Deformation through Transformations

Abstract
Constitutive stress-strain relations for transformational deformation are discussed. A crystal which can be in two possible phase states is considered. A phase transformation begins during the deformation after a certain amount of elastic strain. For each fixed level of strain an equilibrium polydomain microstructure is established which corresponds to a minimum in the free energy of the crystal. The equilibrium microstructure consists of plane-parallel layers of a product phase separated by layers of an initial phase. The product phase itself consists of different domains (twins) forming plane-parallel alternating layers. The volume fractions of the phases and the fractions of the different twin components in the product phase are functions of strain and temperature. The stress-strain curve which reflects the evolution of the equilibrium microstructure is calculated. For deformation under strain control the stressstrain curve has a section with negative or zero slope that corresponds to a negative or zero Young's modulus. If deformation proceeds under stress control, hysteretic stress-strain curves on loading and unloading will result from a section with negative slope.