A hardening model for anisotropic materials

Abstract

Results from proportionate-loading experiments under plane-stress states illustrate the existence of a field of uniform-hardening potentials for the yield and creep deformation behavior of isotropic, slightly anisotropic, aelotropic and orthotropic polycrystalline materials in the initially strain-free condition. For two different plane-stress states, it is shown that a linear functional relationship holds between the plastic-strain increment ratio and the stress ratio in these materials and that, consequently, the field is adequately modeled by a uniform-hardening anisotropic function that is quadratic in the components of deviatoric stress. Anisotropic plane-stress yield functions are formulated for any stage in the deformation process by combining the uniform-hardening function with the kinematic-hardening rule. The resulting functions, which correspond to rigid translations of initial yield loci according to Ziegler's rule, provide good agreement with experimental observations on a marked Bauschinger effect and an absence of cross hardening.