A phase field model for fatigue fracture in piezoelectric solids: A residual controlled staggered scheme

Abstract

Prediction of the fatigue life of piezoelectric devices and structures is of scientific and engineering significance. In this work, a phase field model for fatigue fracture in piezoelectric materials is developed by means of the Hamilton principle. Two classical phase field fracture models are unified in the present framework. A cumulative history variable is introduced to quantify the degradation of the fracture toughness under cyclic loading. The proposed model accounts for three representative electric boundary conditions on crack faces describing the fatigue fracture behaviors in different physical situations. The residual controlled staggered scheme is extended to address the fatigue fracture problems in the context of electro-elasticity. The present algorithm overcomes the convergence problem for the monolithic approach and shows higher accuracy with lower computational effort in comparison to the single-pass staggered scheme. Systematic numerical simulations are carried out in 2D and 3D cases. The effects of the electric boundary condition, external electric field, and the geometry of the crack tip on the fatigue fracture behaviors of piezoelectric solids have been discussed. The effect of the electric boundary conditions on the fatigue life varies depending on the direction of the external electric field. The present work is beneficial to assess the lifetimes of piezoelectric devices in practical applications.