基于剪切非线性三维损伤本构模型的复合材料层合板失效强度预测

基于连续损伤力学,建立了同时考虑复合材料剪切非线性效应和损伤累积导致材料属性退化的三维损伤本构模型。模型能够区分纤维损伤、基体损伤和分层损伤不同的失效模式,并定义了相应损伤模式的损伤变量。复合材料层合板层内纤维初始损伤采用最大应力准则判定,基体初始损伤采用三维Puck准则中的基体失效准则判定,分层初始损伤采用三维Hou准则中的分层破坏准则判定,为了计算Puck失效理论中的基体失效断裂面角度,本文提出了分区抛物线法,通过Matlab软件编写计算程序并进行分析。结果表明,与Puck遍历法和分区黄金分割法对比,本文提出的分区抛物线法有效地降低了求解断裂面角度的计算次数,提高了计算效率和计算精度。推导了本构模型的应变驱动显式积分算法以更新应力和解答相关的状态变量,开发了包含数值积分算法的用户自定义子程序VUMAT,并嵌于有限元程序Abaqus v6.14中。通过对力学行为展现显著非线性效应的AS4碳纤维/3501-6环氧树脂复合材料层合板进行渐进失效分析,验证了本文提出的材料本构模型的有效性。结果显示,已提出的模型能够较准确地预测此类复合材料层合板的力学行为及其失效强度,为复合材料构件及其结构设计提供一种有效的分析方法。      

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。     

纤维增强复合材料层合板缺口尺寸及形状效应数值模拟

通过考虑基体裂纹、纤维断裂、层内劈裂和层间脱层等破坏形式,建立三维有限元模型研究含中心圆孔和中心裂缝的准各向同性复合材料层合板([45/0/-45/90]_(2S))在拉伸载荷下的缺口尺寸效应及缺口形状效应。模拟结果显示:随着缺口尺寸的增大,层合板的破坏强度逐渐降低,然而,在本文研究范围内含中心裂缝的层合板破坏强度始终高于对应的含中心圆孔的层合板破坏强度。进一步分析有限元模拟结果表明,含中心裂缝的层合板亚临界损伤发生得更早,并且亚临界损伤范围更大,亚临界损伤会大大缓解缺口尖端的应力集中,从而使含中心裂缝层合板表现出更高的破坏强度。     

基于连续介质损伤力学的复合材料层合板低速冲击损伤模型

基于连续介质损伤力学（CDM）方法,建立了分析复合材料层合板低速冲击问题的三维数值模型。该模型考虑了层内损伤（纤维和基体损伤）、层间分层损伤和剪切非线性行为,采用最大应变失效准则预测纤维损伤的萌生,双线性损伤本构模型表征纤维损伤演化,基于物理失效机制的三维Puck准则判断基体损伤的起始,根据断裂面内等效应变建立混合模式下基体损伤扩展准则。横向基体拉伸强度和面内剪切强度采用基于断裂力学假设的就地强度（in-situ strength）。纤维和基体损伤本构关系中引入单元特征长度,有效降低模型对网格密度的依赖性。层间分层损伤情况由内聚力单元（cohesive element）预测,以二次应力准则为分层损伤的起始准则,B-K准则表征分层损伤演化。分别通过数值分析方法和试验研究方法对复合材料典型铺层层合板四级能量低速冲击下的冲击损伤和冲击响应规律进行分析,数值计算和试验测量的接触力-时间曲线、分层损伤的形状和面积较好吻合,表明该模型能够准确地预测层合板低速冲击损伤和冲击响应。     

2.5维机织复合材料强度准则

2.5维机织复合材料已有较为广泛的应用,目前对该类复合材料强度理论的研究还相对较少。根据2.5维机织复合材料拉伸破坏的细观机理,基于单向复合材料的三维Hoffman准则,建立了2.5维机织结构复合材料拉伸破坏准则,通过对2.5维机织复合材料3种结构24个试件进行拉伸试验,与计算预测结果的对比表明了本文建立的强度准则的合理性。研究表明,纤维拉伸断裂是2.5维机织复合材料拉伸破坏的主要原因;相比基于最大应力准则、Hashin准则建立的强度准则,基于Hoffman准则建立的强度准则综合考虑了纤维在外载荷作用下各应力分量对纤维断裂破坏的影响,其预测结果与实际试验结果更为接近;在其他条件不变情况下,随纱线取向角增大,纱线拉伸断裂应力呈非线性降低。随纱线纤维体积含量增加,纱线拉伸断裂应力成线性增加。     

