Shielding of a crack tip by its nearby dislocations in cubic piezoelectric crystals

An exact and closed-form solution is obtained for a screw dislocation near a semi-infinite crack in cubic piezoelectric crystals. The solution is expressed explicitly in terms of two complex functions which contain three major sources: (a) the electromechanical field associated with the isolated dislocation, (b) the attendant fields generated by the “image” singularities of the dislocation, and (c) the interaction between the crack and the dislocation. The shielding or anti-shielding contribution from the dislocation to the electromechanical $$K$$ -field of the crack tip is quantitatively assessed. The theoretical findings are discussed and graphically illustrated.