Multiple screw dislocations and a mode III Zener-Stroh crack in a nanowire

We first study an arbitrary number of identical parallel screw dislocations evenly distributed along a concentric circle within a nanowire of radius R. Two equilibrium positions, one stable and the other unstable, co-exist for each screw dislocation. As the number of screw dislocations approaches infinity, each will find a stable equilibrium configuration at a distance 0.7071R from the centerline. Next, we investigate a mode III Zener-Stroh central crack in a nanowire. The crack is simulated by a continuous distribution of screw dislocations which leads to a Cauchy-type singular integral equation whose numerical solution results in the stress intensity factor at the crack tip as well as the Eshelby twist of the rod induced by the imaginary screw dislocations comprising the Zener-Stroh crack. The Eshelby twist will significantly reduce the magnitude of the stress intensity factor at the crack tip.