复合材料位错与圆形夹杂界面缺陷的力、电干涉效应

【作者】 方棋洪；

【导师】 刘又文；

【作者基本信息】 湖南大学 ， 工程力学， 2003， 硕士

【摘要】 复合材料中位错与夹杂及内部缺陷之间的电弹干涉效应问题，是当前固体力学与材料科学研究领域的前沿热点课题。本文首次对位错与圆形弹性夹杂界面典型缺陷的力、电干涉进行研究，解决了无穷远反平面剪切作用下螺型位错与含界面裂纹或界面刚性线圆形夹杂的弹性干涉问题；无穷远纵向剪切和面内电场共同作用下压电螺型位错与含界面裂纹或界面刚性线圆形压电夹杂的力电耦合效应问题：刃型位错与含界面裂纹圆形弹性夹杂的干涉问题。 创造性运用复变函数解析延拓原理，将上述问题转化为Riemann-Hilbert边值问题，结合复应力函数奇性主部分析方法、广义Liouville定理、Cauchy型积分和留数定理，获得了上述问题的一般解答。作为特例，求出了界面含一条裂纹或刚性线夹杂时基体和夹杂区域复势的封闭形式解；同时计算了界面裂纹和刚性线尖端应力和电位移场强度因子。针对以往大多数相关文献^[7]-[16]只求出了位错在x轴上时位错力表达式，本文应用扰动技术，导出了位错在基体或夹杂中任意点的位错力公式；并讨论了位错力随材料相关参数，裂纹或刚性线弧度的变化规律。 分析结果表明，界面裂纹和刚性线夹杂对螺型位错与夹杂的干涉作用具有强烈的扰动效应。当界面裂纹达到一定弧度时，可以将硬夹杂对位错的排斥作用改变为吸引；当刚性线夹杂达到一定弧度时，不但可以将软夹杂对位错的吸引改变为排斥，也可以改变软基体对位错的作用性质。在压电材料中，由于电弹耦合效应，软夹杂也可能排斥位错。刃型位错与含界面裂纹的夹杂干涉效应表明：当位错接近界面时，裂纹对位错平衡位置有很大的影响；平衡位置对两种材料的弹性性质也有很大依赖性。本文的解答包含了以往文献中的若干结果。更多还原

【Abstract】 The electroelastic interaction of dislocation, inhomogeneity and interior defects is a greatly significative subject in the fields of solid mechanics and materials science. The interaction effects between circular interfacial cracks or rigid line inclusions and a screw dislocation located either outside or inside inhomogeneity under antiplane shear, the electroelastic interaction between a piezoelectric screw dislocation located either outside or inside inhomogeneity and circular interfacial cracks and rigid lines under longitudinal mechanical and inplane electrical loads in linear piezoelectric materials and The elastic interaction between an edge dislocation located either outside or inside inhomogeneity and interfacial crack along a circular inhomogeneity are dealt with in this paper.Using Riemann-Schwarz’s symmetry principle of complex functions, the above problems are transformed into Riemann- Hilbert boundary problems. By combining the analysis of singularity of complex functions, generalized Liouville’s theorem, Cauchy model integral and residue theorem, the general solutions of above problems are presented. For special example, the closed form solutions for complex potentials in matrix and inhmogeneity regions are derived explicitly when interface containing single crack or rigid line, and the appropriate expressions of the electro-elastic field intensity factors at the tip of crack or rigid line are examined. Applying perturbation technique, the image force on dislocation is obtained when dislocation located arbitrary point either outside or inside inhomogeneity, however, a number of previous related investigations on above problems only calculated the interactive dislocation force as the dislocation lies on the x-axis. The variation of screw dislocation forces for correlative material parameters and different radians of crack or rigid line is discussed particularly.As a result, analysis and discussion show that the influence of interfacial crack or rigid line inclusion on the interaction between screw dislocation and inhomogeneity is significant. When the radian of crack reaches extensive magnitude, the presence of interfacial crack can change the interaction mechanism between screw dislocation andsoft inclusion. When the radian of rigid line reaches extensive magnitude, the presence of interfacial rigid line inclusion can change not only attraction force on dislocation arisen by soft inhomogeneity into repulsion force, but also the interaction effects between screw dislocation and soft matrix. Soft inhomogeneity can repel screw dislocation in piezoelectric material due to their intrinsic electromechanical coupling behavior. The influence of crack geometrical dimension and materials elastic constants on edge dislocation force is evaluated and discussed when dislocation is located in matrix. It is shown that the interfacial crack has a significant effect on the equilibrium position of the edge dislocation near circular interface. The results also exhibit a strong dependency different between the shear modulus and Poisson’s ratios of the matrix and the inclusion. The present solutions contain a number of previously known results which can be shown to be special cases.更多还原