Statistical physics concepts for the explanation of effects observed in martensitic phase transformations

Abstract

Structural solid-to-solid transformations play a key role for the behaviour of several materials, e.g., shape memory alloys, steels, polymers and ceramics. A novel theoretical approach modelling martensitic phase transformation is demonstrated in the present study. The generally formulated model is based on the block-spin approach and on renormalization in statistical mechanics and is applied to a representative volume element (resp. representative mole element) which is assumed to be in a local thermodynamic equilibrium. The neighbouring representative volume elements are in a generally different thermodynamic equilibrium. This leads to fluxes between those elements. Using fundamental physical properties of a shape memory alloy (SMA) single crystal as input data the model predicts the order parameter ‘total strain’, the martensitic phase fraction and the stress-assisted transformation accompanied by pseudo-elasticity without the requirement of evolution equations for internal variables and assumptions on the mathematical structure of the classical free energy. In order to demonstrate the novel approach the first computations are carried out for a simple one-dimensional case, which can be generalized to the two- and three-dimensional case. Results for total strain and martensitic phase fraction are in good qualitative agreement with well known experimental data according to their macroscopic strain rearrangement when phase transformation occurs. Further a material softening effect during phase transformation in SMAs is predicted by the statistical physics approach. Formulas are presented for the relevant quantities such as volume fraction, total strain, transformation strain, rates of the volume fractions and of the strains.