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.     

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.     

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.     

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.     

Matrix crack-induced delamination in composite laminates under transverse loading

Fibre-reinforced multidirectional composite laminates are observed in experiments under transverse static or low-velocity impact loading to suffer considerable delamination damage. The intensity of this damage depends on the difference in the ply angles above and below the interface. In this paper a fracture mechanics model is presented for investigating the role of matrix cracks in triggering delaminations and the influence of ply angles in adjacent plies on delamination cracking. The fracture mechanics analysis shows that for a graphite fibre-reinforced composite laminate containing a transverse intraply crack, the crack-induced largest interfacial principal tensile stress is a maximum when the difference between the ply angles across the interface is 90 °, and it attains a minimum when the difference is 40 °. When the crack tips touch the interfaces, the minimum mode II stress singularity, which is weaker than the usual square-root type, appears when the difference between the ply angles is about 45 ° for one glass fibre-reinforced laminate and three graphite fibre-reinforced laminates. These results are in agreement with the experimental observation that the largest delaminations appear at the interface across which the difference between the ply angles is the largest i.e. 90 °.     

Modelling delamination onset and growth in pin loaded composite laminates

A three-dimensional (3D) finite element (FE) model is created with cohesive zone elements (CZE) to simulate a mechanically fastened [0°/90°]_s pin-loaded joint in a composite laminate. The model incorporates fully integrated solid elements in the pin-loaded area to accurately capture the high stress gradients. Contact based cohesive elements with a bilinear traction–separation law are inserted between the layers to capture the onset and growth of delamination. The stress distribution around the pin-loaded hole was verified with the widely used cosine stress distribution model. Results from the FE model show that delamination damage initiated at the point of maximum average shear stress at the 0°/90° interface. The delaminated area develops an elliptical shape which grows in a non-self similar manner with increasing pin displacement. It is concluded that a progressive damage model should be included to provide a full understanding of the failure sequence, work that the authors are currently engaged with.     

基于界面元法含分层损伤复合材料层合板的区间分析

基于界面元法研究了含有不确定参数复合材料层合板分层的问题, 以区间数学为基础, 将不确定参数区间定量化, 提出一种含有不确定参数复合材料层合板分层的区间分析方法, 并从数学证明和数值算例两方面与概率方法进行对比, 验证区间分析方法的可靠性。通过区间分析方法给出了不确定参数对DCB (Double cantilever beam) 分层临界载荷的影响, 并且得到在一定初始裂纹长度或铺层数量下, 具有不确定参数DCB 承载临界载荷的上下界值, 这为不确定结构设计提供一定的依据。      

A novel statistical model for predicting matrix cracking in high temperature polymer composite laminates

This paper studied the progressive matrix cracking in high temperature polymer composite laminates that could be used for next generation high speed transport airframe structures and aircraft engine components exposed to elevated temperatures. Damage mechanisms of matrix cracking were identified by X-ray radiography at room temperature and in-test photography technique at high temperature. It was found that the non-deterministic scenario is always involved in the procedure of transverse matrix cracking. Monte Carlo simulations using experimentally obtained materials properties were applied to simulate the multiple transverse cracking and compared with the experiment data. Finally, a novel statistical model combining Weibull theory with shear lag model was proposed to predict the matrix cracking based upon the previously obtained probability density function of crack spacing. It is shown that the predictions of this statistical model agree well with the experimental results and can be used to have an in-depth understanding of the random matrix cracking problem in composite laminates.