Suitability of yield functions for the approximation of subsequent yield surfaces

Abstract Many consitutive models in the plasticity of metals are based on the existence of a yield function, which is not only used to mark the elastic limit but also as a potential function for the plastic strain rate. The construction of this function therefore deserves the utmost interest. Measurements of the elastic limit show the essential features of how the geometry of the yield function contour lines should change with further straining. Against these typical geometric forms of the yield surface existing proposals for invariant formulations of the yield function taking into account isotropic, kinematic and formative hardening are tested. Even if no evolution equations for the constitutive variables contained in the yield functions are specified, best approximations of measured yield surfaces can be computed by optimisation of a quality function. It can be shown that most of the representations are not even able to describe the experimental results qualitatively. The numeric results show further that the yield function is essentially of grade three in the deviatoric stresses. The evolution of internal variables can be deduced from the approximations of the measurements.

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