Lateral constraints in plane strain compression of single crystals

In plane strain compression tests where the walls of a channel suppress lateral flow, the lateral stress developed at the walls varies with the crystal orientation. We have applied a crystal plasticity analysis to calculate the ratio of lateral stress (σ_yy) to the compression stress (σ_xx) for fcc crystals compressed on the (110) plane and extended in various directions in (110). It was found that σ_yy/σ_xx is equal to zero from (110)[001] to ((110)[bar 112]) , at which point it rises discontinuously to a value of 1.5. It then decreases to a value of 1.0 for ((110)[bar 111]) and further to 0.5 for ((110)[bar 110]) . Tests on copper crystals generally confirmed the theoretical predictions. Deviations can be explained in a consistent way by recognizing the inability of the experimental apparatus to suppress small amounts of lateral flow.