D Bouscarrat

M Levesque

B Vieille

Influence of time-dependent phenomena on translaminar fracture of woven-ply C/PPS laminates above the glass transition temperature

Keywords: woven-ply composite, thermoplastic, time-dependency, fracture toughness, translaminar fracture, acoustic emission

The time-dependency of damage development and translaminar fracture mechanisms were investigated in 5-harness satin weave carbon fabric reinforced polyphenylene sulfide composites above their glass transition temperature through an approach combining acoustic emission (AE) monitoring and fracture mechanics. Single edge notch specimens from two stacking sequences (quasiistropic and angle-ply) were subjected to cyclic incremental tensile loading. Tensile tests were carried out for several loading rates or histories featuring creep and/or recovery stages. Both laminates' failure mechanisms do not seem to be influenced by time-dependent phenomena. However, AE monitoring revealed AE activity during creep stages for both stacking sequences, thus highlighting possible time-dependent damage events. If those AE events are indeed related to time-dependent damage, this observation would mean that this damage is only subcritical. Those observations need to be investigated further with acoustic emission coupled to other monitoring tools, such as digital image correlation, in-situ microscopic observations or thermography, to provide a better insight of the physical phenomena associated with the monitored acoustic emission signals.

Introduction

(TS)- [START_REF] Karayaka | Deformation and Failure Behavior of Woven 655 Composite Laminates[END_REF][START_REF] Gao | Damage ac-658 cumulation in woven-fabric CFRP laminates under tensile loading: Part 659 1. Observations of damage accumulation[END_REF][START_REF] Osada | Initial fracture behavior of satin woven fabric composites[END_REF][START_REF] Lomov | Experimental methodology of study of damage initiation and development in textile composites in uniaxial tensile test[END_REF][START_REF] Selezneva | Microscale experimental investigation of failure mechanisms in off-axis woven laminates at elevated temperatures[END_REF][START_REF] Montesano | Elevated temperature off-axis fatigue behavior of an eight-harness satin woven carbon-fiber/bismaleimide laminate[END_REF] and thermoplastic (TP)-based composites [START_REF] Daggumati | Local damage in a 5-harness satin weave composite under static tension: Part I Experimental analysis[END_REF][START_REF] Carnevale | Fibre-matrix interfaces in thermoplastic composites: A meso-level approach[END_REF], at 7 Room Temperature (RT). Those studies either focused on on-8 axis (i.e., the loading is applied parallel to the warp or weft 9 bundles) [1-4, 7, 8] or off-axis (i.e., tensile loading on speci-10 mens for which the warp or weft bundles are not aligned with 11 the loading axis) [START_REF] Karayaka | Deformation and Failure Behavior of Woven 655 Composite Laminates[END_REF][START_REF] Selezneva | Microscale experimental investigation of failure mechanisms in off-axis woven laminates at elevated temperatures[END_REF][START_REF] Montesano | Elevated temperature off-axis fatigue behavior of an eight-harness satin woven carbon-fiber/bismaleimide laminate[END_REF][START_REF] Carnevale | Fibre-matrix interfaces in thermoplastic composites: A meso-level approach[END_REF] solicitations. Intra-bundle cracking, 12 meta-delamination (i.e., debonding between warp and waft fi-13 bre bundles [START_REF] Fujii | Microscopic fatigue processes in a plainweave glass-fibre composite[END_REF]), delamination, fibre-bundle breaking and fibre-14 bundle pull-out are damage mechanisms typically observed in 15 such composites. The on-axis behaviour is characterized by a 16 fibre-dominated failure. By opposition, the off-axis response is 17 dominated by matrix and fibre/matrix interface behavior, hence 18 generally leading to significant elongation and/or necking [START_REF] Carnevale | Fibre-matrix interfaces in thermoplastic composites: A meso-level approach[END_REF], [START_REF] Gross | Stress-Intensity Factors for a Single-Edge-Notch Tension Speciment by Boundary Collocation of a Stress Function[END_REF] as well as significant delamination and fibre-bundle pull-out. [START_REF] Brown | Plane Strain Crack Toughness Testing of High Strength Metallic Materials[END_REF] Damage development in woven composites depends on sev-21 eral testing parameters, like temperature and loading rate. An 22 increase in temperature generally leads to an increase in de-23 lamination and fibre pull-out for off-axis solicitation [START_REF] Selezneva | Microscale experimental investigation of failure mechanisms in off-axis woven laminates at elevated temperatures[END_REF][START_REF] Kawai | Off-axis fatigue behavior of plain weave carbon/epoxy fabric laminates at room and high temperatures and its mechanical modeling[END_REF]. [START_REF] Sumpter | Method for Laboratory Determination 731 of Jc[END_REF] However, no significant differences in failure modes were found 25 for 0 • (i.e., aligned with the warp bundles) nor for 90 • so-26 licitations [START_REF] Kawai | Off-axis fatigue behavior of plain weave carbon/epoxy fabric laminates at room and high temperatures and its mechanical modeling[END_REF]. The factors driving temperature-dependent 27 variations are the matrix shear strength and fiber/matrix inter-28 face degradation [START_REF] Selezneva | Microscale experimental investigation of failure mechanisms in off-axis woven laminates at elevated temperatures[END_REF][START_REF] Montesano | Elevated temperature off-axis fatigue behavior of an eight-harness satin woven carbon-fiber/bismaleimide laminate[END_REF][START_REF] Kawai | Off-axis fatigue behavior of plain weave carbon/epoxy fabric laminates at room and high temperatures and its mechanical modeling[END_REF]. Futhermore, it has been demon-29 strated that an increase in frequency reduced the fatigue lives of angle-ply carbon(C)/epoxy woven laminates, but had little effect on C/Polyphenylene Sulfide (PPS) specimens tested under the same conditions (120 • C) [START_REF] Albouy | Influence of matrix ductility on the hightemperature fatigue behavior of off-axis woven-ply thermoplastic and thermoset laminates[END_REF]. The authors explained this difference by significant autogeneous heating in PPS-based laminates. Such heating increases material ductility and leads to larger plastic strains, locally releasing stress concentrations. The authors have also observed that higher loading frequencies respectively reduced and increased the fatigue lives of quasiisotropic C/PPS and C/epoxy laminates [START_REF] Albouy | Influence of matrix ductility on the hightemperature fatigue behaviour of quasi-isotropic woven-ply thermoplastic and thermoset laminates[END_REF]. The authors justified this result with the combined effects of time-dependent phenomena at lower frequencies that increased the ±45 • bundles contribution to the overall behaviour.

