Phase-field modeling of crack propagation in piezoelectric and ferroelectric materials

This is an accepted manuscript in Journal of the Mechanics and Physics of Solids

Title: Phase-field modeling of crack propagation in piezoelectric and ferroelectric materials with different electromechanical crack conditions

Authors: Amir Abdollahi and Irene Arias, Universitat Politecnica de Catalunya (UPC), Barcelona

Abstract:

We present a family of phase-field models for fracture in piezoelectric and ferroelectric
materials. These models couple a variational formulation of brittle
fracture with, respectively, (1) the linear theory of piezoelectricity, and (2) a
Ginzburg-Landau model of the ferroelectric microstructure to address the full
complexity of the fracture phenomenon in these materials. In these models,
both the cracks and the ferroelectric domain walls are represented in a diffuse
way by phase-fields. The main challenge addressed here is encoding various
electromechanical crack models (introduced as crack-face boundary conditions
in sharp models) into the phase-field framework. The proposed models
are verified through comparisons with the corresponding sharp-crack models.
We also perform two dimensional finite element simulations to demonstrate
the effect of the different crack-face conditions, the electromechanical loading
and the media filling the crack gap on the crack propagation and the
microstructure evolution. Salient features of the results are compared with
experiments.

http://www.sciencedirect.com/science/article/pii/S0022509612001354?v=s5