3-D finite element simulations of indentation on BaTiO3 single crystal using phase-field based constitutive theory

Indentation experiments on BaTiO₃ single crystals have shown domain switching and phase transformation on the indented surface, which have been attributed to normal or circumferential normal stresses. However, the underlying mechanics of indentation-induced phase transformation is not well understood. Though experiments have provided some insights on the phase transformation over the indented surface, but it is very difficult to understand the nature of phase transformation beneath the indenter from these experiments. Thus, the mechanics of indentation-induced phase transformation in BaTiO₃ is still not well understood. Therefore, 3-D finite element (FE) simulations of indentation are performed on [001] poled BaTiO₃ single crystals by employing a phase-field based constitutive model. Results show that compressive normal strain along the indentation direction (${ϵ}_{33}$) must increase beyond a threshold level for tetragonal (T) to orthorhombic (O) or T-to-T phase transformation. Further, if in-plane shear strain (${\gamma }_{12}$) is significant, and in-plane normal strains are identical (${ϵ}_{11}$ = ${ϵ}_{22}$), then T-to-O transformation would occur, otherwise, T-to-T phase transformation takes place. By contrast, T phase transitions to monoclinic (M) phase if ${ϵ}_{33}$ is not compressive enough. It has also been shown that spontaneous strains at a point in the indentation-affected region must reach beyond a threshold level associated with a particular phase for that phase to develop. However, if this condition is unsatisfied, the M phase will develop in the indentation affected zone.