Channel die compression revisited: Application of a set of basic crystal hardening inequalities to (1 1 0) loading

A rigorous analytical investigation of (1 1 0) compression of fcc crystals in a channel die is carried-out for all lattice orientations between lateral constraint directions (channel-wall normals) (001¯) and (11¯2¯). It is proved that a set of basic slip-system hardening inequalities, that are consistent with experiments on fcc crystals in high symmetry, multiple-slip orientations in tension [Havner, K.S., 2005. On lattice and material-frame rotations and crystal hardening in high-symmetry axial loading. Philos. Mag. 85 (25), 2861–2894.], uniquely predict load-axis stability in (1 1 0) channel die compression, with lattice rotation and finite shearing about the loading direction as found experimentally for this range of orientations. It also is established from the inequalities that the evolving lateral constraint stress will be less than that predicted by classic (isotropic) Taylor hardening.