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     

插值矩阵法分析与复合材料界面相交的平面裂纹奇异应力场

提出了用插值矩阵法分析与各向异性材料界面相交的平面裂纹应力奇异性。基于V形切口尖端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,得到关于平面内与复合材料界面相交的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,获得了平面内各向异性结合材料中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。     

有限尺寸下双材料界面附近裂纹位置对裂纹尖端的影响

随着复合材料的应用和发展,不同材料组成的界面结构越来越受到人们的重视。界面层两侧材料的性能相异会引起材料界面端奇异性,同时界面和界面附近存在裂纹会引起裂尖处的应力奇异性。因此双材料界面附近的力学分析是比较复杂的。本文建立双材料直角界面模型,在材料界面附近预设初始裂纹,计算了有限材料尺寸对界面应力场及其附近裂纹应力强度因子的影响。运用弹性力学中的 Goursat 公式求得直角界面端在有限尺寸下的应力场以及其应力强度系数。通过叠加原理和格林函数法进一步得到在直角界面端附近的裂纹尖端应力强度因子。计算结果表明,在适当范围内改变材料内裂纹与界面之间的距离,界面附近裂纹尖端的应力强度因子随着裂纹与界面距离的增加而减少,并且逐渐趋于稳定。分析结果可以为预测双材料结构复合材料界面失效位置提供参考。     

复合材料Reissner板中与界面相交的裂纹奇异性分析

基于切口尖端附近区域位移场的渐近展开,提出了分析复合材料板中与界面相交的切口应力奇异性的新方法。将位移场渐近展开式的典型项代入弹性板的基本方程,得到关于复合材料板中与界面相交的切口应力奇异性指数的一组非线性常微分方程的特征值;采用变量代换法,将非线性特征问题转化为线性特征问题,并用插值矩阵法求解获得了各向异性结合材料中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;最后将计算结果与现有结果进行对比。结果表明:两种结果吻合较好,表明本文方法是有效的。     

各向异性复合材料中界面屈服/脱粘对裂纹扩展的影响

本研究针对层状复合材料中正交于层合面的裂纹,研究裂纹前方层状界面发生屈服或脱粘现象对该裂纹前沿应力场的扰动。通过利用叠加原理,借用滑移型位错密度表征界面的屈服或脱粘。利用Chebyshev数值积分法求解相应的位错密度的奇异积分方程,得到沿界面屈服/脱粘区域的位错密度分布及裂端区应力场。结果表明,若层状复合材料界面为发生屈服或脱粘,将减弱独立层裂尖的应力奇异性,进而抑制独立层中裂纹的扩展。     

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。     

断裂力学判据的评述

从Inglis 和Griffith 的著名论文到Irwin 和Rice 等的奠基性贡献,对断裂力学中的线弹性断裂力学的K判据,界面断裂力学的G判据,和弹塑性断裂力学的J 判据作了扼要的综述. 介绍了在界面断裂力学G判据的基础上提出的界面断裂力学的K判据,以说明断裂力学的判据存在改进的可能性. 在综述中归纳出断裂力学判据中目前还没有较好解决的几个问题. 在总结以往断裂力学研究经验的基础上,指出裂纹端应力奇异性的源是对断裂力学判据存在的问题作进一步研究的切入点. 探讨了裂纹端应变间断的奇点是裂纹端应力奇异性的源的问题,从而对裂纹端应力强度因子的物理意义进行了讨论. 最后,阐述了进行可靠的裂纹端应力场的弹塑性分析是改进弹塑性断裂力学判据的关键,而进行可靠的裂纹端应力场的弹塑性分析的前提是要通过裂纹端应力奇异性的源的研究来获得作用在裂纹端的造成裂纹端应变间断的有限值应力.      

双材料界面Ⅰ型扩展裂纹尖端的弹黏塑性场

双材料界面中存在材料黏性效应, 对界面裂纹尖端场的分布和界面本身性能 的变化起着重要的影响. 考虑裂纹尖端的奇异性, 建立了双材料界面扩展裂纹尖端的弹黏塑 性控制方程. 引入界面裂纹尖端的位移势函数和边界条件, 对刚性-弹黏塑性界面I型界面 裂纹进行了数值分析, 求得了界面裂纹尖端应力应变场, 并讨论了界面裂纹尖端场随各影响 参数的变化规律. 计算结果表明, 黏性效应是研究界面扩展裂纹尖端场时的一个主要因素, 界面裂纹尖端为弹黏塑性场, 其场受材料的黏性系数、马赫数和奇异性指数控制.     

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本文对界面力学若干问题的部分实验成果作一综述,主要集中于以下４个问题;（１）界面层的变形与界面力学模型;（２）异质材料界面端部的应力集中与应力奇异性;（３）界面应力缓释与功能梯度材料;（４）沿界面与垂直界面裂纹的断裂力学问题．并对今后界面力学实验研究的发展前景进行了讨论．     

层状磁电复合材料界面共线裂纹平面问题分析

本文研究了面内电磁势载荷作用下双层压电压磁复合材料中共线界面裂纹问题．考虑了压电材料的导磁性质和压磁材料的介电性质,引入了界面电位移和磁感强度的连续性条件．利用Fourier 变换得到一组第二类Cauchy 型奇异积分方程．进一步导出了相应问题的应力强度因子、电位移强度因子和磁感强度强度因子的表达式,给出了应力强度因子的数值结果．结果表明电磁载荷会导致界面裂纹尖端I、II 混合型应力奇异性,同时还伴随着电位移和磁感强度的奇异性．比较了双裂纹左右端的应力强度因子,发现在面内极化方向上施加面内磁势载荷时共线裂纹内侧尖端区域的两个法向应力场发生互相干涉增强．     

