Roman Gellmann

Continuum damage model for ferroelectric materials and its application to multilayer actuators

In this paper a micromechanical continuum damage model for ferroelectric materials is presented. As a constitutive law it is implemented into a finite element (FE) code. The model is based on micromechanical considerations of domain switching and its interaction with microcrack growth and coalescence. A FE analysis of a multilayer actuator is performed, showing the initiation of damage zones at the electrode tips during the poling process. Further, the influence of mechanical pre-stressing on damage evolution and actuating properties is investigated. The results provided in this work give useful information on the damage of advanced piezoelectric devices and their optimization.

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.

An extended model for electrostatic tractions at crack faces in piezoelectrics

Recently, the theoretical framework of fracture mechanics of piezoelectrics has been extended to include electrostatically induced mechanical tractions in crack models yielding a significant crack closure effect.1-3 However, these models are still simple, neglecting e.g. the piezoelectric field coupling. In this work, an extended model for crack surface tractions is presented yielding some interesting effects. In particular, it is predicted that the Mode-I stress intensity factor is influenced by both a collinear normal stress parallel to the crack faces and a Mode-II shear loading. Also, the direction of electric field vs. poling direction is clearly manifested in the calculated crack loading quantities.