Anti-plane Problem of Interaction between Dislocation and Nanoscale Crack

XIAO Wanshen, XI Junping

Abstract

A new method was presented to exactly solve the anti-plane problem of the interaction between a dislocation and nanoscale crack.Firstly，the problem of straight line crack was turned into an orifice plate problem by using conformal mapping method of the complex function. Secondly，the exact solutions of this problem were obtained by Cauchy integral theorem.Then，the stress field and image force with and without surface effect were formulated.The numerical results show that the stress field near crack tip and image force are decreased due to the surface effect when crack size is reduced to the nanometer level. However the influence of the surface effect can be gradually weakened with the increase of the crack length，and the solutions considering the surface effect approach to the classical elastic theory solutions without the surface effect.

 

Keywords: surface effects,  nanoscale crack,  screw dislocations,  stress field,  image force


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References


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