A misfitting elastic inclusion in an infinite plane containing a crack

The problem discussed in this paper is that of a misfitting circular inclusion in an infinite elastic medium which contains a straight crack. The crack is stress free. The stresses develop in the elastic medium because of the misfit. The point force method is used to solve the problem. The problem reduces to finding two sets of complex potential functions: {(z), (z)}: One for the infinite medium and the other for the misfitting inclusion. The solution has been obtained in closed form. Graphs are drawn for stress intensity at the crack tip and also for normal, shear and hoop stresses at the common interface of medium and misfitting inclusion.