一维六方准晶中带光滑顶点的正三角形孔边裂纹的反平面问题  

Anti-Plane Analysis of an Edge Crack Emanating from a Regular Triangle Hole with Smooth Vertices in One-Dimensional Hexagonal Quasicrystals

作　　者：樊世旺[1] 郭俊宏[1] 

机构地区：[1]内蒙古工业大学理学院,内蒙古呼和浩特010051

出　　处：《数学的实践与认识》2015年第21期187-194,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11262012;11502123;11262017;11462020);内蒙古自治区自然科学基金(2015JQ01;2015MS0129);内蒙古工业大学科学研究项目(ZD201219)

摘　　要：本文通过引入合适的保角映射,利用Stroh公式和复变函数方法研究一维六方准晶材料中含光滑顶点的正三角形孔边裂纹的反平面问题,得到正三角形孔边裂纹尖端的场强度因子和能量释放率的表达式.通过数值算例,讨论了裂纹长度和正三角形孔口边长比值对等效场强度因子和能量释放率的影响,以及耦合系数和机械载荷对能量释放率的影响规律.结果表明:裂尖等效场强因子只与裂纹长度有关,而孔洞大小对其影响可忽略;裂纹长度、耦合系数和机械载荷总是促进裂纹扩展.In this paper, by introducing a new conformal mapping and using the complex variable function method, anti-plane analysis of an edge crack emanating from a regular triangle hole with smooth vertices in one-dimensional hexagonal quasicrystals was studied, and the expressions of the field intensity factors and the energy release rates near the crack tip were obtained. The numerical examples were conducted to show that the influences of the crack length and the side length of triangle hole on field intensity factors and the energy release rate and the effects of the coupling coefficient and the mechanical loads of phonon and phason fields on the energy release rate. The result shows that, the variation of field intensity factors are only related to the crack length, and the effect of the side length of triangle hole on the field intensity factors can be ignored. Moreover, the coupling coefficient and the mechanical loads always promote the crack growth.

关 键 词：一维六方准晶 正三角形孔边裂纹 保角映射 场强度因子 能量释放率 复变方法 

分 类 号：O346.1[理学—固体力学]