Antiplane elasticity crack problem for a strip of functionally graded materials with mixed boundary condition

In this paper, elastic analysis for a collinear crack problem in antiplane elasticity of functionally graded materials (FGMs) is presented. It is assumed that the upper edge of strip is of traction free, and the lower edge is fixed. The Fourier transform method is used to derive an 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. Finally, numerical solutions are provided.