) = -𝐾 𝑃 𝜂 ∇𝑃 (8)
Only a flow orthogonal to the fibers is considered and the fiber bed is assumed compressed to a constant value of 𝜈 𝑓 . Thus, 𝑢 𝑠 = 0 and 𝐾 𝑃 is constant. By resolving the simplified Darcy's law (Eq. ( 9)) and assuming mass conservation, Eq. ( 10) is obtained.

(1 -𝜈 𝑓 )𝑢 𝑙 = (1 -𝜈 𝑓 ) 𝑑𝑟 𝑖 𝑑𝑡 = -𝐾 𝑃 𝜂 𝜕𝑃 𝜕𝑟 ( 9
)
𝑑𝑟 𝑖 𝑑𝑡 = 𝐾 𝑃 𝜂(1 -𝜈 𝑓 )𝑟 𝑖 ln ( 𝑟 𝑖 𝑟 𝑖 0 ) (𝑃 𝑐 + 𝑃 𝑎 -𝑃 𝑔 ) (10)
In Eqs. ( 9) and ( 10), 𝑟 𝑖 (𝑡) is the front flow at time 𝑡, 𝑃 𝑐 is the capillary pressure which is here neglected, 𝑃 𝑎 is the applied pressure during the consolidation and 𝑃 𝑔 is the gas pressure at the front flow. When, 𝑟 𝑖 ≥ 𝑟 𝑐 , 𝑃 𝑔 is equal to atmospheric pressure and for 𝑟 𝑖 < 𝑟 𝑐 the gas law applies and yields

𝑃 𝑔 = 𝑃 𝑎𝑡𝑚 ( 𝑟 𝑐 𝑟 𝑖 ) 2
, where 𝑟 𝑐 is the unimpregnated bundle radius below which the pore is closed. In the present study, the same value that was proposed by Bernet et al. for this critical radius 𝑟 𝑐 was used, i.e. 35 μm.

Application to commingled NCF consolidation

As described in a previous paper [START_REF] Feuillerat | Effect of poly(ether ether ketone) degradation on commingled fabrics consolidation[END_REF], the semi-finished product is composed of yarns that are more juxtaposed than actually commingled. The commingled structure of the preform is thus assumed to be composed of populations of yarns of different sizes. Two populations were considered (Table 3): a population of 3k carbon yarns referring to isolated carbon yarns surrounded by PEEK filaments and a population of two 3k yarns, i.e. composed of 6000 carbon filaments, that corresponds to a situation of two juxtaposed carbon yarns in the preform. Then, since the proportion of one population to the other was difficult to assess in a stack of NCF preforms, it was supposed that the probability of the two situations was equivalent. A bundles fraction 𝜉 𝑏 of 50% for each population was thus taken into account for the simulation of the consolidation of the commingled NCF preforms.

The fiber volume fraction in dry fiber bundles 𝜈 𝑓 is a parameter that depends on the pressure applied to the fibrous preform. It is usually determined by means of compression tests. In the present case, the commingled preform does not allow the determination of this parameter in a simple way. As proposed by Bernet et al. [START_REF] Bernet | An impregnation model for the consolidation of thermoplastic composites made from commingled yarns[END_REF], the 𝜈 𝑓 values were thus adjusted according to the pressure applied to the preform during consolidation considering low temperature and short processing conditions for which degradation could be considered negligible. For pressures below 15 bar, 𝜈 𝑓 was set to 0.762, between 15 and 20 bar 𝜈 𝑓 was 0.767, between 20 and 25 bar 𝜈 𝑓 was 0.768 and above 45 bar 𝜈 𝑓 was 0.769. These values are in good agreement with the values proposed by Bernet et al. and logically reflect the increase in fiber content with the pressure.

The viscosity 𝜂 was calculated through the previously proposed model, which takes into account the degradation phenomenon. In order to assess the PEEK behavior during the total consolidation process, the model was used to simulate the change in viscosity during thermal cycles representative of the compression molding process. As the viscosity model is explicit, the differential form of Eq. ( 6) was used to calculate the change in viscosity during isothermal as well as for non-isothermal time increments 𝛥𝑡. The viscosity was simulated with Eq. ( 11), where Ṫ is the heating or cooling rate during the time increment 𝛥𝑡. The viscosity parameters identified for the PEEK yarns that are summarized in Table 3 were used for the simulation of the commingled NCF preform consolidation.

𝜂(𝑡, 𝑇 (𝑡)) =𝜂(𝑡 -𝛥𝑡, 𝑇 (𝑡 -𝛥𝑡)) + 𝑑𝜂(𝑡, 𝑇 (𝑡))

𝑑𝑡 𝛥𝑡

=𝜂(𝑡 -𝛥𝑡, 𝑇 (𝑡 -𝛥𝑡))

+ 𝛥𝑡

[ 𝜂 0 (𝑇 0 ) exp ( 𝐸 𝑎 𝑅 ( 1 𝑇 - 1 𝑇 0 )) exp ( 𝐴 0 exp ( -𝐸 𝑐 𝑎 𝑅𝑇 ) 𝑡 𝐵 ) … ( -𝐸 𝑎 𝑅𝑇 2 Ṫ + 𝐴 0 𝐸 𝑐 𝑎 𝑅𝑇 2 | Ṫ | exp ( -𝐸 𝑐 𝑎 𝑅𝑇 ) 𝑡 𝐵 + 𝐴 0 exp ( -𝐸 𝑐 𝑎 𝑅𝑇 ) 𝐵𝑡 𝐵-1
)]

(11)

Assessment of void content

From the calculated radius 𝑟 𝑖 (𝑡) of a bundle of each population, is was possible to compute the macroscopic void ratio 𝜙 from the crosssectional areas of the fiber bundles in m 2 according to Eq. ( 12), where 𝐴 𝑣 , 𝐴 𝑓 and 𝐴 𝑚 are the areas associated with voids, fibers and matrix respectively in the 2D representation of the commingled material, defined by Eqs. ( 13), ( 14) and ( 15) respectively.

