Multi-axial electrical switching of a ferroelectric: theory versus experiment

Samples of the polycrystalline ferroelectric ceramic PZT-SH were poled by applying an electric field at room temperature. Subsequently, an electric field was applied to the samples at a range of angles to the poling direction. The measured non-linear responses in electric displacement are used to construct "yield surfaces" in electric field space corresponding to the onset of ferroelectric switching. The results are compared with predictions from three models: (i) a previous self-consistent polycrystal calculation with rate-independent, non-hardening crystal plasticity; (ii) a simplified crystal plasticity model with viscoplastic (rate-dependent) behaviour and a sufficient number of transformation systems to reproduce the polycrystalline behaviour; (iii) a phenomenological model based on rate-independent Row theory, using kinematic hardening and a quadratic yield surface in electric field and stress space. The experiments suggest that the self-consistent crystal plasticity formulation is most able to reproduce the multi-axial electrical response and yield surface of the polycrystal. The phenomenological model is able to reproduce the uniaxial response accurately, but gives relatively poor performance for multi-axial loading paths, in its present form. A tolerable compromise in multi-axial modelling is the simplified crystal plasticity approach. This is able to reproduce multi-axial constitutive behaviour with reasonable accuracy, whilst offering computational simplicity and speed similar to that of the phenomenological model. (C) 2001 Elsevier Science Ltd. All rights reserved.