Interface crack between two interface deformable piezoelectric layers |
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Authors: | Pizhong Qiao Fangliang Chen |
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Affiliation: | (1) Department of Civil and Environmental Engineering, Washington State University, Pullman, WA 99164-2910, USA;(2) Department of Engineering Mechanics, College of Civil Engineering, Hohai University, Nanjing, Jiangsu, 210098, People’s Republic of China |
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Abstract: | Based on an interface deformable piezoelectric bi-layer beam model, a bonded piezoelectric bi-material beam with an interface
crack perpendicular to the poling axis is analyzed within the framework of the theory of linear piezoelectricity. The layer-wise
approximations of both the elastic displacements and electric potential are employed, and each sub-layer is modeled as a single
linearly elastic Timoshenko beam perfectly bonded together through a deformable interface. Using the impermeable crack assumption,
the closed form solutions for the energy release rate (ERR) and crack energy density (CED) are derived for the layered piezoelectric
beam subjected to combined uniformly distributed electromechanical loading. Based on superposition principle, both the ERR
and CED and their components are all reduced to the functions of the crack tip loading parameters. Loading dependence of the
total CED with respect to the applied electric field is manifested with the analytical results, showing that there is a transformation
from an even dependence to an odd dependence for the normalized CED when the applied mechanical loading increases. Compared
with the commonly used equivalent single layer model, the proposed analysis augments the crack driving force by alleviating
the stress concentration along the interface and thus increases the loading parameters at the crack tip. The proposed model
provides improved solutions for fracture analysis of piezoelectric layered structures and sheds light on the loading dependence
of the fracture parameters (i.e., the ERR and CED) with respect to the applied electromechanical loadings. |
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Keywords: | Piezoelectric material Interface deformable bi-layer beam theory Piezoelectric layered structures Interface fracture Energy release rate (ERR) Crack energy density (CED) Electromechanical loading Loading dependence |
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