https://sam.ensam.eu:443 The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material. Mon, 09 Mar 2026 03:08:59 GMT 2026-03-09T03:08:59Z http://hdl.handle.net/10985/8269 Étude numérique du comportement en fatigue à grand nombre de cycles d’agrégats polycristallins de cuivre ROBERT, Camille; SAINTIER, Nicolas; PALIN-LUC, Thierry; MOREL, Franck Numerical study of high cycle fatigue behaviour of copper polycrystalline aggre- gates. An analysis of high cycle fatigue behaviour is undertaken via the numerical simulation of polycrystalline aggregates. The metallic material chosen for investigation is Copper, which has a FCC crystalline structure. The REV, which is composed of 300 randomly orientated equiaxed grains, is loaded at the fatigue limit determined at 10/7 cycles. The aim is to calculate the mechanical quantities at the mesoscopic scale (average quantities in the grains) after cyclic stabilisation has been achieved. The results highlight the fact that the mechanical quantities at this scale have a large scatter. A statistical analysis of the response of the aggregate for different loading conditions (tensile, torsion, and in-phase tension-torsion) is done. Thanks to the sufficiently large number of different microstructures investigated, a critical analysis of the Dang Van and Crossland multiaxial fatigue criteria has been undertaken, using the local mechanical quantities. Sat, 01 Jan 2011 00:00:00 GMT http://hdl.handle.net/10985/8269 2011-01-01T00:00:00Z ROBERT, Camille SAINTIER, Nicolas PALIN-LUC, Thierry MOREL, Franck Numerical study of high cycle fatigue behaviour of copper polycrystalline aggre- gates. An analysis of high cycle fatigue behaviour is undertaken via the numerical simulation of polycrystalline aggregates. The metallic material chosen for investigation is Copper, which has a FCC crystalline structure. The REV, which is composed of 300 randomly orientated equiaxed grains, is loaded at the fatigue limit determined at 10/7 cycles. The aim is to calculate the mechanical quantities at the mesoscopic scale (average quantities in the grains) after cyclic stabilisation has been achieved. The results highlight the fact that the mechanical quantities at this scale have a large scatter. A statistical analysis of the response of the aggregate for different loading conditions (tensile, torsion, and in-phase tension-torsion) is done. Thanks to the sufficiently large number of different microstructures investigated, a critical analysis of the Dang Van and Crossland multiaxial fatigue criteria has been undertaken, using the local mechanical quantities. http://hdl.handle.net/10985/7497 High cycle multiaxial fatigue crack initiation : experimental observations and microstructure simulations AGBESSI, Komlan; SAINTIER, Nicolas; PALIN-LUC, Thierry This study provides an analysis of high cycle multiaxial fatigue crack initiation modes based on SEM observations.The statistical study of crack initiation preferential sites shows that grains with multiple slip have a high probability of crack initiation. The application of Dang Van criterion at the grain scale using finite element analysis (cubic elasticity with / or without crystal plasticity) on 3D synthetic semi-periodic microstructures shows a strong heterogeneity of both the hydrostatic stress and shear. The evolution of this heterogeneity introduced by the material behavior is discussed. Finally, a method based on the extreme values statistics is proposed and applied to the fatigue indicative parameter associated to the Dang Van criterion. The effects of free surface and constitutive material model were analyzed. Tue, 01 Jan 2013 00:00:00 GMT http://hdl.handle.net/10985/7497 2013-01-01T00:00:00Z AGBESSI, Komlan SAINTIER, Nicolas PALIN-LUC, Thierry This study provides an analysis of high cycle multiaxial fatigue crack initiation modes based on SEM observations.The statistical study of crack initiation preferential sites shows that grains with multiple slip have a high probability of crack initiation. The application of Dang Van criterion at the grain scale using finite element analysis (cubic elasticity with / or without crystal plasticity) on 3D synthetic semi-periodic microstructures shows a strong heterogeneity of both the hydrostatic stress and shear. The evolution of this heterogeneity introduced by the material behavior is discussed. Finally, a method based on the extreme values statistics is proposed and applied to the fatigue indicative parameter associated to the Dang Van criterion. The effects of free surface and constitutive material model were analyzed. http://hdl.handle.net/10985/8394 Statistical assessment of multiaxial HCF criteria at the grain scale HOR, Anis; SAINTIER, Nicolas; ROBERT, Camille; PALIN-LUC, Thierry; MOREL, Franck Multiaxial high cycle fatigue modeling of materials is an issue