Damage mechanisms and failure modes in cross-ply laminates under monotonic tensile loading: The influence of fiber sizing

In this study, the effect of fiber-matrix interphase on the damage modes and failure mechanisms in (0, 90₃), cross-ply graphite-toughened epoxy laminates is investigated. Two material systems (designated as 810 A and 810 O) with the same fiber and same matrix, but with different fiber sizings, were used to study the effect of the interphase. The system designated as 810 A contained an unreacted Bisphenol-A (epoxy) sizing, while a thermoplastic polyvinylpyrrolidone (PVP) sizing was used in the 810 O system. Damage accumulation in the cross-ply laminates under monotonic tensile loading was monitored using edge replication, x-ray radiography, acoustic emission, optical and scanning electron microscopy. Results indicate that the fiber-matrix bond strength is lower in the 810 O system compared to the 810 A system. Transverse matrix cracking initiates at a significantly lower stress level in the 810 O laminate. The 810 O laminates also exhibit longitudinal splitting, while the stronger bonding suppress this damage mode in the 810 A laminates. Numerous local delamination occur on the 0/90 interface at the intersection of 0 and 90 degree ply cracks, in the 810 O laminates. These are absent in the 810 A laminates. The failure modes are also different in the two material systems used in this study. The 810 A laminate exhibits a brittle failure, controlled by the local stress concentration effects near broken fibers. In the 810 O laminates, the presence of longitudinal splits result in the reduction of stress concentration effects near fibe fractures. This results in a global strain controlled failure in the 810 O system. It is concluded that the presence of different fiber sizings result in different damage modes and failure mechanisms in the cross-ply laminates used in this study.Research Associate, Research Assistant, Alexander Giacco Professor and Professor respectively.     

Time-dependent boundary element analysis for an interface crack in a two-dimensional unidirectional viscoelastic model composite

Interfacial stress singularities in a unidirectional two-dimensional laminate model consisting of an elastic fiber and a viscoelastic matrix have been investigated using the time-domain boundary element method. First, the interfacial singular stresses between the perfectly bonded fiber and the matrix of a unidirectional laminate subjected to a uniform transverse tensile strain have been investigated near the free surface, but without any edge crack. Such stress singularity might lead to fiber-matrix debonding or an edge crack. Then, the overall stress intensity factor for the case of a small interfacial edge crack of length a has been computed. The numerical procedure does not permit calculation of the limiting case for which the edge crack length vanishes.     

Statistical model of the transverse ply cracking in cross-ply laminates by strength and fracture toughness based failure criteria

Cross-ply laminate subjected to tensile loading provides a relatively well understood and widely used model system for studying progressive cracking of the transverse ply. This test allows to identify material strength and/or toughness characteristics as well as to establish relation between damage level and the composite stiffness reduction. The transverse ply cracking is an inherently stochastic process due to the random variability of local material properties of the plies. The variability affects both crack initiation (governed by the local strength) and propagation (governed by the local fracture toughness). The primary aim of the present study is elucidation of the relative importance of these phenomena in the fragmentation process at different transverse and longitudinal ply thickness ratios. The effect of the random crack distribution on the mechanical properties reduction of the laminate is also considered. Transverse ply cracking in glass fiber/epoxy cross-ply laminates of the lay-ups [0₂/90₂]_s, [0/90₂]_s, and [0/90₄]_s is studied. Several specimens of each lay-up were subjected to uniaxial quasistatic tension to obtain crack density as a function of applied strain. Crack spacing distributions at the edge of the specimen also were determined at a predefined applied strain. Statistical model of the cracking process is derived, calibrated using crack density vs. strain data, and verified against the measured crack spacing distributions.     

