Subcritical Crack Growth in Unpoled and Poled PZT Ceramics under Applied Static and Oscillating Electric Fields. II. Theoretical Analysis Based on the K-V Curve

Abstract

The experimental results of the subcritical crack growth (SCG) of PZT ceramics are analyzed using a power law (Paris law) relationship between the applied stress intensity factor, K, and the crack growth rate, V. A simple model is proposed based on the fact that the K value at the crack tip is contributed from the residual stress of indentation (denoted as K_r) and the applied electric field (denoted as K_v). Good results of curve fitting between the experimental data and model are obtained. It is found that K_v is negative in all cases, which is consistent with some of the theoretical predictions of a negative energy release rate upon crack growth in PZT ceramics. It is suggested that the application of electric field will release the residual stress of indentation and lead to a SCG behavior in PZT, even though it has a shielding effect on the crack growth. Basically, the SCG behavior of PZT can be explained by its dependence on the K_r and K_v value and the slope of the K-V curve can describe the influences of the applied electric field.

Acknowledgment

The authors thank Dr. Susmit Kumar for reviewing the manuscript. Any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Additional information

Funding

This project is supported by National Science Foundation (grant # 1223126).