that concerns many industrial domains (automotive, aerospace, nuclear, etc.) and in which many progress still remains to be achieved. Several approaches exist in the literature: invariants, energy, integral and critical plane approaches all of them having their advantages and drawbacks. These different formulations are usually based on mechanical quantities at the micro or mesoscales using localization schemes and strong assumptions to propose simple analytical forms. This study aims to revisit these formulations using a numerical approach based on crystal plasticity modeling coupled with explicit description of microstructure (morphology and texture) and proposes a statistical procedure for the analyses of numerical results in the HCF context. This work has three steps: First, 2.5D periodic digital microstructures based on a random grain sizes distribution are generated. Second, multiaxial cyclic loading conditions corresponding to the fatigue strength at 106 cycles are applied to these microstructures. Third, the mesoscopic Fatigue Indicator Parameters (FIPs), formulated from the different criteria existing in the literature, are identified using the finite element calculations of the mechanical fields. These mesoscopic FIP show the limits of the original criteria when it comes to applying them at the grain scale. A statistical method based on extreme value probability is used to redefine the thresholds of these criteria. These new thresholds contain the sensitivity of the HCF behavior to microstructure attributes. Finally, the biaxiality and phase shift effects are discussed at the grain scale and the loading paths of some critical grains are analyzed. Wed, 01 Jan 2014 00:00:00 GMT http://hdl.handle.net/10985/8394 2014-01-01T00:00:00Z HOR, Anis SAINTIER, Nicolas ROBERT, Camille PALIN-LUC, Thierry MOREL, Franck Multiaxial high cycle fatigue modeling of materials is an issue that concerns many industrial domains (automotive, aerospace, nuclear, etc.) and in which many progress still remains to be achieved. Several approaches exist in the literature: invariants, energy, integral and critical plane approaches all of them having their advantages and drawbacks. These different formulations are usually based on mechanical quantities at the micro or mesoscales using localization schemes and strong assumptions to propose simple analytical forms. This study aims to revisit these formulations using a numerical approach based on crystal plasticity modeling coupled with explicit description of microstructure (morphology and texture) and proposes a statistical procedure for the analyses of numerical results in the HCF context. This work has three steps: First, 2.5D periodic digital microstructures based on a random grain sizes distribution are generated. Second, multiaxial cyclic loading conditions corresponding to the fatigue strength at 106 cycles are applied to these microstructures. Third, the mesoscopic Fatigue Indicator Parameters (FIPs), formulated from the different criteria existing in the literature, are identified using the finite element calculations of the mechanical fields. These mesoscopic FIP show the limits of the original criteria when it comes to applying them at the grain scale. A statistical method based on extreme value probability is used to redefine the thresholds of these criteria. These new thresholds contain the sensitivity of the HCF behavior to microstructure attributes. Finally, the biaxiality and phase shift effects are discussed at the grain scale and the loading paths of some critical grains are analyzed. http://hdl.handle.net/10985/8814 Overload effects on a ferritic-baintic steel and a cast aluminium alloy: two very different behaviours SAINTIER, Nicolas; PALIN-LUC, Thierry; EL DSOKI, Chalid; BIDONARD, Hadrien; KAUFMANN, Heinz; DUMAS, Christian; VÖLLMECKE, F.J.; SONSINO, Cetin Morris Load controlled fatigue tests were performed up to 107 cycles on flat notched specimens (Kt =2.5) under constant amplitude and variable amplitude loadings with and without periodical overloads. Two materials are studied: a ferritic-bainitic steel and a cast aluminium alloy. These materials have a very different cyclic behaviour: the steel exhibits cyclic strain oftening whereas the Al alloy shows cyclic strain hardening. The fatigue tests show that, for the steel, periodical overload applications reduce significantly the fatigue life for fully reversed load ratio (Rr = – 1), while they have no influence under pulsating loading (Rr = 0). For the Al alloy over-loads have an effect (fatigue life decreasing) only for variable amplitude loadings. The detrimental effect of overloads on the steel is due to ratcheting at the notch root which evolution is overload's dependent. Sat, 01 Jan 2011 00:00:00 GMT http://hdl.handle.net/10985/8814 2011-01-01T00:00:00Z SAINTIER, Nicolas