Screw Dislocation Arrays in a Plate

A simple analysis is presented of linear arrays of screw dislocations in a thin plate. A typical case is shown in which a symmetrical array (normal to the central plane) of positive and negative screw dislocations is blocked at both ends under a uniform shear stress. The relationship between number of dislocations, length of the array, applied stress, and thickness of the plate is derived. The number of dislocations increases rapidly as the ends of the array approach the surface. The equivalence of the symmetrical array to a longitudinal shear crack in a plate is also identified.