Elastic plastic mode III crack under internal shear

A complete solution is presented for the problem of a mode III crack in an infinite elastic perfectly-plastic solid under internal shear stress. This problem is the anti-plane strain equivalent of a mode I crack with internal pressure. The problem is transformed into a boundary value problem for a potential function. The particular case when the applied stress σA is equal to the yield stress σ0 is solved analytically, and the distance to the elastic-plastic boundary is obtained in closed form. The general case when σA σ0 is solved numerically by using the Boundary Element Method for potential problems. Numerical results are given for the distance to the elastic-plastic boundary and the crack tip opening displacement. The extent of the plastic zone ahead of the crack tip is shown to vary linearly with the ratio σA/σ0) when 0.5 ≤ (σA/σ0) ≤ 1.