𝜙 =

𝐴 𝑣 𝐴 𝑣 + 𝐴 𝑓 + 𝐴 𝑚 [START_REF] Ye | Consolidation of unidirectional CF/PEEK composites from commingled yarn prepreg[END_REF])

𝐴 𝑣 = (1 -𝜈 𝑓 ) 𝑛 ∑ 𝑖=1 𝜉 𝑏 𝑖 𝜋(𝑟 𝑖 ) 2 (13
)

𝐴 𝑓 = 𝜋𝑅 2 𝑓 𝑛 ∑ 𝑖=1 𝜉 𝑏 𝑖 𝑁 𝑓 𝑖 ( 14
)
𝐴 𝑚 = (1 -𝑋 𝑓 )
𝑋 𝑓 𝐴 𝑓 [START_REF] Jespersen | Film stacking impregnation model for a novel net shape thermoplastic composite preforming process[END_REF] In Eqs. ( 13) and ( 14), 𝜉 𝑏 𝑖 corresponds to the bundle fraction of the population 𝑖, 𝑋 𝑓 is the fiber volume fraction determined from the areal weights and densities of fiber and matrix in the NCF preform and 𝑁 𝑓 𝑖 is the number of carbon fibers in a commingled bundle of the population 𝑖 (Table 3).

Simulated viscosity and porosity features

Fig. 7 shows the iso-viscosity contours for PEEK yarns calculated in the temperature range above the melting temperature using the viscosity model. For all viscosity levels, the iso-viscosity contours show a particular maximum time with a vertical asymptote that defines a change in the viscous behavior. Whatever the initial temperature, the change in viscosity due to thermo-oxidation can be counterbalanced by gradually increasing the temperature up to this particular point. However, beyond this maximum time, the advancement of degradation no longer allows the same level of viscosity to be maintained. The viscosity of the polymer is no longer recoverable and necessarily increases with time. The curve connecting the maximum value of time of each viscosity level therefore represents a natural limit to PEEK flowability that is independent of the preform characteristics and processing conditions.

By plotting the iso-porosity curves from the impregnation model for a pressure of 25 (Fig. 8), the boundary of irrecoverable PEEK degradation domain transforms into a processability limit. Like the isoviscosity curves, the iso-porosities show vertical asymptotes and the curve connecting the corresponding times represents a dramatic change in the impregnation behavior.

For short times and/or low temperatures, the effect of degradation is moderate and the porosity level decreases progressively over time. In this range of processing conditions, the iso-porosities appear as reciprocal time curves similar to those described in the literature [START_REF] Phillips | Thermal stability of PEEK/carbon fiber in air and its influence on consolidation[END_REF][START_REF] Ye | Consolidation of unidirectional CF/PEEK composites from commingled yarn prepreg[END_REF] as this is 𝜂 0 that controls impregnation. The iso-porosity curves calculated when ignoring the degradation parameters (with Eq. ( 2)) are indeed almost perfectly superimposed at low temperature with the model taking into account degradation (Eq. ( 6)).

However, the two models diverge progressively as the processability limit defined from the vertical asymptotes is approached, due to the intensification of degradation at high temperature. Indeed, this theoretical processing limit is beyond the limit of irrecoverable PEEK degradation (Fig. 7) and impregnation is already critically affected by the increase in viscosity of the matrix. Therefore, beyond this boundary, for a given temperature, the porosity ratio no longer decreases because of the limited flowability of the matrix.

Increasing the consolidation pressure from 25 bar to 50 bar does not broaden the processability window since the processability limit directly arises from the viscosity model. Simply, the levels of porosity that can be obtained before reaching the processability limit are lower due to the application of higher pressure. Under 50 bar, the model predicts a minimum of 9%vol of porosity which is far too high for expecting the material to satisfy aerospace requirements. For the same reason, considering a different degree of commingling by changing the size distribution of the fiber bundles has no effect on the position of the processability limit. According to the model, only a higher pressure would allow reducing further the final porosity ratio. Also, whatever the processing conditions, the lowest porosity ratio that can be obtained within 40 min corresponds to a processing temperature of 380 • C. According to the impregnation model accounting for degradation, this condition therefore represents an optimal setting for the consolidation of the NCF preform.

Model comparison with experimental consolidation data

Time evolution of viscosity and porosity

Thanks to the thermo-kinetic viscosity model and impregnation model, the change in viscosity and porosity evolution could be computed for each processing condition. The actual temperature and pressure recorded during consolidation by the pilot plant were used to be representative of the experimental conditions. Fig. 1 shows an example of a consolidation cycle with simulated viscosity and porosity. The viscosity and resulting impregnation level were computed during the entire cycle when PEEK is in the molten state, i.e. from 343 • C during the heating phase and until 310 • C during the cooling phase. These temperatures were chosen as they correspond to PEEK melting and crystallization temperatures. Nevertheless, the transition temperature has little impact on the simulation results since PEEK viscosity is too high in the transition range of temperature for allowing resin flow whatever the degradation kinetics.

During the heating phase, the viscosity first decreases because the degradation kinetics are slower than the effect of temperature on the initial viscosity 𝜂 0 (𝑇 ). The viscosity then increases throughout the isothermal plateau due to degradation, and this increase intensifies during cooling because the thermo-dependent and degradation effects on the viscosity are cumulative. The consequences on the porosity ratio also depend on the pressure and no porosity evolution thus occurs during the heating phase. Capillary effects could have slightly modified the porosity level during the heating phase, but their contribution is estimated to be of the order of a few kPa [START_REF] Michaud | Infiltration processing of fibre reinforced composites: Governing phenomena[END_REF] and have therefore been neglected in this study. With the application of the consolidation pressure, the porosity rate decreases rapidly until it gradually stabilizes to the final value. The slowdown in impregnation results from the increase in viscosity due to degradation in combination with the effect of temperature during cooling.

Figs. 9-11 compare the experimental porosity ratios with the final void content given by the simulations after the cooling phase. The value of 𝑡 𝑙𝑎𝑚 used in Eq. ( 1) for the determination of the experimental void content is the average of 13 thickness measurements taken at locations on the plates that are representative of their thickness. The error bars displayed for the experimental data represent the variability in porosity content resulting from variation in thickness measurements on compression molded laminates.

