A virtual materials testing approach to calibrate anisotropic yield functions for the simulation of earing during deep drawing of aluminium alloy sheet

We present a pragmatic and computationally efficient scheme to combine polycrystal-plasticity models based on crystallographic texture with phenomenological yield functions into a multilevel modelling framework for consideration of the anisotropic materials response during finite-element (FE) simulations of forming operations. Materials tests are conducted virtually using the visco-plastic self-consistent (VPSC) polycrystal-plasticity model to provide the stresses and strain ratios in uniaxial tension, plane-strain tension and under balanced biaxial conditions. These anisotropic materials data are then utilized to calibrate an advanced phenomenological yield function, viz. Yld2011-27p due to Aretz and Barlat, to simulate the anisotropic materials behaviour during subsequent sheet metal forming operations, here, deep-drawing. Since the simulated materials data can be used just as experimental values, no special fitting procedure for the yield function is required and validation of the simulation results is straightforward. Moreover, the followed modelling scheme enables to combine materials data obtained from experimental and virtual tests in a so-called hybrid approach. The modelling scheme was validated by FE-simulations of the earing behaviour of various Al sheet alloys, including AA 1200-O, AA 3104H19, AA 5182-O and AA 5050A-H44, with distinctively different textures. Since earing is almost entirely controlled by crystallographic texture, analysis of the earing behaviour provides for a meaningful but demanding proof-of-principle for the current hierarchical modelling scheme.