Axisymmetric Plane Stress States of an Annulus Subject to Displacive Shear Transformation

Abstract

We study the equilibrium stress field in an annulus composed of a material that admits stress-induced displacive phase transformation that preserves volume. A standard example is the austenite to martensite transformation in shape memory alloys. Attention is restricted to isothermal and axisymmetric load increase. The constitutive model follows a standard J2 formulation appropriate for small strains and incorporates a single internal variable (the martensite phase fraction). A plane-stress boundary value problem is analyzed so as to determine the partitioning of the annulus into regions of (pure) austenite, (pure) martensite, and austenite/martensite mixture. Structure maps are presented, giving concise descriptions of the phase partitioning as the loads increase.