Prediction of forming limit curves using an anisotropic yield function with prestrain induced backstress

Abstract

The Forming Limit Diagram (FLD), a plot of the maximum major principal strains that can be sustained by sheet materials prior to the onset of localized necking, is a useful concept for characterizing the formability of sheet metal. Both experimental and numerical results in the literature have shown that the level of the FLD is strongly strain path dependent and the prediction of FLD depends on the shape of the initial yield function and its evolution. In this work, to improve the accuracy of FLD prediction under nonlinear strain paths for a given material, the evolution of the yield function is proposed in terms of the changes of its center and its curvature. The center of the subsequent yield surface after preloading and unloading will be determined via a backstress tensor, and the curvature change will be reflected by changing the exponent in the yield function. Both parameters are functions of the effective plastic strain and will be determined using the forming limit strains obtained from two nonlinear tests. Using this approach, a combination of Marciniak–Kuczynski (M–K) analysis (Marciniak, Z., Kuczynski, K. 1967. Limit strains in the processes of stretch-forming sheet metal. Int. J. Mech. Sci. 9, 609.) and a general anisotropic yield criterion developed by Karafillis and Boyce (Karafillis, A.P., Boyce, M.C. 1993. A general anisotropic yield criterion using bounds and transformation weighting tensor, J. Mech. Phys. Solids, 41, 1859) is used to predict nonlinear FLDs of both Al2008-T4 and Al6111-T4. Excellent agreements were obtained between computed FLDs with the experimental data of Graf and Hosford (Graf, A., Hosford, W.F. 1993a. Calculations of forming limit diagrams for changing strain paths. Metall. Trans. A. 24, 2497; Graf, A., Hosford, W.F. 1993b. Effect of changing strain paths on forming limit diagrams of Al 2008-T4. Metall. Trans. A. 24, 2503; Graf, A., Hosford, W.F. 1994. The influence of strain path changes on forming limit diagrams of Al 6111-T4. Int. J. Mech. Sci. 36, 897). This prediction capability provides a powerful tool in the design and optimization process of 3D sheet metal forming where strain path changes are inevitable.