Juan Daniel

Pujols Gonzalez

Benoit Vieille
email: benoit.vieille@insa-rouen.fr

Christophe Bouvet

High temperature translaminar fracture of woven-ply thermoplastic laminates in tension and in compression

Keywords:

A C T

The translaminar fracture behavior of three composite laminates, based on thermoplastic matrix PEEK reinforced by a woven carbon fibers obtained by consolidation process, has been studied by means of Compact Tension (CT) and Compact Compression (CC) tests. An orthotropic laminate and two quasi-isotropic laminates, have been tested at room temperature (RT) and at 150 • C (i.e. for a temperature slightly higher than the glass transition temperature T g ), with the purpose of evaluation the influence of the stacking sequence and the temperature on the damage mechanisms. The CT type tests show that the temperature influence on the overall mechanical response remains low. In contrast, the CC type tests show a decrease in the mechanical resistance and an augmentation in the global ductile behavior. By means of the 2D Digital Image Correlation and the implementation of a algorithm based on the sigma indicator (confidence interval in the area of interest), the crack propagation was measured during loading, then the G-R curves have been obtained from the compliance method. In tension, there is an increase in the translaminar fracture toughness with the laminate thickness and a slight improvement in this one due to the influence of temperature. In compression, the temperature strongly decreases the translaminar fracture toughness.

Introduction

The widespread use of organic matrix composites in many industrial sectors has been confronted with the need to understand and quantify the fracture mechanisms within materials whose behaviour is highly heterogeneous and anisotropic. In addition, they can be subjected to different mechanical loads, but also to different environmental conditions (temperature, humidity, etc.) when it comes to aeronautical applications. Among the main damage modes observed in composite laminates, the breaking of fibers in tension or compression is less studied, compared to delamination. These different damage mechanisms result in the development of a "Fracture Process Zone" (FPZ) in regions where the material is damaged by high stress concentrations, i.e. near holes, notches, or manufacturing defects [START_REF] Jones | Mechanics of composite materials[END_REF][START_REF] Tan | Stress concentration in laminated composites[END_REF]. Depending on the nature of the constituent materials, and the stacking sequence, laminated composites are generally characterized by three primary failure modes (Fig. 1): interlaminar, intralaminar and translaminar failure. These modes are observed at different scales: microscopic scale (fiber/resin interaction), mesoscopic scale (laminate ply) and macroscopic scale (laminate). Translaminar fracture occurs at the mesoscopic scale, with the breakage of fiber bundles. There are two modes of translaminar failure in fiber-reinforced laminates: fiber breakage in tension and in compression [START_REF] Pinho | Fracture toughness of the tensile and compressive fibre failure modes in laminated composites[END_REF][START_REF] Ortega | Translaminar fracture toughness of interply hybrid laminates under tensile and compressive loads[END_REF]. In the case of compressive loadings, fiber failure is mainly due to the formation of fiber buckling bands (also known as kink-bands). Fracture toughness plays a fundamental role in the damage tolerance of a composite structure. It depends on the stacking sequence of the laminate [START_REF] Laffan | Measurement of the in situ ply fracture toughness associated with mode I fibre tensile failure in FRP. Part II: size and lay-up effects[END_REF][START_REF] Teixeira | Translaminar fracture toughness of CFRP: from the toughness of individual plies to the toughness of the laminate[END_REF][START_REF] Teixeira | Thickness-dependence of the translaminar fracture toughness: experimental study using thin-ply composites[END_REF][START_REF] Jose | Intralaminar fracture toughness of a cross-ply laminate and its constituent sub-laminates[END_REF], the loading conditions and the architecture of the reinforcement. Most of the studies dealing with translaminar mode I (opening) failure of multidirectional laminates are based on the quantification of the fracture toughness of unidirectional-ply laminates [START_REF] Pinho | Fracture toughness of the tensile and compressive fibre failure modes in laminated composites[END_REF][START_REF] Laffan | Measurement of the in situ ply fracture toughness associated with mode I fibre tensile failure in FRP. Part I: data reduction[END_REF][START_REF] Laffan | Measurement of the in situ ply fracture toughness associated with mode I fibre tensile failure in FRP. Part II: size and lay-up effects[END_REF][START_REF] Mahmoud | Fracture toughness of single-edge notched fiber reinforced composite[END_REF][START_REF] Catalanotti | Measurement of resistance curves in the longitudinal failure of composites using digital image correlation[END_REF][START_REF] Laffan | Measurement of the fracture toughness associated with the longitudinal fibre compressive failure mode of laminated composites[END_REF][START_REF] Teixeira | Translaminar fracture toughness of CFRP: from the toughness of individual plies to the toughness of the laminate[END_REF][START_REF] Teixeira | Thickness-dependence of the translaminar fracture toughness: experimental study using thin-ply composites[END_REF][START_REF] Allaer | Direct fracture toughness determination of a ductile epoxy polymer from digital image correlation measurements on a single edge notched bending sample[END_REF][START_REF] Moore | Intrinsic characterization of continuous fibre reinforced thermoplastic composites-I: toughness characterization of carbon fibre/polyether ether ketone (CF/PEEK) laminates[END_REF][START_REF] Slepetz | Fracture of composite compact tension specimens[END_REF], while very few studies are dealing with woven-ply laminates [START_REF] Ortega | Translaminar fracture toughness of interply hybrid laminates under tensile and compressive loads[END_REF][START_REF] Vieille | Fracture mechanics of hybrid composites with ductile matrix and brittle fibers: Influence of temperature and constraint effect[END_REF][START_REF] Wang | Effect of interfacial mobility on flexural strength and fracture toughness of glass/epoxy laminates[END_REF][START_REF] Rokbi | On experimental investigation of failure process of woven-fabric composites[END_REF][START_REF] Lisle | Damage of woven composite under translaminar cracking tests using infrared thermography[END_REF][START_REF] Médeau | Robust characterization of crack propagation in 3D woven composites and evidences of size dependency[END_REF].

