Crystallographic Study of Yield Condition of Polycrystalline Metals : (3rd Report, Relation between Slip in Crystals and Yield Condition)

Abstract

In order to reveal the relation between the mathematical yield condition and the number of slip planes or slip directions of a crystal, the yield stress ratio τ/σ of torsion to tension is calculated for several crystals characterized by its numbers of slip planes and slip directions, adopting Sachs model of polycrystalline aggregates. It is shown that the value τ/σ is most affected by the minor number n_m of slip planes and slip directions, and that the value τ/σ becomes smaller with the increase in n_m until it reaches 0.50 corresponding to the crystal in which slip occurs on any plane in any direction. It is also shown that the calculated value τ/σ is equal in fcc and bcc metals. However, in the case of fcc metal, the optional motion of screw dislocation is expected to reduce the value τ/σ slightly.