Computationally efficient modelling of the fatigue behaviour of composite materials

Fatigue of composite structures is a complex process involving several types of failure. Existing approaches either neglect this complexity or require large computational effort. In this work, a simple progressive damage model including strength and stiffness degradation is implemented into finite element (FE) software. To reduce computational time, the major part of stress calculations is carried out by classical lamination theory. At single points of time, FE analysis is employed to support these calculations. The simplified model is tested against a reference model using FEA after each load cycle. Calculations are set up for a tensile specimen and a cap profile with quasi-isotropic layup. The simplified model using CLT is shown to be in good agreement with the reference while significantly reducing computational time.     

Damage model development for SMC composites

This work deals with the development of an SMC composite material model, incorporating a homogenisation model and statistical damage criteria. The model theory and the basis for implementation of the model into a commercial finite element analysis package are both presented here. Coarse model validation is performed by evaluating the model parameters for a set of sample data, and applying these to the modelling of the progressive fracture of an SMC plate under tensile loading.     

A combined elastoplastic damage model for progressive failure analysis of composite materials and structures

The paper is concerned with the development and verification of a combined elastoplastic damage model for the progressive failure analysis of composite materials and structures. The model accounts for the irreversible strains caused by plasticity effects and material properties degradation due to the damage initiation and development. The strain-driven implicit integration procedure is developed using equations of continuum damage mechanics, plasticity theory and includes the return mapping algorithm. A tangent operator consistent with the integration procedure is derived to ensure a computational efficiency of the Newton–Raphson method in the finite element analysis. The algorithm is implemented in Abaqus as a user-defined subroutine. The efficiency of the constitutive model and computational procedure is demonstrated using the analysis of the progressive failure of composite laminates containing through holes and subjected to in-plane uniaxial tensile loading. It has been shown that the predicted results agree well with the experimental data reported in the literature.     

Computational damage mechanics for composite materials based on mathematical homogenization

This paper is aimed at developing a non‐local theory for obtaining numerical approximation to a boundary value problem describing damage phenomena in a brittle composite material. The mathematical homogenization method based on double‐scale asymptotic expansion is generalized to account for damage effects in heterogeneous media. A closed‐form expression relating local fields to the overall strain and damage is derived. Non‐local damage theory is developed by introducing the concept of non‐local phase fields (stress, strain, free energy density, damage release rate, etc.) in a manner analogous to that currently practiced in concrete [1, 2], with the only exception being that the weight functions are taken to be C⁰ continuous over a single phase and zero elsewhere. Numerical results of our model were found to be in good agreement with experimental data of 4‐point bend test conducted on composite beam made of Blackglas™/Nextel 5‐harness satin weave. Copyright © 1999 John Wiley & Sons, Ltd.     

Progressive damage analysis of composite bolted joints with liquid shim layers using constant and continuous degradation models

The structural behaviour of a single-lap, single-bolt composite joint is investigated using a three-dimensional finite element model. In contrast to previous investigations the influence of a liquid shim layer, added between the two laminates, on strength and structural behaviour of the joints is investigated by virtual testing. The finite element model is validated with experimental data. The experiments point out that the structural behaviour of these joints is dominated by progressive damage. Therefore, as a first approach, progressive damage is considered using Hashin’s three-dimensional failure criterion and a constant degradation model. It is shown that this combination yields very conservative results. As a second approach the model is improved by a continuous degradation model. Considering continuous degradation, the numerical results show very good correlation with the experimental data.     

基于渐进损伤分析的复合材料螺栓连接强度包线法研究

针对中国民机采用T800级复合材料这一新材料体系而基础数据匮乏的现状,采用渐进损伤分析(PDA)替代试验以显著降低研究周期和成本。综合渐进损伤方法和工程算法各自的优点,提出以渐进损伤分析替代应力集中减缓因子(SCRFs)测定试验,进而建立强度包线,并进行多钉连接强度预测的数值策略。为验证该数值策略的可行性,针对典型铺层应力集中减缓因子,测定试样,并开展渐进损伤分析,获得了试验件强度预测值来计算应力集中减缓因子,采用旁路载荷修正的强度包线法,绘制了典型铺层复合材料多钉连接旁路载荷修正强度包线,预测多钉连接的失效载荷,并与试验结果进行对比。结果表明:采用该数值策略预测的强度包线、多钉连接的失效载荷和失效模式均与试验结果吻合良好,证明了该数值策略的可行性。     

