Numerical investigation of crack propagation direction in ferroelectric actuators

The functionality of smart structures and microelectromechanical systems, such as ferroelectric multilayer actuators (MLA), macro-fiber composites, etc., can be essentially influenced by crack formation. In the current research possible cracking patterns in PZT MLAs are numerically modeled by finite element method (FEM). Fully coupled electro-mechanical FE analysis is used to investigate the MLA behavior during poling process and under subsequent in-service electromechanical loading. Ferroelectric user elements are developed for commercial software ABAQUS to mimic micromechanical non-linear bulk material behavior. They allow to simulate realistically the poling process of ferroelectric ceramics as a result of tetragonal domain switching. It is known from the experiments, that cracks mainly originate from an electrode tip and then propagate along the electrode interface. There are as well oblique cracks and cross-cracks observed in MLAs. In many cases the type and direction of emerging cracks depend on cofired, non-cofired or partially cofired model of boundary conditions. Initially, the direction of maximum tangential stresses is studied at different positions along the electrode plane. Then electromechanical cohesive elements (EMCZE) are inserted between the bulk ferroelectric elements perpendicular to the direction of action of the maximum tangential stresses. Damage in the CZE is accumulated in accordance with the traction-separation law. As a result of the simulations different patterns of crack propagation in MLAs with cofired, non-cofired or partially cofired ceramics layers are found and studied. The numerical results co-incide with the experimental observations and lead to a better understanding of the complicated multi-physics processes taking place in smart structures.