An eigenstrain approach to predict phase transformation and self-accommodation in partially stabilized zirconia

Abstract This work focuses on micromechanical modeling of the tetragonal to monoclinic phase transformation (t–m transformation) in partially stabilized zirconia (PSZ). Tetragonal particles dispersed in a cubic matrix may transform into the monoclinic phase under sufficiently high mechanical loading or if the material is cooled down below a critical temperature. This phase transformation is supposed to be responsible for the so called transformation toughening effect of PSZ. The transformation is usually accompanied by a self-accommodation process, which reduces the occurring eigenstresses in the surrounding matrix. The influences of particle size and geometry, chemical driving force, temperature, surface energy and remote loading on the t–m transformation are estimated by a thermostatic approach. We assume, that transformations occur, once the Gibbs free energy of the transformed equilibrium state is lower than that of the untransformed reference state. To obtain an analytical solution, the microstructure is modeled as an inclusion of rectangular cross section, restrained by an infinite elastic matrix, under plane strain conditions. The developed model for phase transformation captures the well-known size and temperature dependencies. Furthermore, it indicates a significant influence of the particle geometry, that large aspect ratios of the inclusion’s cross section lower the trigger stress for phase transformation.