Interaction between matrix cracking and edge delamination in composite laminates

Matrix cracking and edge delamination are two main damage modes in continuous-fibre composite laminates. They are often investigated separately, and so the interaction between two damage modes has not yet been revealed. In this paper, a simple parallel-spring model is introduced to model the longitudinal stiffness reduction due to matrix cracking and edge delamination together. The energy release rate of edge delamination eliminating the matrix crack effect and the energy release rate of matrix cracking in the presence of edge delamination are then obtained. Experimental materials include carbon- and glass-fibre-reinforced bismaleimide composite laminates under static tension. The growth of matrix cracks and edge delaminations was recorded by means of NDT techniques. Results show that matrix cracks may initiate before or after edge lamination. This depends on the laminate layup, and especially on the thickness of the 90° plies. Edge delamination may also induce matrix cracking. Matrix cracking has a significant effect on the stiffness reduction in GRP laminates. The present model can predict the stiffness reduction in a laminate containing both matrix cracks and edge delaminations. The mixed-mode delamination fracture toughness obtained from the present model shows up to 50% differences compared with O'Brien's model for GRP laminates. However, matrix cracking has a small effect on the mixed-mode interlaminar fracture toughness of the CFRP laminates.     

Transverse cracking and delamination interaction in the failure process of composite laminates

The transverse crack (TC) failure and delamination of a composite laminate with an outer 90° layer is studied. The stress field near each TC enforces a saturation value for their density and limits the stiffness reduction of the 90° layer for the TC failure mechanism. The failure pattern near a TC, observed by experiments, is found to be similar to a contour map of equal maximum stresses near the tip. A global statistical analysis for the TC accumulation and delamination growth is introduced and the results are compared to experimental data. From the stress field near a delamination crack it is concluded that the delamination process followed by the TCs may be due to dynamic effects. Regular fracture mechanics tools for the prediction of the failure process are limited, since the peeling stress singularity region is too small to be included in the homogenous continuum mechanics range.     

Role of matrix resin in delamination onset and growth in composite laminates

The effect of the matrix resin on the onset and growth of delamination in composite laminates has been investigated in this work. Two kinds of graphite/epoxy composite materials (T300/648-BF₃/MEA and T300/634-DDS) with quite different matrix properties have been used. The study was done on two different layups, [(±30)₃/90₂]_s and [(±45)₂/O₂/90₂]_s. Out-of-plane moiré interferometry and diiodomethane-enhanced X-radiography were used to detect delamination. A strength criterion for the onset of delaminatoin is proposed and an assessment made of the effect of matrix properties on delamination onset. A modified energy release rate model is presented for characterization of delamination growth emphasis being placed on assessing the behavior of delamination resistance curves and delamination growth rate. The results indicate that enhancement of matrix strength and ductility increases the critical loads for delamination onset and delamination resistance in the composite laminates under static loading, and significantly reduces the delamination growth rate under cyclic loading.     

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.     

含矩形边缘分层缺陷层合板的压缩性能

对含矩形边缘分层缺陷层合板的压缩性能进行试验研究和理论分析, 考察了层合板厚度(含铺层形式)、 分层位置、 形状、 面积以及环境等因素对压缩强度的影响, 并采用分层扩展以及软化夹杂两种模型对含分层层合板的压缩强度进行了计算和破坏机理分析。结果表明: 厚板对边缘分层缺陷不敏感, 中等厚度和薄层合板比较敏感; 缺陷的位置和形状对层合板压缩强度有一定的影响; 湿热环境改变了含缺陷板的压缩破坏机理, 并对中等厚度板和薄板的压缩强度有明显的影响。两种模型中软化夹杂模型效果较好, 可用于工程设计计算。      

A criterion for modelling initiation and propagation of matrix cracking and delamination in cross-ply laminates

A variational approach is used to model the behaviour of composite cross-ply laminates damaged by transverse, longitudinal cracking and delamination. An energetic criterion is proposed. It is based on the strain energy release rate associated with each of the three damage modes. The first part of this paper is concerned with the modelling of the transverse and longitudinal cracking. In the second part, a model for studying delamination damage is presented. The numerical results show that these models provide a consistent level of accuracy for a variety of thin laminate material systems and configurations, with various combinations of delaminations and matrix cracks. In this paper several numerical simulations meant to describe initiation for each damage mode are proposed. The estimation of damage modes contributions is achieved for two thin laminates in order to predict the evolution of damage mode transition.     

