Modeling the fracture behavior of piezoelectric materials using a gradual polarization switching model

Polarization switching experiments conducted on polycrystal piezoelectric materials indicate that the polarization switching is gradual (occurs over a range of applied electrical and mechanical loads). An empirical model that considers the gradual change in the polarization direction is proposed to capture the polarization switching phenomena and apply it to modeling the fracture behavior of piezoelectric materials. Changes in the dielectric constants (measured from a 90° polarization switching experiment) and the polarization direction are used to estimate the amount of domain switching for an applied electric field. To model polarization switching in a generalized state of stresses and electric fields, the applied electric field (during the experiment) is converted to the corresponding value of internal energy density causing polarization switching. Internal energy density is used as the parameter to estimate the amount of domain switching and the resulting gradual change in the polarization direction. The gradual polarization switching model computes changes in the material properties and spontaneous strain contributions (arising from crystal shape change in the switching domains) based on the current polarization direction. A finite element solution procedure that incorporates the gradual polarization switching model is developed and interfaced with ABAQUS. Stress–strain variations obtained from the compression experiments and FEA are compared for PZT-4 (Zr/Ti = 52/48) and PZT-5H (Zr/Ti = 53/47). The C(T) specimen that was used in Mode-I fracture experiments is analyzed with a slit crack assumption. Microscopic observations of the region near the crack tip of a C(T) fracture specimen is used to capture the actual crack geometry generated by the machining process. A finite element model with the actual crack geometry is used to investigate the influence of finite dimensions of the crack cavity on the size of the polarization switching zones in the vicinity of the crack tip and its effects on the opening stress and the stress intensity ahead of the crack tip.