Analysis of elastic-plastic accommodation due to volume misfit upon solid-state phase transformation

During solid-state phase transformation, volume misfit between the parent and the product phases leads to strain energy and affects the transformation kinetics. Considering a misfitting spherical inclusion growing/shrinking in a finite elastic-perfectly plastic medium and recognizing the isolated product/present phase as the inclusion at different stages of transformation, complete solutions to the displacement, stress and strain fields for the purely elastic and elastic-plastic accommodations of the transformation misfit are obtained. Then, analytical expressions for the transformed fraction dependences of the total molar accommodation energy and the mechanical driving force at an interphase are presented and incorporated into the transformation kinetics. The present model is evaluated using the austenite-to-ferrite (γ → α) transformation in pure iron with temperature-dependent material properties. During the elastic-plastic accommodation, the elastic strain energies in the matrix and inclusion are negligible compared to the plastic work in the matrix; and meanwhile, the total strain energy is relaxed to a lower value in contrast to the corresponding purely elastic accommodation. Furthermore, during almost the entire process of transformation, the matrix remains completely plastic. The mechanical driving force varies monotonously with the transformed fraction, which counteracts the transformation at the initial stage but favors the transformation at the later stage. Application of the present model in the non-isothermal γ → α transformation of pure iron conducted with a cooling rate of 10 K min−1 is performed, and the effect of the misfit accommodation on the metastable equilibrium temperature is demonstrated. As compared with the chemical driving force, the mechanical driving force is much smaller but has a significant effect on the transformation kinetics.