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.

开发了一种有限形式的解决方案，使螺丝位错在反平面载荷下与结合表面压电的纳米裂纹相互作用。通过边界积分和柯西积分公式将问题转换为一阶微分方程，通过映射技术建立了物理区域的有限形式解。在裂纹尖端，本解决方案的结果表明，当结合了表面压电性时，电位移和应力是有限的，并且去除了奇异点，这与经典解决方案中的相反，并且与其他报道的解决方案不同奇异性减弱但不平凡。数值结果表明，应力