Different configurations of the viscosity model were considered for the comparison: based on the viscosity of raw PEEK or on that of PEEK yarns, and with or without taking degradation into account. This last condition then corresponds to classical modeling approaches proposed in literature [START_REF] Phillips | Thermal stability of PEEK/carbon fiber in air and its influence on consolidation[END_REF][START_REF] Ye | Consolidation of unidirectional CF/PEEK composites from commingled yarn prepreg[END_REF].

Influence of consolidation time

Fig. 9 shows the void content as a function of the isothermal stage duration for a processing temperature of 400 • C and a pressure of 25 bar. Whatever the temperature, the preform consolidation systematically led to a high void content of about 15%. Contrary to what could be expected, increasing the consolidation duration did not result in a lower void content. This is the direct consequence of degradation and was already discussed in a previous article [START_REF] Feuillerat | Effect of poly(ether ether ketone) degradation on commingled fabrics consolidation[END_REF]. As the degradation level and crosslinking effect increase with time, the use of longer consolidation times does not improve impregnation and the porosity ratios remain stable. Nevertheless, it must be noticed that a benefit of consolidation time could be observed for a processing temperature of 430 • C under 50 bar (see Supplementary data).

The porosity ratios predicted with the impregnation model based on PEEK yarns viscosity are in good agreement with experimental results. The viscosity model therefore well describe the effect of consolidation time on degradation and impregnation. For this temperature, the simulations based on NCF matrix show lower porosity ratios than those based on raw PEEK up to 20 min. This is due to the lubricating effect of yarns sizing that lowers PEEK initial viscosity and benefits to impregnation [START_REF] Feuillerat | Effect of poly(ether ether ketone) degradation on commingled fabrics consolidation[END_REF]. The consideration of degradation particularly affects PEEK yarns behavior that exhibit fast degradation kinetics at this temperature. Increasing the isotherm time from 5 to 30 min only reduces the void content from 17% down to 14.5%, while it is decreased to 7% when degradation is dismissed. For raw PEEK, taking degradation into account has little effect on the porosity ratio: crosslinking kinetics is moderate at this temperature.

Influence of temperature

The consequence of PEEK degradation appears even more clearly in Fig. 10 that shows the results for a 10 min isotherm under 25 bar and for a 20 min isotherm under 50 bar. When plotting porosity ratios as a function of the processing temperature, the impregnation model predicts that an increase in the processing temperature results in a higher porosity ratio because of the higher degradation kinetics. According to the simulated data, the influence of degradation becomes predominant beyond 410 • C which indicates that degradation can be detrimental to consolidation at high temperature.

The influence of temperature on experimental porosity data however does not follow the prediction. Instead, for a consolidation pressure of 25 bar, the porosity level remains constant whatever the processing temperature up to 420 • C and decreases when using higher temperatures. This non-linear effect of temperature does not fit Darcy's description of impregnation, whether or not degradation is considered by viscosity. Other phenomena may therefore be activated beyond a temperature level, with a potential interaction with degradation mechanisms.

This non linearity of the porosity level with temperature vanishes under a consolidation pressure of 50 bar. Under high pressure, the porosity level decreases with temperature over the whole range of temperature. Again, neither viscous model conditions fit with experimental data, but contrary to 25 bar, the evolution of porosity follows the trend given by the impregnation model based on the initial viscosity 𝜂 0 although experimental porosity ratios are higher than the ones obtained from the simulation.

Influence of pressure

The influence of pressure on porosity is finally presented in Fig. 11. It appears that for low consolidation pressures, the impregnation model accounting for degradation well predicts the porosity content. However, as it was suggested by the difference in consolidation behavior between Figs. 10(a) and 10(b), it can be seen that the higher the pressure, the less degradation affects impregnation. Degradation thus seems to have moderate effect on consolidation when using high pressures as if it is hindered when consolidation is rapid.

Discussion

Due to their high transition temperatures, high performance polymers such as PEEK undergo irreversible chemical changes at high temperature that alter their behavior. Because of its glass transition of 143 • C, these chemical reactions are activated in the rubbery state [START_REF] Courvoisier | Multi-scale and multi-technique analysis of the thermal degradation of poly(ether ether ketone)[END_REF], but their effect is rapidly noticeable when increasing the temperature above PEEK melting temperature in an oxidative environment. The chemical reactions responsible for the degradation of PEEK result in an increase in molar mass due to crosslinking of PEEK macromolecules [START_REF] Jonas | Thermal stability and crystallization of poly(aryl ether ether ketone)[END_REF][START_REF] Day | Thermal degradation of poly(aryl-etherether-ketone) : Experimental evaluation of crosslinking reactions[END_REF][START_REF] Day | Thermal degradation of poly( aryl-ether-ether-ketone) (PEEK): A differential scanning calorimetry study[END_REF][START_REF] Day | The thermal stability of poly(arylether ether-ketone) as assessed by thermogravimetry[END_REF][START_REF] Day | The thermal degradation of poly(aryl-ether-etherketone) (PEEK) as monitored by pyrolysis-GC/MS and TG/MS[END_REF][START_REF] Cole | Fourier Transform infrared spectroscopic study of thermal degradation in films of poly(etheretherketone)[END_REF] and therefore in a rapid increase in the melt viscosity.

The porosity levels determined after processing the commingled NCF CF/PEEK preforms confirm that the increase in viscosity due to degradation affects impregnation when processing high performance thermoplastic composite laminates. Increasing the duration of the isothermal stage or increasing the processing temperature from 380 to 410 • C has indeed almost no effect on consolidation. These results are in good agreement with the results of Phillips et al. who studied the effect of exposing PEEK films to high temperature on the consolidation of CF/PEEK composites [START_REF] Phillips | Thermal stability of PEEK/carbon fiber in air and its influence on consolidation[END_REF]. In this time-temperature domain, this effect of degradation on the porosity content is well described by the impregnation model taking degradation into account. This is the domain in which iso-porosity curves start diverging from the prediction based on the initial viscosity 𝜂 0 (𝑇 ). This domain corresponds to processing conditions beneath the processability limit defined on the iso-porosity diagrams.

