Anti-plane problem of nanocrack with surface piezoelectricity—a finite-form solution

A solution in finite form for the screw dislocation interacting with the nanocrack incorporating surface piezoelectricity under anti-plane loads is developed. By the boundary integration and the Cauchy’s integral formula to convert the problem into a first-order differential equation, the finite-form solution in physical region is established via the mapping technique. At the crack tip, the results from the present solution indicate that the electric displacements and the stresses are finite and the singularities are removed when the surface piezoelectricity is incorporated, which is against those in the classic solution and also different from other reported solutions where the singularities are weakened but non-trivial. The numerical results shows that the stresses, the electric displacements and the dislocation forces are strongly size dependent and their magnitudes reduce with the decrease in crack length, and the results approach to those by the classic solution with an increasing in the crack length.