纤维增强复合材料圆柱型界面裂纹分析

以裂纹面上的位错函数为未知量将圆柱型界面裂纹问题化成一组奇异积分方程的求解问题．应用Ｍｕｓｋｈｅｌｉｓｈｖｉｌｉ的奇异积分方程理论，分析了圆柱型界面裂纹尖端应力场．针对裂纹尖端分别存在和不存在接触区两种情况，确定了裂纹尖端应力场的奇异性．利用数值方法计算了圆柱型界面裂纹尖端接触区尺寸对剪应力强度因子的影响．     

Interface crack problems for mode Ⅱ of double dissimilar orthotropic composite materials

The fracture problems near the interface crack tip for mode Ⅱ of double dissimilar orthotropic composite materials are studied. The mechanical models of interface crack for mode Ⅱ are given. By translating the governing equations into the generalized bi-harmonic equations,the stress functions containing two stress singularity exponents are derived with the help of a complex function method. Based on the boundary conditions,a system of non-homogeneous linear equations is found. Two real stress singularity exponents are determined be solving this system under appropriate conditions about himaterial engineering parameters. According to the uniqueness theorem of limit,both the formulae of stress intensity factors and theoretical solutions of stress field near the interface crack tip are derived. When the two orthotropic materials are the same,the stress singularity exponents,stress intensity factors and stresses for mode Ⅱ crack of the orthotropic single material are obtained.     

Interface crack problems for mode II of double dissimilar orthotropic composite materials

The fracture problems near the similar orthotropic composite materials are interface crack tip for mode Ⅱ of double disstudied. The mechanical models of interface crack for mode Ⅱ are given. By translating the governing equations into the generalized hi-harmonic equations, the stress functions containing two stress singularity exponents are derived with the help of a complex function method. Based on the boundary conditions, a system of non-homogeneous linear equations is found. Two real stress singularity exponents are determined be solving this system under appropriate conditions about bimaterial engineering parameters. According to the uniqueness theorem of limit, both the formulae of stress intensity factors and theoretical solutions of stress field near the interface crack tip are derived. When the two orthotropic materials are the same, the stress singularity exponents, stress intensity factors and stresses for mode II crack of the orthotropic single material are obtained.     

Singular stress fields of angle-ply and monoclinic bimaterial wedges

The characteristic equations for the order of stress singularity of anisotropic bimaterial wedges subjected to traction boundary conditions are investigated. For an angle-ply bimaterial wedge, both fully bonded and frictional interfaces are considered, whereas for a monoclinic bimaterial wedge, a frictional interface is considered. Here, the Stroh formalism and the separation of variables technique are used. In general, the order of stress singularity can be real or complex, but for the special geometry of a crack along the frictional interface of a monoclinic composite, it is always real. Explicit characteristic equations for the order of singularity are presented for an aligned orthotropic composite with a frictional interface. Numerical results are given for an angle-ply bimaterial wedge and a monoclinic bimaterial wedge consisting of a graphite/epoxy fiber-reinforced composite.     

Elastic-viscoplastic field at mixed-mode interface crack-tip under compression and shear

For a compression-shear mixed mode interface crack, it is difficult to solve the stress and strain fields considering the material viscosity, the crack-tip singularity, the frictional effect, and the mixed loading level. In this paper, a mechanical model of the dynamic propagation interface crack for the compression-shear mixed mode is proposed using an elastic-viscoplastic constitutive model. The governing equations of propagation crack interface at the crack-tip are given. The numerical analysis is performed for the interface crack of the compression-shear mixed mode by introducing a displacement function and some boundary conditions. The distributed regularities of stress field of the interface crack-tip are discussed with several special parameters. The final results show that the viscosity effect and the frictional contact effect on the crack surface and the mixed-load parameter are important factors in studying the mixed mode interface crack- tip fields. These fields are controlled by the viscosity coefficient, the Mach number, and the singularity exponent.     

Finite element analysis of a bimaterial interface crack

In this investigation, the enriched element method developed by Benzley was extended to treat the stress analysis problem involving a bimaterial interface crack. Unlike crack problems in isotropic elasticity, where the stress singularity at the crack tip is of the inverse square root type, the interface crack contains an additional oscillatory singularity. Although the effect of this oscillatory characteristic is confined to a region very close to the crak tip, it nevertheless requires proper treatment in order to obtain accurate predictions on the stress intensity factors. Using appropriate crack tip stress and displacement expressions, the enriched element method can model the stress singularity for an interface crack exactly. The finite element implementation of this method has been made on the code APES. Stress intensity factor results predicted by the modified APES program compare favorably with those available in the literature. This indicates tha the enriched element technique provides an accurate and efficient numerical tool for the analysis of bimaterial interface crack problems.     

Anti-plane shear crack normal to and terminating at the interface of two bonded piezoelectric ceramics

The electroelastic analysis of two bonded dissimilar piezoelectric ceramics with a crack perpendicular to and terminating at the interface is made. By using Fourier integral transform, the associated boundary value problem is reduced to a singular integral equation with generalized Cauchy kernel, the solution of which is given in closed form. Results are presented for a permeable crack under anti-plane shear loading and in-plane electric loading. Obtained results indicate that the electroelastic field near the crack tip in the homogeneous piezoelectric ceramic is dominated by a traditional inverse square-root singularity, while the electroelastic field near the crack tip at the interface exhibits the singularity of power law r^−α, r being distance from the interface crack tip and α depending on the material constants of a bi-piezoceramic. In particular, electric field has no singularity at the crack tip in a homogeneous solid, whereas it is singular around the interface crack tip. Numerical results are given graphically to show the effects of the material properties on the singularity order and field intensity factors.