Elastic equilibrium of a half plane containing a finite array of elliptic inclusions

An accurate analytical method has been proposed to solve for stress in a half plane containing a finite array of elliptic inclusions, the last being a model of near-surface zone of the fibrous composite part. The method combines the Muskhelishvili’s method of complex potentials with the Fourier integral transform technique. By accurate satisfaction of all the boundary conditions, a primary boundary-value elastostatics problem for a piece-homogeneous domain has been reduced to an ordinary well-posed set of linear algebraic equations. A properly chosen form of potentials provides a remarkably simple form of equations and thus an efficient computational algorithm. The theory developed is rather general and can be applied to solve a variety of elastostatics problems. Up to several hundred interacting inclusions can be considered in this way in practical simulations which makes the model of composite half plane realistic and flexible enough to account for the microstructure statistics. The stress concentration factors and effective thermoelastic properties of random structure composites with dilute concentration of fibers are estimated in the vicinity of a free edge. The numerical examples are given showing accuracy and numerical efficiency of the developed method and disclosing the way and extent to which the nearby free or loaded boundary influences the local and mean stress concentration in the fibrous composite.     

Elastic interaction of partially debonded circular inclusions. II. Application to fibrous composite

A complete analytical solution has been obtained of the elasticity problem for a plane containing periodically distributed, partially debonded circular inclusions, regarded as the representative unit cell model of fibrous composite with interface damage. The displacement solution is written in terms of periodic complex potentials and extends the approach recently developed by Kushch et al. (2010) to the cell type models. By analytical averaging the local strain and stress fields, the exact formulas for the effective transverse elastic moduli have been derived. A series of the test problems have been solved to check an accuracy and numerical efficiency of the method. An effect of interface crack density on the effective elastic moduli of periodic and random structure FRC with interface damage has been evaluated. The developed approach provides a detailed analysis of the progressive debonding phenomenon including the interface cracks cluster formation, overall stiffness reduction and damage-induced anisotropy of the effective elastic moduli of composite.     

Stress concentration and effective stiffness of aligned fiber reinforced composite with anisotropic constituents

The paper addresses the problem of calculation of the local stress field and effective elastic properties of a unidirectional fiber reinforced composite with anisotropic constituents. For this aim, the representative unit cell approach has been utilized. The micro geometry of the composite is modeled by a periodic structure with a unit cell containing multiple circular fibers. The number of fibers is sufficient to account for the micro structure statistics of composite. A new method based on the multipole expansion technique is developed to obtain the exact series solution for the micro stress field. The method combines the principle of superposition, technique of complex potentials and some new results in the theory of special functions. A proper choice of potentials and new results for their series expansions allow one to reduce the boundary-value problem for the multiple-connected domain to an ordinary, well-posed set of linear algebraic equations. This reduction provides high numerical efficiency of the developed method. Exact expressions for the components of the effective stiffness tensor have been obtained by analytical averaging of the strain and stress fields.     

Interacting elliptic inclusions by the method of complex potentials

An accurate series solution has been obtained for a piece-homogeneous elastic plane containing a finite array of non-overlapping elliptic inclusions of arbitrary size, aspect ratio, location and elastic properties. The method combines standard Muskhelishvili’s representation of general solution in terms of complex potentials with the superposition principle and newly derived re-expansion formulae to obtain a complete solution of the many-inclusion problem. By exact satisfaction of all the interface conditions, a primary boundary-value problem stated on a complicated heterogeneous domain has been reduced to an ordinary well-posed set of linear algebraic equations. A properly chosen form of potentials provides a remarkably simple form of solution and thus an efficient computational algorithm. The theory developed is rather general and can be applied to solve a variety of composite mechanics problems. The advanced models of composite involving up to several hundred inclusions and providing an accurate account for the microstructure statistics and fiber–fiber interactions can be considered in this way. The numerical examples are given showing high accuracy and numerical efficiency of the method developed and disclosing the way and extent to which the selected structural parameters influence the stress concentration at the matrix–inclusion interface.     

