11 July 2001 Constitutive modeling of repolarization for the ferroelectric process zone of a crack
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Loading of piezoelectric materials leads to high electric fields and mechanical stresses in the near-tip-region of cracks or electrodes. The resulting polarization switching processes can contribute to ferroelectric/ferroelastic crack tip shielding or amplification, equivalent to a change of the fracture toughness. In this paper, we present an approximate constitutive law for repolarization of fully poled materials in load situations where the local poling direction is changed but not the degree of poling. Incremental piezoelectric relations are obtained from a micromechanical switching model. The derivation of the evolution laws for the remanent and material properties and of the tangent moduli resembles plasticity theory: A yield surface is postulated, based on an energy criterion for 90 degree(s) switching of randomly oriented crystallites. The switching barrier corresponds to the yield stress in plasticity. The model is tested on literature data for repolarization of homogeneously poled PZT-samples and in a simulation of the ferroelectric process zone at the tip of a conducting crack or electrode.
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Hannes Kessler, Hannes Kessler, Joerg Drescher, Joerg Drescher, Herbert Balke, Herbert Balke, "Constitutive modeling of repolarization for the ferroelectric process zone of a crack", Proc. SPIE 4333, Smart Structures and Materials 2001: Active Materials: Behavior and Mechanics, (11 July 2001); doi: 10.1117/12.432763; https://doi.org/10.1117/12.432763

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