Constitutive Model for a Fiber Tow Bridging a Delamination Crack

A simple model is introduced for a fibrous tow, stitch, or rod that bridges a delamination crack in a laminate. The model is introduced for mode II delamination cracks but is intended for general mixed-mode cracks. Modeling is guided by prior observations and measurements on laminates reinforced through the thickness by stitches or short rods. Salient phenomena include shear deformation of the bridging tow, its debonding from and sliding relative to the surrounding laminate, and its sideways displacement through the laminate. The tow is represented as a beam that can shear and extend axially. Its axial displacement relative to the laminate is resisted over its debonded periphery by friction. The forces associated with its sideways displacement are estimated by regarding it as a punch being driven through a plastic medium (the laminate). Thus the mechanics of the whole problem are reduced to a set of one-dimensional equations. The distinction between continuous stitches and discontinuous rod reinforcement consists of a boundary condition. With realistic values assigned to undetermined parameters, experimental data for stitches are reproduced over the whole range of displacements up to ultimate failure of the stitch. The model generates a bridging traction law that can be used for optimal design of through-thickness reinforcement for damage tolerance in a wide variety of structures.     

A Discrete Model for Simulation of Composites Plate Impact Including Coupled Intra- and Inter-ply Failure

Laminated composites can undergo complex damage mechanisms when subjected to transverse impact. For unidirectional laminates it is well recognized that delamination failure usually initiates via intra-ply shear cracks that run parallel to the fibres. These cracks extend to the interface of adjacent orthogonal plies, where they are either stopped, or propagate further as inter-ply delamination cracks. These mechanisms largely determine impact energy absorption and post-delamination bending stiffness of the laminate. Important load transfer mechanisms will occur that may lead to fibre failure and ultimate rupture of the laminate. In recent years most Finite Element (FE) models to predict delamination usually stack layers of ply elements with interface elements to represent inter-ply stiffness and treat possible delamination. The approach is computationally efficient and does give some estimate of delamination zones and damaged laminate bending stiffness. However, these models do not properly account for coupled intra-ply shear failure and delamination crack growth, and therefore cannot provide accurate results on crack initiation and propagation. An alternative discrete meso-scale FE model is presented that accounts for this coupling, which is validated against common delamination tests and impact delamination from the Compression After Impact (CAI) test. Ongoing research is using damage prediction from the CAI simulation as a basis for residual strength analysis, which will be the published in future work.     

玻璃纤维-不锈钢网混杂增强环氧树脂层合板对球形弹斜冲击响应特性实验研究

为了研究玻璃纤维-不锈钢网混杂增强环氧树脂层合板在球形弹高速斜冲击下的损伤特性,利用一级气炮对2 mm厚度的玻璃纤维增强环氧树脂复合材料层合板和含一层、三层304不锈钢网的玻璃纤维-不锈钢网混杂增强环氧树脂层合板进行倾角为30°的冲击实验,以揭示304不锈钢网对层合板弹道极限和能量吸收的影响规律,并分析层合板损伤特征及其机理。通过实验发现,含有三层不锈钢网层合板的弹道极限最高,而不含不锈钢网层合板和含一层不锈钢网层合板的弹道极限速度接近。层合板吸收的能量随着弹体速度增加呈现出先增加后趋于平稳,然后急剧上升的趋势。层合板损伤模式为基体开裂和破碎、分层、不锈钢丝拉伸断裂、纤维拉伸断裂和剪切断裂。层合板分层损伤面积随弹体速度增大先增大后减小,最后趋于稳定。当弹体速度较低时,层合板主要发生纤维拉伸断裂、基体开裂、层间有分层损伤产生。随着弹体速度的增大,层合板正面纤维逐渐发生压剪断裂、基体破碎,背面纤维发生严重的拉伸撕裂。      

Environmental durability of z-pinned carbon fibre–epoxy laminate exposed to water

