Analysis of a family of unstable lattice orientations in (110) channel die compression
The family of f.c.c. crystal orientations defined by loading direction (110) and any channel die constraint direction between \((00\bar 1)\) and \((1\overline{12})\) is kinematically unstable. We establish that the experimentally observed finite rotation of the lattice about the loading axis, for initial orientations in this range, is uniquely predicted by the constraints and critical slip-system inequalities without regard to particular hardening theory. We further establish that experimental information on the changing constraint stress would serve to distinguish among theories. Predictions of three specific hardening rules, including classical Taylor hardening and the ``simple theory'', are illustrated for initial constraint directions \((1\;\bar 1 \overline{16})\) and \((3\overline{37})\). For the first of these orientations the predictions include constraint stress, lattice rotation, active and latent hardening, and overall crystal shearing to a logarithmic compressive strain of 1.0.
scientific article; zbMATH DE number 4024891