Experimental validation of non-associated flow rule and hydraulic bulge forming simulation for a 6000 series aluminum alloy sheet

Abstract

Biaxial tensile tests of a 6000 series aluminum alloy sheet were performed using cruciform specimens and tubular specimens fabricated by bending and welding sheet samples. The contours of plastic work and the direction of the plastic strain rate were measured along nine linear stress paths. The test sample exhibited differential hardening because the shape of the work contours gradually changed with increased plastic strain. The direction of the plastic strain rate measured for every stress path was almost constant regardless of the amount of plastic strain and coincided with the direction normal to the work contour associated with a 0.2% plastic strain. Based on these observations, two material models were developed. One was an associated flow rule (AFR) model, in which the material is assumed to follow the AFR with respect to the measured work contours with differential hardening. The other was a non-associated flow rule (NAFR) model, in which the yield function was determined as approximating the work contours with differential hardening and the plastic potential function was chosen to be the work contour associated with a 0.2% plastic strain. A hydraulic bulge forming experiment and simulations with finite element AFR and NAFR models were performed to check the effect of the material models on the accuracy of the forming simulation. The thickness strain at the apex of the test piece $-$ internal pressure curve and thickness strain $-$ initial radial coordinate curve were measured and compared with the finite element simulation results based on both material models. The results revealed that the predictive accuracy of the NAFR model is superior to that of the AFR model for the aluminum alloy sheet used in this study.