Modeling Approaches to Predict Damage Evolution and Life Time of Brittle Ferroelectrics

Reliability and life time of smart materials are crucial features for the development and design of actuator and sensor devices. Being widely used and exhibiting brittle failure characteristics, ceramic ferroelectrics are of particular interest in this field. Due to manifold interactions of the complex nonlinear constitutive behavior on the one hand and the damage evolution in terms of microcrack growth on the other, modeling and simulation are inevitable to investigate influence parameters on strength, reliability and life time. Two approaches are presented, both based on the same constitutive law and damage model. The one is going along with a discretisation scheme exploiting the finite element method (FEM). The so-called condensed approach, on the other hand, considers just one characteristic point in the material, nonetheless accounting for polycrystalline grain interactions. The focus of the simulations is two-fold. Life-time predictions in terms of high cycle fatigue under electromechanical loading conditions are presented based on the condensed approach. Second, the formation of macroscopic cracks at electrode tips in a stack actuator is investigated applying the FEM.