A modified Burzynski criterion for anisotropic pressure-dependent materials

Abstract

In this paper the Burzynski criterion, which was introduced for isotropic pressure-dependent materials, is modified for anisotropic pressure-dependent materials in plane-stress condition. The modified criterion can be calibrated with 10 experimental data points such as tensile stress at 0°, 45° and 90°, compressive stress at 0° and 90° and R-values in tensile stress at 0°, 45° and 90° from rolling direction and also biaxial tensile stress and tensile R-value. To identify the anisotropic parameters an error function is set up through comparison of the predicted yield stresses and R-values with those from experiments. Then the Downhill simplex method is applied to solve 10 high-nonlinearity equations. Finally, considering Al 2008-T4 (BCC), Al 2090-T3 (FCC), AZ31 (HCP) and also Mg–0.5% Th alloy, Mg–4% Li alloy, pure textured magnesium, textured magnesium and Ti–4Al–1/4O 2, which are HCP materials with \( \bar{\varepsilon }^{p} = 1\% ,5\% ,10\% \) as case studies and comparing the results for the modified Burzynski criterion with experiments, it is shown that the Burzynski criterion is appropriate for pressure-dependent anisotropic materials with proper accuracy.