Elastic plastic mode III crack under internal shear

摘要

A complete solution is presented for the problemof a mode III crack in an infinite elastic perfectly-plastic solidunder internal shear stress. This problem is the anti-plane strainequivalent of a mode I crack with internal pressure. The problemis transformed into a boundary value problem for a potentialfunction. The particular case when the applied stress σA is equalto the yield stress σ0 is solved numerically by using theBoundary Element Method for potential problems.Numerical results are given for the distance to theelastic-plastic boundary and the crack tip openingdisplacement. The extent of the plastic zone aheadof the crack tip is shown to vary linearly with theratio (σA/σ0)when 0.5≤(σA/σ0)≤1.