The model however lacks in predicting the porosity ratios when using processing above 410 • C or using a pressure of 50 bar. The processing conditions influence the porosity of laminates according to the model based on 𝜂 0 (𝑇 ), as if degradation is no longer effective under severe processing conditions. The theoretical processability limit that is based on the impregnation model accounting for degradation is thus misnamed: the results of NCF preform consolidation indeed suggest that despite the risk of degrading PEEK matrix the use of very high processing temperatures and pressure may be beneficial for impregnation.

The modification of degradation kinetics also suggests that a kinetic factor is changed beyond a temperature and pressure threshold. Several factors can affect PEEK degradation kinetics, the additives being one of them. The difference in viscous behavior between raw PEEK and PEEK from NCF yarns was actually attributed to the presence of sizing [START_REF] Feuillerat | Effect of poly(ether ether ketone) degradation on commingled fabrics consolidation[END_REF][START_REF] Almeida | Influence of composite preform fabrication on the integrity of poly-aryl-ether-ketone matrices[END_REF]. However, it is unlikely that the change in impregnation kinetics is due to a rapid volatilization of the chemical additives at high temperature without inducing degradation. According to the degradation mechanisms, the main factor that can significantly modify crosslinking kinetics is the presence of oxygen. Many studies actually reported comparisons of degradation kinetics as a function of the atmosphere environment, and oxygen is definitively involved in the degradation mechanisms as a reactive species [START_REF] Courvoisier | Multi-scale and multi-technique analysis of the thermal degradation of poly(ether ether ketone)[END_REF][START_REF] Day | Thermal degradation of poly( aryl-ether-ether-ketone) (PEEK): A differential scanning calorimetry study[END_REF]. The most logical explanation for the discrepancy between experimental and simulation results is therefore that oxygen availability is different when consolidation is achieved at high temperature and high pressure.

Oxygen transport to the PEEK matrix results from two main mechanisms of different kinetics that are schematically described in Fig. 12: convection and diffusion. This transition has actually been demonstrated by Zhang et al. in their study of the out-of-autoclave consolidation of CF/PEEK pre-impregnated tapes [START_REF] Zhang | Design and optimization of oven vacuum bag (OVB) processing for void air removal in high-performance thermoplastic composites[END_REF]. At the beginning of consolidation, the porosities in the melted commingled preform form channels that allow oxygen convection throughout the composite material. Oxygen diffusion is then negligible as regards to the diameter of PEEK filaments or the size of the liquid bed formed by the melted yarns around carbon fiber bundles. But, as impregnation progresses, the open porosities within the composite preform gradually turn into closed porosities. Oxygen convection is no longer possible and the oxygen concentration in the matrix phase then mainly depends on oxygen diffusion through the composite length and/or thickness. Since diffusion is a much slower process than convection, the availability of oxygen to PEEK, i.e. the local concentration in the composite material, is rapidly reduced, which certainly slows down degradation kinetics. Therefore, according to this process, the moment the oxygen supply process within the composite material change from a convection-driven to a diffusion-driven process is crucial, because the earlier it occurs, the less degradation affects impregnation.

Regardless of degradation, the higher the processing temperature and the applied pressure, the faster the impregnation according to Darcy's law. Indeed, the low initial viscosity 𝜂 0 at high temperature above 420 • C as well as a high consolidation pressure (𝑃 𝑎 > 50 bar) induces a rapid reduction of the porosity ratio before degradation is too advanced. The temperature and pressure threshold in iso-porosity diagrams may thus represent a limit beyond which impregnation is fast enough for obtaining a composite microstructure of closed porosities before degradation has affected PEEK viscosity to a critical level.

In addition to the balance between diffusion and convection, the matrix degradation can influence oxygen diffusion. Indeed, by analyzing the property gradient that appears over time through the thickness of PEEK samples subjected to an oxidizing atmosphere at high temperature above 400 • C, Pascual et al. [START_REF] Pascual | On the stability of PEEK for short processing cycles at high temperatures and oxygen-containing atmosphere[END_REF] demonstrated that PEEK degradation kinetics are the result of the balance between oxygen diffusion and temperature-dependent reaction kinetics. They concluded that the different kinetics of both processes lead to the formation of a highly oxidized layer at the surface of samples exposed to temperatures higher than 400 • C. Using a high temperature or a high pressure can therefore be even more beneficial as the degradation of the composite surface can concentrate degradation and preserve the sample core.

However, if the impregnation behavior in CF/PEEK laminates depends on oxygen concentration and the balance between convection and diffusion processes within PEEK matrix, this means the viscosity measurements were also affected with the existence of a gradient of degradation kinetics throughout the radius of the rheology samples during the experiments. The periphery of the cylindrical samples was probably faster degraded than the sample core because of the air flow within the rheometer oven while the sample core was preserved from oxygen and thus from degradation. A thorough investigation of the viscous behavior of PEEK matrix is therefore required for a better representation of the actual behavior of PEEK filaments in a composite preform. To do so, a dimensionless viscous model would be useful in order to consider the actual behavior of a PEEK matrix whatever its shape factor in the composite preform.

Conclusions

In order to better describe the influence of degradation on CF/PEEK composite manufacturing, a viscosity model was developed based on rheological tests. This model well predicts the change in viscosity of raw PEEK and PEEK yarns from NCF matrix that is induced by the crosslinking mechanism. The double Arrhenius exponential law is only based on 4 parameters, two Arrhenius constants and two preexponential factors. The Arrhenius constants express the thermal dependence respectively of the non-degraded viscosity and the crosslinking formation kinetics.

The viscosity model allowed proposing an intrinsic processability criterion for PEEK. This processing limit is simply based on the impossibility after a certain time to counterbalance the viscosity change by increasing the temperature. It differs from the other processing limits available in literature in that it is independent of impregnation parameters.

By implementing the viscosity model into the impregnation model developed by Bernet et al. for commingled preforms, the model demonstrated its ability to describe degradation effects. The discrepancy of simulation results with experimental data at high temperature and pressure however indicates that the degradation process is not continuous over the entire consolidation process. The change of oxygen availability from the moment closed porosities are formed is the most probable assumption for explaining the lack of model prediction at high temperature and pressure.

Fig. 1 .

 1 Fig. 1. Processing cycle recorded during the compression molding of 4 plies of CF/PEEK commingled NCF at 400 • C during 10 min under a pressure of 25 bar. The viscosity and porosity are simulated data determined with a rheological model taking into account the degradation behavior of PEEK matrix (Eq. (6)).

