Plasticity zones in a vicinity of crack tip under longitudinal shear in medium with yield anisotropy (Q2754786)

In infinite elastic plane with semiinfinite crack, antiplane strain is realized. Development of plastic zone near the crack tip is investigated. It is assumed, that yield limit is a function of the angle in a vicinity of the crack tip. From conditions of zero stresses at crack faces, plasticity condition, continuity of stresses at the interface between elastic and plastic zones and the condition at infinity, a boundary value problem for tangential stress is obtained. Its solution is found by the method of conformal mappings. For several yield limit dependencies, shapes of the plastic zones are determined. Rate of dissipation of energy stored in the plastic zone under increasing load is found.