纤维段裂试验的界面端应力奇异性研究

纤维段裂试验是测定纤维复合材料界面剪切强度的细观实验方法之一，其试验结果与其他三种细观试验方法(纤维拔出、纤维压人和微珠脱粘)测得的结果各不相符，相差较大。针对该问题，仔细研究了纤维段裂试验过程，可发现如下两个问题，首先是试件中纤维断裂造成的界面端应力奇异性问题；其次是纤维断成临界长度时界面是否脱粘的问题。针对界面端应力奇异性问题，本文建立了界面端轴对称分析模型，运用渐近展开法，推导出求解界面端特征值的特征方程，并由此得到应力奇异性指数随Dundurs常数的变化规律；采用文献[5]所用试件的纤维／基体性能数据，计算出了界面端的应力奇异性指数，并与文献[7]得到的其他三种试验的界面端应力奇异性指数进行比较，发现纤维段裂试件也存在界面端应力奇异性，而且应力奇异性最强，也说明了与其他三种试验结果不具可比性。本文还对纤维断成临界长度时界面是否脱粘的问题，进行了讨论。     

各向同性材料接头和界面相交裂纹应力奇异性特征分析

提出了用插值矩阵法分析各向同性材料接头以及与界面相交的平面裂纹应力奇异性。基于接头和裂纹端部附近区域位移场渐近展开,将位移场的渐近展开式的典型项代入线弹性力学基本方程,得到关于平面内各向同性材料接头以及与两相材料界面相交裂纹应力奇异性指数的一组非线性常微分方程的特征值问题,运用插值矩阵法求解,获得了两相材料平面接头端部应力奇异性指数以及与界面以任意角相交的裂纹尖端的应力奇异性指数随裂纹角的变化规律,数值计算结果与已有结果比较表明,本文方法具有很高的精度和效率。     

轴对称界面端的扭转问题

基于弹性力学轴对称扭转问题的通解,研究了具有任意几何形状的双材料轴对称界面端,给出了界面端的应力奇异性及其附近的位移场和奇应力场,定义了扭转问题的Ｄｕｎｄｕｒｓ双材料参数。研究结果表明,应力奇异性只与界面端的结合角和扭转问题的Ｄｕｎｄｕｒｓ双材料参数有关,而与界面的角度以及界面端与对称轴之间的距离无关,在任何情况下,特征值均为实数,不会产生振荡应力奇异性。     

界面端应力奇异性与复合材料界面剪切强度细观实验分散性分析

复合材料细观实验方法主要有纤维拔出、纤维压力、纤维段裂和微球脱粘实验等四种；但这四种试验得到的界面剪切强度结果存在很大的分散性。虽经三十余年的研究和改进，仍未能消除。为研究分散性产生的原因，本文以轴对称界面端应力奇异性分析为基础，推导出求解四种试件界面端的特征值的特征方程，并给出了特征值随Dundurs常数的变化情况，由此发现用相同的纤维和基体制作的四种试件在界面端存在奇异性不同的应力场，从而阐明了四种界面剪切强度试验结果巨大分散性的产生原因在于纤维和基体间界面处的应力奇异性。     

双材料自由边界面端部问题的数值分析

对各向异性双材料自由边界面端部奇异性场问题进行了研究,利用有限元分析法所得到的各向异性双材料自由边界面端部的应力奇异性指数以及角分布函数,构造了一个自由边界面端部单元,据此建立了自由边界面端部奇异性场的杂交应力模型,并结合Hellinger-Reissner变分原理导出应力杂交元方程,建立了求解平面各向异性材料裂纹尖端问题的杂交元计算模型.与四节点单元相结合,提出一种求解自由边界面端部广义应力强度因子的杂交元法.考核例结果表明:本文方法的数值解精度高,可应用于各向异性材料双材料自由边界面端部问题.     

双材料反平面问题界面端奇异应力场分析

利用位移函数的级数展开,对任意角度的反平面问题界面端的应力场进行了分析研究,得到了全场解。研究一阶场后发现,奇异规律与一般平面问题界面端有显著区别,在界面端关于界面对称的情况下,平角界面端(θ1 = θ2 = θ = 90°) 应力场没有奇异性,其它形状的界面端随着角度θ 从90°到180°,奇异指数也从0到0.5。当界面端是非对称时,平角界面端(θ1 θ2 = 180°)、直角界面端(θ1 = 90°,θ2 = 180°)以及其它形状界面端的奇异指数是一个与两相材料常数比Γ有关的常数。以上两种情况下的应力强度因子完全类似单相材料中裂纹尖端附近应力强度因子,故可根据定义得到     

