Modeling of Fracture in Ferroelastic Ceramics

Ferroelectric ceramics are used in applications ranging from actuators and sensors to ultrasonic motors. A significant shortcoming of these materials in structural applications is their inherent brittleness. Specifically, most ferroelectrics have fracture toughness levels on the order of KIc MPa m = 1 . The characteristic of ferroelectric ceramics that makes them useful as smart materials is their ability to deform and change polarization irreversibly by the mechanism of domain switching. In a manner akin to transformation toughening, domain switching leads to R-curve behavior and toughness enhancement during crack growth in ferroelectrics. Hence, an understanding of the dissipation due to domain switching and the fracture mechanics governing these materials is crucial for the efficient design of ferroelectric devices. As an initial investigation, this chapter will focus on fracture in unpoled ferroelectric ceramics under mechanical loading. Note that in the absence of electrical loading, unpoled ferroelectrics remain unpoled. Hence, unpoled ferroelectrics loaded mechanically exhibit purely ferroelastic response; i.e. irreversible straining as a result of applied stress. Experimental investigations on unpoled ferroelectric ceramics by Meschke et al. (2000) and Oates et al. (2003) have found toughness enhancements in the range of ∆KIc = − 40 100% of the initiation toughness, which corresponds to ∆G c = − 100 300%. Here ∆KIc represents the difference in the steady state and initiation levels of fracture toughness during crack propagation. Generally, this toughness enhancement has been attributed to ferroelastic domain switching near the crack tip. A number of theoretical investigations of switch toughening have been carried out (Zhu and Yang (1997), Yang and Zhu (1998), Reece and Guiu (2002), and Kreher