Describing the Flexural Behaviour of Cross-ply Laminates Under Cyclic Fatigue

The objective of this work is to derive modelling of the fatigue behaviour of cross-ply laminates from the experimental results obtained in the case of three-point bending tests. Modelling the fatigue behaviour is based on the stiffness reduction of test specimens. Firstly, experimental results are described using interpolation functions. Then, the characteristic coefficients of these functions are studied as function of the laminate properties and loading conditions. This approach allows to predict the fatigue life of composite laminates while avoiding a large number of fatigue tests. Wöhler curves are used to compare the experimental and analytical results, and a good agreement is found between the results. Next, a simple approach is considered to define a damage parameter. It is based on the analogy between the mechanical behaviour and the fatigue damage evolution of composite laminates during fatigue tests. The developed models are applied to analyse the influence of constituents on the fatigue behaviour and damage development of composite materials under fatigue loading.     

Statistical prediction of fatigue failure of fibre reinforced composite materials

A statistical approach is proposed to evaluate the residual strength and life of unidirectional and angle-ply composite laminates subjected to in-plane tensile cyclic stresses. The method is based on the extension of previous static failure criteria describing independently the fibre failure and matrix failure modes, combined with the statistical nature of fatigue failure of fibre-reinforced composites. The static and fatigue strengths of composite laminates at any off-axis angle are evaluated using the fatigue failure functions for the three principal failure modes, which are determined from the fatigue behaviour of unidirectional composites subjected to longitudinal and transverse tension as well as in-plane shear stresses. The evaluations of the fatigue strength of unidirectional E-glass/epoxy laminates under off-axis fatigue loading and angle-ply S-glass/epoxy laminates under in-plane fatigue loading show good agreement between theoretical predictions and experimental results.     

层板复合材料的疲劳剩余寿命预报模型

应用可靠性分析的方法 ,导出了层板复合材料在疲劳载荷作用下的疲劳剩余寿命的预报模型。该模型已用典型层板复合材料在恒幅疲劳载荷作用下的实验数据进行了验证。实验结果表明 ,理论预测结果与实验值的接近程度是合理的     

Fatigue crack growth in thin notched woven glass composites under tensile loading. Part I: Experimental

Helicopter blades are made of composite materials mainly loaded in fatigue and have normally relatively thin skins. A through-the-thickness crack could appear in these skins. The aim of this study is to characterize the through-the-thickness crack propagation due to fatigue in thin woven glass fabric laminates. A technological test specimen is developed to get closer to the real loading conditions acting on these structures. An experimental campaign is undertaken which allows evaluating crack growth rates in several laminates. The crack path is linked through microscopic investigations to specify damage in woven plies. Crack initiation duration influence on experimental results is also underlined.     

Elasto-plastic behavior of thermoplastic composite laminates under cyclic loading

An experimental and numerical study of the elasto-plastic behavior of thermoplastic matrix composite laminates under static and cyclic loads is presented. Off-axis and angle ply specimens cut from laminates of poly(ether ether ketone) (PEEK) reinforced with continuous carbon fibers have been tested under cyclic sinusoidal tensile loads and the hysteresis loops have been monitored. A micro mechanical model, which includes a parabolic criteria based on the plastic behavior of the matrix, has been adopted to study the composite non-linear behavior and a correlation between plastic deformation and a strong rise of damping and temperature at high stresses is outlined. Good agreement is shown between theory and experimental results. The mathematical mdoel presented here can be used to predict the visco-elastic-plastic response of the material at high stresses and its influence in the fatigue damage.     

Fatigue of bolted joints in (0/90) CFRP laminates

The results of an experimental study of the fatigue behaviour of double-lap bolted joints using 1 mm thick (0/90)_2s and 2 mm thick (0/90)_4s laminates from the XAS/914 CFRP system are described. The damage development under fatigue loading was monitored qualitatively by microscopy, and quantitatively by recording the bearing stiffness and permanent joint deformation with cycling. The possibility of a stiffness-based failure criterion is investigated.The importance of the bolt clamp-up torque on the fatigue performance of the laminates was also studied It is shown that damage development under fatigue loading is considerably reduced at higher clamp-ups.     

