压电弹性体中正六边形孔边快速传播裂纹的解析解

Analytic Solutions of Two Fast Propagating Cracks Emanating from a Regular Hexagonal Hole in Piezoelectric Materials

研究了横观各向同性压电材料中正六边形孔边快速传播裂纹的反平面剪切问题。基于复变函数方法,利用保角映射技巧,求得了电渗透和电非渗透两种边界条件下的动态应力强度因子、电位移强度因子和能量释放率的解析解。数值分析给出了场强度因子和能量释放率随缺陷几何尺寸、力电荷载和速度的变化规律,结果表明:能量释放率随着速度的增加而增大,机械载荷总是促进裂纹扩展,而电载荷会抑制裂纹的扩展。

We focus on the anti-plane shear problems of two fast propagating cracks emanating from a hexagonal hole in piezoelectric materials in the paper.Based on complex function method,the analytical solutions of dynamic stress intensity factor,dynamic electric displacement intensity factor and dynamic energy release rate with conditions of electrically permeable and impermeable are obtained by using conformal mapping technique.The numerical analysis reveals the rule of the changes about the field intensity factor and energy release rate with defect geometry dimensions,mechanical and electric loads and velocity,namely that the energy release rate increases with the increase of the velocity,and the mechanical loads always promote the propagation of crack but the electric loads restrain it.