The influence of z-pins on the water absorption properties of a quasi-isotropic carbon fibre–epoxy laminate is assessed. Fibrous composite pins accelerate the moisture absorption rate and increase the total absorbed moisture concentration when the laminate is immersed in water. However, the moisture absorption properties of the laminate are not affected significantly by pins when exposed to hot and humid air. Water diffusion into the z-pinned laminate is aided by interfacial cracks between the pins and laminate. Also, the axial alignment of fibres within the composite pins in the through-thickness direction increases the water absorption rate. Pin pull-out tests reveal that water absorption reduces the mode I crack bridging traction load generated by pins by reducing the shear strength of the pin-laminate interface. This indicates that the mode I delamination toughness induced by pinning is weakened by moisture absorption.     

Simulation of delamination–migration and core crushing in a CFRP sandwich structure

Following the onset of damage caused by an impact load on a composite laminate structure, delaminations often form propagating outwards from the point of impact and in some cases can migrate via matrix cracks between plies as they grow. The goal of the present study is to develop an accurate finite element modeling technique for simulation of the delamination–migration phenomena in laminate impact damage processes. An experiment was devised where, under a quasi-static indentation load, an embedded delamination in the facesheet of a laminate sandwich specimen migrates via a transverse matrix crack and then continues to grow on a new ply interface. Using data from this test for validation purposes, several finite element damage simulation methods were investigated. Comparing the experimental results with those of the different models reveals certain modeling features that are important to include in a numerical simulation of delamination–migration and some that may be neglected.     

基于反平面剪切模型的含分层双金属板片条合成能量解法及其与有限元解的比较

基于反平面剪切模型, 求解得到受出面载荷含分层双金属梁的位移解答, 利用片条合成能量解法构造含分层双金属板附加位移模态, 得到闭合解。利用有限元软件ANSYS建立含对称、非对称矩形分层双金属板有限元模型, 采用接触元模拟非对称分层区, 得到有限元解。结果表明, 与弯曲型闭合解相比, 反平面剪切型闭合解与有限元解更接近。      

Analytical solution for the pull-out response of FRP rods embedded in steel tubes filled with cement grout

Fiber-reinforced plastic (FRP) tendons have been widely used for ground anchors in civil engineering. Although various pull-out tests of FRP rods from grout-filled steel tubes have been conducted to simulate ground anchors in rock, there are relatively few theoretical studies reported in the literature for this type of bonded anchorages. The intention of this paper is to present an analytical solution for predicting the maximum pull-out load of FRP rods embedded in steel tubes filled with cement grout. First, the expression of the shear stress along the thickness direction of the grout layer is obtained analytically. The tensile stress in the rod and the interfacial shear stress at the rod–grout interface are formulated at different loading stages. By modeling interfacial debonding as an interfacial shear crack, the pull-out load is then expressed as a function of the interfacial crack length. Finally, based on the Lagrange multiplier method, the maximum pull-out load and the critical crack length are determined. The validity of the proposed analytical solution is verified with the experimental results obtained from literature. It can be concluded that the proposed analytical solution can predict the maximum pull-out load of spiral wound and indented rods embedded in steel tubes filled with cement grout with reasonable accuracy. The proposed solution can be also applied in predicting the pull-out capacity of steel bars from concrete.     

复合材料层合板静态压痕与损伤行为

发展了层合复合材料面内及分层失效模型,模型考虑了横向压剪残余剪切变形和分层残余相对位移。提出一种块体单元包含若干铺层的模型,以减少复合材料逐层分析时的计算量。对一种碳纤/环氧层合复合材料进行了横向压痕试验,测量了不同压力下凹坑的深度,用超声C扫测得损伤面积。用发展的模型在ABAQUS平台上通过用户材料子程序UMAT模拟了上述试验,分析了试验曲线特征点对应的损伤机制,通过与试验结果的对比,验证了本文模型的合理性。     

