@article{yu_havner_2001, title={Numerical studies of nonuniform deformation, stress state evolution, and subgrain formation in bicrystals in (110) channel die compression}, volume={49}, ISSN={["1873-4782"]}, DOI={10.1016/s0022-5096(00)00021-1}, abstractNote={Abstract 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.}, number={1}, journal={JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS}, author={Yu, PG and Havner, KS}, year={2001}, month={Jan}, pages={173–208} }
 @article{havner_yu_1998, title={On the stress state at the yield point in symmetric bicrystals in (110) channel die compression}, volume={27}, ISSN={["0167-6636"]}, DOI={10.1016/S0167-6636(97)00049-5}, abstractNote={The stress state at the yield point in symmetric fcc bicrystals is analytically investigated for a range of crystal lattice orientations in (110) channel die compression. Although strain-rates and lattice-rotation rates necessarily are nonuniform, it is proved that the stress field satisfying both equilibrium and yield-locus constraints must lie on an edge of the locus and is thereby uniform.}, number={4}, journal={MECHANICS OF MATERIALS}, author={Havner, KS and Yu, PG}, year={1998}, month={Apr}, pages={211–227} }