基于单胞解析模型的复合材料层合板渐进损伤数值分析

基于单胞解析模型,建立一种从复合材料细观组分到宏观层合板的渐进损伤分析模型。根据连续介质力学和均匀化方法构建细-宏观关联矩阵,通过该矩阵将细观组分材料的弹性和损伤性能传递到宏观复合材料中。该模型只需给出纤维和基体的材料属性及纤维体积含量无需层合板的弹性和强度参数,通过组分材料的损伤失效判据确定其是否损伤,如果发生损伤则用损伤因子折算成相应的刚度衰减。通过用户材料子程序UMAT 及VUMAT将单胞解析模型以及损伤理论嵌入到有限元软件ABAQUS 中,对开孔复合材料层合板的渐进损伤过程进行模拟,预测了层合板强度。结果表明：预报的强度与试验值吻合较好,验证了该方法的有效性。     

预测复合材料缺口强度的场强法

本文以复合材料缺口附近的应力应变场为参量,提出了预测复合材料缺口强度的场强法,给出了一个估计复合材料缺口强度的普遍表达式,并由此导出了一个易于使用的工程估算方法。通过对两种材料四组实验结果的分析表明:场强法的预测结果是比较满意的。     

湿热环境下开孔复合材料层合板的强度

通过试验研究T300/5405复合材料层合板在6种湿热环境下开孔拉伸、开孔压缩的极限强度,分析了湿热环境对开孔复合材料层合板强度性能的影响,对比了不同湿热环境下材料的破坏模式。在有限元仿真方面,通过考虑湿热环境对材料刚度和强度的影响,建立了湿热条件下复合材料开孔层合板极限强度的预测方法,模拟了开孔复合材料层合板在不同湿热环境、不同载荷类型下的损伤演化全过程。有限元预测结果与试验结果的误差在20%以内,验证了该预测方法的有效性。     

复合材料加筋层合板的极限强度分析

基于更新拉格朗日格式,应用非线性层合三维退化壳元,结合有效的复合材料失效准则、刚度退化模型以及提出的刚度矩阵奇异判断准则,对复合材料加筋层合板在轴向载荷作用下的压缩极限强度问题进行深入研究。讨论了铺层方式、板厚等对极限强度的影响。通过与试验结果进行比较,表明基于提出的刚度矩阵奇异判断准则,结合增量更新拉格朗日格式下非线性层合三维退化有限元的计算方法,能有效计算复合材料加筋层合板的轴向压缩极限强度,并具有很高的精度。     

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。     

Effect of fibre/matrix adhesion on residual strength of notched composite laminates

Effects of fibre/matrix adhesion and residual strength of notched polymer matrix composite laminates (PMCLs) and fibre reinforced metal laminates (FRMLs) were investigated. Two different levels of adhesion between fibre and matrix were achieved by using the same carbon fibres with or without surface treatments. After conducting short-beam shear and transverse tension tests for fibre/matrix interface characterisation, residual strength tests were performed for PMCLs and FRMLs containing a circular hole/sharp notch for the two composite systems. It was found that laminates with poor interfacial adhesion between fibre and matrix exhibit higher residual strength than those with strong fibre/matrix adhesion. Major failure mechanisms and modes in two composite systems were studied using SEM fractography. The effective crack growth model (ECGM) was also applied to simulate the residual strength and damage growth of notched composite laminates with different fibre/matrix adhesion. Predictions from the ECGM were well correlated with experimental data.     

基于断裂韧性预报复合材料层合板的开孔拉伸强度

开孔层合板的强度预报往往取决于孔边的临界长度,它不仅与材料性能,而且与铺层、孔径都有关。本文基于线弹性断裂力学,提出了一种预报对称铺层层合板开孔拉伸强度的新方法,只需提供正交层合板的断裂韧性和无缺口层合板的拉伸强度,显著降低对实验数据的依赖性。首先,将临界长度表作为层合板断裂韧性和无缺口拉伸强度的函数,再通过正交层合板[90/0]_8s的紧凑拉伸试验和虚拟裂纹闭合技术,确定出0°层断裂韧性,进而计算得到任意对称铺层层合板的断裂韧性。本文测试了T300/7901层合板[0/±45/90]_2s和[0/±30/±60/90]_s的开孔拉伸强度,孔径分别为3 mm、6 mm和9 mm。理论预报结果与试验值吻合较好,最大误差为15.2%,满足工程应用需求。      

复合材料层压板剩余刚度剩余强度关联模型

基于剩余强度和剩余刚度取决于同一损伤状态的假设,给出了基于剩余刚度的损伤定义和基于剩余强度的损伤定义之间的关系,建立了剩余刚度剩余强度关联模型。用3种不同铺层形式的层压板试验数据对本文中提出的剩余刚度模型及剩余强度模型进行了验证,结果表明:本文中提出的剩余刚度和剩余强度模型能很好地描述复合材料层压板疲劳过程中的剩余刚度和剩余强度退化规律;通过关联模型,可以在已知剩余刚度退化规律的前提下,用少量剩余强度试验确定剩余强度退化规律;与剩余刚度关联的剩余强度模型中的参数可以被认为是材料常数。      

