一维六方压电准晶三角形孔边裂纹反平面问题

Anti-plane problem of an edge crack emanating from a triangle hole in one-dimensional hexagonal piezoelectric quasicrystals

通过引入合适的数值保角映射,利用Stroh型公式研究一维六方压电准晶中正三角形孔边裂纹的反平面问题,给出在电非渗透边界条件下三角形孔边裂纹尖端的场强度因子和能量释放率。通过数值算例,讨论场强度因子和能量释放率随缺陷几何尺寸和力电荷载的变化规律。结果表明:随孔边裂纹长度的增加,场强度因子先急剧增加后减小,并趋于定值1,正三角形孔洞的尺寸对其影响可忽略不计;声子场和相位子场机械载荷总是促进裂纹扩展,而电位移对裂纹的扩展极大地依赖于声子场和相位子场载荷的大小。

In this paper, by introducing a numerical conformal mapping and using the Stroh-type formulism, the anti-plane problem of an edge crack emanating from a regular triangle hole in one-dimensional hexagonal piezoelectric quasicrystals is studied and the explicit solutions of the field intensity factors and the energy release rates at the crack tip are obtained. Numerical examples are presented to show the influences of the geometrical parameters of defect, the applied mechanical loads of phonon and phason fields and the electric displacement on the field intensity factor and the energy release rate. The results show that, the field intensity factors are dependent on the crack length, instead of the side of triangle hole. Furthermore, the mechanical loads of the phonon and phason fields always promote the crack growth, but the effect of the electric field on the crack propagationdepends on the mechanical loads of the phonon and phason fields.