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。     

Recent developments on damage modeling and finite element analysis for composite laminates: A review

Under complex environments such as continuous or cyclic loads, the stiffness degradation for the laminated composites such as the carbon fiber reinforced polymer matrix composites is an important physical and mechanical response to the damage and failure evolution. It is essential to simulate the initial and subsequent evolution process of this kind of damage phenomenon accurately in order to explore the mechanical properties of composite laminates. This paper gives a comprehensive review on the general methodologies on the damage constitutive modeling by continuum damage mechanics (CDM), the various failure criteria, the damage evolution law simulating the stiffness degradation, and the finite element implementation of progressive failure analysis in terms of the mechanical response for the variable-stiffness composite laminates arising from the continuous failure. The damage constitutive modeling is discussed by describing the evolvement of damage tensors and conjugate forces in the CDM theory. The failure criteria which interpret the failure modes and their interaction are compared and some advanced methods such as the cohesive theory which are used to predict the damage evolution properties of composites are also discussed. In addition, the solution algorithm using finite element analysis which implements progressive failure analysis is summarized and several applicable methods which deal with the numerical convergence problem due to singular finite element stiffness matrices are also compared in order to explore the whole failure process and ultimate load-bearing ability of composite laminates. Finally, the multiscale progressive failure analysis as a popular topic which associates the macroscopic with microscopic damage and failure mechanisms is discussed and the extended finite element method as a new finite element technique is expected to accelerate its practical application to the progressive failure analysis of composite laminates.     

Progressive damage analyses of angle‐ply laminates exhibiting free edge effects using continuum damage mechanics with layer‐wise finite element method

Capability of continuum damage mechanics (CDM) to predict the damage mechanism evolution of composite laminates has rarely been carried out, and most of the previous CDM works mainly focused on the overall response of the laminates. In this paper, progressive damage and overall response of the composite laminates under quasi‐static, monotonic increasing loading are investigated using three‐dimensional (3D) CDM implementation in a finite element method that is based on the layer‐wise laminate plate theory. In the damage formulation, each composite ply is treated as a homogeneous orthotropic material exhibiting orthotropic damage in the form of distributed microscopic cracks that are normal to the three principal material directions. The progressive damage of different angle‐ply composite laminates under quasi‐static loading that exhibit free edge effects is investigated. It is shown that using CDM global behaviour and various damage mechanisms affected by the complex nature of free edges can be qualitatively well predicted.     

基于应变能耗散的复合材料层合板面内缺口强度分析CDM模型

基于伴随能量释放的渐进损伤演化思想,建立了复合材料层合板面内失效分析的连续介质损伤力学（CDM）分析模型,该模型包含损伤表征、损伤起始判定和损伤演化法则3个方面。基于CDM模型,通过引入损伤状态变量表征损伤,建立了平面应力状态下的材料损伤本构模型。采用损伤参量 f_E改写Hashin准则,以判定损伤的起始。损伤演化由特征长度内的应变能释放密度控制,建立了损伤状态变量关于等效应变的渐进损伤演化法则。模型中还同时考虑了面内剪切非线性和网格敏感性,并进行了对比分析。对含缺口的[90/0/±45]_3s和[（±θ）₄]_s 2类典型复合材料层合板的面内拉伸失效进行了分析,结果表明,本文中的模型能有效预测复合材料层合板的面内拉伸强度。     

单向纤维增强聚合物复合材料压缩渐进破坏单向纤维增强聚合物复合材料压缩渐进破坏

复合材料结构在承压时破坏如何演化,是其强度破坏分析的基础和核心任务。本文提出了基于连续介质损伤力学（CDM）的单向纤维增强聚合物复合材料压缩破坏渐进损伤分析（PDA）模型。建模中考虑了材料非线性行为、失效判断及损伤演化中材料性能退化等基本问题,分别对应于拉压不对称弹塑性本构关系、Puck准则、LaRC05准则及考虑破坏面方向的刚度退化方法。该模型通过用户材料子程序接口VUMAT引入到有限元软件ABAQUS中实现了有限元求解。对文献中提供的纵向、横向及偏轴压缩案例进行了数值计算并与试验数据对比。数值分析结果与试验数据吻合较好,证明了该方法的合理性和有效性,对开展多向层合板压缩破坏分析富有参考价值。      

