Concept of shape change stress and application of Gibbs phase rule to martensitic transformations

Abstract
A concept is developed that inhomogeneous internal stresses called shape change stress (SCS) and elastic back stress (EBS) are generated when a martensite plate forms on cooling. The surrounding parent is subjected to SCS from the plate to be elastically deformed, while the plate is subjected to EBS from the surroundings. In martensitic transformations (MTs), the Gibbs phase rule is expressed as p +f=3, because the number of components c is considered to be 1. When two phases coexist, i.e., p=2, degree of freedom f equats 1. MTs on cooling under no external stress, however, proceed over somewhat broad temperature ranges. This is because internal SCS field is inhomogeneous. With decreasing specimen mass, SCS and EBS generated are expected to decrease. This causes downward shifts of experimental equilibrium temperatures with decreasing specimen mass, as has been so far observed in some shape memory alloys. In the last end of specimen mass zero, no SCS and EBS are generated. Stress-induced MTs in single crystals at a temperature, on the contrary, proceed at an almost fixed stress. This is because the applied external stress is homogeneous throughout the crystal.