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 BaTiO3. 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/BaTiO3 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.