Experimental estimation of translaminar fracture toughness

The ASTM-E1922 standard provides recommendations on specimen geometry for estimating the translaminar fracture toughness of composite materials (Eccentrically loaded Single-Edge-notch Tensile), the use of standards derived from metallic materials is widely used for composite materials [START_REF] Moore | Intrinsic characterization of continuous fibre reinforced thermoplastic composites-I: toughness characterization of carbon fibre/polyether ether ketone (CF/PEEK) laminates[END_REF][START_REF] Laffan | Translaminar fracture toughness testing of composites: A review[END_REF]. Damage growth is characterized by the resistance curve (R-curve), which represents the evolution of the critical strain energy release rate as a function of the macroscopic crack length. There are different specimens geometries to induce stable crack growth and to measure the translaminar fracture toughness: Compact Tension (CT) and Compact Compression (CC) [START_REF] Pinho | Fracture toughness of the tensile and compressive fibre failure modes in laminated composites[END_REF][START_REF] Ortega | Translaminar fracture toughness of interply hybrid laminates under tensile and compressive loads[END_REF][START_REF] Laffan | Measurement of the in situ ply fracture toughness associated with mode I fibre tensile failure in FRP. Part I: data reduction[END_REF][START_REF] Laffan | Measurement of the in situ ply fracture toughness associated with mode I fibre tensile failure in FRP. Part II: size and lay-up effects[END_REF][START_REF] Catalanotti | Measurement of resistance curves in the longitudinal failure of composites using digital image correlation[END_REF][START_REF] Teixeira | Translaminar fracture toughness of CFRP: from the toughness of individual plies to the toughness of the laminate[END_REF][START_REF] Teixeira | Thickness-dependence of the translaminar fracture toughness: experimental study using thin-ply composites[END_REF][START_REF] Slepetz | Fracture of composite compact tension specimens[END_REF][START_REF] Wang | Effect of interfacial mobility on flexural strength and fracture toughness of glass/epoxy laminates[END_REF][START_REF] Rokbi | On experimental investigation of failure process of woven-fabric composites[END_REF][START_REF] Médeau | Robust characterization of crack propagation in 3D woven composites and evidences of size dependency[END_REF][START_REF] Jose | Intralaminar fracture toughness of a cross-ply laminate and its constituent sub-laminates[END_REF], three-/four-point bending [START_REF] Mahmoud | Fracture toughness of single-edge notched fiber reinforced composite[END_REF][START_REF] Laffan | Measurement of the fracture toughness associated with the longitudinal fibre compressive failure mode of laminated composites[END_REF][START_REF] Allaer | Direct fracture toughness determination of a ductile epoxy polymer from digital image correlation measurements on a single edge notched bending sample[END_REF][START_REF] Vieille | Fracture mechanics of hybrid composites with ductile matrix and brittle fibers: Influence of temperature and constraint effect[END_REF][START_REF] Médeau | Robust characterization of crack propagation in 3D woven composites and evidences of size dependency[END_REF] and "Eccentrically loaded Single-Edge-notch Tensile" (ESET) [START_REF] Lisle | Damage of woven composite under translaminar cracking tests using infrared thermography[END_REF][START_REF] Tretyakov | Stable crack growth in composite laminates under various stiffness of the loading system[END_REF][START_REF] John | Stress intensity factor and compliance solutions for an eccentrically loaded single edge cracked geometry[END_REF].

Nomenclature

4PB

Four CT specimens were mainly used to estimate the translaminar fracture toughness, due to the containment of damage around the crack tip due to fiber failure induced by this type of geometry. Similarly, the measurement of the compressive fracture toughness related to the formation of a buckling band of fibers in compression has been reported in many publications using CC specimens, but the values thus obtained are only valid at the initiation of the fracture and not during propagation, because of the energy dissipated by the delamination that comes along with the propagation of the kink-bands [START_REF] Pinho | Fracture toughness of the tensile and compressive fibre failure modes in laminated composites[END_REF][START_REF] Catalanotti | Measurement of resistance curves in the longitudinal failure of composites using digital image correlation[END_REF]. CC specimens are also used to measure compressive fracture toughness related to the formation of a buckling band of fibers in compression In CT specimens there are no significant out-ofplane displacements and the crack propagation data is valid, except only for C8/PEEK orthotropic laminates for which the out-of-plane displacements are observed at testing temperature slightly higher than the glass transition temperature. This may result from its low shear modulus that is obviously much degraded with the temperature [START_REF] Vieille | Prediction of the ultimate strength of quasi-isotropic TP-based laminates structures from tensile and compressive fracture toughness at high temperature[END_REF], and only in this case an anti-buckling device must be used [START_REF] Anderson | Fracture mechanics: fundamentals and applications[END_REF]. In CC specimens, the crack growth is mainly related to micro-buckling of the plies at 0 • . As a result, the data computation is related to the formation of a kink-band.

Many studies have focused on the development of the best technique for quantifying translaminar fracture toughness [START_REF] Laffan | Measurement of the in situ ply fracture toughness associated with mode I fibre tensile failure in FRP. Part I: data reduction[END_REF][START_REF] Laffan | Measurement of the in situ ply fracture toughness associated with mode I fibre tensile failure in FRP. Part II: size and lay-up effects[END_REF][START_REF] Catalanotti | Measurement of resistance curves in the longitudinal failure of composites using digital image correlation[END_REF] in terms of reproducibility and simplicity of results. Laffan et al concluded that the method of compliance calibration based on effective crack length is the most appropriate method, because it does not require optical measurement of crack growth during the test [START_REF] Laffan | Measurement of the in situ ply fracture toughness associated with mode I fibre tensile failure in FRP. Part I: data reduction[END_REF]. The parameters used in this method to determine the length of the crack are a function of a stiffness model (force-displacement) and do not depend on the size of the specimen, they are related to the elastic compliance measured from the force-displacement curve. In another study presented by Catalonatti et al., a digital image correlation technique based on the computation of the J-integral around the crack tip was shown to be suitable for capturing the critical energy release rate associated with the breakage of longitudinal fibers [START_REF] Catalanotti | Measurement of resistance curves in the longitudinal failure of composites using digital image correlation[END_REF].

Some studies have also pointed out that fracture toughness is not an absolute value. Indeed, translaminar fracture toughness depends on the thickness of the plies. Other studies have showed that the increase in fracture toughness is related to the large amount of fiber bundles pullout at 0 • [START_REF] Laffan | Measurement of the in situ ply fracture toughness associated with mode I fibre tensile failure in FRP. Part II: size and lay-up effects[END_REF][START_REF] Teixeira | Translaminar fracture toughness of CFRP: from the toughness of individual plies to the toughness of the laminate[END_REF][START_REF] Teixeira | Thickness-dependence of the translaminar fracture toughness: experimental study using thin-ply composites[END_REF], the blocking effect provided for the two 0 • plies together triples the value of the translaminar fracture toughness while the blocking resulting from the 45 • plies has little effect on the translaminar fracture toughness.

