Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. III. Alternative potentials, critical nuclei, kink solutions, and dislocation theory

In part III of this paper, alternative Landau potentials for the description of stress-and temperature-induced martensitic phase transformations under arbitrary three-dimensional loading are obtained. These alternative potentials include a sixth-degree (2-4-6) polynomial in Cartesian order parameters and a potential in hyperspherical order parameters. Each satisfies all conditions for the correct description of experiments. The unique features of the potentials are pointed out and a detailed comparison of the potentials is made for NiAl alloy. Analytic solutions of the one-dimensional time-independent Ginzburg-Landau equations for the 2-3-4 and 2-4-6 potentials for a constant-stress tensor and invariant-plane strain are obtained and compared. Solutions include martensitic and austenitic critical nuclei and diffuse martensite-austenite and martensite-martensite interfaces. The widths and energies of the nuclei and interfaces are functions of the thermodynamic driving force, the gradient energy coefficient, and a parameter that characterizes the stability of austenite. The splitting of a martensite-martensite interface into two austenite-martensite interfaces is interpreted as a potentially new mechanism-namely, barrierless austenite nucleation-which might be observed experimentally at the interface between two invariant-plane-strain variants. The widths, energies, and gradient energy coefficients of the martensite-martensite and austenite-martensite interfaces are estimated for NiAl. Finally, we outline a version of phase field theory for dislocations based on our theoretical framework for phase transformations.