Fatigue delamination growth rates and thresholds of composite laminates under mixed mode loading

The effect of delamination resistance on fatigue crack growth behavior of composite laminates is studied. The strain energy release rate normalized to fatigue delamination resistance (G_cf) is proposed as a controlling parameter to evaluate the fatigue crack growth rates and thresholds. Compared to previously developed G_cf determination method, the compliance approach presented in this paper shows obvious advantages, such as no interruption to the fatigue crack growth and independence on the specimen dimensions. Based on this approach, the fatigue delamination growth rates and thresholds of carbon/bismaleimide composite laminates under mixed I/II mode loadings are determined experimentally.     

An experimental study on fatigue characteristics of CFRP-steel hybrid laminates

This paper aims to investigate the fatigue characteristics of hybrid laminates consisting of wave carbon fiber reinforced polymer (CFRP) sheets and a thin stainless steel plate under the tension–tension loading. Different loading options (e.g. same stress and same force), layers of CFRP sheets, and lay-ups of laminates (single and double sides) were considered. A series of experimental tests were performed to determine the effectiveness of the CFRP bonding on prolonging fatigue crack initiation life, preventing fatigue crack propagation and extending fatigue life of the hybrid laminates. Three distinct failure modes, classified as delamination, delamination bending and fiber breakage, were observed in the tests. It is shown that the loading conditions and CFRP thickness are the critical parameters affecting the failure modes and fatigue resistance. The crack initiation life and fatigue life of fiber-metal laminates (FMLs) increase by factors ranging from 1.06 to 1.96 and 1.17 to 2.07, respectively, relative to monolithic steel plates under the same force condition; whereas decrease by factors ranging from 0.63 to 0.89 and 0.28 to 0.61 under the same stress condition. Moreover, the double-side bonded FMLs show better fatigue properties and more stable crack propagation than single-side counterpart with the same thickness of CFRP.     

A unified fatigue life model based on energy method

A new unified fatigue life model based on the energy method is developed for unidirectional polymer composite laminates subjected to constant amplitude, tension–tension or compression–compression fatigue loading. This new fatigue model is based on static failure criterion presented by Sandhu and substantially is normalized to static strength in fiber, matrix and shear directions. The proposed model is capable of predicting fatigue life of unidirectional composite laminates over the range of positive stress ratios in various fiber orientation angles. By using this new model all data points obtained from various stress ratios and fiber orientation angles are collapsed into a single curve.

The new fatigue model is verified by applying it to different experimental data provided by other researchers. The obtained results by the new fatigue model are in good agreements with the experimental data of carbon/epoxy and E-glass/epoxy of unidirectional plies.     

The behaviour of Kevlar fibre-epoxy laminates under static and fatigue loading—Part 2: Modelling

A model has been developed for the modulus reduction of cross-ply Kevlar laminates under static loading as a function of applied strain. The effects of strain-rate and temperature have also been considered. The ‘stiffening’ of Kevlar fibres and Kevlar fibre-epoxy (KFRP) laminates under creep or fatigue conditions has been modelled using a kinetic approach. This has enabled stiffening effects to be subtracted out of the residual modulus-with-cycles behaviour of cross-ply KFRP laminates under fatigue loading, leaving a modulus-reduction-with-cycles curve which reflects the damage due to matrix cracking. The analyses compare well with experimental data reported in Part 1.     

Nonlinear response in glass fibre non-crimp fabric reinforced vinylester composites

This paper addresses the nonlinear stress-strain response in glass fibre non-crimp fabric reinforced vinylester composite laminates subjected to in-plane tensile loading. The nonlinearity is shown to be a combination of brittle and plastic failure. It is argued that the shift from plastic to brittle behaviour in the vinylester is caused by the state of stress triaxiality caused by the interaction between fibre and vinylester. A model combining damage and plasticity is calibrated and evaluated using data from extensive experimental testing. The onset of damage is predicted using the Puck failure criterion, and the evolution of damage is calibrated from the observed softening in plies loaded in transverse tension. Shear loading beyond linear elastic response is observed to result in irreversible strains. A yield criterion is implemented for shear deformation. A strain hardening law is fitted to the stress-strain response observed in shear loaded plies. Experimental results from a selection of laminates with different layups are used to verify the numerical models. A complete set of model parameters for predicting elastic behaviour, strength and post failure softening is presented for glass fibre non-crimped fabric reinforced vinylester. The predicted behaviour from using these model parameters are shown to be in good agreement with experimental results.     

