复合材料Ⅰ型层间断裂韧性GIC和初始裂纹长度

从经典梁理论和弹性基础上的正交各向异性梁理论出发，分析了梁的弯曲剪切效应和弹性基础对用双悬臂梁试件测得的复合材料层合板Ⅰ型层间断裂韧性Ｇ＿（ＩＣ）的影响，发现当试件的初始裂纹长度较短时，剪切效应和弹性基础对Ｇ＿（ＩＣ）的影响是显著的，建议将初始裂纹长度取５０毫米。实验结果表明，初始裂纹长度由２０毫米增加到５０毫米时，测得的Ｇ＿（ＩＣ）值的离散系数降低２０％～４０％，数据趋于稳定，分散性减小。     

A continuum damage model for delaminations in laminated composites

Delamination, a typical mode of interfacial damage in laminated composites, has been considered in the context of continuum damage mechanics in this paper. Interfaces where delaminations could occur are introduced between the constituent layers. A simple but appropriate continuum damage representation is proposed. A single scalar damage parameter is employed and the degradation of the interface stiffness is established. Use has been made of the concept of a damage surface to derive the damage evolution law. The damage surface is constructed so that it combines the conventional stress-based and fracture-mechanics-based failure criteria which take account of mode interaction in mixed-mode delamination problems. The damage surface shrinks as damage develops and leads to a softening interfacial constitutive law. By adjusting the shrinkage rate of the damage surface, various interfacial constitutive laws found in the literature can be reproduced. An incremental interfacial constitutive law is also derived for use in damage analysis of laminated composites, which is a non-linear problem in nature. Numerical predictions for problems involving a DCB specimen under pure mode I delamination and mixed-mode delamination in a split beam are in good agreement with available experimental data or analytical solutions. The model has also been applied to the prediction of the failure strength of overlap ply-blocking specimens. The results have been compared with available experimental and alternative theoretical ones and discussed fully.     

Impact and high strain rate delamination characteristics of carbon fibre epoxy composites

Delamination mechanisms and energy dissipation of carbon fibre epoxy composites under impact and high strain rate conditions are studies in terms of a new experimental set-up. The test set-up is designed to separate the Mode-I, -II and mixed mode delamination resistance so that relevant mechanisms can be studied in greater detail. The impact specimens consist of 18 × 18 mm laminated composite pieces bonded to steel bars to form the impact specimens with the normal Charpy and Izod specimen geometry. The impact energy dissipation is recorded and taken as a dynamic delamination toughness measurement, and the transition from the pure Mode-I to Mode-II through the mixed mode delamination is measured. Detailed delamination surface examinations by scanning electron microscopy (SEM) show that different failure mechanisms are involved in the dynamic and usual quasi-static delamination processes. The influence of chopped Kevlar fibres used as low cost interlaminar reinforcement on the energy dissipation is also studied.     

Intrinsic coupling of near-tip matrix crack formation to mode III delamination advance in laminated polymeric matrix composites

Laminated carbon/epoxy specimens are loaded in anti-plane shear to investigate the relationship between near-tip matrix crack formation and the apparent mode III delamination toughness. Specimens are tested with different insert lengths to various load levels and examined fractographically. Near-tip matrix cracks are found to initiate and propagate intralaminarly before the onset of planar growth. These cracks are inclined at approximately 45° to the delamination plane and are perpendicular to the direction of maximum near-tip tensile stress. It is found that this represents an intrinsically coupled sequence of events for anti-plane shear loading of continuous fiber laminated polymeric composites when a preexisting delamination is bounded by plies that have their fiber direction aligned with the direction of macroscopic advance. This sequence of events violates the assumptions used in the reduction of data from common mode III tests. It therefore invalidates the associated toughness measurements, and may account for or strongly contribute to the common observation that laminated polymeric composites exhibit an apparent mode III delamination toughness that is dependent on test geometry.     