复合材料开孔层板压缩渐进损伤试验

为研究碳纤维增强树脂基复合材料开孔层板在压缩加载过程中的损伤起始、演化方式和损伤特点,采用微距拍摄、逐级加载超声C扫描、X光扫描和扫描电子显微镜观测4种观测手段对国产CCF300/5228A[45/0/-45/90]4s、[452/02/-452/902]2s、[454/04/-454/904]s3种铺层方式的开孔层板进行了压缩试验研究。对压缩载荷作用下开孔层板的损伤起始和损伤演化进行了观察和对比。对试验中观测到的纤维微屈曲、纤维挤出、孔边开裂和分层扩展等现象之间的关系进行了分析和说明。试验结果表明:压缩载荷下45°和90°铺层相邻位置为层板易分层位置,含45°和90°铺层相邻位置的开孔层板渐进损伤过程较为明显:开孔层板在压缩载荷下较早出现损伤,损伤的起始和演化缓解了孔边应力集中,促使压缩应变能在孔边逐步释放,推迟开孔层板压缩破坏的发生,提高层板压缩承载能力。研究结果可为材料结构损伤容限设计提供依据。     

Micromechanical modelling for onset of distortional matrix damage of fiber reinforced composite materials

A new multi-scale modelling approach is applied to specimen testing to define the critical strain invariants for the damage onset theory proposed by Gosse, Christensen and Hart-Smith. The onset theory is a micromechanics theory that uses critical strain invariants to predict the onset of damage within fiber polymer composites. To obtain the critical strain invariants for the matrix, finite element analyses are required of unidirectional off-axis specimens that have been tested to failure. The strains remain linear to failure and critical strain invariants can be determined from a linear finite element analysis but the use of continuum models to obtain the critical values requires strain enhancement factors. In this paper a new micromechanics-based modelling approach is proposed. A finite element analysis of the composite specimen is implemented with a square fiber array embedded within the polymeric matrix. Failure initiation sights are identified to obtain the critical values directly without the need for the strain enhancement factors. Numerical examples of the modelling process are provided including a 10° off-axis coupon with rectangular tabs. The results are compared to different modelling approaches. The tests and modelling are repeated for a 20° off-axis coupon but with oblique as well as rectangular tabs.     

GLARE层板挤压渐进损伤分析

对GLARE36/5层板进行挤压性能试验研究,采用超声C扫描、断口微距拍摄和扫描电子显微镜等方法观测GLARE层板挤压渐进损伤过程和最终破坏模式。结果表明:GLARE层板挤压起始损伤为铝合金塑性变形;损伤扩展阶段,0°纤维主要承受挤压正应力,铝合金塑性变形增大,铺层间分层起始并扩展;0°纤维屈曲折断后层内纤维基体损伤和分层损伤急剧扩展,层板最终发生挤压破坏。将GLARE层板挤压失效分为层内失效和层间失效,采用应变描述的Hashin准则和界面单元方法并引入金属塑性建立GLARE层板挤压渐进损伤数值模型,数值模型对层板损伤起始位置、分层产生位置、损伤演化过程、最终破坏模式及破坏载荷进行了预测,计算结果与试验结果吻合较好,说明该计算方法能够有效模拟GLARE层板挤压渐进损伤性能。      

Element-Free Galerkin modelling of composite damage

Delamination and matrix cracking are routine damage mechanisms, observed by post-mortem analysis of laminated structures containing geometrical features such as notches or bolts. Current finite element tools cannot explicitly model an intralaminar matrix microcrack, except if the location of the damage is specified a priori. In this work, a meshless technique, the Element-Free Galerkin (EFG) method, is utilized for the first time to simulate delamination (interlaminar) and intralaminar matrix microcracking in composite laminates.     

