2 - Plastic Zone Transitions

Abstract

This chapter describes an analytical solution for mode III cracking obtained for a finite-width plastic zone model. This model recovers—as special cases—the small-scale yielding elastic-perfectly plastic solution obtained by Hult and McClintock, and a plastic strip model for mode III proposed by Cherepanov, which is analogous in shape to the Dugdale plastic strip model of mode I. The model presented represents a transitional phase of mode III cracking where the elastic-plastic boundary assumes an elliptical form. The stress, strain, and displacement fields are given for both the elastic and plastic regions. For the mode III problem, only the antiplane displacement is nonzero. The elastic-plastic boundary for the plastic strip model given by Cherepanov is a straight line. The elastic-plastic boundary all for the small-scale yielding solution of Hult and McClintock is circular. The additional solution reflects the quadratic nature of the yield condition, and it corresponds to an antiplane loading which is opposite to the loading used to generate the stresses. A change of shape in the plastic zone may be related to an internal variable such as temperature, or it may be related to a three-dimensional effect such as plate thickness. An energy-dissipation analysis for the transition model is also presented.