Inhomogeneity of plastic flow in constrained deformation

Crystals of copper, Cu+6 wt pct Al, and Ag+4 wt pct Sn were compressed along [111] with flow restricted to [ (bar 1bar 12) ]. After deformation, four differently oriented regions were observed. Their origin is explained by the instability of the (111)[ (bar 1bar 12) ] orientation which can rotate to either (112) (bar 1bar 11) or (110)[001] during the imposed shape change. The direction of rotation is determined by which of two initially equally favored pairs of slip systems operate. Surface friction produces shear stresses which favor one pair over the other (depending on the sign of the shear stress) and thus one of the final orientations. Since the sign of the frictional stress varies systematically with position in the deforming crystal, a systematic variation of orientation results. Another orientation (001)[110] has also been observed to behave similarly. During rolling, the frictional forces drawing the crystal into the roll gap are also expected to lead to the division of the crystal into two misoriented regions. The predictions are generalized to include bcc metals of ( (bar 1bar 12) )[111] and (110)[001] orientations. Previously reported observations of rolled crystals of FeNi₃, Fe-3.5 pct Si, and Fe-2 pct Al are in accord with the present analysis.