Simulation of curing process of carbon/epoxy composite during autoclave degassing molding by considering phase changes of epoxy resin

Strain monitoring of a carbon/epoxy composite cross-ply laminate ([0₅/90₅]_s) during thermoforming was conducted by using fiber Bragg grating (FBG) sensors. The entire process was simulated by employing finite element analysis (FEA) by taking into consideration the phase changes of the epoxy resin. For the precise simulation of the curing process, a dielectrometry sensor was used to detect the epoxy-resin dissipation factor, which in turn was used to identify the curing point. To investigate the phase changes and consolidation of the composite laminate by employing FEA, modulus changes with temperature were measured by dynamic mechanical analysis (DMA), and the permeability was estimated by measuring the fiber volume fraction according to the curing temperature. As the epoxy resin changed from a liquid to solid phase, the strain generated along the carbon fibers dynamically changed, and the analysis results generally predicted the strain variation quite well. To apply this simulation technique to practical structures, a composite-aluminum hybrid wheel was analyzed and experimentally verified.     

The mechanical behavior of optical fiber sensor embedded within the composite laminate

Mechanical behavior, such as tensile and fatigue strength, of the optical fiber sensor embedded within the composite laminate was investigated. Tensile and fatigue tests were performed to evaluate the static and fatigue characteristics of optical fibers embedded within three types of laminated composite specimens, [0₆/OF/0₆]_T, [0₂/90₄/OF/90₄/0₂]_T and [0₃/90₃/OF/90₃/0₃]_T. The initiation of damage and fracture of the optical fiber were detected by observation of the intensity drop-off of laser signal transmitted through the optical fiber during test. Experimental results showed that the fatigue strength of optical fiber embedded within the cross-ply laminate is much lower than the fatigue strength of optical fiber within the unidirectional ply laminate. It was also found that the optical fiber embedded within unidirectional ply laminate fractured due to the fatigue damage accumulation of internal defects of optical fiber itself. However the optical fiber embedded within the cross-ply laminate fractured due to the growth of transverse matrix crack of host composite laminate.     

Variational approach development in analysis of matrix cracking and induced delamination of cross-ply composite laminates subjected to in-plane shear loading

Matrix microcracking and induced delamination propagating from the edge of microcracks in cross-ply composite laminates with [0_n/90_m]_s and [90_m/0_n]_s layups under in-plane static shear loading are investigated. An admissible stress field, which satisfies all of equilibrium equations, boundary conditions, and continuity of interfaces, is approximated. Then using the principle of the minimum complementary energy, the stress state is obtained from calculations of variation. The calculated stress state gives the stiffness reduction and the total strain energy of the laminated composite structure. Finally, the strain energy release rate of a general cross-ply laminate due to initiation and propagation of matrix cracking and induced delamination can be deduced. Results of the developed approach are in good agreement with experimental observations and finite element analyses, which confirms its accuracy.     

Determination of damage micromechanisms and fracture resistance of glass fiber/epoxy cross-ply laminate by means of X-ray computed microtomography

The onset and evolution of the damage in three dimensions was studied by X-ray computed micro-tomography (XCT) in a notched glass fiber/epoxy cross-ply laminate subjected to three-point bending. It was found that damage began by formation of intraply cracks in the 90° plies followed by intraply cracking the 0° plies. Fiber fracture in front of the notch tip occurred at 65% of the maximum load and finally fiber kinking and interply delamination took place under the loading point. Finite element (FE) simulations were carried out to understand crack initiation and the redistribution of stresses upon crack propagation. The crack area corresponding to each damage mechanism was quantified from the XCT images, and this information was used to determine the effective fracture resistance curve of the cross-ply laminate.     

The behaviour of cross-ply hybrid matrix composite laminates: Part 1: Experimental results

Two types of cross-ply laminate have been made from prepreg: (a) hybrid matrix laminates consisting of longitudinal plies of glass fibres in epoxy resin and transverse plies of glass fibres in epoxy resin/urethane elastomer blend; and (b) uniform matrix laminates with the same resin in both the longitudinal and transverse plies. The presence of the urethane in the transverse plies increases the applied strains necessary for the initiation and development of transverse cracking during the extension of both hybrid matrix and uniform matrix laminates. The effect is greater with increasing amounts of urethane. The cracking data, stress/strain behaviour, acoustic emission response and ply thickness effects on crack development are discussed in the light of existing theories concerning transverse cracking.     

