A Single Crystal Beam Bent in Double Slip

A theory of plastic bending of single crystal beam with two active slip systems accounting for continuously distributed excess dislocations is proposed. If the resistance to dislocation motion is negligibly small, then excess dislocations pile up against the beam’s neutral line, leaving two small layers near the lateral faces dislocation-free. The threshold value at the onset of plastic yielding, the dislocation density, as well as the moment-curvature curve are found. If the energy dissipation is taken into account, excess dislocations at the beginning of plastic yielding occupy two thin layers, leaving the zone near the middle line as well as two layers near the beam’s lateral faces dislocation-free. The threshold bending moment at the dislocation nucleation and the hardening rate are higher than those in the case of zero dissipation.