Solutions of a Crack Interacting with Tri-Material Composite in Plane Elasticity

In this paper a crack interacting with tri-material composite under a remote uniform tensile load is solved in plane elasticity. An edge dislocation distribution along the prospective site of the crack together with the principle of superposition is used to model a crack. The resulting singular integral equation with logarithmic singular kernels for a line crack is then established. The singular integral equation is solved numerically by modeling a crack in place of several segments. Linear interpolation formulae with undetermined coefficients are applied to approximate the dislocation distribution along the elements, except at vicinity of crack tip where the dislocation distribution preserves a square-root singularity. Once the undetermined dislocation coefficients are solved, the mode-I and mode-II stress intensity factors can be obtained. Some numerical results are performed to show the effects of material property combinations and geometric parameters on the normalized mode-I and mode-II stress intensity factors.