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Microstructural Effects on Piezoelectric Cracking
Published online by Cambridge University Press: 15 February 2011
Abstract
The successful development of smart structures using piezoelectric sensors and actuators depends on a thorough characterization of the mechanical limits of these materials. However, fundamental discrepancies between theoretical predictions and empirical observations of their cracking behavior hinder attempts to provide appropriate design guidelines. The complex microstructure of a piezoelectric ceramic leads to severe nonlinear effects at the crack tip, motivating a physics-based investigation of the fracture mechanics. Specifically, the switching and saturation that occur at the level of individual polar domains require a multiscale viewpoint in order to evaluate the conditions which control crack advance. We introduce a model for domain switching based on discrete electric dipoles superimposed on a homogeneous medium with the macroscopic material properties. Each dipole then represents the deviation of a given domain's polarization vector from the linear constitutive law. Within this framework, we develop a relationship between the apparent loads applied to a cracked sample and the local energetic forces driving the crack. Shrinking the length scale down to the crack tip reveals a “singularity conversion”, from the apparent combination of stress and electrical intensity factors to purely mechanical effective opening forces. Using the energy release rate derived from these local stress singularities to predict the dependence of failure load on applied electric field, we are able to reproduce the trends observed in the laboratory.
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- Copyright © Materials Research Society 2000