New expressions and calibration strategies for Karafillis and Boyce (1993) yield criterion

Abstract

New expressions in terms of stress components of the Karafillis and Boyce (1993) yield criterion are derived. First, it is demonstrated that the isotropic version of this criterion is a homogeneous polynomial in J2 and J32, where J2 and J3 are the invariants of the stress deviator. Moreover, it is shown that irrespective of the value of the interpolation parameter, it has the same mathematical expression as Hershey–Hosford isotropic yield criterion. Making use of these results, new expressions of the Karafillis and Boyce (1993) yield function for orthotropic BCC and FCC materials are derived. This enables to demonstrate that Barlat et al. (1991) and Karafillis and Boyce (1993) orthotropic criteria have the same mathematical form. Most importantly, the benefits of using these new expressions of the Karafillis and Boyce (1993) orthotropic yield criterion for the evaluation of the anisotropy coefficients are demonstrated. It is shown that these coefficients can be evaluated by solving simple algebraic systems of equations involving only experimental flow stresses, or alternatively involving only Lankford coefficients for three orientations. This makes the parameterization of an advanced non-quadratic criterion reliable even when the available mechanical test data are limited.