A delamination gage for carbon fiber composites

A graphite crack gage familiar to fracture testing of nonconductive polymeric materials has been adapted to measure delamination growth in carbon fiber composites. The gage consists of a continuous graphite film whose conductance changes linearly with respect to crack length. The development of an insulation technique so that the electrical film may be applied to carbon fiber composites is described. Further constraints on the gage design occur due to the narrow profiles of conventional delamination specimens. These limitations are reviewed in detail along with appropriate methods for manufacturing and calibration of the gage for delamination experiments. A simple shunt voltage measurement circuit is described along with a derivation of the relationship of crack length to voltage. Two example applications are provided: stable delamination growth in a conventional double cantilever beam (DCB) specimen and dynamic delamination growth in a single-edge-notched (SEN) strip. The electrical delamination length measurements from the DCB tests were found to compare well with the location of the delamination front determined by microscopy and radiography. These results give confidence in dynamic delamination results where growth rates exceeding 1000 m/s were measured. Sample evaluations of delamination toughness are made using the experimental data; compliance methods are used in the case of the DCB analysis, and dynamic finite element methods are used in the case of the SEN strip analysis.     

Influence of the Matrix Type on the Mode I Fracture of Carbon-Epoxy Composites Under Dynamic Delamination

The delamination energy and fracture behaviour under static and dynamic mode I loading of two composites, made of the same unidirectional carbon reinforcement embedded in two different matrices, one tough and the other brittle, was investigated with the aim of analyzing the influence of the employed resin on the fatigue delamination behaviour of both composites. In the case of dynamic loading, the number of cycles necessary for the onset of delamination was determined for a given elastic energy release rate and crack growth rate for different critical energy rates. The double cantilever beam (DCB) test was found to be suitable for promoting the initial delamination. The experimental results confirm the enhanced performance of the tough resin both in terms of crack initiation and growth rate.     

层状纤维圆柱壳轴向压缩破损实验研究

通过对端部引发缺陷层状纤维复合材料圆柱壳在轴向准静态和冲击压缩下的实验研究,分析其渐进压缩破损模式和破坏模式的形成机理．研究此类结构的缓冲性能．实验研究表明随着纤维铺设角度的改变其破损模式的主导形式与分层扩展强度、环向断裂强度和纤维与基体脱胶裂纹相关．它们的断裂韧度的高低决定结构的能量吸收能力     

Experimental and Numerical Study of Paperboard Interface Properties

Laminated paperboard is widely used in packaging products. Interface delamination plays a crucial role in converting paperboard to a carton through the creasing and folding process. Thus, the aim of this study is to experimentally and numerically investigate the interface fracture behavior in pure crack opening mode (mode I) and sliding mode (mode II). Four experimental tests have been evaluated and compared to numerical simulation, namely, the z-directional tensile test (ZDT), double-notch shear test (DNS), double-cantilever beam test (DCB) and end-notched flexure test (ENF). It was shown that, for the paperboard specimens tested, the ZDT test was sufficient to fully characterize the mode I crack growth response. However, the DNS and ENF tests were required to determine the maximum shear stress and the fracture toughness of pure mode II, respectively. Further mixed-mode investigation would enable the analysis of paperboard delamination behavior during the creasing and folding process.     

复合材料Ⅰ、Ⅱ混合型分层试验研究

通过对T300／5405、1300／913、1300／HD03三种航空材料Ⅰ、Ⅱ混合型分层研究，进一步研究了新的Ⅰ、Ⅱ混合型分层断裂测试的JJ法，并和MMB法进行了比较，发现两者较为吻合。但JJ法耗费试件少，简单易行，操作方便，有利于建立混合型分层的失效判据，它可以适用于不同环境下的混合型分层实验的测试。     

On determination of mode II fracture toughness using semi-circular bend specimen

The cracked semi-circular specimen subjected to three-point bending has been recognized as an appropriate test specimen for conducting mode I, mode II and mixed mode I/II fracture tests in brittle materials. The manufacturing and pre-cracking of the specimen are simple. No complicated loading fixture is also required for a fracture test. However, almost all of the theoretical criteria available for mixed mode brittle fracture fail to predict the experimentally determined mode II fracture toughness obtained from the semi-circular bend (SCB) specimen. In this paper, a modified maximum tangential stress criterion is used for calculating mode II fracture toughness K_IIc in terms of mode I fracture toughness K_Ic. The modified criterion is used for predicting the reported values of mode II fracture toughness for two brittle materials: a rock material (Johnstone) and a brittle polymer (PMMA). It is shown that the modified criterion provides very good predictions for experimental results.     

