Anisotropic plasticity model forms for extruded Al 7079: Part I, calibration

The choice of model form used to represent the anisotropic yield response of metals can depend strongly on the type and amount of data available for calibration. This two-part contribution considers the calibration (part I) of three yield functions: von Mises, Hill-48 and Yld2004-18p by Barlat and co-workers. This is followed by model verification exercises (part II). The material used was a 7079 aluminum alloy extruded tube. The calibration data were measurements of yield stress and Lankford ratio from uniaxial tension specimens cut along 12 orientations. Given that the tube was relatively thick-walled, some of the orientations included through-thickness components. This allowed the calibrations to be based exclusively on test data, without the need for parameter assumptions or supplemental crystal plasticity calculations. The Yld2004-18p function provided the best fit to the data available due to its 18 anisotropy parameters plus an unspecified exponent, compared to the quadratic Hill function with 6 anisotropy parameters and to the isotropic von Mises function. Whereas the Yld2004-18p function did not warrant further exploration due to the excellent fit it provided, the results showed that care must be taken when using Hill’s function. Finally, due to its parametrization with only 6 anisotropy parameters, it can significantly misrepresent the yield behavior depending on the calibration data used, possibly rendering it less desirable than a simple isotropic function in some applications.