Upper-bound anisotropic yield locus calculations assuming -pencil glide

Abstract

Deformation by -pencil glide has been analyzed by an upper-bound model which combines a least-shear analysis and Piehler's maximum virtual work analysis. The least-shear analysis gives exact solutions if three slip systems are active, while the maximum work analysis provides solutions for the case of four active slip systems. Independent checks are used to determine which solution method is appropriate.Computer calculations using this model have been made to determine; (1) the orientation dependence of the Taylor factor for axisymmetric deformation; (2) the yield loci for textured materials having [100], [110] and [111] sheet metals and rotational symmetry; (3) the isotropic yield locus for randomly oriented materials; and (4) flow stresses along critical loading paths for various assumed textures with rotational symmetry. The latter calculations indicate that anisotropic yield loci of textured bcc metals with rotational symmetry are much better approximated by where R is the strain ratio and Y is the tensile yield strength with an exponent a = 6 rather than with a = 2 as postulated by Hill. It is not known how well upper-bound calculations like these represent actual yielding behavior.