可收卷复合材料层板大变形弯曲性能研究

该文研究了玻璃纤维编织复合材料制成的可收卷层板在大变形条件下的弯曲静力性能和疲劳性能。通过弯曲静力试验得到了试验件在大变形条件下的应变和位移的关系;通过有限元模拟静力试验并与试验结果对照,确定了疲劳试验的载荷;研究了在大变形条件下不同铺层层板的弯曲疲劳寿命及失效模式和相同铺层层板的疲劳寿命曲线。结果表明:复合材料层板在大变形弯曲时具有明显的非线性行为,且(±45°)铺层层板弯曲疲劳性能明显优于(0°/90°)铺层层板;在最小应变和最大应变比不变的情况下,相同铺层层板的弯曲最大应变和对数疲劳寿命之间存在线性关系。     

变幅载荷下纤维金属层板的疲劳与寿命预测

文章建立了纤维金属层板等幅疲劳载荷下的疲劳裂纹扩展速率与寿命预测模型。在此基础上对玻璃纤维-铝合金层板（GLARE）的疲劳裂纹扩展与分层扩展行为进行了试验研究,探讨了层板过载疲劳行为的机理,提出了纤维金属层板变幅载荷下疲劳寿命预测的等效裂纹闭合模型,并在GLARE层板上得到了验证。     

Flexural Fatigue Behavior of Cross-Ply Laminates: An Experimental Approach

Within an experimental approach we describe the mechanical behavior of different resin-epoxy laminates reinforced with cross-ply Kevlar and glass fibers under conditions of static and cyclic three-point bending. In static tests, we consider the effect of stacking sequence, the thickness of 90°-oriented layers, reinforcement type on the mechanical behavior of laminates under loading and on realization of various damage modes leading to rupture. Cyclic loading studies have been performed in two steps. In the first stage, we inquire into the dependence of the behavior and durability of four glass fiber-reinforced laminate-types on the stacking sequence; the second stage is devoted to studying the dependence of cyclic strength and fatigue behavior of laminates on the reinforcement type. Fatigue tests are carried out in load-control regime for glass and hybrid (Kevlar + glass) fiber laminates. Fatigue curves are constructed in coordinates stress – number of cycles until fracture from the criteria corresponding to a drop in stiffness by 5 and 10%. Analysis of the results obtained permits evaluation of the effect of the stacking sequence and the reinforcement type on the behavior of cross-ply laminates in cyclic loading. The presence of Kevlar fibers accounts for nonlinear behavior of laminates in static tests and for low cyclic strength in fatigue tests under three-point bending.     

Consideration of concurrent transverse cracking and induced delamination propagation using a generalized micro‐meso approach and experimental validation

The aim of this study is to investigate the applicability and more verification of recently developed new micro‐meso approach by the authors. Defining the damage evolution law in traditional classic mesomechanics approaches needs multifarious standard and non‐standard lay‐up tests. By combining the micromechanics and mesomechanics approaches, a relatively new micro‐meso model is proposed to overcome the major disadvantage of traditional meso‐scale modelling. In this study, standard tests are firstly performed to obtain the stress‐strain behaviour of various laminates and then the effects of transverse cracking and induced delamination on laminates responses are examined under uniaxial loading. Furthermore, the recently developed new micro‐meso approach is employed to predict the damage growth and stress‐strain response of examined composite specimens in the experimental study. The experimental results are used to verify this micro‐meso approach and discuss the differences. It is shown that the predicted stress‐strain behaviours using the developed method are in good agreement with the experimental results for various laminates with different lay‐up configurations.     