Translaminar fracture in woven-ply thermoplastic laminates

Over the past fifty years, several studies have been conducted to understand and quantify translaminar fracture toughness in organic matrix composites. Most of them have been dedicated to unidirectional (UD) thermosetting laminates, using two main types of laminates: carbon/epoxy [START_REF] Pinho | Fracture toughness of the tensile and compressive fibre failure modes in laminated composites[END_REF][START_REF] Ortega | Translaminar fracture toughness of interply hybrid laminates under tensile and compressive loads[END_REF][START_REF] Laffan | Measurement of the in situ ply fracture toughness associated with mode I fibre tensile failure in FRP. Part I: data reduction[END_REF][START_REF] Laffan | Measurement of the in situ ply fracture toughness associated with mode I fibre tensile failure in FRP. Part II: size and lay-up effects[END_REF][START_REF] Mahmoud | Fracture toughness of single-edge notched fiber reinforced composite[END_REF][START_REF] Catalanotti | Measurement of resistance curves in the longitudinal failure of composites using digital image correlation[END_REF][START_REF] Laffan | Measurement of the fracture toughness associated with the longitudinal fibre compressive failure mode of laminated composites[END_REF][START_REF] Teixeira | Translaminar fracture toughness of CFRP: from the toughness of individual plies to the toughness of the laminate[END_REF][START_REF] Teixeira | Thickness-dependence of the translaminar fracture toughness: experimental study using thin-ply composites[END_REF][START_REF] Slepetz | Fracture of composite compact tension specimens[END_REF] and glass/epoxy [START_REF] Mahmoud | Fracture toughness of single-edge notched fiber reinforced composite[END_REF][START_REF] Slepetz | Fracture of composite compact tension specimens[END_REF]. Translaminar fracture in woven ply laminates has been little studied compared to UD-ply laminates. Woven-ply laminates allow the processing of parts with complex geometries and have good damage tolerance. As with unidirectional-ply laminates, the various techniques for quantifying toughness have proven to be well applicable to woven-ply laminates. The characterization of translaminar fracture in woven ply laminates focuses mainly on the thermosetting materials carbon/epoxy [START_REF] Ortega | Translaminar fracture toughness of interply hybrid laminates under tensile and compressive loads[END_REF] and glass/epoxy [START_REF] Ortega | Translaminar fracture toughness of interply hybrid laminates under tensile and compressive loads[END_REF][START_REF] Vieille | Fracture mechanics of hybrid composites with ductile matrix and brittle fibers: Influence of temperature and constraint effect[END_REF][START_REF] Wang | Effect of interfacial mobility on flexural strength and fracture toughness of glass/epoxy laminates[END_REF][START_REF] Rokbi | On experimental investigation of failure process of woven-fabric composites[END_REF][START_REF] Lisle | Damage of woven composite under translaminar cracking tests using infrared thermography[END_REF]. Many studies have concluded that in glass/epoxy woven ply laminates, matrix microcracking is the predominant damage phenomenon at the crack tip [START_REF] Wang | Effect of interfacial mobility on flexural strength and fracture toughness of glass/epoxy laminates[END_REF][START_REF] Rokbi | On experimental investigation of failure process of woven-fabric composites[END_REF][START_REF] Lisle | Damage of woven composite under translaminar cracking tests using infrared thermography[END_REF]. Even if this phenomenon is present, the quantification of fracture toughness remains reliable in the case of near-brittle fracture. The behaviour of Polymer Matrix Composites (PMC) is also characterized by temperature dependence [START_REF] Vieille | Fracture mechanics of hybrid composites with ductile matrix and brittle fibers: Influence of temperature and constraint effect[END_REF][START_REF] Coronado | Influence of temperature on a carbon-fibre epoxy composite subjected to static and fatigue loading under mode-I delamination[END_REF][START_REF] Kim | Interlaminar fracture toughness of CF/PEI and GF/PEI composites at elevated temperatures[END_REF][START_REF] Yurchenko | Synthesis, mechanical properties and chemical/solvent resistance of crosslinked poly (arylether-ether-ketones) at high temperatures[END_REF][START_REF] Vieille | Prediction of the notched strength of woven-ply PolyPhenylene Sulfide thermoplastic composites at a constant high temperature by a physically-based model[END_REF][START_REF] Vieille | Prediction of the ultimate strength of quasi-isotropic TP-based laminates structures from tensile and compressive fracture toughness at high temperature[END_REF][START_REF] Vieille | Comparative study on the behavior of woven-ply reinforced thermoplastic or thermosetting laminates under severe environmental conditions[END_REF]. Numerous studies have been carried out on the influence of high temperatures on interlaminar fracture in unidirectional [START_REF] Coronado | Influence of temperature on a carbon-fibre epoxy composite subjected to static and fatigue loading under mode-I delamination[END_REF] and woven-ply thermoplastic (TP) laminates [START_REF] Coronado | Influence of temperature on a carbon-fibre epoxy composite subjected to static and fatigue loading under mode-I delamination[END_REF], but little work has been done on translaminar fracture of woven-ply thermoset laminates [START_REF] Ortega | Translaminar fracture toughness of interply hybrid laminates under tensile and compressive loads[END_REF][START_REF] Rokbi | On experimental investigation of failure process of woven-fabric composites[END_REF][START_REF] Lisle | Damage of woven composite under translaminar cracking tests using infrared thermography[END_REF] and almost no work has been done on woven ply TP laminates [START_REF] Vieille | Fracture mechanics of hybrid composites with ductile matrix and brittle fibers: Influence of temperature and constraint effect[END_REF]. It should be noted that TP matrix composites are known for their excellent damage tolerance. In a work proposed by Vieille et al. [START_REF] Vieille | Fracture mechanics of hybrid composites with ductile matrix and brittle fibers: Influence of temperature and constraint effect[END_REF], the translaminar fracture behaviour of a hybrid woven laminate of reinforced carbon and glass fibers combined with a PEEK matrix was studied. By means of tests carried out on notched specimens in tensile and three-point bending at room temperature and T > T g , it appears that temperature has little influence on the translaminar fracture toughness in mode I. In addition, it seems to foster the intrinsic toughness at the crack tip and the extrinsic toughness at the mechanical loading zones [START_REF] Launey | On the fracture toughness of advanced materials[END_REF], which results in a slight increase of the R-curve. Table 1 summarizes a few translaminar tensile and compressive fracture toughness values available in the Fig. 1. Overview of ply-level failure modes on a weave pattern. literature for unidirectional and woven-ply reinforced polymer matrix laminates.

