A general, flexible and analytical yield criterion framework developed from a novel strategy: Gradual surface-distortion

Abstract

Yield criterion with concise parameters and high accuracy has always been recommended for industrial applications. Based on a novel modeling strategy of gradual surface-distortion (GSD), an analytical yield criterion framework is constructed under the associated flow rule, integrating simplicity, generality and flexibility. Derived from structures of SY2009 criterion, R-value and curvature control terms with independent parameter calibration are developed, resulting in yield surface distortion occurring gradually. Three curvature variables are integrated into a single factor through empirical formulas without additional pure shear and plane strain tension experiments. This framework is an eighth-order homogeneous polynomial, with all parameters uniquely determined through a set of mechanical tests conducted under plane stress conditions. Initially, a simplified GSD version is constructed to characterize yield loci of BCC and FCC materials, requiring a minimum of only seven experimental data ($T_0$, $T_{45}$, $T_{90}$, $T_{\mathrm{EB}}$, $r_0$, $r_{45}$, $r_{90}$). Subsequently, by introducing stresses and R-values in two optional directions, an extended GSD version is proposed to enhance strong anisotropy description. The generality and accuracy of this framework are validated across 19 different materials to predict yield locus, uniaxial stress and R-value curves. The results demonstrate that the simplified model almost replicates Yld2000–2d and enables accurate prediction in the evolution of yield locus under anisotropic hardening. For strongly anisotropic materials, the extended model exhibits high prediction accuracy. By using an implicit finite element method, this framework accurately predicts the earing profile in cup drawing of AA3104-H19. Besides, the convexity trust-domain and the generality of curvature variables are discussed.