Fig. 2 .

 2 Fig. 2. Comparison of experimental raw PEEK viscosity with the rheological model taking into account the degradation behavior (Eq. (6)).

Fig. 3 .

 3 Fig. 3. Comparison of experimental PEEK yarns viscosity (from NCF preform) with the rheological model taking into account the degradation behavior of PEEK yarns (Eq. (6)).

Fig. 4 .

 4 Fig. 4. Arrhenius plot of raw PEEK initial viscosity at 𝑡 = 0. The activation energy of initial viscosity 𝐸 𝑎 is obtained from the slope of the linear regression according to Eq. (2).

Fig. 5 .

 5 Fig. 5. Double logarithmic plot of normalized raw PEEK viscosity versus the logarithmic of time for different temperatures. The time exponent 𝐵 in Eq. (4) is given for each temperature by the slopes of the linear regression of experimental data.

Fig. 8 .

 8 Fig. 8. Iso-porosity contours computed with Bernet's impregnation model (Eqs. (10) and (12)) for a consolidation pressure of 25 bar using material parameters identified from viscosity measurements on PEEK yarns (Table2). Dashed gray lines represent the iso-porosity levels considering the temperature dependency of initial viscosity but without considering degradation kinetics (Eq. (2)); colored lines are obtained using the viscosity model accounting for degradation (Eq. (6)). The red line connecting the minimum time of each iso-porosity contour defines the processing window for impregnation.

Fig. 9 .

 9 Fig. 9. Comparison of the experimental void contents resulting from processing conditions of 400 • C and 25 bar (•) with the predictions obtained with the viscosity model when considering only the temperature dependence (Eq. (2) without degradation, ◊) and when taking into account degradation in addition (Eq. (6), ⧫). The blue symbols (◊) correspond to the simulation performed with the parameters identified for the pure matrix, the red symbols (◊) for the PEEK yarns from the preform. Dotted lines are shown to indicate trends.

Fig. 10 .

 10 Fig. 10. Comparison of the experimental void contents resulting from processing conditions of (a) 10 min and 25 bar and (b) 20 min and 50 bar (•) with the predictions obtained with the viscosity model when considering only the temperature dependence (Eq. (2) without degradation, ◊) and when taking into account degradation in addition (Eq. (6), ⧫). The blue symbols (◊) correspond to the simulation performed with the parameters identified for the pure matrix, the red symbols (◊) for the PEEK yarns from the preform. Dotted lines are shown to indicate trends.

Fig. 11 .

 11 Fig. 11. Comparison of the experimental void contents resulting from processing conditions of 400 • C and 10 min (•) with the predictions obtained with the viscosity model when considering only the temperature dependence (Eq. (2) without degradation, ◊) and when taking into account degradation in addition (Eq. (6), ⧫). The blue symbols (◊) correspond to the simulation performed with the parameters identified for the pure matrix, the red symbols (◊) for the PEEK yarns from the preform. Dotted lines are shown to indicate trends.

Fig. 12 .

 12 Fig. 12. Schematic representation of oxygen transport within a composite preform during compression molding processing.

Table 3

 3 Characteristics and material properties used in the impregnation model (Eq. (10)) and for calculating the final void content with Eq. (12).

	Abbreviation	Parameter	Value
	Model parameters
	𝑅 𝑓	Radius of a single carbon fiber	3.5 μm
	𝑟 𝑐	Critical radius	35 μm
	Description of the commingled NCF preform
	𝑋 𝑓	Nominal fiber volume fraction	0.58
	𝑁 𝑓 1	Number of fibers for the first bundle size	3000
	𝜉 𝑏 1	Ratio of the first bundle size	0.5
	𝑁 𝑓 2	Number of fibers for the second bundle size	6000
	𝜉 𝑏 2

Acknowledgment

The authors wish to thank the Region Occitanie for their financial support.

Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Olivier De Almeida reports financial support was provided by Région Occitanie.

Appendix A. Supplementary data

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.compositesa.2022.106943.


Ram Karthik

Nicolas Ramakrishnan

Stéphane Le Moigne

Olivier Corn

De Almeida

Karthik-Ram Ramakrishnan
email: karthik-ram.ramakrishnan@mines-ales.fr

Nicolas Le Moigne

Stéphane Corn

Olivier De Almeida
email: olivier.dealmeida@mines-albi.fr

A study on the

Keywords: biocomposites, flax, compression moulding, vibration, damping, tensile

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Natural fibres have been studied as potential replacement to traditional composite reinforcements due to their low density, high specific properties, relative abundance, low cost of raw material, and positive environmental profile [START_REF] Shah | Can flax replace E-glass in structural composites? A small wind turbine blade case study[END_REF]. Bast fibres such as flax, hemp, kenaf, jute and ramie exhibit superior flexural strength and elastic modulus and are used in applications with structural requirements as they have high cellulose content and low microfibrillar angle [START_REF] Pickering | A review of recent developments in natural fibre composites and their mechanical performance[END_REF]. The specific longitudinal stiffness of flax in tension is higher than that of glass fibres due to the lower density of flax [START_REF] Pil | Why are designers fascinated by flax and hemp fibre composites?[END_REF] and in the case of plate bending, the specific flexural stiffness of flax composites outperforms steel and aluminium. However, the material properties that can be achieved with the plant fibre composites depends on several factors including the type of the plant fibre, the length of fibres, the resin system used, the composite manufacturing process, and the fabric architecture. Natural fibre thermoplastic composites with short flax fibres and polypropylene manufactured using extrusion had an elastic modulus of 1.5-3.8 GPa and maximum strength of 20-33 MPa [START_REF] Awa S Doumbia | Flax/polypropylene composites for lightened structures: multiscale analysis of process and fibre parameters[END_REF]. However, it is evident that the structural potential of plant fibres as reinforcing agents can only be realized when the highest reinforcement efficiency is employed and this is typically achieved with twistless long continuous fibres. There is limited literature on the mechanical characterisation of plant fibre based thermoplastic composites reinforced with woven long continuous fibres are used.

