Collinear Crack Problem in Antiplane Elasticity for a Strip of Functionally Graded Materials

Abstract

AbstractIn this paper, elastic analysis for a collinear crack problem in antiplane elasticity of functionally graded materials (FGMs) is present. An elementary solution is obtained, which represents the traction applied at a point “x” on the real axis caused by a point dislocation placed at a point “t” on the same real axis. The Fourier transform method is used to derive the elementary solution. After using the obtained elementary solution, the singular integral equation is formulated for the collinear crack problem. Furthermore, from the solution of the singular integral equation the stress intensity factor at the crack tip can be evaluated immediately. In the solution of stress intensity factor, influence caused by the materials property “α” is addressed. Finally, numerical solutions are presented.