纺织复合材料和结构多尺度耦合的数值分析

研究了纺织复合材料和结构多尺度耦合的数值分析模型。建立了微、细观单胞,给出了纺织复合材料平均弹性常数的逐级分析方法,着重研究了由宏观结构、到细观纤维束、再到微观纤维三个尺度耦合的应力分析方案。对于常用的板壳状纺织复合材料结构,在面内载荷下,假设每层细观单胞的平均面内应变是一致的,在弯曲、横向剪切及扭曲等非面内载荷下,在内力等效条件下将沿厚度方向连续分布的宏观应力简化为阶梯状分布,忽略了每层细观单胞范围内宏观应力沿厚度方向的梯度变化,由此利用细观单胞模型实现宏观应力与细观应力之间的传递,再利用微观单胞可得到纤维尺度的微观应力。最后以一种三维机织复合材料为例,用上述多尺度耦合的模型逐级分析了材料的平均弹性常数,并沿相反方向,由宏观结构分析逐级计算出纤维束尺度和纤维尺度的细、微观应力的局部波动。     

复合材料层合板低速冲击响应和损伤分析

通过在有限元软件Abaqus/Explicit中编写用户材料子程序VUMAT，建立了一种基于能量演化的复合材料低速冲击渐进损伤模型．该模型以三维Hashin准则来预测层内损伤的起始，以一种简化的损伤变量来模拟层内损伤的演化，将具有双线性牵引-分离本构的零厚度界面单元插入层间来模拟分层损伤．采用该模型对14.7 J冲击能量下的纤维增强复合材料低速冲击过程进行了仿真分析，计算得到的冲击力-时间曲线、能量-时间曲线和损伤分布与试验结果吻合较好．根据数值模拟结果，分析了纤维、基体和分层损伤的扩展规律，为低速冲击下的复合材料结构设计提供了理论依据．     

Elastic interaction of partially debonded circular inclusions. I. Theoretical solution

A complete solution has been obtained of the elasticity problem for a plane containing a finite array of partially debonded circular inclusions, regarded as the open-crack model of fibrous composite with interface damage. A general displacement solution of the single-inclusion problem has been derived by combining the complex potentials technique with the newly derived series expansions. This solution is valid for any non-uniform far load and is finite and exact in the case of polynomial far field. Applying the superposition principle expands this theory to the multiple inclusion problem and provides a simple and rapidly convergent iterative algorithm. The presented numerical data show an accuracy and numerical efficiency of the proposed method and discover the way and extent to which the elastic interaction between the partially debonded inclusions affects the local fields, stress intensity factors and the energy release rate at the interface crack tips.     

大开口复合材料层合板强度破坏研究

复合材料层合板的各向异性及非均质,使得复合材料层合板内部的破坏形式非常复杂.在复合材料结构的设计中,为满足制造及使用功能上的需求,在复合材料层合板承力结构件上不可避免地需要设计各种开口.然而,含大开口复合材料层合板的强度破坏问题变得更为复杂,使得现有的强度理论面临新的挑战.针对碳纤维增强复合材料大开口层合板受单向拉伸载荷作用下的强度破坏问题进行了数值分析和实验研究.首先,根据Hashin准则和刚度退化模型,对含不同圆形开口尺寸的[0]_(10)单向铺层、[0/90]_5和[±45]_5正交铺层的层合板,进行了单向拉伸载荷作用下渐进失效的数值模拟分析,获得了对应结构的极限载荷和破坏模式.在此基础上,采用数字图像相关方法,进行复合材料大开口层合板强度破坏的实验研究.研究结果表明,大开口复合材料层合板在单向拉伸加载下主要呈现脆性破坏形式,破坏起始位置处于应力集中区.此外,破坏强度和失效模式与复合材料铺层方式和开口尺寸大小密切相关.其中[±45]_5铺层的开口层合板承载能力最弱,分层破坏最严重.开口尺寸越大,结构的极限载荷值越低.同实验测试结果相比,数值模拟对复合材料层合板的损伤失效分析略显不足,往往很难全面分析复合材料层合板破坏失效过程中的各种因素的影响.     