Objectives of the study

In this context, this study focuses on the experimental characterization of the translaminar fracture of three types of carbon fiberreinforced thermoplastic laminates. Using CT and CC specimens to induce translaminar fracture in tension and compression, these laminates were tested at room temperature (RT) and at 150 • C when matrix toughness is exacerbated. To our knowledge no translaminar fracture toughness values are available for woven ply PEEK thermoplastic laminates at room temperature and T > T g [START_REF] Vieille | Fracture mechanics of hybrid composites with ductile matrix and brittle fibers: Influence of temperature and constraint effect[END_REF]. The objective of this study is to analyse the influence of stacking sequence and temperature on the tensile and compressive fracture behaviour of fibers in mode I. This involves measuring the critical energy release rate at initiation and the fracture energy during propagation. Thus, the observation and a post-mortem analysis of damaged areas make it possible to quantify the damage tolerance of TP matrix composites and to understand the influence of temperature on the deformation mechanisms of the TP matrix and ultimately on translaminar fracture.

Materials and methods

Materials

The laminates used in this study are obtained by thermo-compression. They consist of a PEEK thermoplastic matrix reinforced with a continuous carbon fiber fabric (Tenax®-E HTA40 3 K), structured in a 5-harness satin weave (Fig. 1). The average ply thickness of the laminates is 0.31 mm. Three types of woven laminates are tested (Fig. 2). Two laminates with the same ply ratio at 0 • /90 • and ± 45 • , but with different thicknesses qualified as quasi-isotropic [START_REF] Vieille | Fracture mechanics of hybrid composites with ductile matrix and brittle fibers: Influence of temperature and constraint effect[END_REF][START_REF] Vieille | Comparative study on the behavior of woven-ply reinforced thermoplastic or thermosetting laminates under severe environmental conditions[END_REF]:

• [(0/90),(±45),(0/90),(±45),(0/90),(±45),(0/90)] (2.17 mm thick, noted as C7/PEEK)

• [(0/90) V ,(0/90),(±45),(0/90),(±45),(0/90),(±45),(0/90)] S having two outer plies of glass fabric (5-harness satin weave) and PEEK matrix (4.5 mm thick, noted as CG/PEEK), the 0.08 mm thick (0/90) G surface glass fabric is used as corrosion protection and electrical protection with the aim of reducing the galvanic torque and thus avoiding galvanic corrosion of aluminum and steel with carbon. • An eight-ply orthotropic laminate [(0/90)] 8 (2.48 mm thick, noted as C8/PEEK).

The main mechanical properties of the elementary ply are specified in Table 2.

Specimens geometries

The dimensions of the CT and CC specimens were chosen in accordance with ASTM test standard E399-12 [START_REF] Standard | Standard test method for linear-elastic plane-strain fracture toughness KIc of metallic materials[END_REF] (Fig. 3). The specimens are cut from a 600 × 600 mm 2 plate using a water jet machine. The notched area of the CC specimens (Fig. 3b) has been enlarged to avoid contact of the notch faces during compression. The fixing holes of the loading device are machined by means of carbide drills. The ratio between the length of the initial notch and the width of the specimen used is approximately a/w = 0.45 for both types of specimens, where a is the crack length and w is the distance from the load line to the right edge of the specimen.

Experimental set-up and methods

Thermo-mechanical testing

All the tests were conducted with a uniaxial servo-hydraulic tension machine MTS 810 equipped with a 100 kN capacity force cell and a thermal chamber. The specimens are held in position by a standardized device in accordance with ASTM-399, which is maintained by the hydraulic grips of the machine and transmits the mechanical load via pins inserted in the holes of the specimens. Six specimens were tested in each configuration (CT and CC) in displacement-controlled mode (1 mm/min) at two temperatures: room temperature (RT) and 150 • C.

Crack growth measurement by means of a Digital Image Correlation (DIC) technique

A DIC pattern is painted on the specimen surface with a non-periodic texture and without preferred orientation. The use of DIC technique at high temperature requires the use of a high intensity source combined with a fiber optic light guide is used to illuminate the patterns on the surface of the specimen placed into the thermal chamber. A Grasshopper® high-speed monochrome camera allows digital images to be recorded at full resolution (1920 × 1200 pixels), and at a rate of one frames-per-second during thermomechanical loading. The VIC-2D digital image correlation software provides the confidence interval field associated with the convolution factor (sigma indicator) of each pattern in the region of interest [START_REF]Solutions Correlated. Vic 2D reference manual[END_REF]. As was defined by Sutton et al., the VIC-2D system utilizes an optimized correlation method to provide full-field two-dimensional displacement and strain [START_REF] Sutton | Application of an optimized digital correlation method to planar deformation analysis[END_REF]. The method compare the digital images for various small regions (known as subsets) throughout the images before and after deformation using fundamental continuum mechanics concepts, locating the positions of each of these subsets after deformation through digital image analysis. When a material discontinuity appears in the pattern, the homogeneous linear mapping in this region does not present deformed surface and the small subset position is not computed.

Using an algorithm implemented in the Scilab code [35], the crack tip is located via the discontinuity of the strain field resulting from the crack propagation (Catalanotti et al. [START_REF] Catalanotti | Measurement of resistance curves in the longitudinal failure of composites using digital image correlation[END_REF] used a similar technique based on the displacement discontinuity within the pattern). A binarization of the full-field strain obtained by the VIC-2D software is applied (Fig. 4). The identification of the damaged and undamaged areas in the region of interest is associated with a F T function, which takes values of: • F T = 0 corresponds to the region for the undamaged area.

• F T = 1 is the damaged area where a material discontinuity is present next to the initial crack tip and not information is computed using DIC. • F T = -1 is the damaged area where material discontinuity appears due to a secondary crack and not information is computed using DIC.

