Influences of crack-face electric boundary conditions on stress intensity factors of ferroelectric single crystals

Abstract

It is a challenge to determine the crack-tip stress intensity factors (SIFs) of ferroelectrics under large-scale domain switching. An I-integral method has been previously established for an impermeable crack. In order to investigate the influences of crack-face electric boundary conditions on domain switching and the SIFs, this paper develops the I-integral for permeable and conducting cracks to extract the crack-tip SIFs of ferroelectric materials. For all crack-face electric boundary conditions, the I-integral is independent of integration area size, even though the integration area contains domain walls. The phase field model based on the time-dependent Ginzburg-Landau theory combined with the I-integral method is employed to simulate a tensile test of a cracked PbTiO3 single-crystal plate through increasing the tensile stress step by step. The simulations show that the domain evolution process can be divided into three stages by two large-scale polarization reorientations (a local switching and a global switching) for all crack-face electric boundary conditions, including impermeable, permeable and conducting cases. In each stage, almost invariable domain pattern results in a nearly linear variation of the mode-I SIF. The mode-I SIF in the impermeable case is very close or even identical to that in the permeable case but significant larger than that in the conducting case. Except the local switching away from the crack, a local or global switching generally reduces the mode-I SIF obviously. Applied an increasing electric field, the domain evolution process contains two stages separated by a global switching causing a sudden increase of the mode-I SIF for the impermeable case and a sudden fall for the permeable and conducting cases.