复合材料桥连的断裂动力学模型

复合材料产生裂纹后，其纤维处形成“桥连”，这是一个不可避免的现象。由于桥连问题很复杂．在数学方法的处理上有很大困难，至今人们研究大多是桥连的静力学问题．而对其动力学问题研究得很少。为了便于分析复合材料的问题，将桥连处用载荷代替，当裂纹高速扩展时．其纤维也连续地断裂。只有建立复合材料的桥连动力学模型，才能更好地研究复合材料的断裂动力学问题。通过复变函数论的方法，将所讨论的问题转化为Riemann—Hilbert问题。利用建立的动态模型和自相似方法，得到了正交异性体中扩展裂纹受运动的集中力P及阶跃载荷作用下位移、应力和动态应力强度因子的解析解，并通过叠加原理，最终求得了该模型的解。     

Analysis of progressive fiber debonding in elastic laminates

The evolution of fiber debonding, and sliding, in fibrous laminates is modeled by a coupled micro/macro-mechanical analysis scheme. The laminates under consideration have a symmetric layup, and are subjected to mechanical loads. The individual plies are elastic, have a unidirectional reinforcement, and can suffer local damage at the fiber/matrix interface when the resolved normal and shear stresses exceed their ultimate magnitudes. The local fields in the plies are assumed to be periodic, and are approximated by the finite element method for overall loads and local resolved stresses that are in excess of the interface strength. Local effects in the individual plies are scaled up to the laminate analysis through stress transformation factors, which are a function of the elastic properties of the plies and their stacking configuration.The proposed analysis was implemented for a periodic array model of the laminas, and for in-plane loading of the laminate. The model predictions for a unidirectional steel/epoxy system subjected to transverse loading compare remarkably well with experimental measurements. This result, and several other examples given for axial and off-axis loading of SiC/CAS laminates, illustrate the model capabilities in predicting the overall strains in the presence of simultaneous, progressive debonding in the individual plies.     

新修正偶应力层合板理论中的几个基本假设对自由振动计算的影响

基于新修正偶应力理论,在对微细观尺度的复合材料层合梁/板进行力学响应计算时,往往采用一系列假设来简化模型。现有文献都全部或部分应用了这些假设,但对这些假设是否会对计算结果造成影响尚未进行充分讨论分析。本文建立了未经简化的新修正偶应力Reddy层合板模型,并对其自由振动进行了分析。通过数值算例的对比,讨论了常用的几个简化假设对微细观复合材料四边简支方板自振频率的影响以及适用范围。算例结果表明,常用的几个简化假设对于微尺度层合薄板自由振动的影响很小,对于厚板的低阶频率影响也很小,但对厚板的高阶频率影响显著。     

复合材料的裂纹动力学问题的模型

复合材料产生裂纹后，其纤维处形成“桥连”，这是一个不可避免的现象。由于桥连问题很复杂，在数学方法的处理上有很大困难，至今人们研究的大多是桥连的静力学问题，而对其动力学问题研究得很少。只有建立复合材料的桥连动力学模型，才能更好地研究复合材料的断裂动力学问题。为了便于分析复合材料的问题，将桥连处用载荷代替，当裂纹高速扩展时，其纤维也连续地断裂。通过复变函数论的方法，将所讨论的问题转化为Riemann-Hilbet问题。利用建立的动态模型和自相似方法，得到了正交异性体中扩展裂纹受运动的集中力Px/t及均布载荷作用下位移、应力和动态应力强度因子的解析解，并通过迭加原理，最终求得了该模型的解。     

材料非线性对复合材料层合板热自由边界效应的影响

本文用准三维有限元法研究了材料非线性对复合材料层合板热自山边界效应的影响,给出了修正型Hahn-Tsai非线性应力-应变关系的三维形式。由本文非线性分析方法得到的层间应力与以往由线性分析方法得到的层间应力做了比较,结果表明:材料非线性能显著降低层间剪应力的集中程度,但对层间正应力影响不太明显。     

含冲击损伤高强中模碳纤维复合材料层压板压缩剩余强度分析与试验验证

论文以碳纤维复合材料层压板为研究对象,发展了一种模拟复合材料层压板冲击及冲击后压缩的一体化数值分析方法．基于Puck 失效准则和粘聚区模型描述层内损伤与层间损伤,分别采用基于断裂能的双线性型、函数型以及直接折减型等不同损伤折减方法构建了层内损伤预测与演化模型;建立了碳纤维复合材料冲击后压缩数值仿真模型,通过开展不同能量冲击后压缩试验,验证了所发展的数值分析方法的有效性;研究结果表明,采用Puck 失效准则和基于断裂能的双线性损伤演化模型预测冲击后压缩强度时具有较高精度．     

