New mathematical results and explicit expressions in terms of the stress components of Barlat et al. (1991) orthotropic yield criterion

Abstract

In this paper are provided new mathematical results and equivalent expressions of the orthotropic yield criterion of Barlat et al. (1991) for body-centered cubic (BCC) and face-centered cubic (FCC) materials, respectively. Specifically, it is shown that this criterion is expressible as a simple polynomial in terms of the Cauchy stress components. Using these new explicit expressions, it becomes possible to establish new correlations between the anisotropy coefficients and mechanical properties. It is shown that the anisotropy coefficients involved in Barlat et al. (1991) are expressible solely in terms of uniaxial yield stresses, or alternatively only in terms of Lankford coefficients, and can be easily determined by solving simple algebraic systems of equations. Illustrative examples are presented for textured steel and aluminum alloys.