Phase-field model for fatigue crack growth in piezoelectrics: Energetically consistent boundary condition

Piezoelectrics are often subjected to cyclic loads during service, leading to the occurrence of fatigue fracture. Traditional models typically employ the ideal electric boundary conditions to describe the distribution of electric field on crack faces, which may fail to accurately reflect the influence of electric properties on the fatigue life of piezoelectrics. In this work, a phase-field model for fatigue crack growth in piezoelectrics is proposed. By constructing the suitable degradation function, the energetically consistent boundary condition (ECBC) is involved in the present model. The ECBC considers the effect of crack-filled mediums on electric properties, allowing for a more accurate description of electric characteristics on crack faces. Numerical simulations are performed to investigate the effects of the electric boundary condition and external electric field on fatigue behaviors of piezoelectrics. The medium within the crack may significantly affect the fatigue life of piezoelectrics. The higher the relative dielectric constant of the ECBC, the closer the predicted fatigue life is to the situation under electrically permeable boundary condition. The present study may provide theoretical tool for assessing the lifetime of piezoelectrics.