The Critical Shear Stress to Transmit A Peierls Screw Dislocation Across A Non-slipping Interface

Abstract

The critical resolved shear stress to transmit a screw dislocation through a non-slipping (welded) bimaterial interface is studied as a function of the elastic mismatch across the interface and the nonlinear shear stress-relative shear displacement relation across the incoming and outgoing slip planes. This study extends the work of Pacheco and Mura (1969), by using a numerical approach that incorporates a variety of slip plane relations and by adopting a formulation by Beltz and Rice (1991) that accounts for the finite interplanar spacing across a slip plane. The geometry is specialized to the case when slip planes are perpendicular to the interface and numerical results are obtained for values of mismatch, Δμ, in elastic modulus equal to 20% of the average value. Numerical results in this regime confirm the Pacheco and Mura observation that the critical resolved shear stress is proportional to the mismatch in elastic shear modulus. A significant new result is that the critical resolved shear stress increases with the unstable stacking fault energy of the slip planes, but is relatively insensitive to the maximum shear strength of the slip planes. A simple model is constructed which adequately captures the dependence on stacking fault energy and elastic modulus mismatch. It is with pleasure and gratitude that this work is presented on the commemoration of the 60th birthday of Prof. James Rice, who as Ph.D. advisor to one of the authors (PMA), instilled a sense of enthusiasm and formalism to study dislocation-defect interactions of the type described herein.