Multiphase field theory for ferroelastic domain switching with an application to tetragonal zirconia

Abstract

A multiphase field theory and corresponding finite element simulations are developed to describe ferroelastic domain switching in bulk polydomain tetragonal zirconia (t′-zirconia). We consider the ferroelastic switching as mechanical twinning in our model which differs from the Landau-Devinshire theory used in ferroelectric thin films. The approach is advanced in several directions: the thermodynamic potential is developed, introducing interface tension at the domain wall with a multiphase field framework; the ferroelastic features, such as spontaneous strain, coercive stress and hysteresis loop, are explicitly derived from the potential; and a penalizing term in interface energy is introduced to constrain the switching paths between different domains for correctly describing the hysteresis. The phase field model is applied towards prediction of switching rules among three domains of an externally stressed t′-zirconia. Numerical simulations demonstrate fair agreement between phase field solutions and experimental observations that the two sets of domains grow at the expense of the third set upon application of uniaxial compression. The simulations also reproduced a phenomenon that the domain switching occurs and develops inside the colony domain pattern, i.e., the switching rules are dominated by the applied stress tensor and the pre-existing domain patterns of materials. The developed approach can be extended to study the domain switching of any pure ferroelastic material or ferroelectrics subjected to applied stress in the absence of an electric field.