各向异性材料中反平面剪切型裂纹对应力波散射的非局部理论解

Non-Local Theory Solution of the Stress Wave Scattering by a Crack in Anisotropic Materials

利用非局部理论求解了各向异性材料中反平面剪切型裂纹对应力波散射的问题.利用富立叶变换,使问题的求解转换为对一对以裂纹面上位移分布为变量的对偶积分方程的求解;为了求解对偶积分方程,裂纹面上的位移直接展开成雅可比多项式形式.与经典理论的解相比,裂纹尖端处不再有应力奇异性出现,非局部弹性解的应力在裂纹尖端处是一有限值,从而可以利用最大应力假设作为断裂准则.

The dynamic behavior of a crack in anisotropic elasticity materials subject to the harmonic anti-plane shear waves is investigated using the non-local theory.By the Fourier transform, the problem can be solved with the help of a pair of dual integral equations, in which the unknown variable is the displacement on crack surfaces. To solve the dual integral equations, the displacement on crack surfaces is expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularity is present near crack tips. The nonloeal elasticity solutions yield a finite hoop stress at the crack tip, thus allowing us to use the maximum stress as a fracture criterion.