The crack length is then determined from the crack tip position in each pattern, independently of the orientation of crack within the pattern. The spatial resolution of the crack length is defined by the size of the subsets used in the DIC method.

Data reduction methods

ASTM-399 test standard

According to ASTM-399 test standard [START_REF] Standard | Standard test method for linear-elastic plane-strain fracture toughness KIc of metallic materials[END_REF], initially developed and validated for metallic isotropic materials, the critical stress intensity factor (fracture toughness) in mode I (opening) K Ic is given by:

K Ic = P c t ̅̅̅ ̅ w √ f (a/w) (1)
with:

f (a/w) = 2 + a/w
(1a/w)

]

where P c is the critical load ensured at crack initiation, t is the thickness of the specimen, w is the distance from the load line to the right edge of the specimen (Fig. 3), a is the crack length, whose initial value is a 0 and f (a/w) is a geometric correction function for a specimen of finite width [START_REF] Tan | Stress concentration in laminated composites[END_REF][START_REF] Tada | The analysis of cracks handbook[END_REF]. Eq. ( 1) is only defined for isotropic materials though the studied laminates are not completely isotropic. To a fist approximation and for comparison purposes, the function f(a/w) proposed for isotropic materials has been used to compute the values from the method proposed in ASTM-399 test standard. It is acceptable for C7/PEEK and CG/PEEK laminates. For the C8/PEEK orthotropic materials, the solution proposed by Ortega et al for a CT specimen should be considered in order to obtain the linear elastic fracture toughness, the stress intensity factor and the compliance at the load line [START_REF] Ortega | Compact tension specimen for orthotropic materials[END_REF]. The solution applies for any orthotropic material whose principal directions are defined by the crack direction, assuming that the crack grows along the symmetry plane of the specimen.

The critical energy release rate of the laminate G lam Ic is then calculated from K Ic [START_REF] Tada | The analysis of cracks handbook[END_REF][START_REF] Liebowitz | Fracture: an advanced treatise[END_REF]:

G lam Ic = C I K 2 Ic (2)
where C I is the orthotropic elastic coefficient in plane-stress conditions defined by [START_REF] Tada | The analysis of cracks handbook[END_REF]:

C I = ̅̅̅̅̅̅̅̅̅̅̅̅ ̅ 1 2E x E y √ ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ̅ ̅̅̅̅̅ E x E y √ -ν xy + E x 2G xy √ √ √ √
where E x , E y , G xy and ν xy are respectively the Young's modulus in x and y directions (Fig. 1), the shear modulus and the Poisson's ratio of the laminate. The properties used for the computation of the orthotropic elastic coefficient of the equivalent laminate are given in Table 3, they are obtained from the properties of the elementary ply (Table 2) using the laminate theory. The influence of temperature has been taken into account on the properties of the laminates from the standardized tensile tests carried out on different laminates [START_REF] Vieille | Fracture mechanics of hybrid composites with ductile matrix and brittle fibers: Influence of temperature and constraint effect[END_REF][START_REF] Vieille | Comparative study on the behavior of woven-ply reinforced thermoplastic or thermosetting laminates under severe environmental conditions[END_REF].

Compliance method

The compliance method is commonly used to calculate the evolution of the energy release rate from the force-displacement curve at the initiation and propagation of the crack, making it possible to determine the evolution of compliance C = d/P (Fig. 5), where d is the displacement and P the force:

G lam I = P 2 c 2t ( dC da ) (3)
Classically a cubic function of the compliance function versus the crack length has been fitted on the whole test for each experiment [START_REF] Laffan | Measurement of the in situ ply fracture toughness associated with mode I fibre tensile failure in FRP. Part I: data reduction[END_REF][START_REF] Laffan | Measurement of the in situ ply fracture toughness associated with mode I fibre tensile failure in FRP. Part II: size and lay-up effects[END_REF], then an analytical derivation has been done to evaluate the fracture toughness.

Results and discussion

Thermo-mechanical behavior

In order to compare the thermo-mechanical responses of the studied laminates (whose thicknesses are the force was normalized by the thickness of the laminate.

Tensile tests

The propagation of the macroscopic crack is identified from the jumps observed on the force-displacement curves. The method defined in Section 3.2 then makes it possible to monitor the evolution of the crack length via the gradual decrease in load during propagation (Fig. 6). From the curves in Fig. 6, it is observed that quasi-isotropic laminates have similar macroscopic responses with a quasi-linear force-displacement curve before crack propagation, but with a higher initiation load at fracture for the CG/PEEK material. The significant non-linearity observed on the C8/PEEK curve is due to its low shear modulus and to a zone of high plasticity induced by significant damage at the initial crack tip (intrinsic toughness) (Fig. 7) as well as to localized crushing in the zones where the mechanical load imposed by the axes of the intermediate tool (extrinsic toughness) [START_REF] Launey | On the fracture toughness of advanced materials[END_REF][START_REF] Liu | An experimental method to determine the intralaminar fracture toughness of high-strength carbon-fibre reinforced composite aerostructures[END_REF][START_REF] Blanco | Intralaminar fracture toughness characterisation of woven composite laminates. Part I: Design and analysis of a compact tension (CT) specimen[END_REF]. It appears that the shear deformation field of the orthotropic lay-up (Fig. 7) extends beyond the crack tip, causing a more pronounced plastic behaviour. In addition, the larger plasticity zone at the loading axes may justify a slower crack propagation in comparison to quasi-isotropic laminates due to a higher dissipated mechanical load.

Overall, the influence of temperature is not significant, despite the increase in the ductility of the resin at 150 • C. The influence of temperature is also analyzed by examining the post-mortem damage. Macroscopic observations of the damaged area suggest that the ruin of the quasi-isotropic laminates occurs by translaminar failure of the fibers in tension at TA. At 150 • C, the onset of compressive failure in the area opposite the initial notch was observed for the CG/PEEK laminate (Figs. 6 and8b). This compressive fracture is associated with buckling on a macroscopic scale, which can be explained by the significant increase in ductility of the PEEK matrix at T > T g by degrading its shear strength in particular. The C8/PEEK orthotropic laminates exhibit an elastic-ductile behaviour (Fig. 6c). The influence of temperature remains moderate (about 20% on the fracture load of the first fiber bundle), but results in a very pronounced out-of-plane displacement requiring the use of an anti-buckling device. The orthotropic stacking sequence fosters a very gradual propagation of the crack, with jumps of less than 1 mm (Fig. 6c).