A size effect law for notched tensile strength of woven carbon/epoxy laminates

Specimen-size effect and notch-size effect on the tensile strength of woven fabric carbon/epoxy laminates are evaluated and modeled. For two different layups of [(0/90)₁₂] and [(±45)₂/(0/90)₅]_S, respectively, static tension tests were performed on two-dimensional geometrically similar unnotched and double-edge notched specimens scaled to three different sizes. Experimental results demonstrate that the notched strength of the woven CFRP laminates depend on the size of specimen as well as the size of notch. The ratio of notched strength to unnotched strength decreases as the length of notch increases, regardless of the size of specimen. For a given size of notch, the notch strength ratio becomes larger with decreasing size of specimen. A notch-size effect law is derived by means of the Neuber interpolation method. A specimen-size effect is embedded into the notch sensitivity parameter involved by the notch-size effect law to establish a size effect law that can cope with these two kinds of size effect. The engineering size effect law proposed can adequately describe the specimen-size effect as well as notch-size effect on the tensile strength of the woven CFRP laminates. It is also demonstrated that the size effect law allows determining the size independent fracture toughness on the basis of notched strengths of small specimens that fail in a quasi-brittle manner.     

A three-dimensional progressive damage model for bolted joints in composite laminates subjected to tensile loading

A three-dimensional progressive damage model was developed to simulate the damage accumulation and predict the residual strength and final failure mode of bolted composite joints under in-plane tensile loading. The parametric study included stress analysis, failure analysis and material property degradation. Stress analysis of the three-dimensional geometry was performed numerically using the finite element code ANSYS with special attention given to the detailed modelling of the area around the bolt in order to account for all damage modes. Failure analysis and degradation of material properties were implemented using a set of stress-based Hashin-type failure criteria and a set of appropriate degradation rules, respectively. In order to validate the finite element model, a comparison of stress distributions with results from analytical models found in the literature was carried out and good agreement was obtained. A parametric study was performed to examine the effect of bolt position and friction upon damage accumulation and residual strength.     

A comparative analysis of approaches to the strength assessment of composite laminates

We present a comparative analysis of the approaches to the strength assessment of composite laminates, which are based on application of different strength criteria to individual plies in a stack or to a stack as a whole. The Mises-Hill and Goldenblat-Kopnov strength criteria are considered. __________ Translated from Problemy Prochnosti, No. 4, pp. 36–42, July–August, 2008.     

三维复合材料层合板渐进损伤非线性分析模型

为有效反映复合材料层合板层间相互作用和材料损伤非线性,建立了中等尺度的三维复合材料层合板渐进损伤分析模型。非线性渐进损伤分析过程包括应力求解、材料损伤失效判据及材料性能退化方案3个方面。讨论了损伤材料性能退化方案,引入与材料损伤模式相对应的损伤变量表征材料点的损伤状态,材料的刚度矩阵按损伤变量退化。基于该模型可成功预测复合材料层合板损伤起始、扩展直至最终失效的整个过程和极限强度。经文献试验数据验证,12种不同铺层顺序层合板的计算强度与试验数据均吻合较好,表明该模型在复合材料层合板极限强度预测上的有效性。     

A CDM-based failure model for predicting strength of notched composite laminates

This paper investigates the ultimate tensile failure strength of laminated composites containing a central circular hole. Based on continuum damage mechanics, a Principal Damage Model is developed by combining the generalized standard material model with the Principal Damage concept of composite materials. Three in-plane failure modes: fiber breakage, matrix cracking, and fiber/matrix interface debonding are included in the present model. After obtaining material constants and damage relations from standard tensile tests, the material constitutive relations with damage model are implemented into commercial finite element code, abaqus. By comparing the predicted results with the experimental data, the proposed model has proven to be capable of predicting failure strength and load–deflection relations of notched laminated composites. The effects of hole size and specimen width are discussed in detail. In addition, the advantage of the present model is demonstrated through comparison with other existing models.     

复合材料层板低速冲击后剩余压缩强度

对两种材料体系和铺层的复合材料层合板进行低速冲击后压缩强度试验 , 以研究低速冲击后层合板的压缩破坏机理。讨论了表面凹坑深度、 背面基体裂纹长度、 损伤面积以及剩余压缩强度与冲击能量的关系。在试验研究的基础上 , 建立了复合材料低速冲击后剩余强度估算的一种椭圆形弹性核模型。该模型将冲击损伤等效为一刚度折减的椭圆形弹性核 , 采用含任意椭圆核各向异性板杂交应力有限元分析含损伤层合板的应力应变状态 ,并应用点应力判据预测层板的压缩(或压、 剪)剩余强度。理论分析与试验结果对比表明 , 该模型简单有效。