含脱层损伤复合材料层合梁的冲击动力屈曲

针对含初始缺陷和脱层损伤的复合材料层合梁的轴向冲击动力屈曲问题进行了分析。基于Hamilton原理导出了考虑初始缺陷、轴向和横向惯性、横向剪切变形以及转动惯性影响时含脱层损伤复合材料梁的非线性动力屈曲控制方程;基于B-R准则,采用有限差分方法求解了受轴向冲击载荷作用下含脱层损伤复合材料梁的动力屈曲问题;讨论了冲击速度、初始几何缺陷、铺层角度以及脱层长度等因素对复合材料层合梁动力屈曲的影响。     

蜂窝夹芯试件破坏行为分析

通过平面拉伸试验和双悬臂梁试验研究了蜂窝夹芯试件的破坏行为. 在平面拉伸试验中， 发现的破坏模式不是预期的面芯界面脱胶破坏而是面板层间分层破坏；在双悬臂梁试验中， 发现了一种与以往文献报导中不同的破坏模式(面板层间分层，预制裂纹偏转和面板分层扩 展依次出现). 针对试验中所发现的新的破坏模式，结合粘结模型，建立了基于 蔡-希尔破坏准则和能量准则的计算模型. 模拟结果与试验结果对比发现，所建立 的计算模型能够很好地模拟所发现的破坏行为.     

SEMI-ANALYTICAL SOLUTION FOR TWO KINDS OF DELAMINATION MODELS OF LAMINATED CYLINDRICAL SHELLS

为了研究层合壳脱层,本文首先建立了柱坐标系下Hamilton 正则方程的8 节点等参元列式;然后分别采用了"先分后合" 模型和"弱粘接" 模型对开口壳的脱层损伤进行了模拟;通过利用层间的力学关系建立了整个壳的求解方程;最后分别从粘接完好和脱层两类情况对开口壳进行研究,并计算脱层前缘裂纹扩展的能量释放率. 数值实例的分析结果表明环向脱层受外载荷影响大于轴向脱层外载荷影响,脱层深度对两类脱层模型影响较大.     

Dynamic analysis of composite plate with multiple delaminations based on higher-order zigzag theory

In a recent paper, Cho and Kim [Journal of Applied Mechanics] proposed a higher-order cubic zigzag theory of laminated composites with multiple delaminations. The proposed theory is not only accurate but also efficient because it work with a minimal number of degrees of freedom with the application of interface continuity conditions as well as bounding surface conditions of transverse shear stresses including delaminated interfaces. In this work, we investigate the dynamic behavior of laminated composite plates with multiple delaminations. A four-node finite element based on the efficient higher-order zigzag plate theory of laminated composite plates with multiple delaminations is developed to refine the prediction of frequencies, mode shape, and time response. Through the dynamic version of the variational approach, the dynamic equilibrium equations and variationally consistent boundary conditions are obtained. Natural frequency prediction and time response analysis of a composite plate with multiple delaminations demonstrate the accuracy and efficiency of the present finite element method. To prevent penetration violation at the delamination interfaces, unilateral contact constraints by Lagrange multiplier method are applied in the time response analysis. The present finite element is suitable for the prediction of dynamic response of thick composite plates with multiple and arbitrary shaped delaminations.     

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.     

Mode I stress intensity factor solutions for spot welds in lap-shear specimens

The analytical solutions of the mode I stress intensity factor for spot welds in lap-shear specimens are investigated based on the classical Kirchhoff plate theory for linear elastic materials. First, closed-form solutions for an infinite plate containing a rigid inclusion under counter bending conditions are derived. The development of the closed-form solutions is then used as a guide to develop approximate closed-form solutions for a finite square plate containing a rigid inclusion under counter bending conditions. Based on the J integral, the closed-form solutions are used to develop the analytical solutions of the mode I stress intensity factor for spot welds in lap-shear specimens of large and finite sizes. The analytical solutions of the mode I stress intensity factor based on the solutions for infinite and finite square plates with an inclusion are compared with the results of the three-dimensional finite element computations of lap-shear specimens with various ratios of the specimen half width to the nugget radius. The results indicate that the mode I stress intensity factor solution based on the finite square plate model with an inclusion agrees well with the computational results for lap-shear specimens for the ratio of the half specimen width to the nugget radius between 4 and 15. Finally, a set of the closed-form stress intensity factor solutions for lap-shear specimens at the critical locations are proposed for future applications.     