Compressive tests

In CC specimens, crack growth is mainly related to micro-buckling of the plies at 0 • , which results in fiber breakage in compression and the formation of a kink-band. Using the same protocol as for the CT specimens, the crack tip in the area damaged by compression fiber breakage could be located by image analysis. It can be seen that the crack growth is gradual (Fig. 9), but the correspondence between the increases in crack length and the jumps observed on the force-displacement curve is not obvious. In addition, it appears that the first fiber failure does not correspond to the maximum force, but that the load continues to increase for some time after this first failure. This is because the fiber breakage in compression is less abrupt than in tension, and that after the failure in compression a crushing stress continues to be transmitted.

From the curves in Fig. 9, it can be noted that quasi-isotropic laminates are characterized by similar macroscopic responses, the force-displacement curve is quasi-linear until the start of propagation, but unlike the case of the CT tests, the load continues to increase after the start of propagation up to about 5 mm crack length. It is also observed that the failure of the first fiber bundle occurs almost at the same time in the force-displacement curve for quasi-isotropic laminates. The glass plies, as well as the greater thickness of the CG/ PEEK, therefore do not seem to significantly influence the resistance to fracture initiation, but delay the growth of the crack.

In compression, the influence of temperature is very pronounced with a decrease of about 35% in fracture initiation resistance for quasi-isotropic laminates. At room temperature, the specimens are characterized by a final quasi-brittle fracture, which results in a two-part separation of the specimens along the axis of the initial crack (Fig. 10a); this self-similar translaminar fracture [START_REF] Jones | Mechanics of composite materials[END_REF] occurs when the crack length reaches a critical value due to the stress concentration accumulated on the free-edge of the specimen during the test. The onset of a tensile fiber breakage at the free-edge of the specimen is observed at 150 • C for quasi-isotropic laminates (Fig. 9a andb). At 150 • C, the more pronounced ductility of the PEEK matrix fosters the localized crushing of the plies in compression inducing ductile failure, especially for the orthotropic laminate.

The force-displacement curve of the C8/PEEK orthotropic laminate (Fig. 9c) is non-linear even before propagation begins. At room temperature, and at 150 • C, the orthotropic C8/PEEK laminate does not exhibit fiber breakage in tension; the fibers all fail in compression. This is explained by the absence of plies at ±45 • , which limits the transmission of shear forces. At 150 • C, the test was interrupted before the final break to avoid contact between the notch faces of the specimen, but the specimen was not completely broken (the load does not decrease to 0). This interruption is likely to prevent the development of a tensile crack, observed in quasiisotropic laminates. The influence of temperature is more pronounced compared to the quasi-isotropic laminates with a reduction of about 50% of the resistance at the initiation of the fracture.

Estimation of the strain energy release rate

The resistance of a laminate to translaminar crack initiation and propagation are characterized by a resistance curve, called the Rcurve. The first point of the R-curve can be defined as the critical energy release rate related to crack initiation G C I , while the propagation values G C I during propagation generally tend towards an asymptote [START_REF] Pinho | Fracture toughness of the tensile and compressive fibre failure modes in laminated composites[END_REF][START_REF] Laffan | Measurement of the in situ ply fracture toughness associated with mode I fibre tensile failure in FRP. Part I: data reduction[END_REF][START_REF] Laffan | Measurement of the in situ ply fracture toughness associated with mode I fibre tensile failure in FRP. Part II: size and lay-up effects[END_REF][START_REF] Mahmoud | Fracture toughness of single-edge notched fiber reinforced composite[END_REF][START_REF] Catalanotti | Measurement of resistance curves in the longitudinal failure of composites using digital image correlation[END_REF][START_REF] Laffan | Measurement of the fracture toughness associated with the longitudinal fibre compressive failure mode of laminated composites[END_REF][START_REF] Teixeira | Translaminar fracture toughness of CFRP: from the toughness of individual plies to the toughness of the laminate[END_REF][START_REF] Teixeira | Thickness-dependence of the translaminar fracture toughness: experimental study using thin-ply composites[END_REF][START_REF] Slepetz | Fracture of composite compact tension specimens[END_REF][START_REF] Rokbi | On experimental investigation of failure process of woven-fabric composites[END_REF][START_REF] Lisle | Damage of woven composite under translaminar cracking tests using infrared thermography[END_REF][START_REF] Médeau | Robust characterization of crack propagation in 3D woven composites and evidences of size dependency[END_REF]. Here, the ASTM-399 test standard is only applied to determine the value of the critical initiation energy release rate, the critical load associated with crack initiation was identified using digital image analysis. The compliance method is used to monitor the evolution of the energy release rate during propagation as well.

Tensile tests

The mean R-curves obtained for the three laminates are shown in Fig. 11. No value was taken for a crack length greater than 11 mm due to the appearance of a secondary crack (compression crack for the CT test and tensile crack for the DC test), which contributes to dissipation of mechanical energy during fracture, which disturbs the evaluation of the strain energy release rate.

The compliance method makes it possible to monitor the evolution of the energy release rate during crack propagation (Fig. 11). The values of G C I | tension at initiation determined from the ASTM-399 standard seem to validate its use for quasi-isotropic woven laminates; the difference observed at the values obtained with the compliance method remains small (Fig. 14). For the orthotropic C8/ PEEK laminate, the mean value of G C I | tension at initiation calculated from ASTM-399 gives a value at RT of 29.9 kJ/m 2 compared to 117.3 kJ/m 2 for the compliance method. It is reasonable to assume that the higher value of G C I | tension at initiation is due to a very high plasticity at the points of load application accompanied by a greater area of plasticity at the crack tips (Fig. 7). It is worth noting that ASTM-399 is applicable for materials with elastic-brittle behaviour, which is not observed for orthotropic laminates (Fig. 6-c).