Modelling off-axis ply matrix cracking in continuous fibre-reinforced polymer matrix composite laminates

The fracture process of composite laminates subjected to static or fatigue tensile loading involves sequential accumulation of intra- and interlaminar damage, in the form of transverse cracking, splitting and delamination, prior to catastrophic failure. Matrix cracking parallel to the fibres in the off-axis plies is the first damage mode observed. Since a damaged lamina within the laminate retains certain amount of its load-carrying capacity, it is important to predict accurately the stiffness properties of the laminate as a function of damage as well as progression of damage with the strain state. In this paper, theoretical modelling of matrix cracking in the off-axis plies of unbalanced symmetric composite laminates subjected to in-plane tensile loading is presented and discussed. A 2-D shear-lag analysis is used to determine ply stresses in a representative segment and the equivalent laminate concept is applied to derive expressions for Mode I, Mode II and the total strain energy release rate associated with off-axis ply cracking. Dependence of the degraded stiffness properties and strain energy release rates on the crack density and ply orientation angle is examined for glass/epoxy laminates. Suitability of a mixed mode fracture criterion to predict the cracking onset strain is also discussed.     

Multi-directional stiffness degradation induced by matrix cracking in composite laminates

A model was developed for predicting the stiffness degradation of fiber reinforced plastics (FRP), with ply configuration [0_m/±θ_n]_S, induced by matrix cracking under in-plane tension. The model assumes that the cracks in off-axis plies are uniformly distributed and a damage variable D is defined. Based on the theory of fracture mechanics, the elastic moduli of cracked matrix are obtained and indicated by the damage variable D, then the reduction of elastic moduli of laminates caused by the matrix cracks was studied. Comparison with experimental values for the glass/epoxy [90₃/0]_S, [0/90]_S and [0/±45]_S laminates shows good agreement with the theoretical prediction given by the presented model.     

复合材料层合板基体裂纹的协同损伤演化模型

首先,为研究复合材料层合板在准静态载荷下的基体裂纹演化特征,提出了一个基于能量的协同损伤演化模型。然后,通过模型对损伤进行了多尺度分析:从微观角度,采用三维有限元方法求得裂纹表面位移;从宏观角度,结合裂纹表面位移,推导了萌生基体裂纹的能量释放率。最后,根据裂纹萌生准则对基体裂纹的演化过程进行预测。模型考虑了演化过程中损伤的相互影响、残余应力、基体材料非线性、材料初始损伤分布及损伤演化的不均匀性。根据演化分析流程计算了[±θ/904]s铺层玻璃纤维复合材料的基体裂纹演化过程。结果表明:这一模型能够准确地预测准静态载荷下复合材料层合板基体裂纹的损伤演化规律。     

XFEM simulation of delamination in composite laminates

In this paper, the extended finite element method (XFEM) is extended to simulate delamination problems in composite laminates. A crack-leading model is proposed and implemented in the ABAQUS® to discriminate different delamination morphologies, i.e., the 0°/0° interface in unidirectional laminates and the 0°/90° interface in multidirectional laminates, which accounts for both interlaminar and intralaminar crack propagation. Three typical delamination problems were simulated and verified. The results of single delamination in unidirectional laminates under pure mode I, mode II, and mixed mode I/II correspond well with the analytical solutions. The results of multiple delaminations in unidirectional laminates are in good agreement with experimental data. Finally, using a recently proposed test that characterizes the interaction of delamination and matrix cracks in cross-ply laminates, the present numerical results of the delamination migration caused by the coupled failure mechanisms are consistent with experimental observations.     

含面内波纹缺陷的复合材料层合板刚度性能

基于经典层合板理论（CLT）,并考虑面内波纹引起的拉伸-弯曲耦合作用,提出了含面内波纹缺陷的复合材料层合板刚度预测模型,定量研究了波纹比、纤维偏转角和波纹位置等面内波纹参数对其三维刚度性能的影响。结果表明：理论模型预测值与文献中的结果吻合较好;面内波纹对纵向弹性模量、横向弹性模量、面内剪切模量、主泊松比和面内弯曲刚度均产生了显著影响。该建模方法为研究波纹缺陷对复合材料力学性能影响提供了参考。     

Fatigue life prediction of woven composite laminates with initial delamination

An engineering approach for fatigue life prediction of fibre‐reinforced polymer composite materials is highly desirable for industries due to the complexity in damage mechanisms and their interactions. This paper presents a fatigue‐driven residual strength model considering the effect of initial delamination size and stress ratio. Static and constant amplitude fatigue tests of woven composite specimens with delamination diameters of 0, 4 and 6 mm were carried out to determine the model parameters. Good agreement with experimental results has been achieved when the modified residual strength model has been applied for fatigue life prediction of the woven composite laminate with an initial delamination diameter of 8 mm under constant amplitude load and block fatigue load. It has been demonstrated that the residual strength degradation‐based model can effectively reflect the load sequence effect on fatigue damage and hence provide more accurate fatigue life prediction than the traditional linear damage accumulation models.     

