A theoretical examination of the plastic properties of bcc crystals deforming by 〈111〉 pencil glide

Abstract

Yielding under an arbitrary stress state and constrained deformation by polyslip were examined for bcc crystals deforming by 〈111〉 pencil glide,i.e., slip with equal ease on any plane containing a 〈111〉 slip direction. The pencil-glide equivalent of the generalized Schmid’s law was derived. The yield expression for the initiation of slip in each 〈111〉 direction is a coupled quadratic function of all six stress components, and all four expressions reduce to the von Mises yield criterion when only principal stresses are applied along the cubic axes. In order to accommodate an arbitrary imposed shape change by pencil glide, polyslip stress states were examined which simultaneously operate four or three 〈111〉 slip directions. A maximum-work procedure is proposed to choose that particular polyslip stress state required to enforce a given shape change.