含内部分层复合材料层板三维问题的三角级数能量解法

本文根据叠加原理分解含内部分层复合材料层板的受力状态, 使分层问题归结为分层表面受附加剪切载荷作用时附加状态的分析, 然后根据边界条件, 利用三角级数构造位移模态, 进而由势能原理确定位移解答, 并做收敛性验证。计算表明, 结果收敛, 挠度收敛尤为迅速。      

复合材料层板损伤过程的刚度分析

本文对典型铺设的[0₂/±45₂/90₂]_s碳/环氧复合材料层板中的典型损伤状态进行了实验观察,测定出损伤对层板刚度引起的下降率.建立了横向裂纹扩展、分层伴以横向裂纹扩展的三维有限元分析模型,计算出对层板刚度引起的下降率,并与实验值进行了比较.结果表明,横向裂纹和分层是层板的主要损伤型式,分层损伤扩展是一个主导性的稳定的损伤扩展过程,是导致刚度下降的主要因素.     

雷击冲击力作用下复合材料层合板动力学响应及损伤特性

采用基于连续介质损伤理论（CDM）的复合材料三维渐进损伤分析模型,以ABAQUS有限元分析软件为平台,结合VUMAT子程序,对雷击冲击力作用下的复合材料层合板进行了三维动力学分析,研究了雷击冲击力作用下层合板的动力学响应及损伤特性。结果表明,在雷击冲击力作用下,层合板做降幅振荡运动,冲击力做功与层合板内能和动能相互转换,同时伴随着黏性耗散能,冲击力做功大小可用雷电流库伦量与作用积分的函数表示;层合板损伤由外力做功大小决定,对于同种材料,基体、纤维及分层损伤分别存在不同的损伤能量临界值,当冲击力做功大于该值,层合板会产生对应的损伤;在相同边界支持条件下,冲击力总功最大值决定了不同损伤类型损伤状态变量的大小,与波形参数和峰值电流无关。     

复合材料层合板缺口强度的CDM三维数值模型

针对复合材料层合结构缺口强度问题,基于连续损伤力学（CDM）提出了一种三维损伤数值模型。模型区分了层内损伤（纤维失效、纤维间失效）和层间分层损伤的不同失效模式。采用三维Puck准则与Aymerich准则对上述2类损伤进行判定,材料失效后基于CDM中线性软化模型对材料损伤进行演化。模型考虑了复合材料层合板子层的就位效应和剪切非线性行为。对Carlsson的AS4/3501-6缺口拉伸强度试验进行数值模拟。结果表明:分析结果与试验结果吻合良好,证明了该模型能够准确地预测含缺口复合材料层合板面内拉伸强度。      

复合材料层合板三维分层问题的断裂力学分析

对复合材料层板中椭圆分层的断裂力学问题进行了研究。根据层板平面剪切型分层和反平面剪切型分层尖端附近位移场、应力场与应力强度因子的关系,利用法向切片法,得到椭圆分层前缘应力强度因子与能量释放率的关系。结合由附加位移所确定的总位能,确定了能量释放率和应力强度因子沿分层前缘分布的表达形式。数值计算给出了二者随分层区形状、载荷以及各层厚度比等参数变化的分布情况。     

具有分层损伤复合材料加筋与无加筋层合板热-机械力屈曲性态

基于复合材料一维剪切理论——Mindlin 理论, 给出了材料性质与温度有关的含分层损伤复合材料加筋和无加筋层合板的线性和非线性热-机械力耦合情况下的屈曲问题有限元分析方法, 并研究了含分层损伤的加筋和无加筋层合板的两种不同类型的热- 机械力屈曲问题。通过典型算例分析, 讨论了热-机械力耦合效应和分层大小对含分层损伤结构的屈曲性态的影响关系。     

Stress analysis of imperfect composite laminates with an interlaminar bonding theory

Delamination is a major damage mode in laminated composites since it can cause severe structural degradation. Based on an interlaminar shear stress continuity theory and a linear shear slip theory, a so-called Interlayer Shear Slip Theory was presented in a previous study. This theory was verified to be feasible for shearing-mode delamination analysis. However, in order to account for opening-mode delamination in laminated composites, the continuity of interlaminar normal stress and the modelling of normal separation on the composite interface should also be considered. The present study gives a complete discussion on the Interlaminar Bonding Theory. The effects of interlaminar bonding condition on the laminate deformation and stress distribution are also presented. It is concluded from numerical results that the present theory is suitable for analysis of composite laminates with imperfect interfaces.     