PALIN-LUC, Thierry EL DSOKI, Chalid BIDONARD, Hadrien KAUFMANN, Heinz DUMAS, Christian VÖLLMECKE, F.J. SONSINO, Cetin Morris Load controlled fatigue tests were performed up to 107 cycles on flat notched specimens (Kt =2.5) under constant amplitude and variable amplitude loadings with and without periodical overloads. Two materials are studied: a ferritic-bainitic steel and a cast aluminium alloy. These materials have a very different cyclic behaviour: the steel exhibits cyclic strain oftening whereas the Al alloy shows cyclic strain hardening. The fatigue tests show that, for the steel, periodical overload applications reduce significantly the fatigue life for fully reversed load ratio (Rr = – 1), while they have no influence under pulsating loading (Rr = 0). For the Al alloy over-loads have an effect (fatigue life decreasing) only for variable amplitude loadings. The detrimental effect of overloads on the steel is due to ratcheting at the notch root which evolution is overload's dependent. http://hdl.handle.net/10985/10764 Microstructure-dependent predictions of the effect of defect size and shape on the high-cycle fatigue strength GUERCHAIS, Raphaël; MOREL, Franck; SAINTIER, Nicolas This study aims to investigate the effects of both the microstructure and void on the high-cycle fatigue behavior of metallic materials. To deal with this matter, finite element analyses of polycrystalline aggregates are carried out, for different configurations of crystalline orientations, in order to estimate the mechanical state, at the grain scale, in the vicinity of a small elliptical hole. Fatigue criteria are then applied to predict the average fatigue limit in fully reversed tension, for different defect sizes and ellipse aspect ratios. The constitutive models and the fatigue criteria are calibrated using experimental data obtained from specimens made of 316L austenitic steel . The predictions are then confronted to experimental trends . Fri, 01 Jan 2016 00:00:00 GMT http://hdl.handle.net/10985/10764 2016-01-01T00:00:00Z GUERCHAIS, Raphaël MOREL, Franck SAINTIER, Nicolas This study aims to investigate the effects of both the microstructure and void on the high-cycle fatigue behavior of metallic materials. To deal with this matter, finite element analyses of polycrystalline aggregates are carried out, for different configurations of crystalline orientations, in order to estimate the mechanical state, at the grain scale, in the vicinity of a small elliptical hole. Fatigue criteria are then applied to predict the average fatigue limit in fully reversed tension, for different defect sizes and ellipse aspect ratios. The constitutive models and the fatigue criteria are calibrated using experimental data obtained from specimens made of 316L austenitic steel . The predictions are then confronted to experimental trends . http://hdl.handle.net/10985/10874 Microstructural-based analysis and modelling of the fatigue behaviour of cast Al-Si alloys; Analyse et modélisation du comportement en fatigue des alliages d'aluminium de fonderie LE, Viet-Duc; MOREL, Franck; BELLETT, Daniel; PESSARD, Etienne; SAINTIER, Nicolas; OSMOND, Pierre This paper describes a microstructural-based high cycle fatigue behaviour model applied to cast Al-Si alloys used in an automobile context. These materials are characterized by the presence of different microstructural heterogeneities at different scales: the aluminium matrix (DAS/SDAS and the precipitation hardening level), inclusions (Si particles and intermetallic) and casting defects (porosity). It is shown that the effects of these factors on the HCF damage mechanisms are important and can depend on the loading mode. A multiaxial fatigue test campaign has been carried out using three cast aluminium alloys, fabricated by different casting processes (gravity die casting and lost foam casting), associated with several heat treatment(T7 and Hot Isostatic Pressing-HIP). The HIP treatment is used to eliminate or minimise the porosity. The first part of the article is dedicated to the experimental characterization of the HCF damage mechanisms. With regard to the effect of the casting defects, a study of natural fatigue crack growth and artificial long crack growth is presented and subsequently used to choose an appropriate fatigue strength criterion to take into account the effect of defects, for different loading modes (tension, torsion and combined tension-torsion). Finally, a flexible modelling framework, providing the possibility of combining any two suitable criteria, which leads to the construction of a multiaxial Kitagawa-Takahashi diagram, is used. Thu, 01 Jan 2015 00:00:00 GMT http://hdl.handle.net/10985/10874 2015-01-01T00:00:00Z LE, Viet-Duc MOREL, Franck BELLETT, Daniel PESSARD, Etienne SAINTIER, Nicolas OSMOND, Pierre This paper describes a