Gotoh’s 1977 Yield Stress Function with Kinematic Hardening for Modeling Strength Differential Yielding of Orthotropic Sheet Metals

Abstract

AbstractWhen a sheet metal is subjected to both tensile and compressive stresses in a forming process, there is a need to formulate a yield stress function that can accurately account for its strength differential effect in anisotropic yielding. The earliest classical approach is to combine Hill’s 1948 quadratic yield stress function with Prager’s kinematic hardening concept. Consistent with the requirement that a polynomial stress function admits only even-order shear stress components for an orthotropic sheet metal, the resulting quadratic yield stress function in plane stress has up to five material parameters for on-axis yielding but only one material parameter for off-axis yielding. The latter feature limits its modeling capabilities in general sheet metal forming simulations. In this paper, we present a user-friendly approach of formulating a non-quadratic yield stress function with tension-compression asymmetry by combining Gotoh’s 1977 quartic yield stress function with kinematic hardening. The new fourth-order yield stress function in plane stress has up to a total of eleven material constants: seven for on-axis yielding and four for off-axis yielding. The nonlinear parameter identification by least-square minimization with positivity and convexity constraints on the yield stress function is detailed for various sheet metals exhibiting strength differential effects. The results show that the new Gotoh-Prager yield stress function has adequate capabilities for modeling both on-axis and off-axis asymmetric yielding of many orthotropic sheet metals investigated over the years.