Institute of Metals Division - Torsional Deformation of Aluminum and Magnesium Single Crystals

The torsional deformation of aluminum and magnesium crystals is investigated, with particular reference to the dependence of proportional limit on crystal orientation. The proportional limit is found to be governed by the average value of the resolved shear stress on the most highly stressed slip systems, but the proportional limit does not strictly obey a critical-resolved-shear-stress law. The behavior of a cylindrical single crystal stressed in tension is well known: plastic flow begins when the resolved shear stress on the most highly stressed slip system reaches a critical value. There is much less understanding of the effect of torsion on such a crystal and on the way in which the critical-resolved-shear-stress law should be applied to torsional deformation. In the present paper particular attention is paid to the dependence of plastic yielding on crystal orientation and lesser attention to the mechanism of flow after yielding has occurred. New work on aluminum and magnesium crystals is presented, and previous results obtained in this laboratory on magnesium1 are re-examined. STRESS DISTRIBUTION The problems involved in torsional deformation of single crystals are due entirely to the complexity of the stress distribution. In tension, if loading conditions are perfect, the shear stress on any particular slip plane is completely uniform over the entire area of that plane. In torsion, on the other hand, the stress on any selected plane in a particular direction varies not only from center to edge of the specimen but also around its perimeter. It is convenient to express the stress at any point in terms of t0, which is the shear stress acting at the surface of a cylindrical specimen on a plane normal to the axis and in a direction tangential to the cylinder. At point P of Fig. 1 this stress acts in the direction of axis 2 and is given by To = 2T/pr3 [1] where T is the applied torque and r the specimen radius. This stress can be resolved on any chosen slip system, and details are given in the Appendix. Let P be the point on the specimen surface where the stress is to be evaluated; P is defined by its angular distance A from an arbitrary reference line through 0 normal to the axis. his line is usually taken as the direction of incidence of the X-ray beam used to determine the crystal orientation.) Then the shear stress t, acting at P in direction Dona plane whose normal is N is given by Ts/TO = sin ? 0, cos ?d sin (?0, - ?) + cos ?, sin ?d sin (?d - ?) [2] where 0, and Od are the angles between N and D, respectively, and the axis, ?0 and ?d are the angles between the projections of N and D, respectively, on the transverse plane and the reference line through 0. By means of Eq. [2], the stress 7, acting in any given slip direction can be computed. In the previous work on magnesium1 only gross slip tangential to the specimen surface was considered, and this