The Prediction of Plastic Properties of Polycrystalline Aggregates of BCC Metals Deforming by Pencil Glide

The Bishop and Hill-type isostrain analysis for the deformation of BCC crystals by pencil glide has been re-examined. Expressions have been derived for slip-plane orientations and shears for simultaneous slip along four directions. The expressions for shears, in conjunction with expressions for the stress states previously calculated by Piehler and Backofen, permit comparison of external and internal work, which must be equal for the active stress state. Additional relations are introduced which must be satisfied for simultaneous operation of three slip systems. These relations permit a straightforward computational procedure for determining possible stress states, and insure that external and internal work are equal. If for a possible stress state involving activation of three slip directions, the shear stress on the supposedly inactive system is less than the yield stress, that stress state is active.