A limited number of authors investigated, experimentally, the rate-dependency of interlaminar fracture toughness of TS [START_REF] Zabala | Loading rate dependency on mode I interlaminar fracture toughness of unidirectional and woven carbon fibre epoxy composites[END_REF] and TP [START_REF] Mall | Loading Rate Effect on Interlaminar Fracture Toughness of a Thermoplastic Composite[END_REF] woven composites. It was concluded that a decrease in interlaminar strain energy release rate (SERR) is associated with an increase in loading rate. However, to the best of our knowledge, no study quantified the effects of timedependent behaviour in the case of translaminar fracture (i.e., fracture associated with longitudinal tensile failure through fibre failure [START_REF] Laffan | Translaminar fracture toughness testing of composites: A review[END_REF][START_REF] Bullegas | Engineering the translaminar fracture behaviour of thin-ply composites[END_REF]) in woven composites.

This paper studies the effect of time-dependent phenomena on the translaminar fracture in woven-ply laminates. The material under investigation is a 5-harness satin weave C/PPS. Two stacking sequences were considered: a Quasi-Isotropic (QI) sequence, having a fibre-dominated behaviour, and an Angle-Ply (AP) sequence, characterized by a matrix-dominated behaviour. Tensile tests were carried out on Single-Edge-Notch (SEN) specimens subjected to different quasi-static loading histories (different loading rates and creep/recovery steps) at 120 •

Background information for the determination of fracture toughness parameters

There are different ways to consider fracture mechanics: locally through stress and strain fields around the crack tip, and more globally with an energy criterion like the strain energy release rate [START_REF] Anderson | Fracture mechanics: fundamentals and applications[END_REF]. Furthermore, different fracture mechanics frameworks and fracture toughness parameters are used depending on the material behaviour (e.g., linear elasticity or elasto-plasticity).

Linear Elastic Fracture Mechanics

The Linear Elastic Fracture Mechanics (LEFM) framework relies on the assumption that only small scale yielding (SSY) occurs. In other words, when the plastic zone is very small when compared to the "singularity dominated zone" (SDZ) (i.e., the zone where the crack-tip fields are affected by the presence of the crack). The Stress Intensity Factor (SIF) in mode I (crack opening), K I , which uniquely characterizes crack-tip conditions, can be computed as:

K I = σ remote √ πa 0 f cor (a 0 /W), (1)
where

σ remote = F B.W (2)
is the stress far from the crack. F is the applied load, W and B are the specimen's width and thickness, respectively.

f cor (a 0 /W) is a finite-width correction factor [START_REF] Tada | The analysis of cracks handbook[END_REF]. A function f cor (a 0 /W) has been proposed by Gross and Brown [19,[START_REF] Brown | Plane Strain Crack Toughness Testing of High Strength Metallic Materials[END_REF] for Single-Edge-Notch specimens in Tension (SENT) and is expressed as: 3) yields an accuracy of 0.5% for a/W ≤ 0.6 [START_REF] Tada | The analysis of cracks handbook[END_REF].

f cor (a/W) = 1.122 -0.231(a/W) + 10.550(a/W)
The SERR, G I , can be computed from the SIF, K I , as per:

G I = K 2 I C I , (4) 109
where 110

C I = 1 2E x E y E x E y -ν xy + E x 2G xy (5) 111
for orthotropic materials [START_REF] Laffan | Translaminar fracture toughness testing of composites: A review[END_REF], in which E x , E y and G xy are the 112 stiffness in the x and the y directions and the shear modulus in 113 the x-y plane, respectively. Elastic Plastic Fracture Mechanics (EPFM) is required when 116 the plastic zone expands to a larger zone since the previous frac-117 ture toughness parameters, K I and G I , rely on the assumption 118 that plastic strains are small.

