Abstract

Based on the complex variable method and the perturbation technique, Green's functions for the anti-plane problems in an infinite piezoelectric medium with a crack under remote uniform loadings are derived. The analysis is conducted on the electrically unified crack boundary condition with the introduction of the electric crack condition parameter that can describe all the electric crack boundary conditions. The two ideal crack boundary conditions, namely, the electrically impermeable and permeable crack assumptions are obtained as two special cases for the current solution. The explicit expressions of the mechanical and electrical fields produced by a line-force, a line-charge and a screw dislocation are derived and the field intensity factors are calculated. The image forces on the dislocation due to the crack and the remote uniform loadings are computed as functions of dislocation position and material constant combinations. Numerical examples are performed to show how the electric crack condition parameter affects the field intensity factors and the force on the dislocation.

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