The nonlocal solution of two parallel cracks in functionally graded materials subjected to harmonic anti-plane shear waves

• 来源期刊: 力学学报（英文版）
• 年，卷（期）: 2007,（4）
• 页码范围: 427-435
• 页数: 9页
• 语种: 英文

摘要

In this paper, the dynamic interaction of two parallel cracks in functionally graded materials (FGMs) is investigated by means of the non-local theory. To make the analysis tractable, the shear modulus and the material den-sity are assumed to vary exponentially with the coordinate vertical to the crack. To reduce mathematical difficulties, a one-dimensional non-local kemel is used instead of a two-dimensional one for the dynamic problem to obtain stress fields near the crack tips. By use of the Fourier transform,the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displace-ments across the crack surfaces are expanded in a series of Jacobi polynomials. Unlike the classical elasticity solu-tions, it is found that no stress singularity is present at the crack tips. The non-local elastic solutions yield a finite hoop stress at the crack tips. The present result provides theoret-ical references helpful for evaluating relevant strength and preventing material failure of FGMs with initial cracks. The magnitude of the finite stress field depends on relevant param-eters, such as the crack length, the distance between two parallel cracks, the parameter describing the FGMs, the fre-quency of the incident waves and the lattice parameter of materials.