Thermodynamic analysis of shape memory phenomena — I. Effect of transformation plasticity on elastic strain energy

Abstract

The effect of plastic strains accompanying the thermoelastic transformation on shape memory phenomena is evaluated. It is shown that transformation plasticity can be formally included in Eshelby's macroscopic elastic analysis by defining a net transformation strain equal to the difference of the crystallographic transformation strain and the associated plastic strain. A two variant analysis for a thermoelastic martensite transformation is developed which enables calculation of the variant structure along the path of minimum elastic energy. It is shown that plastic strain accompanying the formation of a martensitic plate reduces the elastic energy stored during the forward transformation. The equilibrium variant structure is shown to be determined by both the applied stress and the fraction of martensite. If the plastic strains accompanying the forward and reverse transformations do not cancel, residual elastic stress fields remain after completion of the reverse transformation. The residual elastic strain fields influence subsequent transformation behaviour and provide the driving force for two-way shape memory behaviour.