Phase-field fracture modeling of piezoelectric solids with a novel crack driving force incorporating an intrinsic material parameter

Fracture failure is an essential concern on the design, manufacture and utilization of piezoelectric functional materials. Both traditional piezoelectric ceramics and new flexible piezoelectric materials demand objective modeling of fracture under the coupled action of electric and mechanical fields. Currently, the widely developed electromechanical fracture phase-field model (EM-PFM), which employs the mechanical energy release rate as the crack driving force, cannot sensibly predict some of the classical experimental reports. In this work, the necessity of the mechanical energy release rate as the fracture criterion is revised based on a semi-analytical demonstration on the EM-PFM, and a new crack driving force formulation is proposed. More specifically, the new crack driving force consists of the mechanical energy release rate contributed from the effective stress and a part of the electro-mechanical coupled energy release rate, where the transformation rate of the latter is controlled by an intrinsic material parameter. The proposed EM-PFM is numerically implemented in a multi-field finite element framework in the commercial software ABAQUS via a user element subroutine. A representative one-dimensional ideal numerical test demonstrates the rationality of the present model. Most importantly, for the first time, we achieved numerical reproduction of Park and Sun’s classical experiments in the EM-PFM without changing any piezoelectric coefficients. The present work contributes to a better understanding of piezoelectric materials and is beneficial in predicting the fracture of piezoelectric materials realistically.