Nonlinear progressive damage model for composite laminates used for low-velocity impact

In order to effectively describe the progressively intralaminar and interlam- inar damage for composite laminates, a three dimensional progressive damage model for composite laminates to be used for low-velocity impact is presented. Being applied to three-dimensional （3D） solid elements and cohesive elements, the nonlinear damage model can be used to analyze the dynamic performance of composite structure and its failure be- havior. For the intralaminar damage, as a function of the energy release rate, the damage model in an exponential function can describe progressive development of the damage. For the interlaminar damage, the damage evolution is described by the framework of the continuum mechanics through cohesive elements. Coding the user subroutine VUMAT of the finite element software ABAQUS/Explicit, the model is applied to an example, i.e., carbon fiber reinforced epoxy composite laminates under low-velocity impact. It is shown that the prediction of damage and deformation agrees well with the experimental results.     

材料非线性对复合材料层合板热自由边界效应的影响

本文用准三维有限元法研究了材料非线性对复合材料层合板热自山边界效应的影响,给出了修正型Hahn-Tsai非线性应力-应变关系的三维形式。由本文非线性分析方法得到的层间应力与以往由线性分析方法得到的层间应力做了比较,结果表明:材料非线性能显著降低层间剪应力的集中程度,但对层间正应力影响不太明显。     

Variational principle of hybrid energy and the fundamentals of 3-D laminate theory—A new approach for the analysis of interlaminar stresses in composite laminates

This paper discusses the discontinuity of stresses and strains at interlaminar surfaces of the composue laminate and presents a 3-D laminate theory for composite materials. This paper also presents a new type of elastic energy based on the globally continuous variables in laminates, different from the traditional potential energy and complementary energy. Then, a variational principle corresponding to the 3-D laminate theory is developed. The theory and the principle could be a basis of verifying the 2-D laminate theory and determining the interlaminar stresses near the free edges.     

含冲击损伤高强中模碳纤维复合材料层压板压缩剩余强度分析与试验验证

论文以碳纤维复合材料层压板为研究对象,发展了一种模拟复合材料层压板冲击及冲击后压缩的一体化数值分析方法．基于Puck 失效准则和粘聚区模型描述层内损伤与层间损伤,分别采用基于断裂能的双线性型、函数型以及直接折减型等不同损伤折减方法构建了层内损伤预测与演化模型;建立了碳纤维复合材料冲击后压缩数值仿真模型,通过开展不同能量冲击后压缩试验,验证了所发展的数值分析方法的有效性;研究结果表明,采用Puck 失效准则和基于断裂能的双线性损伤演化模型预测冲击后压缩强度时具有较高精度．     

Fracture process zone concept and delamination of composite laminates

Delaminations occur at the free edges of composite laminates because of high interlaminar stresses, which develop due to a mismatch in elastic properties between adjacent plies and the limited toughness of the matrix. The process of delamination is modelled using the concept of a fracture process zone. A finite element analysis that can be used with a constant or linear stress-displacement relationship within the fracture process zone is presented. It is found that the simple constant stress model gives an accurate prediction of the delamination on the free edge of a tensile specimen.     

Numerical simulation of interlaminar damage propagation in CFRP cross-ply laminates under transverse loading

This paper proposes a numerical simulation of interlaminar damage propagation in FRP laminates under transverse loading, using the finite element method. First, we conducted drop-weight impact tests on CFRP cross-ply laminates. A ply crack was generated at the center of the lowermost ply, and then a butterfly-shaped interlaminar delamination was propagated at the 90/0 ply interface. Based on these experimental observations, we present a numerical simulation of interlaminar damage propagation, using a cohesive zone model to address the energy-based criterion for damage propagation. This simulation can address the interlaminar delamination with high accuracy by locating a fine mesh near the damage process zone, while maintaining computational efficiency with the use of automatic mesh generation. The simulated results of interlaminar delamination agreed well with the experiment results. Moreover, we demonstrated that the proposed method reduces the computational cost of the simulation.     

