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 °.     

A study of the propagation of an embedded crack in a composite laminate of finite thickness

In this paper, the mechanism for the propagation of a crack embedded in the central layer of a composite laminate is studied based on energy criteria. As the crack may propagate in the transverse direction or in the tunneling direction, the critical stresses for these two propagations are presented. The theoretical analysis is applied to a fibre-reinforced composite laminate. Critical stresses for the initiation of crack propagation are calculated taking into account the influence of the adjacent ply angle and the crack size. It is found that for the considered typical fibre-reinforced composite laminate, the critical stress for the transverse propagation is less than that for the tunneling propagation. Therefore, transverse cracking is a more possible fracture mode in composite laminates with initial crack-like defects. This finding supports the calculation of the in situ transverse strength based upon the transverse crack propagation.     

Micromechanical characterization of local deformation in interlaminar-toughened CFRP laminates

The in situ SEM micro-line/grid methods were applied for quantitative evaluation of microscopic deformation in interlaminar-toughened CFRP cross-ply laminates with transverse cracks. Both the local deformation in the interlaminar region around the transverse crack tip and the crack opening displacement (COD) were observed at different temperatures to evaluate the effect of thermal residual stress. A two-dimensional approximate elastic analysis of stress and displacement fields in interlaminar-toughened cross-ply laminates with transverse cracks was conducted and compared with the experimental results. A reasonable agreement was obtained which implied the applicability of the analysis. The analysis will be a basis for the optimal design of interlaminar-toughened composite laminates.     

不同界面SiC/SiC复合材料的断裂行为研究

碳化硅纤维增强碳化硅复合材料(SiC/SiC)是极具前景的高温结构材料。通过先驱体浸渍裂解(PIP)工艺分别制备了PyC界面和CNTs界面SiC/SiC复合材料, 对两种SiC/SiC复合材料的整体力学性能以及界面剪切强度等进行了测试表征, 并对材料中裂纹的产生与扩展进行了原位观测。结果表明, 两种界面SiC/SiC复合材料弯曲强度相近, 但PyC界面SiC/SiC复合材料的断裂韧性约为CNTs界面SiC/SiC复合材料的两倍。在PyC界面SiC/SiC复合材料中, 裂纹沿纤维-基体界面扩展, PyC涂层能够偏转或阻止裂纹, 材料呈现伪塑性断裂特征; 而在CNTs界面SiC/SiC复合材料中, 裂纹在扩展路径上遇到界面并不偏转, 初始裂纹最终发展为主裂纹, 材料呈现脆性断裂模式。     

各向异性复合材料开孔板拉伸强度预测及模型验证

基于有限断裂力学方法建立了一种预测多向复合材料开孔板拉伸强度的通用和半经验模型。该模型同时采用基于应力形式的失效准则和基于能量形式的失效准则预测失效。模型仅需铺层弹性常数、无缺口层合板的强度以及0°铺层的断裂韧性等参数。基于线弹性断裂力学建立了多向复合材料层合板的断裂韧性与0°铺层断裂韧性之间的关系, 进而预测了任意铺层复合材料开孔板发生纤维主导拉伸失效时的强度。将模型预测结果与开孔板拉伸强度的试验数据进行了对比验证, 预测误差最大为9.7%, 与点应力和平均应力等方法的对比表明, 该模型的预测精度高于传统的特征长度方法。      

基于断裂韧性预报复合材料层合板的开孔拉伸强度

开孔层合板的强度预报往往取决于孔边的临界长度,它不仅与材料性能,而且与铺层、孔径都有关。本文基于线弹性断裂力学,提出了一种预报对称铺层层合板开孔拉伸强度的新方法,只需提供正交层合板的断裂韧性和无缺口层合板的拉伸强度,显著降低对实验数据的依赖性。首先,将临界长度表作为层合板断裂韧性和无缺口拉伸强度的函数,再通过正交层合板[90/0]_8s的紧凑拉伸试验和虚拟裂纹闭合技术,确定出0°层断裂韧性,进而计算得到任意对称铺层层合板的断裂韧性。本文测试了T300/7901层合板[0/±45/90]_2s和[0/±30/±60/90]_s的开孔拉伸强度,孔径分别为3 mm、6 mm和9 mm。理论预报结果与试验值吻合较好,最大误差为15.2%,满足工程应用需求。      

Fracture control for composite structures

A fracture control technique for composite structures is presented which takes advantage of the unique capability of composite materials to be tailored in stiffness and fracture toughness. Crack arrestment is achieved through the use of integral ‘buffer’ strips in the primary load-carrying laminate. Experimental uniaxial tension data obtained from damaged laminates containing such buffer strips indicate residual strength capacity in excess of the limit design stress for the selected laminate.     