Natural fibres used as reinforcement in composites are exposed to high temperatures during processing. Liang et al. [START_REF] Liang | Thermo-compression forming of flax fibrereinforced polyamide 6 composites: influence of the fibre thermal degradation on mechanical properties[END_REF] noted that the manufacturing conditions of plant fibre-based composites are limited by the thermal degradation of fibres at high temperatures. This is due to the presence of thermally sensitive constituents such as cellulose, hemicelluloses and lignin and the high melting point of thermoplastics. The thermal degradation of flax fibres is dependent on both the temperature of exposure and the duration. Gourier et al. [START_REF] Gourier | Mechanical analysis of elementary flax fibre tensile properties after different thermal cycles[END_REF] studied the effect of thermal cycles on the mechanical behaviour of elementary fibres of flax and found that modification of the fibre structure and of the interactions between components occurred at high temperatures such as 250° C. In order to minimise the damage of the fibre, Van de Velde and Baetans [START_REF] Van De Velde | Thermal and Mechanical Properties of Flax Fibres as Potential Composite Reinforcement[END_REF] recommended that composite production temperatures higher than 180° C have to be avoided, unless the duration is short. It was reported that 15 minutes of exposure of flax to 180° C results in lower residual tensile stress and strain than two hours exposure to 120° C. Nassiopoulos and Njuguna [START_REF] Nassiopoulos | Thermo-mechanical performance of poly(lactic acid)/flax fibre-reinforced biocomposites[END_REF] revealed that deformational behaviour of flax-PLA composite changes from brittle to more ductile-like characteristics with increasing temperature and concluded that the material properties exhibited a strong dependence on temperature. Bourmaud et al. [START_REF] Bourmaud | Influence of processing temperature on mechanical performance of unidirectional polyamide 11-flax fibre composites[END_REF] studied the effect of the processing temperature on mechanical performance of unidirectional flax fibre composites in polyamide 11 matrix and found that a thermal cycle of 8 minutes at 210° C reduced both the stiffness and strength of the composite. John and Anandjiwala [START_REF] Jacob | Anandjiwala, Chemical modification of flax reinforced polypropylene composites[END_REF] also noted the low thermal stability of natural fibres and recommended the use of polypropylene as matrix as it has a relatively low processing temperature. Van de Velde and Kiekens [START_REF] Van De Velde | Effect of Flax/PP Panel Process Parameters on Resulting Composite Properties[END_REF] studied the effect of processing parameters, temperature and time, on the mechanical properties of non-woven flax/PP composites and recommended that temperature of 200° C was sufficient to obtain good mechanical properties. In this paper, the effect of processing conditions on the mechanical properties of woven commingled fabric of flax fibre and polypropylene is studied to improve the understanding of the process-structure-property relationship of these composites.

One advantage of natural fibre composites compared to synthetic fibre composites is their damping properties. Duc et al. [START_REF] Duc | Damping of thermoset and thermoplastic flax fibre composites[END_REF] reported that the damping of flax fibre reinforced composites was higher than that of carbon and glass fibre reinforced composites, with unidirectional flax fibre epoxy composite exhibiting a 100% increase in loss factor compared to glass fibre reinforced epoxy. Typically, damping and stiffness are inversely related with low damping value indicating high elasticity and high damping suggesting a material with high, non-elastic strain component. Similarly, an improvement in the fibre/matrix interface results in the reduction of damping factor, since mobility of the molecular chains at the fibre/matrix interface decreases. El Hafidi et al. [START_REF] El-Hafidi | Determination of dynamic properties of flax fibres reinforced laminate using vibration measurements[END_REF] noted that damping is induced by several microscopic mechanisms, such as viscoelastic elongation of the matrix and/or fibres, and local friction at the interface between both components. For the natural fibre composites such as flax fibre reinforced polymer composites, the friction between elementary fibres inside bundles represents an additional mechanism of energy dissipation, which also contributes to the overall damping. The entanglement of the fibres, void in the lumen, heterogeneity of the cell walls and reversible hydrogen bonding between the different components of the cell walls are also considered important contribution to the intrinsically good damping properties observed in plant fibres [START_REF] Joo | The damping -modulus relationship in flax-carbon fibre hybrid composites[END_REF].

There are many different definitions and ways of measuring damping such as the loss factor, the quality factor, the specific damping capacity, the logarithmic decrement or the damping ratio. There is limited literature on the damping properties of flax-PP composites, especially on the effect of processing conditions on the vibration response of composites. Duc et al. [START_REF] Duc | Damping of thermoset and thermoplastic flax fibre composites[END_REF] used DMA device in the single cantilever mode to characterise the damping behaviour of the composites under flexural loading. Le Guen et al. [START_REF] Joo | The damping -modulus relationship in flax-carbon fibre hybrid composites[END_REF] quantified the damping coefficient of flax fibre-reinforced composites and flax-carbon hybrid composites and used rule of hybrid mixtures to study the impact of reinforcement hybridisation on the damping coefficient, and tensile and flexural elastic modulus and strength of hybrid composite. Le Guen et al. [START_REF] Le Guen | Tailoring the vibration damping behaviour of flax fibre-reinforced epoxy composite laminates via polyol additions[END_REF] also used vibration in longitudinal and flexural modes and found that improved damping performance due to polyglycerol additives. This was explained by the formation with polyglycerol of hydrogen bonded bridges between concentric layers of cell walls, causing friction between the two layers through stick-slip molecular motion. Monti et al. [START_REF] Monti | Experimental and finite elements analysis of the vibration behaviour of a bio-based composite sandwich beam[END_REF] studied the flexural vibration response of bio-based sandwich and laminates beams using free vibration tests and analysed the damping property of different configurations of unidirectional and cross-ply composites as well as sandwich structures with different core thicknesses. In this paper, the flax thermoplastic composite is manufactured with different processing parameters of temperature, pressure and duration. The different composites are then tested in uniaxial tension to measure the elastic and ultimate properties. Free vibration tests are conducted on cantilever beams of selected composites and the damping properties are compared statistically to investigate the effect of processing conditions.

