Non-Chemical Potentials and Dissipative Forces in Thermoelastic Martensitic Transformation

Abstract

*Institute of Metal Physics, National Academy of Sciences of the Ukraine,Department of Phase Transitions, 36 Vernadsky Str., 252142, Kiev, Ukraine**Departament de Fi´sica, Universitat Illes Balears. E-07071 Palma de Mallorca, Spain(Received October 16, 1997)(Accepted in revised form March 6, 1998)IntroductionDuring a martensitic transformation cycle, a shape memory alloy (SMA) runs a sequence of heterophasestates in which the fraction of martensitic phase increases continuously on cooling and decreases onheating showing a definite temperature hysteresis. At each step of both the forward and the reversetransformations the microstructure of SMA consists of a great number of plate-like martensite crystalsin an austenite matrix, appearing and growing on cooling and shrinking and disappearing on heating.Started with the works by Kurdjumov and Kurdjumov & Khandros (1–3), the problem of thermoelasticequilibrium in SMA remains still opened and has been the subject of extended discussions anddevelopments (4–13). Paskal & Monasevich (8, 9) postulated the existence of fraction dependent Gibbsfree energy potentials describing the direct and reverse martensitic transformation. They also derivedconstitutive thermodynamic force balance equations accounting for the temperature dependence of themartensite volume fraction in a global hysteresis cycle through minimisation of these, strictly speaking,non-equilibrium potentials. Some problems arise from this procedure: first, considering the configura-tion dependent thermodynamic functions as solely dependent on the martensite fraction is onlyphysically reasonable provided the microstructure sequence followed during the forward martensitictransformation is followed in the opposite sense during the reverse transformation. Such “microscopicreversibility” principle was qualitatively formulated by Olson & Cohen (5), who pointed out that growthand shrinkage of the martensitic plates take place in a well defined sequential order, the first platesformed on cooling being the last ones to disappear on heating. Second, introduction of non-equilibriumfree energies containing dissipative or frictional terms, and especially application of minimisationprinciple to them can be a source of misleading physical conclusions. Finally, the usual splitting of thefraction dependent thermodynamic potentials into pure chemical and non-chemical (elastic) compo-nents is practically useful, in the sense of their determination from the experiment, only if the purechemical equilibrium temperature T