Optimum in situ strength design of laminates under combined mechanical and thermal loads

In this paper, optimum laminate configurations are sought for multidirectional fibre-reinforced composite laminates under combined in-plane mechanical and thermal loads. The design objective is to enhance the value of the loads over and above the first-ply-failure loads which are judged by a transverse failure criterion and the Tsai-Hill criterion, respectively. The in situ strength parameters previously obtained are incorporated in these criteria. It is found that the optimum designs under combined mechanical and thermal loads are not the same as those under pure mechanical loads for three of the four loading cases studied. For all cases the optimum loads are significantly larger than those for a quasi-isotropic design.     

Thermal and mechanical load induced damage behaviour of a low alloy steel: Mechanisms and modelling

A series of experiments, including macroscopic damage measurement and in situ microscopic observation at room temperature and tensile tests at eight different temperatures ranging from 20 to 900°C, is carried out. Mechanical load induced ductile damage evolution law and micromechanisms are presented, where damage evolution law is measured through a new a.c. potential system and the micromechanisms of damage and fracture are observed through an in situ technique in conjunction with a scanning electron microscope (SEM) equipped with a tensile platform. A continuum damage mechanics (CDM) model for ductile fracture proposed by Wang [Engng Fracture Mech. 42, 177–183 (1992)] is employed to model and to analyse the evolution law of damage in the steel. Comparison of experimental and modelling results is presented and good agreement is found. The effect of stress triaxiality on damage evolution is also discussed in the framework of CDM. The effect of temperature rise on tensile properties including Young's modulus, yield and ultimate tensile strength and ductility (elongation and reduction in area), is also reported.     

Failure of fibre-reinforced composites by pull-out fracture

A simple model is proposed to predict the ultimate tensile strength of fibre-reinforced composites when the failure is governed by fibre debonding. The theoretical analysis is based on the concept of fracture mechanics where the debonded zone is considered as an interfacial crack. The analysis is first applied to the classical pull-out test in order to determine the specific work of interfacial cracking. Using this value, the uniaxial tensile strength of the composites can be predicted from an approximate, closed-form equation proposed here. The theoretically predicted results seem to compare favourably with experimental values for fibrere-inforced cement based composite.     

Synthesis and mechanical properties of niobium aluminide-based composites

Niobium aluminide-based composites reinforced with in situ and externally added Al₂O₃ and TiC particulates were fabricated by hot-pressed sintering at 1400 °C. In particular, Nb₂Al–Al₂O₃–TiC in situ composites were successfully obtained from the raw powder mixtures of Nb60Al40 (in at.%)–TiO₂20C8 (in wt.%) by means of this process. The influences of ceramic particulates on the microstructures, flexural strength and fracture toughness were examined. The experimental results indicate that the presence of ceramic particulates yielded a remarkable improvement in both the strength and fracture toughness in comparison with previous results for monolithic niobium aluminide compounds.     

Optimal design of composite wing structures with blended laminates

In this paper we formulate the problem of wing box design optimization using composite laminates with blending constraints. The use of composite laminates necessitates the inclusion of fiber orientation angle of the layers as well as total thickness of the laminate as design variables in the design optimization problem. The wing box design problem is decomposed into several independent local panel design problems. In general such an approach results in a nonblended solution with no continuity of laminate lay ups across the panels, which may not only increase the lay up cost but may also be structurally unsafe due to discontinuities. The need for a blended solution increases the complexity of the problem many fold. In this paper we impose the blending constraints globally by using a guide based design methodology within the genetic algorithm optimization scheme and compare the results with the published ones. Two different blending schemes – outer and inner blending are presented. The result shows that the optimum design obtained using the current methodology has better continuity of laminate lay ups and also the reported weight of the composite wing box is on the lower side. Finally, a parametric study of the effect of global deflection constraint on the total weight of the optimum design is presented.     

Z-pin增强复合材料Ⅰ型断裂韧性数值分析

采用细观力学方法以及虚拟裂纹闭合法(VCCT)对含有Z-pin增强复合材料双悬臂梁(DCB)结构Ⅰ型断裂韧性进行了研究。利用有限元法建立了结构模型,采用实体单元模拟复合材料层压板结构和非线性弹簧元模拟Z-pin。通过计算应变能释放率对含有不同体积分数Z-pin的复合材料层压板Ⅰ型断裂韧性与不含Z-pin的复合材料层压板Ⅰ型断裂韧性进行了对比分析。研究表明,含有Z-pin增强复合材料双悬臂梁(DCB)结构Ⅰ型断裂韧性在裂纹扩展过程中受到Z-pin桥联作用的影响而显著增强,且其增强效果与Z-pin的体积分数、处在桥联区的Z-pin数目均相关,这表明Z-pin增强方法能够有效提高复合材料层压板的分层扩展阻力。     

Interfacial separation of fibres in fibre reinforced composites

An analytical model is proposed to predict the ultimate tensile strength of fibre-reinforced composites when the failure is governed by fibre debonding.

The analytical analysis is based on the principle of the compliance method in fracture mechanics with the presence of an interfacial crack at the fibre/matrix interface. The model is developed on the basis of the assumption that both the matrix and the fibre behave elastically and the matrix strain at a zone far from the matrix-fibre interface is equal to the composite strain. Furthermore, it is assumed that a complete bond exists between the fibre and the matrix and that the crack faces are traction free.

