Under the action of applied electromechanical loadings, the electroelastic analysis of a cracked piezoelectric material has been made within the framework of the theory of linear piezoelectricity. The associated mixed boundary-value problems are different from those studied previously. The electric boundary conditions are governed by the CODs. By using the Fourier and Hankel transforms to solve the electroelasticity problems related to a crack of finite length and a penny-shaped crack, respectively, a full electroelastic field is deter- mined explicitly. In particular, the asymptotic electroelastic field near the crack front are derived, and the field intensity factors are given. The dependence of field intensity factors on applied electric field for various dielectric permittivities is displayed graphically. Fur- thermore, similar to the strain intensity factor, the COD intensity factor can be used as a suitable fracture criterion of a cracked piezoelectric material. Based on this criterion, the results indicate that applied positive electric fields decrease fracture toughness and negative ones increase fracture toughness for prescribed remote stress. In contrast, applied positive electric fields increase fracture toughness and negative ones decrease fracture toughness for prescribed remote strain or displacement. Therefore, far-field mechanical boundary con- ditions play a crucial role in studying the stability of a crack embedded in a piezoelectric ceramic, which might account for conflicting experimental observations.
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Editor: Peter L. Reece, pp. 113-157 © 2006 Nova Science Publishers, Inc.
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