The elastoplastic transition in channel die compression of fcc crystals

A comprehensive analysis of the elastoplastic transition in fcc crystals in (110) channel die compression is presented. This range of very small crystal deformations and lattice rotations, of order 10−3 or less (typically with only two equally-stressed slip systems significantly active), precedes the 4-fold (or higher) large multiple-slip deformations that have been studied extensively, both experimentally and theoretically. General equations are derived for the strains, rotations, and crystal shearing in the elastoplastic transition, including a predictive equation for the compressive strain at the onset of finite deformation. From crystal elastic properties and experimental stress data for aluminum and copper in various lattice orientations, these very small elastoplastic strains, rotations, and shears are calculated over the range of possible lateral constraint directions. The results are contrasted with experimental and theoretical values of finite shears and lattice rotations in the same initial orientations, and a justification for the disregard of lattice straining in the finite deformation realm is given.