DETERMINATION OF THE ASYMPTOTIC CRACK-TIP FIELDS FOR A CRACK PERPENDICULAR TO AN INTERFACE BETWEEN ELASTIC-PLASTIC MATERIALS

The singular behavior near a crack tip at the interface between two po wer-law hardening materials with the crack perpendicular to the interf ace is studied for both Mode I and Mode II loading under either plane strain or plane stress conditions. The mathematical model developed ca n be expressed as a fourth order ordinary differential equation with h omogeneous boundary condition. A shooting method is applied to obtain the eigenvalues and to solve the differential equation with homogeneou s boundary conditions. When both materials have the same hardening exp onent, N, another material parameter, beta, representing the relative resistance of two materials to plastic deformation, is introduced to r eflect the joint effect of the two materials on the singularity. Resul ts indicate that if both materials have the same N, the singularity at the crack tip is reduced as beta increases; however, when beta become s large there appears to be little change in the singularity for a fix ed N. When the hardening exponents are not the same, the mathematical model assumes stress continuity across the interface. The results show that the order of the singularity depends largely on the softer mater ial, with the largest stresses in the harder material.