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 e p ¼ 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.

Archives of Metallurgy and Materials

“…Recently, the most popular in the studies of elastic-plastic deformation processes in anisotropic solid, particularly in orthotropic one, is the approach based on the transformed-tensor method summarized by [22]. Such an approach was applied also in [16,17] where the [2,3] hypothesis states that the elastic energy density of distortion and certain part of the energy density of volumetric changes are involved in formulating the measure of material effort. In the paper the authors attempted to show that the application of the mentioned above energy-based approach by [2,3] provides the similar formulation of limit conditions with clear physical interpretation.…”

“…In the papers of [16,17] the experimental data for the commercial Al2008-T4 aluminium alloy sheet of the yield stress directionality measured for uniaxial tensile and uniaxial compression tests were applied for the verification of considered yield criteria, Fig. 4.…”

“…During the optimization process the algorithm fits the function with free parameters to a set of experimental data points by minimizing the sum of the squares of the errors between the experimental data and the function. [16,17] The parameters used to describe experimental observations are reported in Table 1. A good agreement is observed between the Burzyński model and experiments.…”

“…Fig.4. Comparison of the proposed criterion with the experimental data and simulation results taken from[16,17] …”