影响双材料界面端三维应力奇异性的几何因素研究

应用常规有限单元分析技术,对几种典型接头形式的三维双材料结构界面端点附近应力奇异性进行了研究,重点分析了棱角(两自由平面的夹角)大小对界面端点附近应力奇异性指数的影响。数值分析结果表明:棱角大小对界面端应力奇异性指数有明显影响,棱角越大,奇异性指数越小;当棱角趋于180°时,端点附近的应力奇异性指数收敛于界面端线上的值(等于平面应变条件下的理论值)。研究发现,如果采用圆弧对三维双材料结构的棱边进行倒角,使相应的界面端线变成光滑连续曲线,则原界面端点附近的应力奇异性会完全退化为界面端线附近的应力奇异性,即界面端点独特的应力奇异性现象消失。     

QFP结构中引脚焊缝界面端的奇异性热应力问题研究

由于引脚、印制电路板和焊接剂的热-机材料属性不同,在受到热载荷或机械载荷时,引脚焊接界面端会产生奇异性应力,有可能产生界面开裂.为了基于界面端奇异场来评价QFP结构引脚界面端力学行为,本文拟采用数值方法求解引脚焊缝任意角度尖劈界面端的应力强度系数.具体步骤为:首先,基于高次内插有限元特征分析法确定两相任意角度尖劈界面端的奇异性指数和应力角分布函数,并引入常数热应力项,获得热-机耦合奇异性应力场表达式;采用有限元分析技术和最小二乘拟合法来获得应力强度系数的数值解.文中考察了热-机材料属性对热载荷下焊接剂/印制电路板界面端应力强度系数的影响,并给出改善界面端热应力状态的建议.     

三维双材料结构的应力奇异性分析

应用有限单元法子模型技术，对具有不同界面角的三维双材料结构的应力奇异性进行了分析。结果表明，应用子模型技术估算三维双材料结构的应力奇异性指数是有效的。然后分析了界面端线和界面端点处附近奇异性指数，得到了一些重要而有趣的结果。最后对消除三维双材料结构应力奇异性的几何条件进行了讨论。     

异质材料粘接界面强度——三维应力奇异性影响

通过实验并结合有限元分析研究了三维应力奇异性对异质材料粘接接头界面强度的影响.有限元分析结果表明:如果对三维双材料结构的棱边进行圆弧倒角,使相应的界面端线变成光滑连续曲线,则原界面端点附近的三维应力奇异性会退化为界面端线附近的二维应力奇异性,进而降低应力奇异性程度.设计了一系列有圆弧倒角与无圆弧倒角的聚甲基丙烯酸甲酯(PMMA)/铝(AL)和聚碳酸酯(PC)/铝(AL)双材料试样并进行了四点弯曲实验.实验结果表明:界面尺寸对试样失效载荷无明显影响;与未圆弧倒角的试样相比,有圆弧倒角试样的失效载荷明显得到提高.这一结果证明三维应力奇异性对粘接界面强度有明显影响.     

A new variable-order singular boundary element for calculating stress intensity factors in three-dimensional elasticity problems

A new three-dimensional variable-order singular boundary element has been constructed for stress analysis of three-dimensional interface cracks and internal material junctions. The singular fields in the vicinity of crack front or junction have been accurately represented by the singular elements by taking account the variable order of singularities and the angular profiles of field variables. Both the singular stress fields and displacement fields are independently formulated by the element’s shape functions. Different kinds of displacement formulations are investigated. The formulation combining singular and linear terms is found to be the most accurate one. The mixed-mode stress intensity factors are treated as nodal unknowns. The variation of stress intensity factors along the line of singularity can be obtained directly from the final system of equations and thus no post processing, such as three-dimensional J-integral or domain integral, is necessary. Numerical examples involving stress singularity, such as penny-shaped cracks in homogeneous and dissimilar material interface, plates with through-thickness cracks, and a dissimilar inclusion, are investigated. The analysis results are in good agreement with those reported in the literature.     

