State equation for shape-memory alloys: Application to Cu-Zn-Al

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Abstract
We deal with the hysteretic behavior of partial cycles in the two-phase region associated with the martensitic transformation of shape-memory alloys. We consider the problem from a thermodynamic point of view and adopt a local equilibrium formalism, based on the idea of thermoelastic balance, from which a formal writing follows a state equation for the material in terms of its temperature T, external applied stress σ, and transformed volume fraction x. To describe the striking memory properties exhibited by partial transformation cycles, state variables (x,σ,T) corresponding to the current state of the system have to be supplemented with variables (x,σ,T) corresponding to points where the transformation control parameter (−σ and/or T) had reached a maximum or a minimum in the previous thermodynamic history of the system. We restrict our study to simple partial cycles resulting from a single maximum or minimum of the control parameter. Several common features displayed by such partial cycles and repeatedly observed in experiments lead to a set of analytic restrictions, listed explicitly in the paper, to be verified by the dissipative term of the state equation, responsible for hysteresis. Finally, using calorimetric data of thermally induced partial cycles through the martensitic transformation in a Cu-Zn-Al alloy, we have fitted a given functional form of the dissipative term consistent with the analytic restrictions mentioned above.