Characterising fibre compression fracture toughness of composites using bearing tests

In this paper we propose the use of a bearing test with a coupled experimental–numerical approach to characterise the critical strain energy release rate, or “fracture toughness”, for fibre compression failure in bearing. This property is used in continuum damage mechanics (CDM) approaches for progressive failure analysis of composite laminates. In the proposed approach, experimental results for a standard bearing test are used to calibrate the fracture toughness with a progressive failure analysis using a CDM damage model. The approach is demonstrated for a plain weave carbon/epoxy material using the CDM damage model available in a commercial finite element package (Abaqus). The results indicate that the bearing test method provides a simple and convenient means of quantifying fibre compression fracture toughness. Analysis results applying the characterised value show good comparison with experimental results, and confirm the value of the bearing test as part of a novel material characterisation technique.     

Determination of material parameters for discrete damage mechanics analysis of carbon-epoxy laminates

Discrete damage mechanics (DDM) refers to micromechanics of damage constitutive models that, when incorporated into commercial finite element software via user material subroutines, are able to predict intralaminar transverse and shear damage initiation and evolution in terms of the fracture toughness of the composite. A methodology for determination of the fracture toughness is presented, based on fitting DDM model results to available experimental data. The applicability of the DDM model is studied by comparison to available experimental data for Carbon Epoxy laminates. Sensitivity of the DDM model to h- and p-refinement is studied. Also, prediction of modulus vs. applied strain is contrasted with ply discount results and the effect of in situ correction of strength is highlighted.     

复合材料层合板低速冲击的接触力和能量响应仿真

以连续介质损伤力学（CDM）为基础,提出了一个有效的数值分析模型来模拟碳纤维增强复合材料（CFRP）层合板低速冲击的接触力响应和能量响应。该模型考虑了不同的失效模式,引入了不可逆的损伤变量和新的刚度折减方式以考虑损伤造成的刚度变化,定义了耗散能的计算方式以考虑损伤造成的能量变化。通过在Abaqus/Explicit平台上编写VUMAT子程序具体实现模型,数值仿真与试验结果吻合较好,验证了该模型的有效性。此外,还综合考虑了Hashin准则与LaRC04准则各自的优缺点,用Hashin和LaRC04相混合得到的准则对低速冲击进行了模拟。结果表明：在冲击外载作用下当CFRP层合板中存在较多基体压缩失效时,采用混合的失效准则模拟得到的接触力响应和能量响应结果更接近试验结果,而使用纯Hashin准则得到的预测结果偏保守。     

Determination of material parameters for Abaqus progressive damage analysis of E-glass epoxy laminates

A methodology for determination of material parameters for the progressive damage analysis (PDA) model implemented in Abaqus is presented. The methodology is based on fitting PDA model results to available experimental data. The applicability of the PDA model is studied by comparison to a broad set of experimental data for E-glass epoxy laminates, as well as contrasting PDA with ply discount results. Also, sensitivity of the Abaqus PDA model to h- and p-refinement is studied.     

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。      

复合材料层板开孔压缩损伤分析

针对纤维增强复合材料层板开孔压缩, 将复合材料层板的失效分为层内失效和层间失效, 建立了复合材料层板开孔压缩损伤分析模型。该模型基于逐渐损伤分析, 对不同复合材料开孔层板进行了失效预测, 并与文献中试验结果进行了对比, 破坏强度和失效模式均与文献试验结果非常吻合。结果表明, 本文中所建立的层板开孔压缩损伤分析模型能够模拟含孔层合板压缩过程中的损伤起始、损伤扩展和最终破坏, 并最终预测含孔层合板压缩失效模式和破坏强度。     

