Modeling of the near-tip zones of a crack between two anisotropic materials

Abstract

We study a crack between two anisotropic half planes under the action of normal and shear loads applied at infinity. To eliminate the singularities of stresses on the continuation of the crack, we introduce plastic bands with certain laws of variation of stresses inside the bands. We reduce the problem under consideration to the Riemann boundary-value problem and use the exact solution of the problem. As a result, we obtain transcendental equations for the length of the indicated bands and analytic expressions for stresses inside these bands. Under the assumption that the material is perfectly plastic inside the plastic bands and the half planes are orthotropic, we obtain numerical values of the length of these bands as functions of the external load and mechanical characteristics of the material.