Fig. 11 shows that all the R-curves tend to converge for a crack length greater than about 4-11 mm depending on the case, this would mean that the size of the FPZ is reached from the beginning and does not change much. For quasi-isotropic laminates, it is observed that the increase in thickness implies a significant increase in G C I | tension at initiation and during propagation (Fig. 11 and Fig. 14). The presence of two glass-PEEK plies can be considered negligible compared to the proportion of carbon-PEEK plies in the CG/ PEEK hybrid laminate [START_REF] Vieille | Prediction of the notched strength of woven-ply PolyPhenylene Sulfide thermoplastic composites at a constant high temperature by a physically-based model[END_REF], so the large increase observed can be attributed mainly to the increase in the thickness of the laminate [START_REF] Laffan | Measurement of the in situ ply fracture toughness associated with mode I fibre tensile failure in FRP. Part II: size and lay-up effects[END_REF][START_REF] Teixeira | Translaminar fracture toughness of CFRP: from the toughness of individual plies to the toughness of the laminate[END_REF][START_REF] Teixeira | Thickness-dependence of the translaminar fracture toughness: experimental study using thin-ply composites[END_REF][START_REF] Jose | Intralaminar fracture toughness of a cross-ply laminate and its constituent sub-laminates[END_REF], which leads to an increase in the size of the damaged areas (Fig. 12). A simple thresholding method applied in the images (Fig. 12) shows that the fracture surface increase with the thickness and with the presence of 45 • laminate ply. Temperature contributes to a small increase (7-10%) in the translaminar fracture toughness of quasi-isotropic laminates at initiation; this trend is also observable during propagation (Figs. 11 and14).

Overall, the C8/PEEK orthotropic laminate has a very high translaminar tensile fracture toughness compared to the quasi-isotropic laminates, while the number of fibers to be broken is lower (Fig. 12). In practice, cutting a 0 • /90 • ply requires cutting only the fibers at 0 • , whereas cutting a ±45 • ply requires cutting the fibers at +45 • and -45 • [START_REF] Teixeira | Translaminar fracture toughness of CFRP: from the toughness of individual plies to the toughness of the laminate[END_REF]. The greater toughness of the orthotropic laminate could be due to a zone of extensive plasticity caused by blunting at the initial crack tip (Fig. 7) as well as significant plastic deformations at the load application points, thus inducing energy dissipation, which is added to those due to the crack propagation. However, this calls into question the computation of the critical strain energy release rate from a global computation using the forcedisplacement curve (Fig. 11), and must be confirmed by a local computation of the integral J type or infrared thermography [START_REF] Lisle | Damage of woven composite under translaminar cracking tests using infrared thermography[END_REF].

Compressive tests

In this case, R-curves were obtained for crack growth values up to about 16 mm (Fig. 13). An increasing trend of G C I | compression during propagation is observed for all laminates. This evolution is because after a compressive failure in the form of a kink-band, a crushing stress is transmitted (contrary to the case of a tensile test). Thus, the evolution of the critical energy release rate during the formation of a kink-band does not accurately describe the absorbed energy, since other modes of damage are present in particular the crushing of the fibers or the delamination. Thus, the values at initiation seem to be the best measure of the critical strain energy release rate associated with the appearance of the kink-band (Fig. 14). For quasi-isotropic laminates, an increase in translaminar fracture toughness can be observed with thickness, but not to the same magnitude as in tension. There is also a very marked decrease in translaminar fracture toughness on all the laminates studied at 150 • C (Figs. 13 and 14), in contrast to the tensile characterized by a slight increase, suggesting that a test temperature T > T g contributes to the formation of plastic buckling bands in compression due to increased ductility of the PEEK matrix. At RT the crushing is more pronounced than the buckling and at 150 • C the out-of-plane buckling is more pronounced than the crushing, because the softening of the matrix in the overlapping areas facilitates the out-ofplane displacement of the fiber bundles.

Conclusions

In order to study the damage tolerance of the high performance TP laminates used for aeronautical applications in high temperature conditions, the quantification of translaminar fracture toughness plays a key role. One of the main objectives of this study was to determine translaminar fracture toughness values for composite woven-ply thermoplastic-based laminates to be used under high temperature conditions. To authors best knowledge there are few references dealing with the translaminar fracture behavior and the quantification of fracture toughness of high-performance thermoplastic composites. In addition, an accurate measurement of the crack physical length during loading is challenging at room temperature, and even more at high temperature. This study was aimed at proposing an in situ crack growth measurement based on a Digital Image Correlation (DIC) technique implemented in a thermal chamber combined with a high intensity light source and a binarization algorithm. In orthotropic laminates, tensile tests also reveal that the plastic area is very large at the crack tip due to its low shear modulus (intrinsic toughness). Local plasticity also causes an important toughness linked to localized crushing in the area of force application (extrinsic toughness). In quasi-isotropic laminates, thickness contributes to increase the initiation load at fracture and slows the propagation of the crack. Compressive failure by plastic buckling on the edge opposite the notch is facilitated by the ductility of the PEEK matrix at T > T g .

Compression tests show that compressive failure is driven by the fiber breakage at 0 • and the formation of a plastic kink-band. As for tension tests, for the orthotropic laminate, the low shear modulus induces an important zone of plasticity, an important extrinsic toughness and makes it difficult the evaluation of the fracture toughness. At high temperature, ductile failure associated with localized crushing of the plies is promoted by the plastic deformation of the PEEK matrix at T > T g .

Toughness evaluation based on ASTM-399 proved to be relevant for quasi-isotropic woven laminates giving similar values compared to the compliance method. For highly orthotropic laminates, the computation of toughness based on an overall behaviour (force-displacement curve) is related to energy dissipation at the points of load application accompanied by greater plasticity mechanisms at the crack tip, which are combined with those related to crack propagation. In tension, the R-curves tend to converge towards an asymptote with an almost constant value, while in compression the R-curves tend to increase due to localized crushing which results in constant crushing stress.

Finally, at a temperature (e.g. 150 • C) slightly higher than the glass transition temperature of the materials there is a moderate increase in the translaminar fracture toughness in tension. Thickness increases the fiber pull out length causing an increase in the translaminar fracture toughness in tension. In compression, the thickness does not seem to influence the size of the kink-band (which is associated with the fiber diameter and to the matrix shear mechanical behavior). The compressive translaminar fracture toughness decreases sharply with the temperature, as the softening of the matrix in the overlapping areas facilitates the out-of-plane movement of the fiber bundles. For orthotropic laminates, the computation of the translaminar fracture toughness will have to be confirmed by a local computation of the J-integral type or infrared thermography due to the ductile fracture behaviour.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 2 .