MATERIALS AND METHODS

Manufacturing of composite samples

The woven commingled fabrics of Flax/PP were supplied by Composites Evolution as Biotex Flax/PP with surface density of 400g/m 2 and made from twistless natural flax fibre and polypropylene (PP) fibre in a balanced 2x2 Twill architecture. The relatively low melting point of polypropylene makes it a more suitable matrix for flax fibres as thermal characterisation analysis by TGA show that the fibres begin to degrade at temperatures higher than 200 °C. The flax fibre volume fraction of the fabrics was 40%, with an estimated thickness of 0.3-0.35 mm per ply. The composites were fabricated using a compression moulding method in which the fabrics are moulded into rigid fibre-reinforced thermoplastic composite parts by applying heat and pressure to melt the thermoplastic, wet-out the flax and consolidate. Eight plies of the flax/polypropylene commingled fabric were cut to 280 mm x 280 mm and placed between the two rigid steel plates in a hydraulic press. The fabrics were pre-dried before composite production to remove the excess moisture. A schematic diagram showing the upper and lower plate of the mould and the woven fabric and the thermopress system (induction press system EdyCo platform, Mines Albi) used for the fabrication of the plates is shown in Figure 1. The mechanical properties of the thermoplastic composite are highly dependent on the processing conditions. Therefore several processing parameters were considered for this study. All samples were prepared in the thermopress following a specific cycle comprised of three phases: an initial heating period, an isotherm (or constant temperature phase) and the final cooling down phase. The composite plates were manufactured using different experimental parameters for temperature, pressure and consolidation time.

The conditions were chosen based on thermal analysis of the flax-PP fibres. The peak melting temperature of the polypropylene was found to be approximately 168 °C. The chosen temperature should be sufficiently high as to completely melt the PP matrix. At higher temperatures, the viscosity of the resin is low allowing the flow of the matrix and perhaps better diffusion. However, at high temperatures, there is degradation of the flax fibre. 18 composite plates were manufactured and the parameters used are summarised below in Fig 2 . The nomenclature for the samples follows the rule xC_ym_zb, which corresponds to the temperature in °C degrees, consolidation time in minutes and pressure in bars, respectively. The temperature of the press, the pressure applied, generator power applied for the heating and the platen position were recorded for each condition. A typical processing cycle for the manufacturing of flax/PP composite is shown in Figure 3. It can be seen that the isotherm corresponding to this cycle is at 200 °C. Maximum power is applied to the press for the heating cycle and power is shut off before the press reaches the assigned temperature as there is a delay. The temperature is allowed to stabilise for 2 minutes before the pressure (20 bars in this case) is applied and the clock is started to measure the duration of the consolidation phase. At the end of the consolidation phase (10 minutes in this case), the cooling system is turned on and the temperature is allowed to decrease rapidly until 140 °C. The cooling rate is reduced at this temperature to aid the crystallisation of the polymer. The pressure is maintained during the entire cooling cycle and it can be seen from the platen position that there is thickness reduction during the consolidation.

Figure 3. Typical processing cycle data from induction press

A typical SEM micrograph of the flax fibre reinforced PP matrix composite manufactured using the induction press is shown in Figure 4. The composite specimen in the figure corresponds to plate manufactured at 190°C and consolidation time of 10 minutes. During the compression moulding, the PP fibres in the commingled yarn melts and diffuses within the flax yarns and bundles before the freezing of the matrix during the cooling phase. It can be seen in the left that the composite consists of both longitudinal and transversal fibres (warp and weft). Flax fibres are typically in the form of fibre bundles with individual elementary fibres visible in the Figure 4(b). We can also note the microstructure of the fibre with lumen and cell walls as well as some macro porosities in the composite.

Tensile testing of composite samples

A Zwick Z010 testing machine, shown in the Figure 5 was used to perform tensile tests based on the ISO 527-4 standard. These tests were all performed in room temperature in a controlled environment (ca. temperature of 25°C and 50% humidity) after having been conditioned for at least three hours in a humidity controlled oven (temperature of 30 C and 3.5% humidity). The width and thickness of each sample was measured before every test (ca. 18 mm-21 mm and 2.4 mm-2.8 mm, respectively) and the length between the fixing jaws was 110 mm (length of actual samples: 165 mm). Five samples were tested per condition and each test was conducted in two stages; a first stage at a crosshead speed of 1 mm/min using an extensometer to determine the tensile modulus (calculated by taking the slope of a linear trendline of the stress-strain curve between a displacement of 0.05% and 0.3%) and a second stage at a cross-head speed of 5 mm/min until rupture to determine the tensile strength. A typical stress strain curve showing the two loading phases is shown in Figure 5.

Vibration testing of composite samples

The damping measurements were achieved on cantilever beams of the flax/PP composite that were clamped in a bench at one end and excited by a short impulse. Initially, three processing conditions corresponding to the extreme cases were chosen for the vibration tests. The setup used for the vibration test and typical timeform signal is shown in Figure 6. The dimensions of the beam were 80 mm in length and 10 mm width. However, some part of the beam was clamped in the fixture so that 60 mm was the free length of the beam. The clamping torque of 2 Nm was kept constant by using a torque wrench. The vibration tests were performed at room temperature and humidity. A short impulse was applied at the free end of the beam, similar to the method used by Regazzi et al. [START_REF] Regazzi | Reversible and irreversible changes in physical and mechanical properties of biocomposites during hydrothermal aging[END_REF]. For each beam, the tests were repeated at least five times and the results were averaged. A SunX laser vibrometer sensor was used to measure the transient response of the beam and the time signal was converted to frequency response by FFT. The advantage of the laser sensor was that it is a non-contact measurement and there is no added mass on the composite beam (contrary to the use of an accelerometer). The eigen-frequency and the damping factor of the fundamental flexural mode of vibration were determined using a rational polynomial fit of the frequency response function in Modalview software.

Figure 6. Setup for vibration test and typical time signal measured by laser vibrometer

The time signal is converted to the frequency domain. A typical frequency response with the first flexural mode identified for a flax-PP beam is shown in Figure 7. It can be seen that the corresponding resonant frequency is approximately 350 Hz. The real part and the imaginary part of the complex frequency response function were plotted against each other to provide a Nyquist plot, which is nearly a complete circle as expected in the vicinity of a resonance peak.