A generalized damage model for woven ply laminates under static and fatigue loading conditions

A generalized non-linear cumulative damage model for woven ply laminates subjected to static and fatigue loading is developed in this paper. The damage, consisting of small cracks running parallel to the fibers, leads to a loss of stiffness in the warp, weft and shear directions. The model presented here describes the evolution of the damage up to failure of the first ply. By replacing the woven ply by two stacked unidirectional plies corresponding to the warp and weft thicknesses, this general model is extended to cover a broad range of plies, from quasi-unidirectional to balanced woven plies. A continuum damage approach (CDM) is then used to define the behaviour of the two virtual unidirectional plies under static and fatigue loading conditions. The model is applied here to an unbalanced woven ply with glass reinforcement and the results of the simulations are compared with experimental data.     

复合材料层压板剩余刚度剩余强度关联模型

基于剩余强度和剩余刚度取决于同一损伤状态的假设,给出了基于剩余刚度的损伤定义和基于剩余强度的损伤定义之间的关系,建立了剩余刚度剩余强度关联模型。用3种不同铺层形式的层压板试验数据对本文中提出的剩余刚度模型及剩余强度模型进行了验证,结果表明:本文中提出的剩余刚度和剩余强度模型能很好地描述复合材料层压板疲劳过程中的剩余刚度和剩余强度退化规律;通过关联模型,可以在已知剩余刚度退化规律的前提下,用少量剩余强度试验确定剩余强度退化规律;与剩余刚度关联的剩余强度模型中的参数可以被认为是材料常数。      

复合材料层合板低速冲击后压-压疲劳试验研究及寿命预报

进行了复合材料层合板低速冲击和冲击后压-压疲劳试验。在疲劳试验过程中详细测量了损伤扩展情况,获得了损伤扩展规律。将冲击损伤等效为一圆形开孔,应用含椭圆形夹杂的杂交应力单元分析含圆孔有限大板的应力分布,采用特征曲线和点应力判据相结合的方式并通过引入损伤扩展规律建立了含低速冲击损伤复合材料层板压-压疲劳寿命预测模型。通过与试验数据的对比,证明了该模型的有效性。同时,该模型还可预报在疲劳载荷下含冲击损伤层板的剩余压缩强度。     

拉压加载下纤维增强铝合金层板疲劳裂纹扩展的压载荷效应与预测模型

基于增量塑性损伤理论与纤维增强金属层板疲劳裂纹扩展唯象方法, 推导出在拉-压循环加载下, 纤维增强金属层板疲劳裂纹扩展速率预测模型。并通过玻璃纤维增强铝合金层板在应力比R=-1,-2的疲劳裂纹扩展实验对预测模型进行验证。结果表明, 纤维增强铝合金层板疲劳裂纹扩展的压载荷效应分为两种情况: 在有效循环应力比R_C>0时, 表现为压载荷对铝合金层所承受残余拉应力的抵消作用; 当R_C<0时, 表现为压载荷抵消残余拉应力后, 对纤维增强铝合金层板金属层的塑性损伤, 对疲劳裂纹扩展存在促进作用。纤维铝合金层板疲劳裂纹扩展的压载荷效应不可忽略, 本文中得出的在拉-压循环加载下疲劳裂纹扩展速率预测模型与实验结果符合较好。     

Wavelet analysis of plate wave propagation in composite laminates

A new approach is presented for the analysis of transient waves propagating in composite laminates. The wavelet transform (WT) using the Gabor wavelet is applied to the time–frequency analysis of dispersive plate waves. It is shown that the peaks of the magnitude of WT in the time–frequency domain are related to the arrival times of group velocity. Experiments are performed using a lead break as the simulated acoustic emission source on the surface of quasi-isotropic and unidirectional graphite/epoxy laminates. For predictions of the dispersion of the flexural mode, Mindlin plate theory is shown to give good agreement with the experimental results. The planar source location based on the flexural wave is performed using a triangulation method. The use of frequency-dependent arrival time of output signal and angular dependence of group velocity provides accurate results of source location for anisotropic laminates.