Modelling complex progressive failure in notched composite laminates with varying sizes and stacking sequences

The emergence of advanced computational methods and theoretical models for damage progression in composites has heralded the promise of virtual testing of composite structures with orthotropic lay-ups, complex geometries and multiple material systems. Recent studies have revealed that specimen size and material orthotropy has a major effect on the open hole tension (OHT) strength of composite laminates. The aim of this investigation is develop a progressive failure model for orthotropic composite laminates, employing stepwise discretization of the traction–separation relationship, to predict the effect of specimen size and laminate orthotropy on the OHT strength. The results show that a significant interaction exists between delamination and in-plane damage, so that models without considering delamination would over-predict strength. Furthermore, it is found that the increase in fracture toughness of blocked plies must be incorporated in the model to achieve good correlation with experimental results.     

Identification of Fracture Toughness for Discrete Damage Mechanics Analysis of Glass-Epoxy Laminates

A methodology for determination of the intralaminar fracture toughness is presented, based on fitting discrete damage mechanics (DDM) model predictions to available experimental data. DDM is constitutive model that, when incorporated into commercial finite element software via user material subroutines, is able to predict intralaminar transverse and shear damage initiation and evolution in terms of the fracture toughness of the composite. The applicability of the DDM model is studied by comparison to available experimental data for Glass-Epoxy laminates. Sensitivity of the DDM model to h- and p-refinement is studied. Also, the effect of in-situ correction of strength is highlighted.     

复合材料层合板多尺度交互渐进损伤分析

纤维增强复合材料强度的准确表征是复合材料力学性能研究的核心问题之一。该文以碳纤维增强树脂基复合材料层合板为研究对象,基于宏观-细观多尺度分析方法,根据复合材料的物理失效模式分别给出了基体和纤维的细观失效准则,同时考虑基体失效对复合材料层合板纤维轴向力学性能的影响。提出了新的刚度退化方式,可准确表征复合材料层合板的损伤演化过程,开展了复合材料层合板四点弯模型的多尺度交互渐进损伤分析和试验验证。结果表明:基于多尺度方法的复合材料层合板宏-细观交互渐进损伤分析结果与试验结果吻合较好,新的刚度退化方式可以准确模拟层合板的失效过程。     

Lamb wave-based quantitative identification of delamination in CF/EP composite structures using artificial neural algorithm

Delamination in composite structures plays a major role in lowering structural strength and stiffness, consequently downgrading system integrity and reliability. A Lamb wave-based quantitative identification technique for delamination in CF/EP composite structures was established. Propagation of Lamb waves in a series of composite laminates, individually bearing a delamination, was evaluated using dynamic FEM analyses. Taking advantage of wavelet transform and artificial neural algorithms, an Intelligent Signal Processing and Pattern Recognition (ISPPR) package was developed, by which the spectrographic characteristics of simulated Lamb wave signals in the time-frequency domain were extracted and digitised as Digital Damage Fingerprints (DDF), to construct a Damage Parameters Database (DPD). The DPD was then used offline to train a multi-layer feedforward artificial neural network (ANN) under supervision of an error-backpropagation (BP) algorithm. Assisted by an active online structural health monitoring (AO-SHM) system with an active piezoelectric actuator/sensor network, the proposed methodology was validated online by identifying actual delaminations in CF/EP (T650/F584) quasi-isotropic composite laminates.     

Modelling low-speed drop-weight impact on composite laminates

The impact responses of typical laminates are investigated numerically in this research. Delamination responses among plies and fibre and/or matrix damage responses within plies are simulated to understand the behaviours of laminates under different impaction conditions. Damage resistance of a laminate is highly dependent upon several factors including geometry, thickness, stiffness, mass, and impact energies (impact velocities), which are here considered by the finite element (FE) method. Three groups of composite laminates are simulated and the numerical results in general are in good agreement with corresponding experiments. Models containing different stacking sequences and impact energies are built to study their influence on impact responses and demonstrate that clustered (or nearly clustered) plies in the laminate can effectively reduce the degree of interface damage. Models containing different indenters and plate shapes are also built to systematically study their influence on the low-speed drop-weight behaviour of composite laminates. Suggestions are proposed for designing impact tests for particular purposes.     