RESULTS AND DISCUSSION

A box plot showing the modulus and strength for selected subset of processing cycles is shown in Figure 8. The fibre volume fraction of the composites varied from 39% to 41.1%. It can be seen from the variation of the modulus and strength that there is a positive effect of the fibre content on the mechanical properties. The increase in the modulus of the composite with higher fibre weight fraction is an indication of stiffening due to the fibres, while the increase in the strength of the composite is explained by the fact that the addition of flax fibres leads to uniform and effective stress transfer within the composite.

Figure 8. Boxplot of tensile modulus and strength for different processing cycles

Figure 9 shows the variation of both the tensile strength and modulus in Ashby style chart to study the effect of the processing conditions. It can be seen that the effect of the temperature on the initial modulus is negligible but there is significant effect on the tensile strength of the composite. The composites manufactured at 240°C have the lowest strength with almost 35% reduction in strength compared to composites manufactured at 200°C. According to Bourmaud et al. [START_REF] Nassiopoulos | Thermo-mechanical performance of poly(lactic acid)/flax fibre-reinforced biocomposites[END_REF], at higher temperatures there is a significant modification of the flax fibres such as its biochemical composition and macromolecular arrangement. These modifications affect the cellulose micro fibrils, and therefore lead to a decrease of Young's modulus and strength. Initially, two composite samples were selected for the vibration tests corresponding to the two extreme cases for the tensile tests. However, it can be seen that the initial modulus is almost identical for the two extreme cases. It was hypothesised that since the vibration response is measured at low strains, there may not be a strong effect of processing conditions on damping. Therefore, a third sample corresponding to the lowest modulus in the Ashby chart (200C_5m_20b) was also chosen.

The frequency-amplitude graph for each sample was analysed using Modalview software. The frequency range around the resonance peak was chosen according to the classical 3db method and an automatic polynomial fit was applied to extract the eigen frequency and damping factor. Table 1 shows the results of the damping factor (in %) measured for composites manufactured at 190C_10m_40b. Five samples were tested and multiple trials were conducted for each sample. It can be seen that the variation of the damping factor for the multiple trials on same sample is very low (standard deviation of 0.01 to 0.02). This confirms that the vibration measurement system that is proposed is highly repeatable. However, it can be seen that the variation between the samples of supposedly the same material is rather high, varying from 1.43 to 1.54 (standard deviation of 0.04). This can be explained by the fact that the damping factor is highly sensitive to local microstructure and presence of voids, any variation in the fibre volume fraction or in the intrinsic properties of the components will have a strong influence on the measured damping. It was also found that while the eigen frequency was very stable for the measurement, the damping factor was influenced by the impulse magnitude and by the selection of the frequency range for the calculation. It is also interesting to note that the dynamic modulus assessed from the eigen frequency by using the classical Euler-Bernoulli formula are well correlated to the modulus measured by the tensile tests. For example, the tensile modulus of 240C_5m_40b is 9.8 GPa and the dynamic modulus for the same sample is 9.6 GPa.

The mean damping factor, which is taken as the mean of the means of the different composite beams, was found to be 1.47, 1.50 and 1.39% for the 190C, 200C and 240C samples respectively. Figure 11 plots the damping factor measured from the vibration tests and the Young's modulus measured from the tensile tests for the three samples. It can be seen from the error bars that there is a large scatter in the properties of the composite. A statistical comparison of the composites is necessary to identify the degree of correlation A Wilcoxon signed-rank test was performed for the comparison of the three composite samples. The Wilcoxon method is a nonparametric test that can be used to determine whether two dependent samples were selected from populations having the same distribution. This test is recommended as an alternative to the paired Student's t-test for small sample sizes and when the population cannot be assumed to be normally distributed. A p-value of less than 0.01 is considered highly statistically significant while a p-value higher than 0.05 is considered not statistically significant, meaning that there is no effect of the processing conditions.

For the comparison of the 190C and 240°C samples, it was found that the p-value was 2.85E-05 which clearly shows that there is an effect of the processing temperature. However, the comparison of the 190C and 200C samples did not have the same result, with a p-value of 0.0734. Contrary to the initial hypothesis that composites with similar modulus will have similar damping factors, these results show that there was an effect of the higher processing temperatures on the damping factor. We can see that the damping factor is reduced for the samples manufactured at 240 ºC. Therefore the thermal degradation of the fibre and the change in the microstructure such as fibre-matrix interface and the Table 1. Damping factor in (%) for 190C_10m_40b composite fibre volume fraction will impact the vibration response of the composite. In the future study, the damping parameters of the composites manufactured at all the different conditions are correlated to the elastic properties.

CONCLUSIONS

In this study, thermoplastic composites from flax/PP commingled fabrics were manufactured using thermocompression. The influence of the processing conditions on the elastic and ultimate properties from uniaxial tensile test was studied. Additionally, the vibration damping properties were measured using free vibration analysis of cantilever beams with laser vibrometer. It was found that the temperature, pressure and duration of the compression moulding cycle has a strong effect on the modulus and strength of the composite. The strength of the composite was particularly affected by high temperatures which resulted in fibre degradation. The damping properties of the composite from the vibration test also show that it is sensitive to the microstructural parameters such as porosities and fibre volume fraction. In the future study, the damping parameters of the composites manufactured at all the different conditions are correlated to the elastic properties.

Figure 1 .

 1 Figure 1. Schematic diagram of thermocompression process and the induction press used for manufacturing flax/PP composites

Figure 2 .

 2 Figure 2. Summary of experimental conditions used in press for fabrication of flax/PP composite

Figure 4 .

 4 Figure 4. SEM image of fracture surface for composite manufactured at 240°C

Figure 5 .

 5 Figure 5. Tensile testing setup and typical stress -strain curve of flax/PP composite

Figure 7 .

 7 Figure 7. Typical frequency domain signal with first bending mode and Nyquist plot

Figure 9 .

 9 Figure 9. Ashby chart of modulus and strength for flax/PP composite

Figure 10 .

 10 Figure 10. Comparison of extreme cases (190 C and 240 C composite)

Figure 11 .

 11 Figure 11. Damping factor vs. Modulus for the three composite samples (190C, 200C and 240C)

ACKNOWLEDGMENTS

This project was funded by the European Union's Horizon 2020 Programme (HERMES project, grant agreement n° 636520).