纤维增强复合材料层板高速冲击损伤数值模拟

推导了复合材料应变率相关三维本构关系, 并将其用于复合材料层板高速冲击损伤的数值模拟。该模型在复合材料层间引入界面单元模拟层间分层, 结合三维Hashin失效准则进行单层板面内损伤识别, 引入材料刚度退化, 采用非线性有限元方法, 研究了复合材料层板高速冲击的破坏过程及层板的损伤特性。数值分析结果表明, 剩余速度预报结果与实验结果吻合较好, 层板的主要损伤形式是层间分层、 基体微裂纹和纤维断裂, 减小弹体直径、 增大铺层角度和层板厚度能够有效降低层板损伤面积。      

单丝复合体系渐进损伤过程模拟及组分性能对损伤过程的影响

为研究单丝复合体系在单向加载过程中的应力传递及损伤演化规律,基于剪滞模型建立了渐进损伤过程的三维数值分析模型。单丝复合体系的渐进损伤过程曲线和临界状态下的纤维段数、应变载荷及纤维轴向应力分布均与文献试验结果非常吻合,表明本文所提出的单丝复合体系渐进损伤模型能够有效模拟单丝断裂过程中的损伤起始、损伤演化和断裂临界状态。研究了模型中组分材料的模量和强度对损伤过程的影响。结果表明：保持组分材料强度不变,增加纤维的模量能够加快损伤过程,基体模量和界面模量的增加对单丝复合体系渐进损伤过程影响不大;在组分材料模量及界面强度不变的情况下,随着纤维强度的增加,单丝复合体系渐进损伤过程的起始应变载荷和临界应变载荷均增加,临界状态下的纤维断点数减少。     

复合材料三维损伤模型在大开口结构强度预测中的应用

为了预测复合材料大开口结构的强度及损伤扩展情况,开展了3种不同复合材料三维损伤退化模型(瞬间退化模型、渐进损伤退化模型和连续损伤退化模型)在复合材料大开口结构强度预测中的应用研究,完成了含口框加强件的复合材料大开口结构面内纯剪切试验,并采用3种损伤退化模型对试验件及相关文献算例进行了数值模拟。数值模拟结果与试验结果的对比表明:3种损伤退化模型均可以较为精确地预测复合材料大开口结构的极限强度;与其他模型相比,连续损伤退化模型的预测精度最高、通用性最好且网格依赖度最低。研究结果为复合材料大开口结构力学性能的研究提供了理论指导。     

A new damage model for composite laminates

Aircraft composite structures must have high stiffness and strength with low weight, which can guarantee the increase of the pay-load for airplanes without losing airworthiness. However, the mechanical behavior of composite laminates is very complex due the inherent anisotropy and heterogeneity. Many researchers have developed different failure progressive analyses and damage models in order to predict the complex failure mechanisms. This work presents a damage model and progressive failure analysis that requires simple experimental tests and that achieves good accuracy. Firstly, the paper explains damage initiation and propagation criteria and a procedure to identify the material parameters. In the second stage, the model was implemented as a UMAT (User Material Subroutine), which is linked to finite element software, ABAQUS™, in order to predict the composite structures behavior. Afterwards, some case studies, mainly off-axis coupons under tensile or compression loads, with different types of stacking sequence were analyzed using the proposed material model. Finally, the computational results were compared to the experimental results, verifying the capability of the damage model in order to predict the composite structure behavior.     

A fatigue damage model of composite materials

The mechanical properties of composite materials degrade progressively with the increasing of the number of cyclic loadings. Based on the stiffness degradation rule of composites, a phenomenological fatigue damage model is presented in this paper, which contains two material parameters. They are proportional to the fatigue life of materials and inversely proportional to the fatigue loading level. Thirteen sets of experimental data of composite stiffness degradation were employed to verify the presented model, and the statistical results showed that this model is capable of describing the damage evolution of composite materials. The characteristics of damage development and accumulation of composite materials subjected to variable loading were studied in this paper. Four sets of two-level loading experimental data were cited to verify the damage model, and the results showed that the predicted life is in good agreement with the experimental ones.     