119

The most widely used fracture toughness parameter for 120 elastic-plastic materials is the J-integral [START_REF] Rice | A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks[END_REF] and considers an 121 elastic-plastic material as a nonlinearly elastic material. J has 122 a similar mathematical definition that the SERR G I , but the 123 physical interpretation is different. G I is defined as the poten-124 tial energy required for an increment of crack extension within 125 an elastic body, whereas J rather characterizes the difference 126 in elastic-plastic work for specimens with different crack sizes 127 [START_REF] Dowling | Fatigue Crack Growth During Gross Plasticity and the J-Integral[END_REF]. However, J can still characterize the crack-tip stresses and 128 strains fields. J can be seen as an energy parameter as well as a 129 stress intensity parameter [START_REF] Anderson | Fracture mechanics: fundamentals and applications[END_REF].

130

Several experimental methods have been developped to de-131 termine J. Rice et al. [START_REF] Rice | Some Further Results of J-Integral Analysis and Estimates[END_REF] proposed the first single-specimen 132 method from the strain energy release rate formulation of J by 133 separating it into elastic, J el , and plastic, J pl , components, as:

134 J = J el + J pl . ( 6
) 135
Sumpter and Turner [START_REF] Sumpter | Method for Laboratory Determination 731 of Jc[END_REF] proposed another expression for J as: 136

J = η el A el Bb + η pl A pl Bb , (7) 137
where A el and A pl are the elastic and plastic works done, respec-138 tively. η el and η pl are parameters that depend on the specimen's 139 geometry and loading conditions. B and b are the specimen's 140 thickness and the uncracked ligament length, respectively. A el 141 and A pl are calculated from the load-Load Line Displacement 142 (LLD) curves, as schematized in Figure 1a. Several approaches 143 can be used to determine η el and η pl . Sharobeam and Landes 144 [START_REF] Sharobeam | The load separation criterion and 734 methodology in ductile fracture mechanics[END_REF] proposed a methodology based on the load separation as-145 sumption allowing to represent the load as the multiplication of 146 a material deformation function and a crack geometry function. 147 This method was used [START_REF] Chabchoub | Determination of J-R curves by load separation criterion in highly duc-738 tile TP-based composites under high temperature conditions[END_REF] to determine η pl for a Single-Edge-148 Notch (SEN) C/PPS dogbone specimen subjected to a clamped 149 tensile loading. The authors used the compliance method to 150 compute η el . The computed values are summarized in Table 1. 151 Since the J-integral was developed under the nonlinear elas-152 ticity assumption, analyses based on this assumption should 153 not be valid for an elastic-plastic material if unloading oc-154 curs. Dowling and Begley [START_REF] Dowling | Fatigue Crack Growth During Gross Plasticity and the J-Integral[END_REF][START_REF] Dowling | Geometry Effects and the J-Integral Approach to Elastic-741 Plastic Fatigue Crack Growth[END_REF] were the first to apply 155

F δ A pl A el (a) F δ ∆J = C I ∆K 2 + η pl A cycle Bb A cycle (b)
Figure 1: Typical Load-LLD curves for an elasto-plastic material subjected to (a) a monotonic loading and (b) a cyclic loading with a crack closure effect [START_REF] Dowling | Geometry Effects and the J-Integral Approach to Elastic-741 Plastic Fatigue Crack Growth[END_REF]. The y-axis is the applied load, while the x-axis is the displacement between the points where the load is applied. A el and A pl are the elastic and plastic works done, respectively. AE monitoring has several advantages. The first is that it enables volume measurements of damage propagation, unlike DIC. Therefore, AE analysis may be used to identify the onset of subcritical damage, while DIC detects the onset of macrocrack propagation. Another advantage is that AE enables a possible distinction between the different damage mechanisms occurring within the specimens through data clustering [35].

Materials and methods

Material and specimen geometry

The material under investigation is a carbon fabric reinforced polyphenylene sulfide (C/PPS). The fabric is a balanced 5harness satin weave (5HS) of carbon fibres (T300 3K) purchased from Soficar. The PPS matrix (Fortron 2014) was supplied by Ticona. Its glass transition temperature is about 95

• C [38].
The quasi-isotropic and angle-ply laminated plates were manufactured by hot press consolidation of 0.317 mm thick prepregs with a volume fraction of carbon fibres equal to 50%. The consolidation process was achieved at 310 ± 15 • C and 10 bars, as schematically shown in Figure 2. Two unsymmetric stacking sequences were considered, namely:

• Quasi-isotropic (QI):
[(0/90), (±45), (0/90), (±45), (90/0), (±45), (90/0)]

• Angle-ply (AP): [(±45) 3s (±45)] 200 mm long specimens were waterjet-cut from 600 × 600 mm 2 plates. The specimen geometry is that proposed in [START_REF] Albouy | Influence of matrix ductility on the hightemperature fatigue behavior of off-axis woven-ply thermoplastic and thermoset laminates[END_REF][START_REF] Albouy | Influence of matrix ductility on the hightemperature fatigue behaviour of quasi-isotropic woven-ply thermoplastic and thermoset laminates[END_REF], with an additional notch, as illustrated in Figure 3. The single-edge-notch specimens were obtained by machining a central notch with a precision endless diamond wire saw having a radius of 0.085 mm. The notch length was chosen to obtain a ratio a 0 W ≈ 0.3, a 0 being the initial notch length and W the specimen's width. Ratios ranging from 0.25 to 0.32 were obtained.