A novel model of delamination bridging via Z-pins in composite laminates

A new micro-mechanical model is proposed for describing the bridging actions exerted by through-thickness reinforcement on delaminations in prepreg based composite materials, subjected to a mixed-mode (I–II) loading regime. The model applies to micro-fasteners in the form of brittle fibrous rods (Z-pins) inserted in the through-thickness direction of composite laminates. These are described as Euler–Bernoulli beams inserted in an elastic foundation that represents the embedding composite laminate. Equilibrium equations that relate the delamination opening/sliding displacements to the bridging forces exerted by the Z-pins on the interlaminar crack edges are derived. The Z-pin failure meso-mechanics is explained in terms of the laminate architecture and the delamination mode. The apparent fracture toughness of Z-pinned laminates is obtained from as energy dissipated by the pull out of the through-thickness reinforcement, normalised with respect to a reference area. The model is validated by means of experimental data obtained for single carbon/BMI Z-pins inserted in a quasi-isotropic laminate.     

Three-dimensional modelling of elastic bonding in composite laminates using layerwise differential quadrature

In an effort to overcome the limitations of existing rigid bonding analysis of composite laminates, the current three-dimensional elastostatic model is proposed. In this model, the three-dimensional interlaminar elastic stress field is determined using the technique of layerwise differential quadrature. The new formulations allowed us to determine the influence of a natural bonding layer upon the field variables in the laminated structure. The interfacial characteristics of continuity and discontinuity satisfy the kinematic continuity conditions through the elastic-bonding layer. A number of case studies are examined, comparisons with rigid bonding and finite element analyses are provided, and the influence of the pertinent parameters on the interlaminar stress field is evaluated and discussed.     

复合材料层合板固化过程的数值模拟

在文［１］中作者采用了有限元和有限差分相结合的交替迭代法及Ｅｕｌｅｒ－Ｃａｕｃｈ解偶算法分析了复合材料层合板固化全过程中板内温度场和固化度场。在此基础上，本文进一步根据层合板在固化过程中不同阶段材料物性变化及损伤破坏特征，提出了两种不同破坏准则和后破坏模型，并采用非线性瞬态热弹性问题的Ｈａｍｉｌｔｏｎ半解析法，研究了层合板在固化全过程中的损伤破坏和热应力、变形的变化规律。通过数值模拟和分析，发现层合板在固化过程中，板内热应力出现多峰值和变号特征，这将是导致层合板早期破坏的原因，本文工作将对材料工艺工作者选择固化工艺参数具有参考价值。     

缝纫复合材料层合板面内弹性模量分析

基于对缝纫孔附近局部细观结构的分析,提出了一种预测缝纫复合材料层合板面内力学性能的理论模型．从分析缝孔单胞的纤维弯曲几何特征入手,最终得到单向板及层合板的弹性常数．通过有限元分析研究了缝纫参数对复合材料层合板面内等效模量的影响．研究结果表明,缝纫造成单向板及层合板面内材料性质的不均匀,随着缝纫密度和缝纫线直径的增加,层合板的等效模量逐渐降低．     

Steady-state aeroelasticity of fluid flow over a laminated composite plate

A stress-function-based variational approach is used to determine the interlaminar stresses in a multilayered strip of laminate subject to arbitrary combinations of axial extension, bending, and the steady-state aerodynamic loading of fluid flow over the upper surface of laminated composite plate. Symmetric four-layer, cross-ply and angle-ply laminates are considered in details. Some numerical solutions by using a personal computer are obtained. The present results for four-layer laminates show that the aerodynamic loading has significant effects on the interlaminar stresses near the free-edge regions.     