缝合复合材料层板低速冲击损伤数值模拟

建立了缝合复合材料层板在低速冲击载荷下的渐进损伤分析模型。模型中采用空间杆单元模拟缝线的作用;采用三维实体单元模拟缝合层板,通过基于应变描述的Hashin准则,结合相应的材料性能退化方案模拟层板的损伤和演化;采用界面单元模拟层间界面,结合传统的应力失效判据和断裂力学中的应变能释放率准则判断分层的起始和扩展规律。通过对碳800环氧树脂复合材料（T800/5228）层板的数值仿真结果和试验结果相比较,验证了模型的正确性,同时讨论了不同冲击能量下缝合层板的损伤规律。研究结果表明：缝线能够有效地抑制层板的分层损伤扩展;相同冲击能量下缝合与未缝合层板的基体损伤和纤维损伤在厚度分布上相似,缝合层板的损伤都要小于未缝合层板。     

正交铺设陶瓷基复合材料单轴拉伸行为

采用细观力学方法对正交铺设陶瓷基复合材料单轴拉伸应力-应变行为进行了研究。采用剪滞模型分析了复合材料出现损伤时的细观应力场。采用断裂力学方法、 临界基体应变能准则、 应变能释放率准则及Curtin统计模型4种单一失效模型确定了90°铺层横向裂纹间距、 0°铺层基体裂纹间距、 纤维/基体界面脱粘长度和纤维失效体积分数。将剪滞模型与4种单一损伤模型结合, 对各损伤阶段应力-应变曲线进行了模拟, 建立了复合材料强韧性预测模型。与室温下正交铺设陶瓷基复合材料单轴拉伸应力-应变曲线进行了对比, 各个损伤阶段的应力-应变、 失效强度及应变与试验数据吻合较好。分析了90°铺层横向断裂能、 0°铺层纤维/基体界面剪应力、 界面脱粘能、 纤维Weibull模量对复合材料损伤及拉伸应力-应变曲线的影响。      

The effect of residual thermal stresses on transverse cracking in cross-ply laminates: an application of the coupled criterion of the finite fracture mechanics

A model to predict transverse cracking in cross-ply laminates in the presence of residual thermal stresses is developed here. This model is based on the coupled criterion of the finite fracture mechanics. This criterion has been successfully used for different materials, structures and scales to predict crack initiation. It is based on two main hypotheses: (i) crack initiation occurs as a finite-length crack onset and (ii) the crack onset requires that both stress and energy criteria are fulfilled simultaneously. The present model is developed under the generalized-plane-strain hypotheses combining the results obtained using the laminate theory and a boundary element code. The present analysis shows that the residual thermal stresses affect both the stress and the energy criteria in the form of adding a residual elastic-strain to the strain imposed by external mechanical loads. An explicit expression for this residual elastic-strain is provided. For certain composite materials as carbon/epoxy the value of this residual elastic-strain is shown to be relatively large in comparison with the nominal critical transverse strain of the material. The comparison with experiments shows that considering the residual thermal stresses using the strategy proposed here improves drastically the accuracy of the model predictions.     

An experimental investigation of the sequence effect in block amplitude loading of cross-ply composite laminates

