Numerical studies of nonuniform deformation, stress state evolution, and subgrain formation in bicrystals in (110) channel die compression

An elastoplastic numerical model for f.c.c. bicrystals in (110) channel die compression is investigated to a logarithmic strain of 10% and compared with the analytical rigid-plastic solution at the yield point. Three lattice orientations of an aluminum bicrystal are calculated between constraint directions [00 1 ̄ ] and [1 1 ̄ 2 ̄ ] . It is found that the elastoplastic results for each of stress state, velocity field and lattice-rotation rate (indicating subgrain formation) pass very close to the analytical solution at 0.2% strain for two of the orientations. This is in spite of small tangential velocity discontinuities along characteristic directions of that solution which are not permitted in the numerical (finite element) modeling. The results are never as close in the third orientation, for which there are much greater tangential velocity discontinuities in the rigid-plastic model. It is suggested that the elastoplastic comparisons with the rigid-plastic model may provide insight into realistic strain levels at the beginning of fully plastic response. However, it also is concluded that a deeper analytical representation of the tangential velocity discontinuities is needed.