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Fracture mechanical investigations of piezoelectric materials as components of smart structures have become popular in the last 30 years. In the early years of research, boundary conditions at crack faces have been adopted from pure mechanical systems under the assumption that boundaries were traction free. From the electrostatic point of view, cracks have been assumed to be either free of charge or fully permeable. Later, limitedly permeable crack boundary conditions have become popular among the community, nevertheless still assuming traction-free crack faces. Recently, the theoretical framework has been extended to include electrostatically induced mechanical tractions in crack models yielding a significant crack closure effect. However, these models are still simple, neglecting, e.g., the piezoelectric field coupling. In this work, we present an extended model for crack surface tractions yielding some interesting effects. In particular, the orientation of the electrical field with respect to the poling axis becomes important. Furthermore, applying a collinear stress parallel to the crack faces influences the Mode-I stress intensity factor and a Mode-II shear loading couples to the Mode-I SIF.

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.

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In this work we study contributions to the effective fracture toughness of ferroelectric materials arising from effects on macroscopic and mesoscopic scales of the system. On the macroscopic scale, the crack in a ferroelectric material is modeled taking into account an extended theory of stresses at interfaces in dielectric solids [1‐3]. We predict several new effects, such as the “poling effect”, “collinear effect” and the coupling of a Mode‐II shear loading and the Mode‐I SIF. Further, on the mesoscopic scale, we study the influence of polarization switching limited to the fracture process zone (small scale switching) on the fracture toughness. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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In this paper we present two subjects of our actual research in the field. The first deals with the boundary conditions at the crack faces. The well known model by Hao and Shen gives opportunity to take the finite dielectric permeability of the crack into account, without having to solve the two-or three-dimensional coupled boundary value problem of solid material and crack medium. This approach, however, is based on the assumption of the electric field being perpendicular to the crack faces. We investigate this problem for arbitrary poling and field directions based on a combined analytical-numerical approach. The second focus of the paper is on the effective properties of piezoelectrics with cracks. Here, homogenization procedures are applied and extended towards coupled field problems including e.g. Maxwell stresses at internal boundaries and interfaces. Effective elastic, dielectric and piezoelectric constants exhibit interesting effects.