Effect of z-pin surface treatment on delamination and debonding properties of z-pinned composite laminates

The effect of z-pin surface treatment on the delamination fracture properties of z-pinned unidirectional carbon fibre/epoxy prepreg laminate is presented in this paper. Cryogenic and plasma treatments were used to increase the pin/composite interface properties. Z-pin pullout tests were carried out to study the relations between the bridging force and the displacement. Mode-I double-cantilever beam tests were used to characterize the improvements in delamination toughness. It was pointed out that appropriate treatments could effectively increase the delamination fracture properties. Oxygen-containing functional groups could be induced on the pin surface through cold plasma treatment. An increasing surface energy is improving the wettability so that more chemical reactions can be generated between the epoxy group and z-pin surface. Furthermore, the surface roughness of z-pins can be extended with a plasma or cryogenic treatment. The pins obtained a larger surface area, which could wet by the epoxy matrix during the z-pin-insertion and curing process.     

Experimental study on delamination migration in composite laminates

The transition of delamination growth between different ply interfaces in composite tape laminates, known as migration, was investigated experimentally. The test method used promotes delamination growth initially along a 0/θ ply interface, which eventually migrates to a neighbouring θ/0 ply interface. Specimens with θ = 60° and 75° were tested. Migration occurs in two main stages: (1) the initial 0/θ interface delamination turns, transforming into intraply cracks that grow through the θ plies; this process occurs at multiple locations across the width of a specimen, (2) one or more of these cracks growing through the θ plies reaches and turns into the θ/0 ply interface, where it continues to grow as a delamination. A correlation was established between these experimental observations and the shear stress sign at the delamination front, obtained by finite element analyses.Overall, the experiments provide insight into the key mechanisms that govern delamination growth and migration.     

纤维桥联效应下复合材料层合板的屈曲及分层扩展模拟

纤维增强复合材料层合板由于层间力学性能弱,容易出现分层损伤。分层的扩展往往伴随着纤维桥联效应,纤维桥联能显著增大层合板尤其是多向层合板分层扩展的阻力。考虑纤维桥联效应的三线性内聚力模型能表征分层扩展实验中断裂韧性的“R曲线”特征,比传统的双线性模型能更为准确地描述复合材料的分层扩展行为。本论文基于三线性内聚力模型,对含圆形分层复合材料层合板的轴向压缩进行数值模拟,探讨纤维桥联效应对分层扩展及后屈曲行为的影响规律。研究结果发现,纤维桥联对层合板的屈曲载荷影响较小;混合屈曲模式下,三线性模型预测的上下子板相对法向位移明显低于双线性模型;相同分层深度下,三线性模型预测的层合板后屈曲更早转变为整体屈曲模式。随着分层深度的增加,层合板的屈曲模式由局部屈曲逐步过渡为混合屈曲和整体屈曲;当分层深度较浅时,Ⅰ型分层扩展占主导;随着分层深度的增加,Ⅰ型分层逐渐减弱,而Ⅱ型和Ⅲ型分层扩展则显著增强;当分层接近板中面时,Ⅰ型分层停止扩展,以Ⅱ型及Ⅲ型分层为主。     

Experimental investigation of delamination buckling of stitched composite laminates

In the current investigation, effects of through-the-thickness stitching with two different types of aramid threads, Kevlar^® and Twaron^® threads, on the buckling loads of delaminated glass/epoxy composite laminates are studied. Buckling loads are predicted based on the Southwell, Vertical displacement and Membrane strain plot methods by using the experimental data. From the Southwell, Vertical displacement and Membrane strain plot methods it is observed that stitching either by Kevlar^® or Twaron^® threads is effective in improving the buckling strength of glass/epoxy composite laminates when the delamination length is greater than 0.5L, L being the length of the laminate. For long delaminations, Kevlar^® stitched glass/epoxy composite laminate is best in retaining its buckling strength when re-loading is done. Southwell plot method tends to overestimate the buckling loads as the data obtained from this method are influenced by the breakages in the glass/epoxy composite laminate buckling test specimens.     

Cohesive modeling of delamination in Z-pin reinforced composite laminates

The mode I interlaminar fracture in Z-pin reinforced composite laminates is modeled using a cohesive volumetric finite element (CVFE) scheme. The test configuration used in this study is a Z-pin reinforced double cantilever beam specimen. A bilinear rate-independent but damage-dependent cohesive traction–separation law is adopted to model the fracture of the unreinforced composite and discrete nonlinear spring elements to represent the effect of the Z-pins. The delamination toughness and failure strength of the Z-pin reinforced composites are determined by a detailed comparison study of the numerical modeling results with experimental data. To further reduce the computational effort, we introduce an equivalent distributed cohesive model as a substitute for the discrete nonlinear spring representation of the Z-pins. The cohesive model is implemented on various test problems with varying failure parameters and for varying spatial Z-pin reinforcement configurations showing good agreement with the experimental results.