Analysis of an infinite shape memory alloy plate with a circular hole subjected to biaxial tension

This paper presents an exact solution for the stresses in an in_nite shape memory alloy plate with a circular hole subjected to biaxial tensile stresses applied at in_nity[ The solution obtained by assumption of plane stress is based on the two!dimensional version of the Tanaka constitutive law for shape memory materials[ The plate is in the austenitic phase\ prior to the application of external stresses[ However\ as a result of tensile loading\ stress!induced martensite forms\ beginning from the boundary of the hole and extending into the interior\ as the load continues to increase[ Therefore\ in a general case\ the plate consists of three annular regions] the inner region of pure martensite\ the intermediate region where martensite and austenite coexist\ and the outer region of pure austenite[ The boundaries between these annular regions can be found as functions of the external stress[ Two methods of solution are presented[ The _rst is a closed!form approach based on a replacement of the actual distribution of the martensitic fraction by a piece!wise constant function of the radial coordinate[ The second method results in an exact solution obtained by assuming that the ratio between the radial and circumferential stresses in the region where austenite and martensite coexist is governed by the same relationship as that in the encompassing regions of pure austenite and pure martensite[ 0887 Elsevier Science Ltd[ All rights reserved