Prediction of springback in anisotropic sheet metals: The effect of orientation and friction

Abstract

In this paper, springback of anisotropic sheet based on the modified form of the asymmetric non-quadratic yield function (YLD96) for plane stress conditions due to Barlat et al. (Yield function development for aluminium alloy sheets. J Mech Phys Solids 1997; 45: 1727–1763), suitable for describing mixed (isotropic and kinematic) hardening in aluminium alloy sheets under the Bauschinger Effect was compared with the results of tests. Simulation of uniaxial tensile and cyclic tests including both nonlinear isotropic and nonlinear kinematic hardening showed the necessity of including the Bauschinger effect in the constitutive equations at both small and large strains. Following the application to prediction of springback in draw bending of these alloys oriented in the rolling direction, draw-bending tests on AA2024-O and AA7075-O alloy sheets are described. The springback parameters of specimens with axes oriented at 45° and 90° to the rolling direction were measured and compared with prediction based on the modified form of the YLD96, which captured the hardening response at small and large strains when combined with the mixed hardening model, predicting springback in very good agreement with experimental results. The number of components of back stress used in this model depends on the nature of the nonlinear behaviour of the material. For alloys AA2024-O and AA7075-O, excellent agreement with experiments required the use of up to three nonlinear components of back stress. Prediction suggested values of friction consistent with published values and showed that friction inversely affected the radius of sidewall curl, but was not sensitive to lower and upper opening angle. This was consistent with the findings of Carden et al. (Measurement of springback. Int J Mech Sci 2002; 44: 79–101), although those authors also reported that very low friction may increase springback in their proposed draw-bending test. The results confirmed the efficacy of the yield surface model based on YLD96, modified to include nonlinear isotropic and nonlinear kinematic hardening, for predicting deformation subject to the Bauschinger effect.