考虑横法向热应变的C~0型整体-局部高阶层合梁理论

通过考虑横法向热变形,本文建立了预先满足层间应力连续的C0型整体-局部高阶层合梁理论,并用于分析复合材料层合梁热膨胀和热弯曲问题。虽然考虑了横法向应变,不增加额外的位移变量。此理论位移场不含有横向位移一阶导数,便于构造多节点高阶单元。基于虚功原理推导了复合材料层合梁平衡方程,并分析了简支多层复合材料梁热膨胀和热弯曲问题。数值结果表明,建立的模型能准确分析复合材料层合梁热膨胀和热弯曲问题,忽略横法向应变的理论分析热膨胀问题误差较大。     

Direct Measurement of the Cohesive Law of Adhesives Using a Rigid Double Cantilever Beam Technique

Engineering adhesive joints are being increasingly used in industry because of the advantages they offer over other joining methods such as fastening or welding. The development and the use of adhesives in a design environment require accurate mechanical tests in order to measure their strength and toughness. Standard techniques such as the shear lap test are commonly used to measure shear strength, but the results they produce generally depend on geometry and on initial defects within the bond line. Fracture tests such as the double cantilever beam (DCB) tests overcome these limitations, but rely on elasticity models and assumptions to determine toughness. In this study, we present a novel technique to directly determine the mode I fracture toughness of engineering adhesive joints as well as their full cohesive law, without any initial assumption on its shape. Our new method is remarkably simple in terms of experimental setup, execution and analysis. It is similar to the standard double cantilever beam (DCB) test with the difference that the material and dimensions of the beams are chosen so that they are assumed to be rigid compared to the bond line. In this rigid DCB (RDCB) technique the crack opening is known everywhere along the interface, which we use to compute the cohesive law of the adhesive directly from the load-displacement data obtained from experiment and the geometry of the RDCB specimen. The RDCB method is validated and applied to three typical commercial adhesives (polyurethane, epoxy, and silicone), to determine their cohesive law and fracture toughness.     

Delamination of laminated composite plates by p-convergent partial discrete-layer elements with VCCT

The simulation of the delamination process in laminated composite plates is quite complex and requires advanced finite element modeling techniques. Failure analysis tools must be able to predict initiation, size and propagation of delamination process. This paper presents the p-convergent partial discrete-layer elements with the virtual crack closure technique (VCCT) for the delamination analysis of laminated composite plates. The proposed element can be formulated by the suitable dimensional reduction from three-dimensional solid to two-dimensional plate. It is assumed that the piecewise linear variation of in-plane displacements and the constant value of out-of-plane displacements across the thickness. The higher-order approximation based on integrals of Legendre polynomials is used to define displacement fields. The three-dimensional VCCT is also slightly modified to incorporate with the proposed elements to estimate the energy release rate. The initiation of delamination occurs when the energy release rate for a displacement increment is same as the critical energy release rate corresponding to fracture toughness. The approach is to use a fracture mechanics criterion, but to avoid the complex moving mesh technique. At first, the validation and characteristic of the proposed elements are investigated on isotropic plates and orthotropic laminated plates, compared with referenced values. Then for fracture analysis, the efficiency of proposed approach is demonstrated with the help of additionally two problems such as the double-cantilever-beam test and the orthotropic laminated square plate with interior delamination.     

Nonlinear dynamic analysis of Timoshenko beams by BEM. Part I: Theory and numerical implementation

In this two-part contribution, a boundary element method is developed for the nonlinear dynamic analysis of beams of arbitrary doubly symmetric simply or multiply connected constant cross section, undergoing moderate large displacements and small deformations under general boundary conditions, taking into account the effects of shear deformation and rotary inertia. Part I is devoted to the theoretical developments and their numerical implementation and Part II discusses analytical and numerical results obtained from both analytical or numerical research efforts from the literature and the proposed method. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions as well as to axial loading. To account for shear deformations, the concept of shear deformation coefficients is used. Five boundary value problems are formulated with respect to the transverse displacements, to the axial displacement and to two stress functions and solved using the Analog Equation Method, a BEM based method. Application of the boundary element technique yields a nonlinear coupled system of equations of motion. The solution of this system is accomplished iteratively by employing the average acceleration method in combination with the modified Newton–Raphson method. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. The proposed model takes into account the coupling effects of bending and shear deformations along the member, as well as the shear forces along the span induced by the applied axial loading.