特征值为二重根的压电材料异材界面端奇异性

横观各向同性压电材料的特征值的不同,其一般解的形式也不同,压电结合材料问题的求解,可以归结为寻找合适的调和函数,针对材料特征值为二重根（s1^2≠s2^2=s3^2)的情况,将变量分离形式的调和函数作特征展开,推导了横观各向同性压电材料轴对称异材界面端附近的奇民异应力场和奇异电位移场,给出院 决定奇异性的特性方程,结果表明,电位移场和应力场具有相同的奇异性,奇异性次数不仅与界面端形状以及材料的机械性质有关。也与材料的压电特性有关。     

纤维端部的界面裂纹分析

基于弹性力学空间轴对称问题的通解,研究了短纤维增强复合材料中纤维端部的轴对称币形和柱形界面裂纹尖端的应力奇异性,得到了裂纹尖端附近的奇异应力场．研究结果表明,这两种轴对称界面裂纹尖端的应力奇异性相同,并且与平面应变状态下相应模型的应力奇异性一致,材料性能对裂纹尖端附近奇异应力场的影响可用三个组合参数描述     

Dissimilar material joints with and without free-edge stress singularities: Part I. A biologically inspired design

An integrated experimental and numerical investigation was conducted for removing the free-adge stress singularities in dissimilar material joints. A convex inter-face/joint design, inspired by the shape and mechanics of trees, will result in reduced stress singularities at bimaterial corners for most engineering material combinations.In situ photoelasticity experiments on convex polycarbonate-aluminum joints showed that the free-edge stress singularity was successfully removed. As a result, the new design not only improves the static load transfer capacity of dissimilar meterial joints, but also yields more reasonable interfacial tensile strength evaluation. For convex polycarbonate-aluminum and poly(methyl methacrylate)-aluminum joint specimens, the ultimate tensile load increased up to 81% while the total material volume was reduced by at least 15% over that of traditional butt-joint specimens with severe free-edge stress singularities.     

Analysis of a three-dimensional dissimilar material joint with one real singularity using a conservative integral

In the present study, a conservative integral based on the Betti reciprocal principle is formulated to determine the intensity of singularity at a vertex of the interface in three-dimensional dissimilar material joints with one real singularity. Eigenanalysis formulated using a three-dimensional finite element method (FEM) is used to calculate the order of stress singularity, angular functions of displacements and stresses. Models with various element sizes and various integral areas are used to investigate the effect of the integration area on the accuracy of the results. The results are compared with those obtained from the boundary element method (BEM) using a curve-fitting technique to calculate the intensity of singularity. In addition, models of various lengths and various material combinations are used to investigate the stress singularity characteristics in three-dimensional dissimilar material joints. The results of the present study indicate that the conservative integral can be used to determine the intensity of singularity in three-dimensional bi-material joints. The accuracy of the results can be improved by mesh refinement. Finally, the relationships among the intensity of singularity, the order of stress singularity and the model geometry are discussed.     

Singularities in auxetic elastic bimaterials

In this paper we study the effects of negative Poisson's ratios on elastic problems containing singularities. Materials with a negative Poisson's ratio are termed auxetic. We present a brief review of such materials. The elasticity problem of a bimateral wedge is presented, then two particular cases of this problem are investigated: the free-edge problem and the interface crack problem. We study the effect on the stress singularity due to one portion of the bimaterial becoming auxetic. We find that the auxetic material has a significant effect on the singularity order, even causing the singularity to vanish for certain values of the elastic constants.     

On discontinuous strain fields in incompressible finite elastostatics

Piece-wise homogeneous three-dimensional deformations in incompressible materials in finite elasticity are considered. The emergence of discontinuous strain fields in incompressible materials is studied via singularity theory. Since the simplest singularities, including Maxwell’s sets, are the cusp singularities, cusp conditions for the total energy function of homogeneous deformations for incompressible materials in finite elasticity will be derived, compatible with strain jumping. The proposed method yields simple criteria for the study of discontinuous deformations in three-dimensional problems and for any homogeneous incompressible material. Furthermore the homogeneous stress tensor is also not restricted. Neither fictitious nor simplified constitutive relations are invoked. The theory is implemented in a simple shearing problem.     

On discontinuous strain fields in finite elastostatics

A general method for the study of piece-wise homogeneous strain fields in finite elasticity is proposed. Critical homogeneous deformations, supporting strain jumping, are defined for any anisotropic elastic material under constant Piola–Kirchhoff stress field in three-dimensional elasticity. Since Maxwell’s sets appear in the neighborhood of singularities higher than the fold, the existence of a cusp singularity is a sufficient condition for the emergence of piece-wise constant strain fields. General formulae are derived for the study of any problem without restrictions or fictitious stress–strain laws. The theory is implemented in a simple shearing plane strain problem. Nevertheless, the procedure is valid for any anisotropic material and three-dimensional problems.