AE sensors

Figure 3: Notched specimen geometry. The dogbone specimens were waterjetcut from plates. The notches were manufactured with a precision endless diamond wire saw having a radius of 0.085 mm. The notch length to width ratio is about 0.3. The specimen length, width and thickness were around 200, 15 and 2.3 mm, respectively. The two AE sensors were PAC micro80 sensors and were used to spatially filter the AE events.

Mechanical testing

All the quasi-static tests were performed on a MTS 810 servo-hydraulic testing machine with a 100 kN load cell. The Table 2 summarizes the testing configurations for AP and QI stacking sequences.

Acoustic emission monitoring

The acoustic emission activity was monitored by means of two PAC micro80 sensors and a PCI-2 data acquisition 3, to spatially filter the AE 260 events. Every signal was amplified by 20 dB using 2/4/6 261 pre-amplifiers. The acquisition was done through the soft-262 ware AEwin vE4.70. The acquisition threshold was set to 263 45 dB and the Peak-Definition-Time/Hit-Definition-Time/Hit-264 Lockout-Time were set to 30/100/300 µs. Noesis (v7.0) and 265 Matlab software were used for the post-analysis. The follow-266 ing analysis is based on all events localized between the two 267 sensors by keeping the hit from the nearest sensor. The fracture toughness parameters G I , for elastic behaviours, 270 and ∆J, for inelastic ones, were computed.

271

G I can be evaluated from Equation (4) using Equations (1) 272 and (5). Its critical value, G c , can be obtained from the critical 273 stress causing crack extension, σ remote c . This method was used 274 as a first approximation.

275

Even though the method to determine ∆J was developed 276 for elastic-plastic materials under cyclic loading, a similar ap-277 proach is used in this paper to evaluate the ∆J-like integral for 278 visco-elasto-plastic materials under incremental load-unload 279 solicitation. Thus, for a visco-elastic-plastic material subjected 280 to a cyclic loading, Equation ( 7) becomes:

F δ ∆A i irrev ∆A i rev i i -1
Figure 5: Typical Load-LLD curves for a visco-elasto-plastic material subjected to an incremental load-unload test with no crack closure effect. ∆A irrev is the energy dissipated during a cycle, while ∆A rev is the reversible work. Figure 8 shows the failure surface of a representative QI specimen. This crack grows self-similarly (i.e., crack propagation occurs in the plane of the initial notch), resulting in an opening mode failure, as illustrated in Figure 8a. The main damage mechanisms involved by this configuration are intra-bundle transverse cracking and breakage of 0 • and ±45 • bundles. Intrabundle cracking is not limited to the crack path vicinity, as shown in Figure 8b. Furthermore, it seems that no extensive delamination can be observed while some fibre bundle pull-out can be observed in Figure 8c, especially at the edges of ±45 • oriented plies due to edge effects. The main fracture mode is therefore translaminar. It also seems that there is no visible qualitative difference in the fracture morphology between the different loading conditions, suggesting no significant influence of time-dependent phenomena on failure mechanisms. Figure 9 displays the critical strain energy release rate, G c for each configuration. The LEFM framework was considered here as a first approximation. These values were computed from Equation (4) and the maximum stress for each test by assuming: i) that no prior crack extension occurred and ii) that the QI specimens had a macroscopically quasi-isotropic behavior. Figure 9 shows that G c values exhibit no significant difference between the loading conditions. These results suggest that the influence of time-dependent phenomena on G c is negligible in QI specimens, whose macroscopic failure mode is fibre-dominated.

∆J = ∆J rev + ∆J irrev = η rev ∆A rev Bb + η irrev ∆A irrev Bb , (8

AE activity

Figure 10 shows the cumulative events per loading cycle as a function of the maximal remote stress reached during each cycle for the LU5, LU50 and LU500 test configurations. The discontinuous symbols correspond to whole sets of experimental data points, while the continuous lines are exponential regressions. This figure suggests that the higher the solicitation rate, the slower the AE activity as a function of the remote stress is. However, this trend is not that obvious between the LU5 and LU50 configurations due to data dispersion in the LU5 data set. This tendency should be confirmed by additional tests with complementary techniques. than those from the LU5 and LU50 test conditions. The higher σ remote r for the LcUr50 loading might be due to the lower notch ratio more than a time-dependent effect. r is not time-dependent. σ remote r and r do not seem to be significantly influenced by time-dependent phenomena, as illustrated in Figures 13a and13b.

Angle-ply laminates

Table 4 summarizes the number of cycles to failure of all AP specimens for the different loading conditions. It appears that the loading configuration does not influence significantly the number of cycles to failure.

