Modeling the Rotation of Orthotropic Axes of Sheet Metals Subjected to Off-Axis Uniaxial Tension

Abstract

A simplified version of a newly developed anisotropic plasticity theory is presented to describe the anisotropic flow behavior of orthotropic polycrystalline sheet metals under uniaxial tension. The theory is formulated in terms of the intrinsic variables of principal stresses and a loading orientation angle and its uniaxial tension version requires a non-quadratic stress exponent and up to five anisotropic material functions of the loading orientation angle to specify a flow condition, a flow rule for plastic strain rates, a flow rule for macroscopic plastic spin, and an evolution law of isotropic hardening. In this investigation, the proper analytical form and the associated parameter identification of the anisotropic material functions defining the flow rule of macroscopic plastic spin are discussed for sheet metals with persistent but rotated orthotropic symmetry axes under off-axis uniaxial tension. It is shown that the proposed flow rule of macroscopic plastic spin can successfully model the experimental data on the rotation of orthotropic symmetry axes in the three sheet metals reported, respectively, by Boehler et al. (Boehler and Koss, 1991, Advances in Continuum Mechanics, O. Bruller et al., eds., Springer, Heidelberg, pp. 143–158; Losilla, Boehler, and Zheng, 2000, Acta Mech. 144, pp. 169–183); Kim and Yin (1997, J. Mech. Phys. Solids 45, pp. 841–851); and Bunge and Nielsen (1997 Int. J. Plasticity 13, pp. 435–446).