碳/双马来酰亚胺层板加压冲击后的损伤研究

本文对预压碳/双马来酰亚胺层板进行了冲击试验.运用超声C扫描,金相技术和揭层法对冲击损伤进行了细致观察与描述,得到了较全面的细观损伤面貌.研究表明,分层是其主要损伤形式,并几乎分布在所有界面上.分层的形状不规则,但主方向均沿着界面下层纤维方向.分层面积与相邻两层的铺层方向间的夹角及铺层顺序有关.预加压对其内部分层分布有较大影响,最大的分层处于层板背面部分接近中面的界面上.     

Development of smart composite structures with small-diameter fiber Bragg grating sensors for damage detection: Quantitative evaluation of delamination length in CFRP laminates using Lamb wave sensing

The authors and Hitachi Cable, Ltd. have recently developed small-diameter optical fiber and its fiber Bragg grating (FBG) sensor for embedment inside a lamina of composite laminates without strength reduction. The outside diameters of the cladding and polyimide coating are 40 and 52 μm, respectively. First, a brief summary is presented for applications of small-diameter FBG sensors to damage monitoring in composite structures. Then, we propose a new damage detection system for quantitative evaluation of delamination length in CFRP laminates using Lamb wave sensing. In this system, a piezo-ceramic actuator generates Lamb waves in a CFRP laminate. After the waves propagate in the laminate, transmitted waves are received by an FBG sensor attached on or embedded in the laminate using a newly developed high-speed optical wavelength interrogation system. This system was applied to detect interlaminar delamination in CFRP cross-ply laminates. When the Lamb waves passed through the delamination, the amplitude decreased and a new wave mode appeared. These phenomena could be well simulated using a finite element analysis. From the changes in the amplitude ratio and the arrival time of the new mode depending on the delamination length, it was found that this system could evaluate the delamination length quantitatively. Furthermore, small-diameter FBG sensors were embedded in a double-lap type coupon specimen, and the debonding progress could be evaluated using the wavelet transform.     

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.     

含椭圆形分层层板的状态分解-片条合成能量解法

根据叠加原理将含有椭圆形非穿透分层的层板在横向载荷作用下的受力状态进行分解,从而将分层问题归结为在分层表面上的附加剪切载荷作用下层板附加位移与附加应力的分析,并据此建立了一个仅包含分层区的力学模型。进而在层板分层区中切取平行于坐标平面的切片,将切片视为含分层的层合梁,其位移模态以相应层合梁的附加位移模态来表示。这样,可构造层板分层区内满足位移边界条件的位移场。最后,应用最小势能原理确定位移幅值的闭合解。计算结果表明,挠度幅值远远大于中面位移幅值,且与由双三角级数能量解法所得挠度幅值吻合很好。      

含矩形内部分层的复合材料层板的 状态分解-片条合成能量解法

根据叠加原理将含有矩形内部分层的层板在横向载荷作用下的受力状态进行分解, 从而 将分层问题归结为在分层表面上的附加剪切载荷作用下层板附加位移与附加应力的分析, 并据此 建立了一个仅包含分层区的力学模型。进而在层板分层区中切取平行于边界的切片, 将切片视为 含分层的层合梁, 其位移模态以相应层合梁的附加位移模态来表示。这样, 可构造层板分层区内满 足位移边界条件的位移场。最后, 应用最小势能原理确定位移幅值的闭合解。计算结果表明, 挠度 幅值远远大于中面位移幅值, 且与由双三角级数能量解法所得挠度幅值吻合很好。