Fracture morphology and strain energy release rate

Figure 14 illustrates the fracture and damage mechanisms occurring within SEN AP specimens. As shown in Figure 14a, it appears that the crack does not grow self-similarly, contrary to what was observed in QI specimens. Indeed, the crack seems to propagate along the (±45 • ) bundles leading to a mixed-mode I-II (opening-shear) failure, as already observed in the same ma- Figure 10: Cumulative events for QI SEN specimens subjected to LU5/50/500 test conditions at 120 • C. The symbols correspond to whole sets of experimental data points, while the continuous lines are exponential regressions. It appears that higher solicitation rates lead to slower AE activity as a function of the remote stress. This tendency is less obvious between the LU5 and LU50 test conditions. terial [START_REF] Chabchoub | Determination of J-R curves by load separation criterion in highly duc-738 tile TP-based composites under high temperature conditions[END_REF]41]. Figures 14a and14d show that failure occurred 385 after an extensive delamination and meta-delamination leading 386 to fibre bundles pull-outs. Thus, this experimental configuration . Complete self-similarity of a fracture process is hardly ever found experimentally in fiber-reinforced polymer laminates. Equation 7was already used to compute the fracture toughness during non-self-similar propagation [41,42]. Therefore, Equation 8 is assumed valid to calculate a J-like parameter as a first approximation in order to compare the different loading configurations, regardless the crack propagation path (self-similar or not self-similar). In the present work, the computation of ∆J is based on the computation of the energy dissipated during a cycle. However, the theoretical validity of this approach should be confirmed. Figure 15 suggests that the data dispersion is quite significant, especially for LcU tests, hence hindering the time-dependent phenomena influence on ∆J irrev . However, an emerging trend can be guessed from the early stage of the test. ∆J irrev values computed from the LcUr configuration are higher than those extracted from the LU configurations, while ∆J irrev values computed from the LcU configurations are positioned between those extracted from LU and LcUr loading cases.

AE activity

Figure 16 shows the cumulative events and cumulative absolute energy per cycle as a function of the maximal remote stress during each cycle. Figure 16a shows that the LU load configuration results in lower amount of AE events than that of the LcU and LcUr loading conditions for stresses higher than 60 MPa. However, the same conclusion is not immediate for stresses close to ultimate failure due to data dispersion. This dispersion could result from a failure mechanism that is not purely translaminar (see Section 4.2.2). These results suggest that there is more damage accumulation in specimens subjected to creep stages. However, conclusions can hardly be drawn about the criticality of damage depending on the loading conditions because there is no significant difference in the evolution of the cumulative absolute energies (see Figure 16b). when compared to the amount of events appearing during the 443 loading phases (Figure 17a). This observation suggests that sig-

QI stacking sequence

The experimental results presented in Figures 6 to 11 suggest that potential time-dependent phenomena have little influence on QI specimens fracture mechanisms, at the macroscopic scale. Though it appears that the LcUr50 configuration has a higher σ remote r (Figure 7a), this difference can be explained by the shorter crack length. Indeed, the LcUr50 configuration presents a notch ratio significantly different (about -17%) from the other ones. As time-dependent effects are limited in QI specimens, and assuming that QI specimens display linearly elastic and brittle fracture without prior crack propagation, the critical energy release rate G c should be material-dependent and not dependent on the crack length. Therefore, G c is a more relevant parameter than the σ remote r to compare the influence of loading configurations on translaminar failure. This is confirmed in Figure 9 as no significant differences in G c are observed for the different loading configurations. Furthermore, no significant difference was observed in terms of fracture morphology (Figure 8) and number of cycles to failure (Table 3). However, AE seems to indicate that the higher the solicitation rate, the slower the evolution of cumulative events as a function of the remote stress is (Figure 10). In addition, the tests conducted with creep and recovery stages show that creep stages may induce some time-dependent damage, as suggested from the AE activity (Figure 11). However, the influence of creep seem to be significantly influenced by time-dependent behaviors involved during creep stages. This could either mean that the creep steps only affect subcritical damage or that the macrocrack propagation is mainly unstable after its initiation, thus leading to similar fracture surfaces. The first observation is supported by the AE activity analysis that suggests an influence of time-dependent phenomena on the onset of damage accumulation and subcritical damage accumulation. Indeed, damage development globally occurs earlier for the LcU and LcUr tests, when compared to what happens during the LU tests, based on the evolution of the cumulative AE events (Figure 16). This observation becomes less obvious close to ultimate failure. This could underline that critical damage accumulation is virtually not influenced by time-dependent phenomena for the studied time scale and that sub-critical damage does not influence the ultimate failure of the specimens, as highlighted by the number of cycles to failure in Table 4. This analysis also points out significant events, and thus probably damage, involved during creep stages, when compared to the events occurring during loading phases (Figure 17).

The analysis of ∆J irrev as a function of the cumulative AE absolute energy (Figure 15) yields curves whose shape is similar to the conventional J-R curves. However, no definitive conclusion about the influence of the time-dependent phenomena on the fracture toughness can be drawn without a reliable AE crite-

