The plastic deformation of bicrystals under mixed deformation by plane-constrained uniaxial tension and shear was investigated, within continuum dislocation theory, with regard to the nucleation of dislocations and dislocation pile-ups near to the phase boundaries of a model bicrystal having one active slip system within each single crystal. For plane uniaxial tension, a closed-form analytical solution was presented for the evolution of the plastic distortion and of the dislocation network in the case of symmetrical slip planes (twins), which exhibited an energetic as well as a dissipative threshold for dislocation nucleation. The general solution for non-symmetrical slip systems was obtained numerically. For combined deformation in tension and shear, the possibility was analyzed of linearly superposing results obtained for each loading mode independently. All of the solutions also exhibited the Bauschinger effect of translational work hardening, and the size-effect which was typical in problems of crystal plasticity.

Dislocation Pile-Ups in Bicrystals within Continuum Dislocation Theory. D.M.Kochmann, K.C.Le: International Journal of Plasticity, 2008, 24[11], 2125-47