The bending of a strip in plane strain was analyzed by using discrete dislocation plasticity, where the dislocations were modelled as line defects in a linear elastic medium. At each stage of loading, superposition was used to represent the solution in terms of the infinite medium solution for discrete dislocations. A complementary solution, which was non-singular and was obtained from a linear-elastic finite-element solution, enforced the boundary conditions. The lattice resistance to dislocation motion, dislocation nucleation and dislocation annihilation were incorporated via a set of constitutive rules. Solutions were presented for cases with multiple slip systems and with a single slip system. A relationship for bending moment versus rotation, and the evolution of the dislocation structure, were outcomes of the boundary value solution. The effects of slip geometry, obstacles to dislocation motion and specimen size upon the moment versus rotation response were considered. The evolution of the dislocation structure was studied, with emphasis being placed on the role of geometrically necessary dislocations. The dislocation structure which developed led to well-defined slip bands, with the slip-band spacing scaling with the specimen height.

A Discrete Dislocation Analysis of Bending. H.H.M.Cleveringa, E.Van der Giessen, A.Needleman: International Journal of Plasticity, 1999, 15[8], 837-68