Comparison between QI and AP laminates

AP specimens exhibited a highly time-dependent behaviour, when compared to QI specimens (see Figures 6 and12). Furthermore, the AP specimens exhibited a strain at failure 10 times higher than that of the QI specimens. However, the stress at failure is about twice as low as in AP specimens, resulting in greater computed ∆J irrev in AP laminates, when compared to the values of G c in QI laminates. This difference is primarily due to different failure mechanisms resulting from specific microstructures. On the one hand, AP specimens display a highly visco-elasto-plastic behaviour that could slow down the prop-559 agation of the macro-crack through stress redistribution lead-560 ing to more extensive secondary damage development around 561 the notch, as illustrated in Figure 14. Furthermore, AP spec-562 imens are characterized by extensive delamination, fibre bun-563 dle/matrix debonding and pull-out, leading to higher computed 564 ∆J irrev , when compared to the strain energy release rate of QI 565 specimens, for which interfacial failure is limited. On the other 566 hand, QI specimens, whose macroscopic behaviour is fibre-567 dominated, are characterized by less plasticity, less secondary 568 damage and a smaller FPZ. This observation is also supported 569 by the AE analysis of the LU50 configuration. Indeed, the fail-570 ure of AP samples generates slightly more AE events than their 571 QI counterparts, suggesting that more extensive damage devel-572 ops in AP laminates.

573

It should be recalled that this fracture mechanics-based anal-574 ysis is a qualitative comparison. This approach only provides 575 rough estimations of the translaminar fracture toughness of the 576 studied specimens. In addition, QI and AP specimens exhibit 577 different fracture mechanisms, and therefore require specific 578 experimental procedures. QI specimens present elastic-brittle 579 behaviour characterized by unstable brittle failure without prior 580 stable growth, therefore a critical value can be defined un-581 ambiguously. However, AP specimens exhibit highly elasto-582 plastic behaviour characterized by little stable crack propaga-583 tion and ultimately an unstable propagation. Thus, the fracture 584 toughness results are presented in a form equivalent to a J-R 585 curve for AP specimens, what was not possible for QI speci-586 mens due to unstable failure. Ultimately, further investigations are required, and the exper-627 imental protocol should be improved to obtain more quantita-628 tive and accurate results. A few improvements can be consid-629 ered to enhance the quantitative capabilities of the experimental 630 protocol, namely

631

• Develop of a stable crack propagation. This problem 632 can be solved by using other specimen geometries. Tests 633 under displacement-controlled conditions should be used 634 as force-controlled tests generally lead to an early crack 635 growth instability.

636

• Use complementary monitoring tools along with AE to 637 follow the macro-crack initiation and its propagation to 638 obtain more reliable quantitative results from the fracture 639 mechanics analyses. This could be achieved using an ad-640 ditional monitoring technique, as DIC or IR thermogra-641 phy. Though AE data presents a significant scatter in this 642 study, such technique provides real-time and in-situ quali-643 tative information regarding damage evolution and the in-644 teraction between damage and time-dependent effects at 645 the microscopic scale. In addition, AE activity may be 646 correlated with the macro-crack propagation [33,34]. To 647 reduce data scattering, additional filters (either feature-648 based or spatial filters) may be needed to specifically work 649 on events, which originate from the FPZ. Furthermore, 650 an optimization of the experimental procedure resulting 651 in a crack growth with less unwanted interlaminar failure 652 mechanisms may result in less scatter in AE data.

1

  Woven-ply composites exhibit damage mechanisms at the2 micro-(scale of the fibre and matrix), meso-(scale of the bun-3 dles) and macroscopic (scale of the laminate) scales. Damage 4 development under tensile loading in woven composite lami-5 nates has been investigated by several researchers for thermoset 6

  C to investigate the effect of time-dependent phenomena on failure mechanisms and corresponding fracture toughness. An AE setup was used as an in-situ monitoring of damage development and a potential damage state parameter. The novelty of our work lies in the study of the influence of time-dependent behaviour on translaminar failure of woven laminates through a fracture mechanics framework. Section 2 describes the framework on which the fracture mechanics analysis is based. The materials and methods used to study the influence of time-dependent phenomena on the fracture behaviours of AP and QI 5-harness satin weave C/PPS composites at 120 • C > T g are detailed in Section 3. The experimental results are presented in Section 4. Section 5 discusses the results and Section 6 concludes this work.

114 2 . 2 .

 22 Elastic Plastic Fracture Mechanics 115

Figure 2 :

 2 Figure 2: Manufacturing cycle for hot press C/PPS consolidated plates. The consolidation process of seven 0.317 mm thick C/PPS prepregs was achieved at 310 ± 15 • C and 10 bars.

  specimens were heated in a MTS 651 environmental chamber at 120 • C. Longitudinal strains were measured by means of a blade-extensometer having a gage length l 0 equal to 25 mm. The SEN specimens were subjected to different incremental force-controlled loading configurations, as shown in Figure 4, namely: • Load-unload (LU) at 5-50-500 N/s • Load at 50 N/s -15 minutes creep -unload at 50 N/s (LcU) • Load at 50 N/s -15 minutes creep -unload at 50 N/s -15 minutes recovery (LcUr) The LU condition was designed to study the influence of loading rate on damage while the LcU and LcUr conditions were designed to investigate the influence of creep periods on fracture mechanisms. The creep time has to be long enough to exacerbate the viscoelastic effects depending on the testing temperature. In the present case, the temperature is about 120 • C above the matrix T g . In addition, Albouy has observed that 90 to 95% of the full creep strain occurred within 15 minutes in the case of 24 h creep tests for the same material under the same temperature [39]. As a result, a creep time of 15 minutes is assumed long enough to make a significant difference on the influence of time-dependent effects on damage in the fracture process zone around the crack tip. Creep times of 15 minutes were therefore a good compromise between test duration and the representativeness of the influence of the viscoelastic behavior on crack growth. The solicitation rate for LcU and LcUr configurations was fixed to 50 N/s for both stacking sequences as a compromise between minimizing the machine overshoot and minimizing creep effects during the loading phase. The load levels were determined based on the ultimate load obtained through forcecontrolled monotonic tensile tests. The ultimate loads are about 5400 N and 3400 N for QI and AP specimens, respectively.

