A phase-field model for crack growth in electro-mechanically coupled functionally graded piezo ceramics

Abstract

The analysis and design of piezoelectric actuators and sensors require the understanding of their failure due to the coupled electromechanical interactions. We present a phase-field model for damage to capture the brittle fracture associated with piezoelectric ceramics. A homogeneous PZT-4 specimen is used to demonstrate the interaction of various geometric parameters and polarization direction on the growth and arrest of a crack. In addition, the effect of holes and their arrangement on the fracture load is also discussed to assist in topology optimization. It was found that an ordered arrangement of holes could enhance the reliability of these ceramics more than a single hole with a similar amount of material removed. Finally, the functional gradation of material properties is modelled to understand the fracture in a piezoelectric composite containing PZT-4 and BaTiO 3 . The effect of the relative orientation of the material with respect to the polarization direction, on the fracture load is studied to improve the life of such piezoelectric composites. The resistance of fracture is found to be the maximum when the crack propagates into the tougher region of the domain. Whereas, the field enhances the fracture load irrespective of its magnitude when the gradation of material properties for the PZT-4/BaTiO 3 ceramic is along the polarization direction. The aim of the study is to identify the factors that arrest crack propagation by analyzing the coupled system for the better design of piezoelectric sensors and actuators.

A phase-field model for electro-mechanical fracture with an open-source implementation of it using Gridap in Julia

“…For modeling fracture in brittle materials under electro-mechanical loading, Park and Sun [4] proposed that one should consider the fracture process as purely mechanical and use only the mechanical energy as the driving force for crack propagation. Miehe et al [21] and Mohanty et al [24] have computed the same results as Park and Sun [4], implementing their suggestion of considering only the mechanical energy as the driving force for crack propagation in piezoelectric ceramics under electro-mechanical loading. Sridhar and Keip [23] have generated results by considering two cases, namely, total electro-mechanical energy as the driving force and only mechanical energy as the driving force for crack propagation.…”

“…However, piezoelectric ceramics are inherently brittle, and thus fracture analysis of these materials becomes extremely important to ensure their reliability while in use. To understand the fracture mechanism in the piezoelectric ceramics, there are several attempts in the literature both from the experimental [3][4][5][6][7][8][9][10][11] and the theoretical fronts [12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

“…Recently, there is a growing interest to develop phase-field models for simulating brittle fracture under electro-mechanical loading [20][21][22]24,48] and to explore the effect of electro-mechanical coupling on the fracture response. In all the phase-field models, for regularizing the sharp cracks, the length scale parameter has to be chosen sufficiently small and very fine meshing has to be done in the area where crack propagation is expected.…”