The interaction between a semi-infinite crack and a screw dislocation under antiplane mechanical and in-plane electrical loading in a linear piezoelectric material is studied in the framework of linear elasticity theory. A straight dislocation with the Burgers vector normal to the isotropic basal plane near a semi-infinite crack tip is considered. In addition to having a discontinuous electric potential across the slip plane, the dislocation is subjected to a line-force and a line-charge at the core. The explicit solution for the model is derived by means of complex variable and conformal mapping methods. The classical 1/r singularity is observed for the stress, electric displacement, and electric field at the crack tip. The force on a screw dislocation due to the existence of a semi-infinite crack subjected to external electromechanical loads is calculated. Also, the effect of the screw dislocation with the line-force and line-charge at the core on the crack-tip fields is observed through the field intensity factors and the crack extension force. [S0021-8936(00)01501-4]
This paper analyzes the static response of a functionally graded spherical shell made of piezoelectric materials. A hollow piezoelectric sphere is polarized in the radial direction. Spherically symmetric problems of piezoelectric spherical shells as sensors or actuators are considered. For the gradient of power-law behavior, closed-form explicit expressions for the electroelastic field are derived. These solutions can serve as benchmarks for functionally graded piezoelectric hollow spheres. For arbitrarily varying gradient, an analytic approach for reducing the problem to a Fredholm integral equation is suggested to obtain the responses of the electroelastic field. Numerical results for a spherical piezoelectric vessel are obtained for special radial nonhomogeneity, and the distribution of the radial and circumferential stresses as well as the response of the electric potential for sensors and actuators are presented graphically under electrical and mechanical stimuli, respectively. Our results indicate that the gradient index strongly affects the stress distribution and electric response. The obtained results are helpful for optimizing the design of hollow spherical piezoelectric transducers.
Previous studies assumed that a crack is either impermeable or permeable, which are actually two limiting cases of a dielectric crack. This paper considers the electroelastic problem of a three-dimensional transversely isotropic piezoelectric material with a penny-shaped dielectric crack perpendicular to the poling axis. Using electric boundary conditions controlled by the boundaries of an opening crack, the electric displacements at the crack surfaces are determined. The Hankel transform technique is employed to reduce the considered problem to dual integral equations. By solving resulting equations, the results are presented for the case of remote uniform loading, and explicit expressions for the electroelastic field at any point in the entire piezoelectric body are given in terms of elementary functions. Moreover, the distribution of asymptotic field around the crack front and field intensity factors are determined. Numerical results for a cracked PZT-5H ceramic are evaluated to examine the influence of the dielectric permittivity of the crack interior on the field intensity factors, indicating that the electric boundary conditions at the crack surfaces play an important role in determining electroelastic field induced by a crack, and that the results are overestimated for an impermeable crack, and underestimated for a permeable crack.
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