与两相材料界面接触的裂纹对SH波的散射

利用积分变换方法得出了两相材料中作用简谐集中力时的格林函数．根据所得的格林函数并利用Betti-Rayleigh互易定理得出了与界面接触裂纹的散射波场．裂纹的散射波场可分解为两部分，一部分为奇异的散射场，另一部分为有界的散射场．利用分解后的散射场，可得裂纹在SH波作用下的超奇异积分方程．根据裂纹散射场的奇异部分和Cauchy型奇异积分的性质得出了裂纹和界面接触点处的奇性应力指数和接触点角形域内的奇性应力．利用所得的奇性应力定义了裂纹和界面接触点处的动应力强度因子．对所得超奇异积分方程的数值求解可得裂纹端点和接解点处的应力强度因子。

SCATTERING OF SH WAVE BY A CRACK TERMINATING AT THE INTERFACE OF BI-MATERIAL

By using Fourier transform method, the Green function of a point harmonic force applied at a bi-material plane is obtained. In terms of the obtained Green function along with the Betti-Rayleigh theorem, the scattered field of a crack terminating at the interface of bi-material is derived. The scattered field of the crack is divided into a singular part and a regular part. Utilizing the separated scattered field of the crack as well as the boundary condition along the crack surface, the hypersingular integral equation of the crack is established. In virtue of the singular scattered field of the crack together with the property of Cauchy type integral, the singular stress and singular stress order at the terminating point are calculated. The dynamic stress intensity factor (DSIF) at the terminating point is defined in terms of the singular stresses at the point. Numerical solution of the obtained hypersingular integral equation yields the dynamic stress intensity factors at the crack tip as well as the terminating point.