The Palmgren–Miner rule has been shown to be inexact in many cases for various composite materials. Several empirical models have been conceived to account for this discrepancy, as well as the effect of block sequence. The approach taken here is based on the underlying mechanisms. A cross-ply laminate was used as a model material. In general, composites show both initiatory and progressive mechanisms under fatigue loading. The former is active at high static stresses, whereas the latter predominates at lower stress amplitudes where they are given sufficient time to propagate. Initiatory mechanisms give rise to damage from which the progressive mechanisms can start, and conversely the progressive mechanisms continually alter the local stress state which results in further damage accumulation caused by the initiation controlled mechanisms. In a cross-ply laminate, the initiatory mechanism is the formation of transverse cracks, and the progressive mechanism is mainly delamination growth initiated from the transverse cracks. In an experimental investigation of carbon fiber/epoxy cross-ply laminates, the interaction of these mechanisms has shown why a sequence of high–low amplitude levels results in shorter lifetimes than a low–high order. Such a sequence effect seems to be a common behavior for many other composite materials, and can be mechanistically explained by a similar kind of interaction. Advantages and drawbacks of the mechanistic approach compared with empirical rules are also discussed.     

The role of microdamage in tensile failure of graphite/epoxy laminates

Damage development during quasistatic tensile loading of several laminates of graphite/epoxy material is examined and compared to damage development in laminates of a similar graphite/epoxy material subjected to tension-tension fatigue loading. Emphasis is placed upon following damage development at the microstructural level. Evidence of the important role of off-axis ply cracks in localizing and controlling fiber fracture in adjacent load-bearing plies for both loading modes is resented. The relationship between fiber fracture density and static load level is presented for tensile loading of unidirectional and cross-ply laminates by direct observation of fiber fracture in situ. The frequencies of occurrence of multiple adjacent fiber fractures are also reported. The cross-ply laminate results are compared with those from fatigue testing. Significant differences are described and discussed.     

Effect of micro-randomness on macroscopic properties and fracture of laminates

Composite materials demonstrate a considerable extent of heterogeneity. A non-uniform spatial distribution of reinforcement results in variations of local properties of fibrous laminates. This non-uniformity not only affects effective properties of composite materials but is also a crucial factor in initiation and development of damage and fracture processes that are also spatially non-uniform. Such randomness in microstructure and in failure evolution is responsible for non-uniform distributions of stresses in composite specimens even under externally uniform loading, resulting, for instance, in a random distribution of matrix cracks in cross-ply laminates. The paper deals with statistical features of a distribution of carbon fibres in a transversal cross-sectional area in a unidirectional composite with epoxy matrix, based on various approaches used to quantify its microscopic randomness. A random character of the fibres’ distribution results in fluctuations of local elastic moduli in composites, the bounds of which depend on the characteristic length scale. A lattice model to study damage and fracture evolution in laminates, linking randomness of microstructure with macroscopic properties, is discussed. An example of simulations of matrix cracking in a carbon fibre/epoxy cross-ply laminate is given.     

Time-dependent damage in carbon fibre-reinforced polymer composites

Time-dependent damage (matrix cracks) evolution in AS4/3501-6 cross-ply laminates was studied using constant strain rate and constant stress tests. First ply failure stress and strain as well as the matrix crack density at a given stress level were found to be strongly dependent on strain rate. Matrix crack density increased with creep time at a constant stress level. The compliance and creep rate of the laminate increased in the presence of these cracks. These results emphasize the importance of the knowledge of time-dependent damage evolution in a lamina/laminate of a polymer composite for reliable prediction of creep and creep rupture.     

Micromechanical Analysis of Interphase Damage for Fiber Reinforced Composite Laminates

In the present study, the initiation and evolution of the interphase damage and their influences on the global stress-strain relation of composite laminates are predicted by finite element analysis on a micromechanical unit cell model. A thin layer of interphase elements is introduced and its stress-strain relation is derived based on a cohesive law which describes both normal and tangential separations at the interface between the fiber and matrix. In addition, a viscous term is added to the cohesive law to overcome the convergence difficulty induced by the so-called snap-back instability in the numerical analysis. The matrix behavior is described by a recently developed nonlinear viscoelastic constitutive model. As application examples, glass fiber/epoxy unidirectional laminates under off-axis loadings are analyzed. One-quarter of the unit cell is used in the analysis accounting for the geometrical symmetry of the model, and the corresponding periodic boundary conditions for combined global shear and normal loading are derived. Results show that the initiation and evolution of the interphase damage can be well simulated and the predicted global stress-strain responses are in good agreement with the experimental results.     

