On the macroscopic free energy potential for Shape Memory Alloys treated as a two-phase continuum

Abstract

In the present paper, a macroscopic free energy potential for shape memory alloys in the pseudoelastic range of their behavior is derived. It is assumed that the macro-element made of Shape Memory Alloy (SMA) is composed of austenitic and martensitic phase. It is stipulated that on the mezo-scale level, the micro-constituents obey generalized thermoelastic Hooke's law, in which eigenstrains connected with martensitic phase transformation are present. The primary target of the paper is not determination of the specific form of the macro free energy but revealing its structure resulting from the micro-macro transition. This structure is of a fundamental significance for subsequent development of macroscopic constitutive relations for Shape Memory Alloys. Micro-macro transition procedure allows for identifying the correspondence between the actual micro-phenomena and individual terms appearing in the free energy macro-potential. The performed calculations throw a new light on the so-called accommodation energy, a part of which is the interaction (coherence) energy appearing in contemporary literature. On the application side, it was possible to explain a certain paradox appearing in the attempts made to describe the behavior of some TiNiX ternary alloys (TiNi alloy) undergoing R-phase transformation.