纤维金属层板低速冲击试验和数值仿真

为开展纤维金属层板（FML）低速冲击有限元数值仿真研究,改进了传统的连续损伤力学（CDM）模型,然后对FML落锤低速冲击试验进行数值仿真,并与实验结果进行对比验证。分别采用5.11 J 和10.33 J冲击能量对FML进行落锤低速冲击试验,得到冲击载荷、位移和能量时程曲线,分析FML的动态响应和失效模式。建立了考虑塑性应变、压缩刚度衰减特征和纤维拉伸断裂损伤的新CDM模型,描述S2-玻璃纤维/环氧树脂（S2-galss/epoxy）复合材料的损伤本构,并编写VUMAT子程序,通过ABAQUS/Explicit求解器对FML落锤冲击试验进行数值仿真。研究结果表明：低能量冲击条件下,FML背面主要为鼓包和裂纹等失效模式,位移峰值随冲击能量的提高而增加,冲击载荷峰值在穿透前也随冲击能量的提高而增加;采用改进的CDM模型描述FML中S2-galss/epoxy复合材料铺层后,有限元数值计算可以较好地预测FML低速冲击载荷下的动态响应;有限元数值仿真结果表明,FML中第2层复合材料铺层发生的纤维断裂损伤比第1层的更严重。     

准静态压痕力作用下复合材料层压板的损伤阻抗分析

建立了一种复合材料层压板在准静态压痕力作用下的损伤阻抗的预测方法。首先分别针对基体破坏、分层、 纤维断裂等失效模式引入相应的失效变量 , 并建立不同失效模式下的刚度折减方法 , 然后采用基于应变描述的 Hashin和 Yeh失效准则并结合有限元方法 , 对复合材料层压板在准静态压痕力作用下的破坏过程进行渐进损伤分析 , 在此基础上进一步预测了层压板的损伤阻抗。采用商用有限元软件 ABAQUS/ Standard 的 UMAT用户子程序实现数值模拟。计算结果表明 , 分层起始与扩展是导致载荷2位移曲线发生第 1 次卸载的主要原因 , 当接触力达到其最大值时出现较明显的纤维断裂。分层起始载荷和最大接触力的预测结果与实验数据吻合良好。     

Composite laminate failure analysis using multicontinuum theory

Damage in a composite material typically begins at the constituent level and may, in fact, be limited to only one constituent in some situations. An accurate prediction of constituent damage at sampling points throughout a laminate provides a genesis for progressively analyzing failure of a composite structure from start to finish. Multicontinuum Theory is a micromechanics based theory and associated numerical algorithm for extracting, virtually without a time penalty, the stress and strain fields for a composites’ constituents during a routine finite element analysis. A constituent stress-based failure criterion is used to construct a nonlinear progressive failure algorithm for investigating the material failure strengths of composite laminates. The proposed failure analysis methodology was used to simulate the nonlinear laminate behavior and progressive damage of selected laminates under both uniaxial and biaxial load conditions up to their ultimate strength. This effort was part of a broader project to compare the predictive capability of current composite failure criteria.     

复合材料层板开孔拉伸损伤分析

针对纤维增强复合材料层板开孔拉伸, 将复合材料层板的失效分为层内失效和层间失效, 建立了复合材料层板开孔拉伸损伤分析模型。该模型基于逐渐损伤分析, 对不同复合材料开孔层板进行了失效预测, 并与文献试验结果进行了对比, 破坏强度和失效模式均与文献试验结果非常吻合。结果表明本文中所建立的层板开孔拉伸损伤分析模型能够模拟含孔层合板拉伸过程中的损伤起始、 损伤扩展和最终破坏模式, 并最终预测含孔层合板拉伸失效模式和破坏强度。