横观各向同性压电材料中正三角形孔口快速传播裂纹的解析解

利用复变函数方法,通过引入合适的数值保角映射研究了横观各向同性压电材料中正三角形孔口快速传播裂纹的反平面剪切问题,并在电非渗透型与电渗透型两种边界条件下,结合柯西积分,导出了力-电耦合作用下以速度v传播时的Ⅲ型裂纹的动态应力强度因子和电位移强度因子的解析解.最后,考虑面内电载荷和面外机械载荷共同作用,分析了三角形孔尺寸、裂纹尺寸、外载变化对裂尖场强度因子的影响.

Analytical Solution of the Fast Propagating Crack in a Triangular Hole in Transversely Isotropic Piezoelectric Materials

By using the complex function method and introducing the appropriate numerical conformal mapping,the anti plane shear problem of the fast propagating crack at the regular triangular orifice in the transversely isotropic piezoelectric material is studied.Under the two boundary conditions of the electric non-permeability type and the electric permeability type,combined with the Cauchy product,the dynamic stress of the type III crack under the force electric coupling is derived Finally,considering the combined action of in-plane electric load and out of plane mechanical load,the influence of triangle hole size,crack size and external load change on the crack tip field strength factor is analyzed.