Figure 4 :

 4 Figure 4: Illustration of the different incremental tensile loading conditions: (a) Load-unload at 5/50/500 N/s, (b) Load at 50 N/s -15 minutes creep -unload at 50 N/s and (c) Load at 50 N/s -15 minutes creep -unload at 50 N/s -15 minutes recovery

268 3 . 4 .

 34 Determination of fracture toughness parameters 269

Figure 11 Figure 6 :Figure 7 :

 1167 Figure 11 reports the AE activity for the LcUr test configuration for QI laminates. This figure shows that a significant amount of AE events appeared during the high stress level creep stages.

361 4 . 2 . 1 .Figure 12 Figure 13

 4211213 Figure12reports the stress-strain curves for SEN AP spec-

Figure 8 :Figure 9 :

 89 Figure 8: Microscopic observations of (a) the fracture surface, (b) a secondary intra-bundle cracking and (c) the edges of a QI SEN C/PPS specimen subjected to LU500 at 120 • C (the red dot line is an indication of the extent of the fracture process zone and the solid yellow lines indicate secondary intra-bundle cracking). The crack grew in a self-similar manner resulting in a mode I failure. The main damage mechanisms involved are intra-bundle cracking and breakage of bundles. The failure is translaminar at the macroscopic scale. No difference in fracture morphology was observed between the different loading conditions.

387

  does not lead to a pure translaminar failure, which is accompa-388 nied by damage mechanisms associated with interlaminar fail-389 ure. Many secondary intra-bundle cracks (Figure 14b), as well 390 as some inter-bundle/interfacial cracks (Figure 14c) away from 391 the main crack's vicinity, are observed, hence revealing a large 392 damaged zone around the crack. Furthermore, no significant 393 difference was observed on the fracture morphology between 394 the different loading conditions, suggesting no substantial influ-395 ence of time-dependent phenomena on the failure mechanisms 396 at the macroscopic scale.

  397

Figure 15

 15 Figure 15 represents the cumulative ∆J irrev evolution as a

Figure 11 :

 11 Figure 11: Density of AE events occurring during a LcUr50 test at 120 • C. It appears that a significant amount of AE events occurred during the creep steps for high stresses. These events might result from time-dependent damage.

Figure 17 Figure 12 :Figure 13 :

 171213 Figure17shows a similar approach except that the AE ac-

444Figure

  Figure 17b.449

Figure 14 :Figure 15 :

 1415 Figure 14: Microscopic observation of (a) the fracture surface, (b) a secondary intra-bundle (continuous yellow line) and (c) secondary inter-bundle/interfacial cracking (continuous red line), as well as (d) the edges of an AP SEN C/PPS specimen subjected to LU50 at 120 • C (the red dot line is an indication of the extent of the fracture process zone). The crack path seems to follow the ±45 • ) bundles leading to a mixed-mode I-II. An extensive delamination appeared during failure resulting in mixed translaminar-interlaminar failure. No difference in fracture morphology were observed between the different loading conditions.

Figure 16 :

 16 Figure 16: (a) Mean cumulative AE events and (b) Mean cumulative AE absolute energy per cycle for AP SEN specimens subjected to various test conditions at 120 • C (the "error" bars represent the min and max values for each cycle).The LU test condition triggered a lower amount of AE events than the LcU and LcUr load configurations, indicating less damage accumulation. However, the evolution of the cumulative AE absolute energy indicates that the criticality of damage is the same for all the test configurations.

587 6 .Figure 17 :

 617 Figure 17: (a) Mean cumulative AE events and (b) Mean cumulative AE absolute energy during loading and creep for AP SEN specimens subjected to various test conditions at 120 • C (the "error" bars represent the min and max values for each cycle). More events appear during the creep stages indicating possible timedependent damage. However, no significant difference can be observed in the evolution of the cumulative AE absolute energies between the loading and creep phases.

  2

Table 1 :

 1 Values of η el and η pl evaluated in C/PPS angle-ply SEN dogbone specimens subjected to tensile loading at T > T g[START_REF] Chabchoub | Determination of J-R curves by load separation criterion in highly duc-738 tile TP-based composites under high temperature conditions[END_REF]