Numerical analysis of damage progression and strength of countersunk composite joints

A numerical investigation is conducted into the damage progression and strength of bolted joints between fibre-reinforced composite laminates using countersunk fasteners. Experimental tests were previously conducted on a bearing test specimen and countersunk fastener single-lap joints. In this work, computational models are developed for Abaqus/Explicit, with continuum shells employed to model in-plane ply failure. The bolt-nut assembly is modelled with rigid elements, and the models account for bolt torque and frictional contact. The material properties required in the computational model are determined from standard tests, with the compression fracture toughness of composite plies calibrated against experimental data from the bearing test. The analysis approach captures the load-carrying capability of all configurations, and provides reasonable accuracy in predicting damage patterns. The effects of bolt torque, clearance and countersink height ratio are investigated, and the analysis results compare well with experimental findings. Furthermore, the analysis provides rich insight into the damage progression and joint behaviour at the ply level, with the in-plane and through-thickness damage patterns mapped for increasing applied load. Delamination is incorporated using a cohesive element layer at the start of the countersunk region, though has minimal influence on damage progression and load-carrying capability, which agrees with the experimental results.     

Experimental investigation of damage progression and strength of countersunk composite joints

An experimental investigation is conducted into the damage progression and strength of bolted joints with fibre-reinforced composite laminates and countersunk fasteners. The main goal of the experimental investigation is to characterise the effect of the countersink geometry on the load-carrying capacity of single lap joints in comparison to the straight-shank case. The effects of bolt torque, clearance and countersink height ratio on the damage progression and joint strength are also studied. Experimental tests and detailed microscopy studies are conducted on a bearing test specimen with a straight-edged hole, and several single-lap joint configurations with countersunk fasteners. It is found that introduction of the countersunk hole roughly halves the bearing stress, and causes delamination for some configurations. This delamination is primarily located at the start of the countersink region, though is found to be triggered by other damage mechanisms and has only minor influence on the results. Bolt torque increases the density of through-thickness damage though limits its extension from the hole edge, whilst bolt clearance causes localisation of the damage region. Increasing the ratio of the countersink depth to the laminate thickness reduces the extent of bearing and promotes bending, with a change to net section failure at large ratios.     

An efficient algorithm for modelling progressive damage accumulation in disordered materials

This paper presents an efficient algorithm for the simulation of progressive fracture in disordered quasi‐brittle materials using discrete lattice networks. The main computational bottleneck involved in modelling the fracture simulations using large discrete lattice networks stems from the fact that a new large set of linear equations needs to be solved every time a lattice bond is broken. Using the present algorithm, the computational complexity of solving the new set of linear equations after breaking a bond reduces to a simple triangular solves (forward elimination and backward substitution) using the already Cholesky factored matrix. This algorithm using the direct sparse solver is faster than the Fourier accelerated iterative solvers such as the preconditioned conjugate gradient (PCG) solvers, and eliminates the critical slowing down associated with the iterative solvers that is especially severe close to the percolation critical points. Numerical results using random resistor networks for modelling the fracture and damage evolution in disordered materials substantiate the efficiency of the present algorithm. In particular, the proposed algorithm is especially advantageous for fracture simulations wherein ensemble averaging of numerical results is necessary to obtain a realistic lattice system response. Copyright © 2005 John Wiley & Sons, Ltd.     

Progressive damage modeling for large deformation loading of composite structures

A nonlinear constitutive model for large deformation loading at different strain rate condition was developed to represent tensile progressive damage of the nonlinear large deformation rate dependent behavior of polymer-based composite materials. The material was characterized by using off-axis composite specimens at different strain rates. A new failure criterion was proposed for the analysis of different loading directions and strain rates. Based on a method of combining the nonlinear constitutive theory and the proposed failure criterion for different strain rates, the progressive damage behavior of large deformation composites was represented. The strength of the material was also successfully represented with a single material constant.     

复合材料层合板阶梯形挖补胶接修理渐进损伤分析

建立了复合材料层合板阶梯形挖补胶接修理构型的渐进损伤分析三维有限元模型, 同时考虑了复合材料母板、 补片和胶层的损伤扩展以及它们之间的相互影响。层合板采用含正交各向异性损伤的连续介质损伤力学(CDM)本构方程进行描述, 材料积分点处的损伤状态采用二阶张量形式的内部状态变量表征。胶层采用含各向同性损伤的CDM本构方程进行描述, 材料积分点处的损伤状态采用常数形式的损伤变量表示。计算结果与试验数据符合较好, 说明该模型可较好预测挖补胶接修理的复合材料层合板拉伸强度及其失效模式。