Micromechanical estimates of the interaction energy for shape memory alloys based on a two-phases microstructure

The interaction energy is a fundamental ingredient in the modeling of Shape Memory Alloys (SMA) and several micromechanical estimates are available in the literature Some of the models describe SMA by Multi-Variant Microstructures (MVM) made of a mixture of Austenite and several variants (or groups of variants) of Martensite. Others, rely upon Two-Phase Microstructures(TPM) in which only one type of Martensite arises. Besides the different approaches there is a common issue to most micromechanical estimates: they tend to largely overestimate the values of the interaction energy. In this work the quantitative relevance of the overestimation of the interaction energy is evaluated, in a sample case, showing that some models based on TPM may lead to violations of the second law of thermodynamics. While various solutions to this problem have been proposed in the framework of MVM by enriching the description of the microstructure, it seems that similar remedies are not yet available in the two-phases setting. In a previous work it was shown that, for SMA modeled by TPM, any estimate of the effective compliance immediately lead to a corresponding estimate of the interaction energy. Among the several estimates available in the literature, Dvorak's Average Field Approximation (AFA) turns out to be very useful in this context. In this micromechanical scheme mechanical concentration tensors are approximated by embedding inclusions in a comparison material subject to a suitable stress field that models, in an indirect way, the interaction between phases. The use of this scheme in the framework of leads to estimates of the interaction energy that depend on the elastic properties of the comparison material. While in the composite materials applications of the AFA scheme the comparison material is used to model the interactions between the phases, here the idea is to model, in an overall and indirect way, the secondary accommodation phenomena that take place during phase transformations by a comparison material less stiff than parent phase. This might be interpreted also as a kind of effective microscale damage occurring around the product phase regions. The elastic properties of the comparison material may thus be tuned in order to model the reduction of stiffness induced by the, otherwise unspecified, secondary accommodation phenomena. Finally, it is shown that this gives rise to physically plausible values of the interaction energy consistent with the thermodynamical bounds.