MARTENSITIC-TRANSFORMATION AND STRESS-STRAIN RELATIONS OF SHAPE-MEMORY ALLOYS

A micromechanical theory is developed to predict the stress-strain rel ations of shape-memory alloys (SMAs) at various temperatures above the martensitic-start temperature M-s. The theory is based upon the irrev ersible thermodynamic principle associated with the stress-induced mar tensitic transformation where the reduction in Gibbs' free energy is e valuated by considering the morphology of the product phase. The volum e concentration, inclusion shape, and the normal and shear components of the transformation strain have all been incorporated. The influence of applied stress through the mechanical potential energy and the inf luence of temperature through the chemical free energy have also been established. Departing from the traditional constant-entropy assumptio n, a linear entropy-temperature relation is introduced to calculate th e chemical free energy. The resulting chemical energy is non-linear, a nd is found to have strong influence on several basic properties of SM As, including a non-linear stress-dependence for M-s and the austeniti c-start temperature A(s). Despite the complexity of the microgeometry, the outcome is a set of explicit constitutive equations which provide a direct link between the applied stress and the evolution of the pro duct phase, and between the stress and overall strain of the transform ing system. Finally, the theory is applied to study the stress-strain relations of a Ti-49.8 at% Ni single crystal during the forward austen ite-to-martensite transformation and the reversed martensite-to-austen ite transformation. Apart from several noble qualitative features of t he theory, the quantitative predictions are found to be in accord with experimental observations over a wide range of temperature. (C) 1997 Elsevier Science Ltd.