A multi-surface model for ferroelectric ceramics - application to cyclic electric loading with changing maximum amplitude

Abstract

Depending on the maximum amplitude of externally applied cyclic electric fields, ferroelectric ceramics show minor or major hysteresis. The materials also show asymmetric butterfly hysteresis in a prepoled material. Aiming at capturing these behaviour in a phenomenological constitutive model, a multi-surface modelling approach for ferroelectrics is introduced. In this paper, with the note on the motivation for a multi-surface model related to the results of new experimental investigations and also to experimental data reported in the literature, the constitutive relation for a rate dependent multi-surface ferroelectric model is developed. Following this, a brief graphical illustration shows how this model captures the objective phenomena. Consequently, the numerical implementation of the model to capture experimental results is demonstrated. Finally, the performance of this model to represent behaviour of decaying polarisation offset of electrically fatigued specimen is shown.

Keywords:

• Ferroelectrics
• switching
• asymmetric butterfly curves
• coupled problems
• modelling
• experiment

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Financial support by the NRW Graduate School of Energy Efficient Production and Logistics is gratefully acknowledged. Partial financial support was also provided by the German Research Foundation (DFG) within the research unit 1509 ‘Ferroic Functional Materials’ under project P6, which is gratefully acknowledged.