It is shown that the separation strain energy release rate for fibre-reinforced composites can be obtained for cases with and without the existence of an interfacial crack. Numerical examples are presented and compared with results obtained in the literature by finite element analyses and from experimental tests. The comparison demonstrates the accuracy and the convergence of the model.     

A finite fracture mechanics model for the prediction of the open-hole strength of composite laminates

A new model based on finite fracture mechanics is proposed to predict the open-hole tensile strength of composite laminates. Failure is predicted when both stress-based and energy-based criteria are satisfied. The material properties required by the model are the ply elastic properties, and the laminate unnotched strength and fracture toughness. No empirical adjusting parameters are required. Using experimental data obtained in quasi-isotropic carbon–epoxy laminates it is concluded that the model predictions are very accurate, resulting in improvements over the traditional strength prediction methods. It also is shown that the proposed finite fracture mechanics model can be used to predict the brittleness of different combinations of materials and geometries.     

Topology optimization of particle‐matrix composites for optimal fracture resistance taking into account interfacial damage

This paper presents a topology optimization framework for optimizing the fracture resistance of two‐phase composites considering interfacial damage interacting with crack propagation through a redistribution of the inclusions phase. A phase field method for fracture capable of describing interactions between bulk brittle fracture and interfacial damage is adopted within a diffuse approximation of discontinuities. This formulation avoids the burden of remeshing problem during crack propagation and is well adapted to topology optimization purpose. Efficient design sensitivity analysis is performed by using the adjoint method, and the optimization problem is solved by an extended bidirectional evolutionary structural optimization method. The sensitivity formulation accounts for the whole fracturing process involving crack nucleation, propagation, and interaction, either from the interfaces and then through the solid phases, or the opposite. The spatial distribution of material phases are optimally designed using the extended bidirectional evolutionary structural optimization method to improve the fractural resistance. We demonstrate through several examples that the fracture resistance of the composite can be significantly increased at constant volume fraction of inclusions by the topology optimization process.     

Optimizing energy absorption in multi-layered materials through controlled delamination

The intent of this paper is to investigate the mechanics of delamination growth in an isotropic, ideally-brittle layered material under an impact load and to present guidelines for the design of more energy absorbent structures. Using a finite element model, both two- and three-layered configurations are considered. Prompted by the results from this model, closed-form solutions for the interlaminar shear strength and the interfacial fracture toughness corresponding to maximum energy absorption are derived for the two-layered laminate. These solutions were used to develop guidelines for the optimal design of two- and three-layered laminates.     

Fatigue and residual strength of composite laminates

The mechanics of fatigue failure of laminated composite materials are completely different from that of conventional materials. The mechanics of fatigue failure of conventional materials involve the initiation and propagation of a single crack, which causes the material to fail. Laminated composite material can arrest the propagating crack to within a single lamina, thus avoiding immediate failure. Only after accumulation of cracks the laminate fails. The fatigue life of the laminate is best described by S-N curves. A theory for residual strength is developed which is based on a cumulative damage theory. The theory predicts that the static strength of the laminate is maintained almost to the final failure by fatigue. Experimental results verify this phenomenon.     

Strength of carbon/epoxy laminates with countersunk hole

The aim of this study is to predict the static strength of carbon/epoxy laminates with countersunk hole. Also, three-point bend (TPB) specimens with the same lay-up were analysed. For this purpose, the notched strength of the laminates was analysed by a damage zone model (DZM), where damage around the notch is represented by an ‘equivalent crack’ with cohesive forces acting between the crack surfaces. The DZM requiring only basic properties of the laminate such as unnotched tensile strength, δ₀, fracture energy, G_c^*, and stiffnesses of the laminate. However, the complex geometry around the countersunk hole implies that both δ₀ and G_c^* will vary in this area, and in order to avoid this problem an approximate geometry of the countersunk hole is used in the DZM-calculations. With this approximation, good agreement between experimental and calculated strength was observed for the laminates with countersunk hole. This was also the case for the TPB specimens.     

Damage tolerance assessment by bend and shear tests of two multilayer composites: Glass fibre reinforced metal laminate and aluminium roll-bonded laminate

The damage tolerance of an aluminium roll-bonded laminate (ALH19) and a glass fibre reinforced laminate (GLARE) (both based on Al 2024-T3) has been studied. The composite laminates have been tested under 3-point bend and shear tests on the interfaces to analyze their fracture behaviour. During the bend tests different fracture mechanisms were activated for both laminates, which depend on the constituent materials and their interfaces. The high intrinsic toughness of the pure Al 1050 layers present in the aluminium roll-bonded laminate (ALH19), together with extrinsic toughening mechanisms such as crack bridging and interface delamination were responsible for the enhanced toughness of this composite laminate. On the other hand, crack deflection by debonding between the glass fibres and the plastic resin in GLARE was the main extrinsic toughening mechanism present in this composite laminate.