A new thermodynamically-consistent model for uniform phase transitions in shape memory alloys

What is it about?

The paper derives a thermodynamic scheme for uniform phase-changes in shape memory alloys. The new idea of the thermodynamic approach is the formulation of the second law where also the entropy production is given by a constitutive equation. Also by analogy with the usual one-dimensional experimental setting, this work describes a thin parallelepiped-shaped body subject to the standard balance equations. The shape-memory material is characterized by constitutive equations where the temperature, the stress and the mass fraction of a phase (martensite) are the variables along with their time derivatives.. The thermodynamic analysis leads to a skeleton surface consisting of equilibrium states and to a rate equation governing the evolution of the fields, outside the skeleton/equilibrium surface. It emerges that the single rate equation allows a whole account of hysteretic transition loops induced by temperature (at constant stress) or by stress (at constant temperature).

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Why is it important?

The operative aspect of the theory is emphasized in Sect. 19.6 by using a linearized version of the skeleton/equilibrium surface. The rate equations governing the evolution of the fields yields ordinary differential equations that can be integrated in closed form. Hence, detailed (bilinear) hysteretic loops are derived accordingly as they are induced by temperature (at constant temperature) or by stress (at constant temperature). As a result, pseudoelastic (bilinear) hysteretic loops and sub-loops are derived in the stress-strain plane. Note that some characteristic parameters of the model related to experimentally measurable quantities.

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