microstructural-based high cycle fatigue behaviour model applied to cast Al-Si alloys used in an automobile context. These materials are characterized by the presence of different microstructural heterogeneities at different scales: the aluminium matrix (DAS/SDAS and the precipitation hardening level), inclusions (Si particles and intermetallic) and casting defects (porosity). It is shown that the effects of these factors on the HCF damage mechanisms are important and can depend on the loading mode. A multiaxial fatigue test campaign has been carried out using three cast aluminium alloys, fabricated by different casting processes (gravity die casting and lost foam casting), associated with several heat treatment(T7 and Hot Isostatic Pressing-HIP). The HIP treatment is used to eliminate or minimise the porosity. The first part of the article is dedicated to the experimental characterization of the HCF damage mechanisms. With regard to the effect of the casting defects, a study of natural fatigue crack growth and artificial long crack growth is presented and subsequently used to choose an appropriate fatigue strength criterion to take into account the effect of defects, for different loading modes (tension, torsion and combined tension-torsion). Finally, a flexible modelling framework, providing the possibility of combining any two suitable criteria, which leads to the construction of a multiaxial Kitagawa-Takahashi diagram, is used. http://hdl.handle.net/10985/10857 Multiaxial high cycle fatigue damage mechanisms associated with the different microstructural heterogeneities of cast aluminium alloys; Mechanismes d'endommagement en fatigue multiaxiale à grand nombre de cycles associés aux différentes hétérogénéités microstructurales des alliages d'aluminium de fonderie LE, Viet-Duc; MOREL, Franck; BELLETT, Daniel; SAINTIER, Nicolas; OSMOND, Pierre This article is dedicated to the high cycle fatigue (HCF) behaviour of cast Al-Si alloys. In particular, three similar alloys with different microstructural characteristics are investigated. The result of an experimental campaign are presented, in order to characterise the fatigue behaviour, and more specifically the fatigue damage mechanisms related to the different microstructural heterogeneities (i.e. casting porosity, dendrite size, SDAS, non-metallic inclusions and silicon particles), observed under different multiaxial loading conditions: pure tension, plane bending, pure torsion and combined tension-torsion with a load ratio R=-1. It is shown that casting porosity has a very detrimental influence on the uniaxial and combined tension-torsion fatigue strengths. However, a much lower influence is observed for the torsional fatigue strength. For the porosity-free alloy, it is observed that the formation of persistent slip bands (PSB) in the aluminium matrix is the major fatigue crack initiation mechanism regardless of the loading modes, at a load ratio of R=-1. It is also shown that the aluminium matrix has a large role in the formation of PSB and that the Si particles facilitate the formation of PSB. Fri, 01 Jan 2016 00:00:00 GMT http://hdl.handle.net/10985/10857 2016-01-01T00:00:00Z LE, Viet-Duc MOREL, Franck BELLETT, Daniel SAINTIER, Nicolas OSMOND, Pierre This article is dedicated to the high cycle fatigue (HCF) behaviour of cast Al-Si alloys. In particular, three similar alloys with different microstructural characteristics are investigated. The result of an experimental campaign are presented, in order to characterise the fatigue behaviour, and more specifically the fatigue damage mechanisms related to the different microstructural heterogeneities (i.e. casting porosity, dendrite size, SDAS, non-metallic inclusions and silicon particles), observed under different multiaxial loading conditions: pure tension, plane bending, pure torsion and combined tension-torsion with a load ratio R=-1. It is shown that casting porosity has a very detrimental influence on the uniaxial and combined tension-torsion fatigue strengths. However, a much lower influence is observed for the torsional fatigue strength. For the porosity-free alloy, it is observed that the formation of persistent slip bands (PSB) in the aluminium matrix is the major fatigue crack initiation mechanism regardless of the loading modes, at a load ratio of R=-1. It is also shown that the aluminium matrix has a large role in the formation of PSB and that the Si particles facilitate the formation of PSB. http://hdl.handle.net/10985/9596 Creep-fatigue interactions in pure Tantalum under constant and variable amplitude MARÉCHAL, David; SAINTIER, Nicolas; PALIN-LUC, Thierry; NADAL, François Due to its specific mechanical properties, tantalum is often used in strength-demanding military applications. High cycle fatigue (HCF) behaviour of pure tantalum, however, has been