On isotropy and anisotropy in the theory of plasticity

Test results on the plastic behaviour of a range of engineering metals and alloys under proportionate loading are examined in terms of the isotropic hardening rule with homogeneous yield functions of the form $f(J'_2, J'_3)$. It is shown that the inclusion of $J'_3$ accounts for the differences observed between experiment and the Levy-Mises flow rule, that is in the associated constitutive relations, Lode parameter equality and equivalent stress-plastic strain correlations. Non-symmetrical functions account for nonlinear plastic strain paths and the presence of second-order strain under torsional loading. Alternative yield functions are presented where deformation behaviour has been identified with initially anisotropic material. The distinction between isotropic and anisotropic yield functions is clarified by an examination of component plastic strain paths in a tension test. It is shown that anisotropy due to plastic strain can be modelled by combining the rules of isotropic and kinematic hardening. Functions describing the model are consistent with experimental observations in that they display a marked Bauschinger effect and an absence of cross-hardening.