Stress intensity factors for cracks in functionally graded annular planes under anti-plane loading

• Anti-plane analysis of functionally graded annular domains has been developed.
• The obtained solutions of stress and displacement fields allow multiple cracks.
• Effects of crack length, orientation and location are shown by multiple examples.

First, through the finite Fourier sine and cosine transforms, the stress solution of a functionally graded (FG) annular plane weakened by a screw dislocation is obtained. Next, by means of dislocation solution, integral equations are formulated for the same circular plane weakened by several cracks. The ensuing singular integral equations are of Cauchy types which are solved numerically in order to find the dislocation density function on crack borders. Several examples are presented to study the effect of FG material as well as the crack orientation/location on the ensuing stress intensity factors at crack tips of annular planes.