rarely reported and the mechanisms at stake to account for deformation under cyclic loadings are still badly understood [1-2]. This presentation aims at better understanding the HCF damage mechanisms encountered in pure tantalum under such loadings. HCF loadings at various frequencies were performed in tension at room temperature on commercially-pure tantalum. Mean stress effects and frequency effects were investigated in the aim of clarifying the interaction between fatigue and creep. For symmetrical loadings (R=-1, i.e. under zero mean stress), fracture mechanisms were observed to vary from intergranular to transgranular when the maximum stress was decreased. For non-symmetrical loadings (R>0, with sufficiently large mean stress), a transition was also observed from extensive necking to intergranular initiation. Important creep activation was deduced from the presence of necking. This prevalence of creep at room temperature was actually confirmed by two other phenomena: a) The large influence of the frequency on fatigue life, indicating time-dependent damage. b) Important creep deformation during room-temperature creep tests. Finally, complex sequential loadings, representative of in-service loadings, were applied to pure tantalum specimens. The contribution of each loading sequence to the overall damage was quantified. It was shown that linear cumulative damage rules (analogous to Miner’s law to account for fatigue damage and for creep damage) failed to predict life duration of pure tantalum. The ONERA model [3-4], which specifically accounts for creep-fatigue interactions, granted better results. However, it is important to notice that this model uses engineering stresses as input, assuming that the specimen cross-section does not evolve drastically during fatigue/creep deformation. Such hypothesis needs to be revisited as the true stress seems a more realistic input to account for creep damage. Thu, 01 Jan 2015 00:00:00 GMT http://hdl.handle.net/10985/9596 2015-01-01T00:00:00Z MARÉCHAL, David SAINTIER, Nicolas PALIN-LUC, Thierry NADAL, François Due to its specific mechanical properties, tantalum is often used in strength-demanding military applications. High cycle fatigue (HCF) behaviour of pure tantalum, however, has been rarely reported and the mechanisms at stake to account for deformation under cyclic loadings are still badly understood [1-2]. This presentation aims at better understanding the HCF damage mechanisms encountered in pure tantalum under such loadings. HCF loadings at various frequencies were performed in tension at room temperature on commercially-pure tantalum. Mean stress effects and frequency effects were investigated in the aim of clarifying the interaction between fatigue and creep. For symmetrical loadings (R=-1, i.e. under zero mean stress), fracture mechanisms were observed to vary from intergranular to transgranular when the maximum stress was decreased. For non-symmetrical loadings (R>0, with sufficiently large mean stress), a transition was also observed from extensive necking to intergranular initiation. Important creep activation was deduced from the presence of necking. This prevalence of creep at room temperature was actually confirmed by two other phenomena: a) The large influence of the frequency on fatigue life, indicating time-dependent damage. b) Important creep deformation during room-temperature creep tests. Finally, complex sequential loadings, representative of in-service loadings, were applied to pure tantalum specimens. The contribution of each loading sequence to the overall damage was quantified. It was shown that linear cumulative damage rules (analogous to Miner’s law to account for fatigue damage and for creep damage) failed to predict life duration of pure tantalum. The ONERA model [3-4], which specifically accounts for creep-fatigue interactions, granted better results. However, it is important to notice that this model uses engineering stresses as input, assuming that the specimen cross-section does not evolve drastically during fatigue/creep deformation. Such hypothesis needs to be revisited as the true stress seems a more realistic input to account for creep damage. http://hdl.handle.net/10985/8397 High-Cycle Fatigue Behaviour of Pure Tantalum under Multiaxial and Variable Amplitude Loadings MARECHAL, David; SAINTIER, Nicolas; PALIN-LUC, Thierry; NADAL, François Due to its specific mechanical properties, tantalum is often used in strength-demanding military applications. High-cycle fatigue (HCF) behaviour of pure tantalum, however, has been rarely reported and the mechanisms at stake to account for deformation under cyclic loadings are still badly understood. This paper aims at better understanding the fatigue behaviour of tantalum and at clarifying the mechanisms of damage formation encountered under