Failure analysis of quasi-isotropic CFRP laminates under high strain rate compression loading

Dynamic compressive strength of quasi-isotropic fiber composite is investigated experimentally and also numerically simulated. In-plane compression tests at strain rates around 400/s quasi-isotropic laminates were performed using the Split Hopkinson Pressure Bar (SHPB). The material system used was Texipreg^® HS160 REM, comprising high strength unidirectional carbon fiber and epoxy resin. The dynamic strength of quasi-isotropic laminates exhibits a considerable increase when compared to the static values. The finite-element model used ABAQUS™ three-dimensional solid elements C3D8I with 8 nodes and user-defined interface finite elements with 8 nodes [Gonçalves JPM, de Moura MFSF, de Castro PMST, Marques AT. Interface element including point-to-surface constraints for three-dimensional problems with damage propagation. Eng Comp: Int J Comput Aided Eng Software 2000;17(1):28–47; de Moura MFSF, Pereira AB, de Morais AB. Influence of intralaminar cracking on the apparent interlaminar mode I fracture toughness of cross-ply laminates. Fatigue Fract Eng Mater Struct 2004;27(9):759–66.]. These interface elements which connect the three-dimensional solid elements modeling the composite layers, include a cohesive damage model allowing the simulation of delamination initiation and propagation. Hence the present model assumes that the phenomenon of failure under these conditions is mainly dictated by interface delamination. This is supported by experimental tests which showed that all quasi-isotropic laminates split into several almost intact sublaminates. The model compares very well with experimental results, confirming the formulated hypothesis that the internal layer damage does not markedly contribute to the quasi-isotropic laminate failure.     

Application of extended finite element method in damage progress simulation of fiber reinforced composites

Damage initiation and propagation in unidirectional glass fiber reinforced epoxy matrix composites under tension load were simulated in this study. Cell models with both single fiber and multi-fiber were modeled by extended finite element method (XFEM) in ABAQUS environment. The damage progresses in the cells were investigated and then the nominal stress–strain curves as well as stress distributions in the fiber and matrix were obtained. Results indicate that the XFEM is an effective modeling technique to study the initiation and propagation of a crack along an arbitrary, mesh-independent, solution-dependent path. In addition, convergence difficulties are familiar issues while carrying out damage and fracture analysis when employing numerical simulation. Several methods, which are helpful to resolve these convergence problems, were presented. Baseline simulations about damage initiation and propagation in composites indicate that a larger value of viscous regularization causes the peak of the reaction force to be higher. A smaller viscosity parameter is better than bigger one. Other advanced techniques, include using automatic stabilization and customized general solution controls, are also adoptable to improve convergence in ABAQUS/Standard analysis.     

Predicting evolution of ply cracks in composite laminates subjected to biaxial loading

An energy-based model is developed to predict the evolution of sub-critical matrix crack density in symmetric multidirectional composite laminates for the case of multiaxial loading. A finite element-based numerical scheme is also developed to evaluate the critical strain energy release rate, G_Ic, associated with matrix micro-cracking, a parameter that previously required fitting with experimental data. Furthermore, the prediction scheme is improved to account for the statistical variation of G_Ic within the material volume by using a two-parameter Weibull distribution. The variation of G_Ic with increasing crack density is also accounted for based on reported experimental evidence. The simulated results for carbon/epoxy and glass/epoxy cross-ply laminates demonstrate the ability of the improved model to predict the evolution of multidirectional ply cracking. By integrating this damage evolution model with the synergistic damage mechanics approach for stiffness degradation, the stress-strain response of the studied laminates is predicted. Finally, biaxial stress envelopes for ply crack initiation and pre-determined stiffness degradation levels are predicted to serve as representative examples of stiffness-based design and failure criterion.