光纤光栅传感网络应用于玻璃纤维复合材料构件损伤检测的试验研究

将光纤光栅传感网络埋入玻璃纤维复合材料试件后,通过无损试件与有损试件的准静态弯曲对比试验研究,分析了测量过程中反映损伤位置以及损伤程度的光纤光栅参数。然后使用ANSYS有限元软件对其进行数值模拟计算,并将数值模拟的结果与试验测得的结果相对比,验证了应用光纤光栅传感网络利用准静态加载方法测量损伤的可行性以及准确性。本文研究结果可为利用FBG光纤传感网络对实际工程中复合材料结构的在线健康监测提供实验基础。     

含共晶界面陶瓷复合材料的损伤应变场分析

研究了含共晶界面陶瓷复合材料的损伤应变场及其尺度效应。根据含共晶界面复合陶瓷的细观结构特性,利用含共晶界面陶瓷复合材料中三相胞元内的应力场分布规律,得出棒状共晶体内的无损应变场分布规律。针对棒状共晶体内存在损伤的现象,通过引入损伤变量,利用三相模型法得到了棒状共晶体内存在损伤时的应变场分布规律;根据应变和纤维状夹杂直径之间的关系,分析了棒状共晶体内的损伤应变场及其尺度效应。结果表明,含共晶界面陶瓷复合材料内三相胞元中基体、界面相和纤维夹杂内的损伤应变场对纤维夹杂直径具有明显的尺度效应。     

An elastic–plastic crack bridging model for brittle-matrix fibrous composite beams under cyclic loading

A fibrous composite beam with an edge crack is submitted to a cyclic bending moment and the crack bridging actions due to the fibers. Assuming a general elastic-linearly hardening crack bridging model for the fibers and a linear-elastic law for the matrix, the statically indeterminate bridging actions are obtained from compatibility conditions. The elastic and plastic shake-down phenomena are examined in terms of generalised cross-sectional quantities and, by employing a fatigue crack growth law, the mechanical behaviour up to failure is captured. Within the framework of the proposed fracture mechanics-based model, the cyclic crack bridging due to debonding at fiber–matrix interface of short fibers is analysed in depth. By means of some simplifying assumptions, such a phenomenon can be described by a linear isotropic tensile softening/compressive hardening law. Finally, numerical examples are presented for fibrous composite beams with randomly distributed short fibers.     

复合材料框架结构刚度几何双尺度优化设计

航空航天结构对超轻质大跨度框架类结构提出了迫切的需求,考虑纤维增强复合材料框架结构宏观与微观的可设计性,基于结构与材料一体化优化理念,研究了复合材料框架结构宏观拓扑与微观纤维铺层参数并发优化的双尺度优化问题。以宏观管件构件内半径与微观连续纤维缠绕角度为两类独立的设计变量,建立了以最小化结构柔顺性为目标函数、材料用量为约束的双尺度复合材料框架结构优化列式,给出了宏微观设计变量灵敏度信息的求解算法。讨论并对比了单尺度微观纤维缠绕角度优化、宏观截面拓扑优化与宏微观双尺度并发优化。数值算例表明,双尺度并发优化设计可进一步发掘结构与材料的承载潜力,实现既定性能下的结构轻量化设计。     

模拟长纤维增强树脂层合板冲击损伤的数值方法

建立了一套模拟树脂层合板低速冲击下损伤过程的方法.该方法采用Mindlin板模型并考虑板的大变形,使用以前提出的一种修正的Newmark时间积分方案进行层板的动态分析,全面考虑了复合材料的脱层破坏、基体开裂和纤维断裂等破坏形式及其相互作用.还建立了一种适合于 Mindlin板的计算应变能释放率的方法;构造了一种连续的罚函数来动态加人弹簧约束以考虑脱层间的接触效应;证明了球板之间的冲击过程是刚性系统,应使用A（α）稳定的数值方法求解;实现了模拟过程中的自适应分析.使用所开发的软件NBHULI完成了长纤维增强碳/环氧复合材料层板在低速冲击下损伤过程的模拟,取得了一些重要的结果.     

45#钢的损伤演化方程和层裂准则研究

通过唯象分析和细观物理统计相结合的方法建立了一种韧性材料的损伤演化方程。在试验结果和内变量理论的基础上得到了45#钢的含损伤热—粘塑性本构关系。用有限差分方法计算了45#钢平板撞击所产生的应力波传播规律、损伤演化规律及层裂进程。通过自由面速度历史的数值模拟,并基于计算结果与试验结果间的最佳一致性,得到了损伤演化方程中的材料参数和极限损伤数值,并以此为依据建立了材料的应力率层裂准则。