such loadings. HCF experiments performed at room temperature on commercially-pure tantalum are presented. Mean stress effects were investigated in the aim of clarifying the interaction between fatigue and creep. Fracture mechanisms were observed to vary from intergranular to transgranular depending on applied stress amplitude and mean stress. Damage mechanisms were investigated under tension and torsion. Results are analyzed in the light of existing fatigue criteria, the limitations of which are discussed. Finally, complex sequential loadings, representative of in-service loadings, were applied to tantalum smooth specimens. The contribution of each loading sequence to the overall damage was quantified and analyzed in terms of linear or non-linear cumulative damage rule Wed, 01 Jan 2014 00:00:00 GMT http://hdl.handle.net/10985/8397 2014-01-01T00:00:00Z MARECHAL, David SAINTIER, Nicolas PALIN-LUC, Thierry NADAL, François Due to its specific mechanical properties, tantalum is often used in strength-demanding military applications. High-cycle fatigue (HCF) behaviour of pure tantalum, however, has been rarely reported and the mechanisms at stake to account for deformation under cyclic loadings are still badly understood. This paper aims at better understanding the fatigue behaviour of tantalum and at clarifying the mechanisms of damage formation encountered under such loadings. HCF experiments performed at room temperature on commercially-pure tantalum are presented. Mean stress effects were investigated in the aim of clarifying the interaction between fatigue and creep. Fracture mechanisms were observed to vary from intergranular to transgranular depending on applied stress amplitude and mean stress. Damage mechanisms were investigated under tension and torsion. Results are analyzed in the light of existing fatigue criteria, the limitations of which are discussed. Finally, complex sequential loadings, representative of in-service loadings, were applied to tantalum smooth specimens. The contribution of each loading sequence to the overall damage was quantified and analyzed in terms of linear or non-linear cumulative damage rule http://hdl.handle.net/10985/7934 Multiscale fatigue damage characterization in short glass fiber reinforced polyamide-66 ARIF, Muhamad Fatikul; CHEMISKY, Yves; ROBERT, Gilles; FITOUSSI, Joseph; MERAGHNI, Fodil; SAINTIER, Nicolas This paper aims at studying fatigue damage behavior of injection molded 30 wt% short glass fiber reinforced polyamide-66 composite (PA66/GF30). The evolution of dynamic modulus, hysteresis area, cyclic creep and temperature during fatigue tests were analyzed and discussed. Damage analyses by X-ray micro-computed tomography (lCT) technique on interrupted fatigue tests at several percentages of total fatigue life were performed to further understand the damage mechanisms and evolution during fatigue loading. It can be observed that experimental results related to the evolution of dynamic modulus, strain, temperature and energy dissipation are important and consistently complement each other for damage evaluation of PA66/GF30. During fatigue loading, diffuse damage occurs over the entire specimen though the damage does not necessarily exhibit the same level between different locations inside the specimen. The lCT analysis of voids characteristics demonstrates that the damage continuously increases during fatigue loading. The damage is developed notably along fiber interface in the form of fiber/matrix interfacial debonding. Wed, 01 Jan 2014 00:00:00 GMT http://hdl.handle.net/10985/7934 2014-01-01T00:00:00Z ARIF, Muhamad Fatikul CHEMISKY, Yves ROBERT, Gilles FITOUSSI, Joseph MERAGHNI, Fodil SAINTIER, Nicolas This paper aims at studying fatigue damage behavior of injection molded 30 wt% short glass fiber reinforced polyamide-66 composite (PA66/GF30). The evolution of dynamic modulus, hysteresis area, cyclic creep and temperature during fatigue tests were analyzed and discussed. Damage analyses by X-ray micro-computed tomography (lCT) technique on interrupted fatigue tests at several percentages of total fatigue life were performed to further understand the damage mechanisms and evolution during fatigue loading. It can be observed that experimental results related to the evolution of dynamic modulus, strain, temperature and energy dissipation are important and consistently complement each other for damage evaluation of PA66/GF30. During fatigue loading, diffuse damage occurs over the entire specimen though the damage does not necessarily exhibit the same level between different locations inside the specimen. The lCT analysis of voids characteristics demonstrates that the damage continuously increases during fatigue loading. The damage is developed notably along fiber interface in the form of fiber/matrix interfacial debonding.