 2 Fig. 2. Lay-up and thickness of the woven-ply composite laminates studied.

Fig. 3 .

 3 Fig. 3. Test specimen dimensions (in mm) for: (a) tension and (b) compression translaminar fiber-breaking fracture toughness tests.

Fig. 4 .

 4 Fig. 4. FT function implemented on a CT specimen.

Fig. 5 .

 5 Fig. 5. Force-displacement curve representative of a stable crack propagation.

Fig. 6 .

 6 Fig. 6. Macroscopic mechanical responses and evolution of the crack length (based on the DIC analyze) of the different laminates in the case of CT specimens at RT and 150 • C.

Fig. 7 .

 7 Fig. 7. (a) CT specimens at RT: shear deformation field at laminates' surface before failure of the first fibers bundles in the case -(b) Stress-Strain curve of angle-ply C8/PEEK laminates showing the onset of the plastic behavior at about 0.3% strain.

Fig. 8 .

 8 Fig. 8. Microscopic observations after failure of CT specimens: (a) C8/PEEK at RT -(b) CG/PEEK at 150 • C.

Fig. 9 .

 9 Fig. 9. Macroscopic mechanical responses and evolution of the crack length (based on the DIC analyze) of the different laminates in the case of CC specimens: (a) RT and (b) 150 • C.

Fig. 10 .

 10 Fig. 10. Microscopic observations after failure of CG/PEEK CC specimens: (a) RT -(b) 150 • C.

Fig. 11 .

 11 Fig. 11. R-curves obtained with the compliance method from CT specimen tests: (a) RT and (b) 150 • C.

Fig. 12 .

 12 Fig. 12. Microscopic observations of the fracture surface of studied laminates in the case of CT specimens.

Fig. 13 .

 13 Fig. 13. R-curves obtained with the compliance method from CC specimen tests: (a) RT and (b) 150 • C.

Fig. 14 .

 14 Fig. 14. Influence of the stacking sequence and the temperature on the tensile and compressive fracture toughness.

Table 1

 1 Summary of experimental data obtained from characterization of the tensile and compressive translaminar failure mode.

	Laminate type	Study (year)	Specimen	Polymeric resin	Methods of data	Fracture toughness G C I (kJ/
			configuration	Fiber reinforcement	reduction	m 2 )
						Initiation	Propagation
	Unidirectional ply	Tension
	composite laminate	Slepetz et Carlson	CT	Epoxy	Compliance calibration	21.2	-
		[14] (1975)		Carbon T300/5208
		Mahmoud [7]	SENT	Polyester	ASTM E399	4.95	-
		(2003)		E-glass
		Pinho et al. [3]	CT	Epoxy	VCCT and rule of	91.6	133.0
		(2006)		Carbon T300/913	mixtures
		Laffan et al. [6]	CT	Epoxy	Modified compliance	57.0	69.0
		(2010)		Carbon T300/920	calibration
		Catalonatti et al. [8]	CT	Epoxy	Digital Image	98.7	133.7
		(2010) Teixeira et al. [11] a	CT	Carbon IM7-8552 Epoxy	Correlation Modified compliance	46.0-104.0	49.0-160.0
		(2016)		Carbon T800s/M21	calibration
		Compression
		Pinho et al. [3]	CC	Epoxy	VCCT and rule of	79.9	-
		(2006)		Carbon T300/913	mixtures
		Catalonatti et al. [8]	CC	Epoxy	Digital Image	47.5	-
		(2010)		Carbon IM7-8552	Correlation
		Laffan et al. [9]	4 PB	Epoxy	VCCT	25.9	-
		(2012)		Carbon IM7/8552
	Woven ply composite laminate	Tension Rokbi et al. [17] b	CT	Epoxy	Compliance calibration	31.9-37.4	42.0-51.0
		(2011) Lisle et al. [18] c	ESET	E-Glass Epoxy	Infrared thermography	15.8-21.6	61.5-62.5
		(2017)		E-Glass
		Ortega et al. [4]	CT	Epoxy	Cohesive law and rule of	97.0	-
		(2017)		Hybrid: Carbon	mixtures
		Vieille at al. [15] d	SENB	G0926/Glass S2 PEEK	ASTM E1820	41.0-44.0	-
		(2018)		Hybrid: Carbon
				HTA40/E-Glass
		Compression
		Ortega et al. [4]	CC	Epoxy	Cohesive law and rule of	-	-
		(2017)		Hybrid: Carbon	mixtures
				G0926/Glass S2

a Four different 0 • ply-block thicknesses ranging from 0.03 mm to 0.12 mm. b Two different fiber directions (warp and weft). c Two different lay-up sequences ([0 • ] 2 and [±45 • ] 2 ). d Two different temperatures.

Table 2

 2 A few properties of the elementary ply of woven carbon and glass fibers reinforced PEEK at RT and 150 • C.

		Carbon/PEEK		Glass/PEEK
	Nominal ply thickness (mm)	0.31		0.08
	T g ( • C)	143		143
		TA	150 • C	TA	150 • C
	Longitudinal modulus E x (GPa)	60	55.04	22
	Transverse modulus E y (GPa)	60	55.04	20
	Shear modulus G xy (GPa)	4.83	4.43	6.55
	Poisson's coefficient νxy	0.04	0.037	0.04

Table 3

 3 Elastic properties of the equivalent orthotropic laminate.

		C7/PEEK quasi-isotropic [(0/90),(±45),(0/90),	CG/PEEK quasi-isotropic [(0/90) G ,(0/90),(±45),	C8/PEEK orthotropic [(0/90)] 8
		(±45),(0/90),(±45),(0/90)]		(0/90),(±45),(0/90),(±45),(0/90)] S
		Ex(GPa)	Ey(GPa)	Gxy(GPa)	vxy	Ex(GPa)	Ey(GPa)	Gxy(GPa)	vxy	Ex(GPa)	Ey(GPa)	Gxy(GPa)	vxy
	TA	46.57	46.57	15.12	0.25	45.73	45.66	14.82	0.25	60	60	4.83	0.04
	150 • C	42.73	42.73	13.91	0.25	42.03	41.96	13.65	0.25	55.04	55.04	4.43	0.04

Acknowledgement

The authors would like to thank the Ministerio de Educación Superior, Ciencia y Tecnología (MESCYT) of the Dominican Republic for the funds invested in this research.