An enhanced beam-theory model of the mixed-mode bending (MMB) test—Part I: Literature review and mechanical model

The paper presents a mechanical model of the mixed-mode bending (MMB) test used to assess the mixed-mode interlaminar fracture toughness of composite laminates. The laminated specimen is considered as an assemblage of two sublaminates partly connected by an elastic–brittle interface. The problem is formulated through a set of 36 differential equations, accompanied by suitable boundary conditions. Solution of the problem is achieved by separately considering the two subproblems related to the symmetric and antisymmetric parts of the loads, which for symmetric specimens correspond to fracture modes I and II, respectively. Explicit expressions are determined for the interfacial stresses, internal forces, and displacements.     

Layup optimization with GA for tapered laminates with internal plydrops

Layup optimization of the maximum strength of laminated composites with internal ply-drops is performed by genetic algorithm (GA). Interlaminar stresses are considered in estimating the strength of laminates and calculated by the stress function based complementary virtual work principle. Out-of-plane stress functions are expanded in terms of harmonic series through the thickness direction and initially satisfied the traction free boundary conditions of laminates automatically. As the number of expansion terms is increased, stress concentration near the dropped plies is predicted with better accuracy. Since the proposed analysis is relatively simple and efficient in the prediction of interlaminar stress concentration near the ply-drops, the layup optimization of composite laminates with dropped plies considering interlaminar strength can be easily performed by GA. In the formulation of genetic algorithm, a repair strategy is adopted to satisfy given constraints and multiple elitism scheme is implemented to efficiently find multiple global optima or near-optima.     

碳纳米管/碳纤维增强复合材料层合板低速冲击响应和破坏的数值模拟

碳纳米管/碳纤维增强复合材料（carbon nanotube/carbon fibre reinforced plastic,CNT/CFRP）是一种多尺度复合材料,比传统CFRP有更好的综合性能和更广阔的应用前景。对CNT/CFRP在低速冲击下的响应和破坏进行了数值模拟研究。首先,基于先前的研究通过引入基体增韧因子、残余强度因子并改进损伤耦合方程,建立了新的FRP动态渐进损伤模型;然后,利用新建立的本构模型并结合黏结层损伤模型,对4种碳纳米管含量的增韧碳纤维增强树脂基复合材料层合板在5个能量下的冲击实验进行了数值模拟;最后,将模拟结果与文献中的相关实验结果进行了比较,并讨论了冲击速度的影响。结果表明:新建立的FRP本构模型能够预测CNT/CFRP层合板在低速冲击载荷作用下的响应、破坏过程和分层形貌,模拟得到的载荷-位移曲线和破坏形貌与实验吻合较好;冲击速度会影响CNT/CFRP层合板拉伸和压缩破坏的比例,相同的冲击能量下,更大的冲击速度会造成更多的拉伸破坏。     

用Hamilton半解析法分析固化降温过程中的层间热应力

推导了增量形式Ｈａｍｉｌｔｏｎ半解析法公式；给出了层合板瞬态热弹性问题的求解过程；对复合材料层合板在固化降温过程中的热应力进行了分析。结果表明，在降温过程中层合板内将会出现较大的应力峰值，这些应力峰值将是导致层合板在固化工艺过程中出现破坏的原因。本文的工作将对固化工艺研究具有参考价值。     

3-D numerical study on the bending of symmetric composite laminates

３－ＤＮＵＭＥＲＩＣＡＬＳＴＵＤＹＯＮＴＨＥＢＥＮＤＩＮＧＯＦＳＹＭＭＥＴＲＩＣＣＯＭＰＯＳＩＴＥＬＡＭＩＮＡＴＥＳＣｈｉｅｎＷｅｉ－ｚａｎｇ（钱伟长）;ＨｕａｎｇＱｉａｎ（黄默）;ＦｅｎｇＷｅｉ（冯伟）（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｔｙｏｆＴｅｃ...     

Interlaminar hygrothermal stresses in laminated plates

Within the elasticity formulation the most general displacement field for hygrothermal problems of long laminated composite plates is presented. The equivalent single-layer theories are then employed to determine the global deformation parameters appearing in the displacement fields of general cross-ply, symmetric, and antisymmetric angle-ply laminates under thermal and hygroscopic loadings. Reddy’s layerwise theory is subsequently used to determine the local deformation parameters of various displacement fields. An elasticity solution is also developed in order to validate the efficiency and accuracy of the layerwise theory in predicting the interlaminar normal and shear stress distributions. Finally, various numerical results are presented for edge-effect problems of several cross-ply, symmetric, and antisymmetric angle-ply laminates subjected to uniform hygrothermal loads. All results indicate high stress gradients of interlaminar normal and shear stresses near the edges of laminates.     

Deformation of Cross-Ply Composite Laminates with Cracked Ceramic Matrix

The deformation of cross-ply ceramic-matrix composite laminates under biaxial loading is studied theoretically. Experimentally, microscopic damage evolution in cross-ply ceramic-matrix composite laminates has not been well characterized yet, mainly due to the difficulties involved in testing of anisotropic plates under biaxial loading. It is assumed that the initial damage mechanism observed in ceramic-matrix composite laminates is the formation of tunneling macrocracks both in the 90°- and 0°-plies. The paper addresses the stiffness-deterioration behavior of cross-ply ceramic-matrix laminates with transverse and longitudinal macrocracks. The analysis is based on the equivalent-constraint model of a damaged laminate. Numerical results for SiC/CAS cross-ply laminates of various lay-ups are presented and discussed__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 37–46, January 2005.     

Nonlinear analysis of a composite panel with a cutout repaired by a bonded tapered composite patch

This study presents a solution method to analyze the geometrically nonlinear response of a patch-repaired flat panel (skin) with a cutout under general loading conditions. The effect of induced stiffening due to tensile loading on the in-plane and, particularly, the out-of-plane behaviors of the patch-repaired skin are investigated. The damage to the skin is represented in the form of a cutout under the patch. The patch with tapered edges is free of external tractions. The skin is subjected to general boundary and loading conditions along its external edge. The solution method provides the transverse shear and normal stresses in the adhesive between the skin and the patch, and in-plane and bending stresses in the patch and skin. Both the patch and skin are made of linearly elastic composite laminates, and the adhesive between them is homogeneous and isotropic, exhibiting a bi-linear elastic behavior. Modified Green’s strain–displacement relations in conjunction with von Karman assumptions are employed in determining the in-plane strains in the skin and patch; however, the transverse shear strains in the adhesive are determined based on the shear-lag theory. The present solution method utilizes the principle of virtual work in conjunction with complex potential functions.     

冲击作用下复合材料叠层板层间开裂演化模型

采用双线性特性破坏模型研究了复合材料叠层板层间开裂裂纹的演化, 通过引入弹性/剪切模量的损伤参数, 推导出损伤参数与应变之间的微分方程, 并得到裂纹耗散功率与损伤参数变化率之间的关系. 计算不同初始冲击速度下复合材料叠层板某界面上应变、应变率响应以及损伤参数的演化, 即可得到该界面发生层间开裂的情形及其对剪切模量的影响.通过检查界面各点处的损伤参数是否发生改变, 预测了冲击完成之后复合材料叠层板第1, 2层之间发生层间开裂区域的大小与位置; 该预测结果与实验数据及其他破坏准则计算结果基本相符. 计算结果表明, 在冲击过程中当界面上任意点处的剪应力超过剪切强度后, 该点附近的剪切模量开始发生衰减, 衰减大小随铁球初始冲击速度的增大而增大, 并从靠近冲击中心的位置逐渐向周围递减. 在四边简支边界条件下, 复合材料叠层板的层间开裂区域同样最先出现在界面中靠近冲击点的位置, 区域面积随初始冲击速度的增大不断扩大. 当初始冲击速度足够高时, 第1, 2层界面的两条对称轴上开始出现多个独立的开裂区域.