Crack tip plasticity in mixed mode loading under contained yielding conditions

Mode I, mode II and mixed mode I/II asymptotic crack tip fields have been studied under contained yielding conditions using plane strain and plane stress boundary layer formulations. The effect of the non-singular term in the asymptotic elastic expansion (Williams, 1957) on the plastic zone at the crack tip has been determined. Plane stress mode I, mode II and mixed mode I/II crack tip fields have also been investigated analytically. Analytical solutions were developed by assembling constant stress, fan and elastic sectors. Slip line theory (Hill, 1950) was used to solve constant stress and fan sectors while the stress fields in elastic sectors were solved using the semi-infinite wedge solution of Timoshenko and Goodier (1970). Analytical solutions were validated by numerical results, and represented as slip line fields