		η el	η pl
		0.8674	0.7718
	156	the J-integral concept to cyclic loading to predict fatigue crack
	157	growth and introduced the ∆J concept. The ∆J concept is based
	158	on changes in quantities (e.g., displacement, strain, etc.) from
	159	a reference state. The onset of crack opening/closure is gener-
	160	ally defined as the reference state. Dowling [27] proposed an
	161	estimation method similar to Equation 7 using the hysteresis
	162	loops of the Load-LLD cycles to compute the plastic compo-
	163	nent ∆J pl , as illustrated in Figure 1b, while the elastic compo-
	164	nent was evaluated using ∆K, which is the equivalent of ∆J for
	165	elastic materials. The applicability of the ∆J concept as a frac-
	166	ture toughness parameter for cyclic loading is still controver-
	167	sial from a theoretical standpoint. However, the authors noted a
	168	good correlation between ∆J and fatigue crack growth rates.
	169	2.3. Damage and crack propagation monitoring
	170	Several methods can be used to evaluate, qualitatively or
	171	quantitatively, the extent of crack development during notch
	172	propagation experiments. Crack development can be evaluated
	173	through the unloading compliance method [28], Digital Image
	174	Correlation (DIC) [29, 30], infrared (IR) thermography [31, 32]
	175	or Acoustic Emission (AE) [31, 33-37].
	176	The acquisition of AE signals enables the monitoring of dam-
	177	age events around the crack. One approach consists in tracking
	178	damage accumulation and in possibly identifying crack initia-
	179	tion/propagation through any change in AE activity (i.e, cumu-
	180	lative events/counts or cumulative energy) [33-36]. Another
	181	approach is to directly track the crack propagation through the
	182	localization of AE events generated at the crack tip [31, 34, 37].
	183	Some of the previous authors also correlated crack extension
	184	with AE activity, either with cumulative hits [33] or with cu-
		mulative AE energy [34].

Table 2 :

 2 Summary of tests carried out on QI and AP laminates for each loading configuration

		Loading #	B 1	W 1	Notch	Load
				(mm)	(mm)	ratio 2	increment
		LU5	3 2.26 16.27 0.292-0.313	10%
		LU50 3 2.31 16.27 0.289-0.317	10%
	QI	LU500 3 2.25 16.27 0.288-0.305	10%
		LcU50 -	-	-	-	-
		LcUr50 3 2.16 16.27 0.245-0.258	5%
		LU5	-	-	-	-	-
		LU50 2 2.33 14.81 0.307-0.317	5%
	AP	LU500 -	-	-	-	-
		LcU50 3 2.36 14.79 0.309-0.318	5%
		LcUr50 3 2.34 14.85 0.304-0.309	5%
	1 Mean values
	2 Min-max values
	card. The sensors were separated by 60 mm in a linear ar-259
	rangement, as shown in Figure

Table 3 :

 3 Number of cycles to failure for the different loading configurations in the case of QI specimens

	305
	306	and r respectively, for the LU (5-50-500 N/s) and LcUr
	307	(50 N/s) loading conditions. Figure 7a suggests that σ remote r	for
	308	specimens subjected to loading LU500 is slightly higher than
	309	those obtained for specimens subjected to loadings LU5 and
	310	LU50. In addition, σ remote r	obtained for loading LcUr50 might
	311	be higher than those resulting from other loadings due to its
	312	slightly lower notch ratio. On the contrary, Figure 7b shows
		that r is insensitive to both loading rate and creep stages.

)

282

where ∆A rev and ∆A irrev can be evaluated from the Load-LLD 283 curves, as illustrated in Figure

5

. It should be noted that no 284 crack closure phenomena, as illustred in Figure

1b

, were ob-285 served during the tests. Furthermore, only the irreversible com-286 ponent was investigated because the component J el is only sig-287 nificant at the onset of mechanical loading, whereas the compo-288 nent J pl becomes prominent throughout the test

[START_REF] Chabchoub | Determination of J-R curves by load separation criterion in highly duc-738 tile TP-based composites under high temperature conditions[END_REF]

. As a first 289 approximation, η irrev was considered to be equal to η pl (Table

290

1). This value was determined by Chabchoub et al.

[START_REF] Chabchoub | Determination of J-R curves by load separation criterion in highly duc-738 tile TP-based composites under high temperature conditions[END_REF]

for 291 the same material, the same geometry and for identical loading 292 conditions.

293 4. Results

294 4.1. Quasi-isotropic laminates 295 4.1.1. Stress-strain macroscopic response 296 Figure 6 shows the stress-strain curves for SEN QI speci-297 mens subjected to LU (5-50-500 N/s) and LcUr (50 N/s) load-298 ings. This figure shows that QI laminates exhibit a slightly non-299 linear behaviour, probably due to slight plasticity and progres-300 sive damage development as the applied stress approaches the 301 ultimate strength [40]. Furthermore, it appears that QI speci-302 mens submitted to the LcUr condition undergo some viscoelas-303 tic, viscoplastic and/or time-dependent damage phenomena. 304 Figure 7 shows the remote stress and strain at failure, σ remote r 313 Table 3 summarizes the number of cycles to failure of all 314 tested specimens for the different loading conditions in the case 315 of QI specimens. It can be seen that the loading configuration 316 does not influence significantly the number of cycles to failure, 317 even for different load increments.

318

Table 4 :

 4 Number of cycles to failure for the different loading configurations in the case of AP specimens

	Configuration Load increment	Number of cycles to failure # 1 # 2 # 3
	LU50	5%	23	22	-
	LcU50	5%	20	23	21
	LcUr50	5%	21	22	22

Growth Monitoring in Ceramic Matrix Composites by Combined Infrared