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Nowadays the forming limit curves is very useful in forming of metal sheets and the effect of yield criteria is one of the most important parameters in prediction of the limit strain especially in anisotropic aluminum sheets. In this paper, first the effects of advanced BBC2008, Soare2008, Plunkett2008 and Yld2011 yield criteria on limit strain calculation and then on forming limit stress diagram will be investigated. Plastic instability model is studied based on Marciniak-Kuczynski model and the non-linear equations are solved by using Newton-Rophson method. These functions are used to evaluate the limit forming predictability of AA2090-T3 aluminum sheet based on the Swift hardening law and is compared with the forming limit curves predicted by Hill’s 1948 classic yield criterion. It was observed that the classic yield functions is not appropriate for anisotropic aluminum sheets forming estimation. Numerical results obtained from the forming limit diagram for AA5754 with Plunkett2008 yield function and Swift hardening law, although the experimental results confirm at close range to plane strain case, but CPB06ex2 yield criterion to predict the behavior of anisotropic aluminum sheets. The limit strain prediction for AA3104-H19 by using Yld2011 yield criterion and Voce hardening law show better conformity with experimental results.

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In the new sheet metal forming process as incremental sheet forming and spinning forming, this is not perfectly true in Marciniak-Kuczyinski model to assume that sheet deformation occurs in the plane-stress state indispose there are normal compressive stress and through-thickness stress. In this type of forming processes, the obtained limit strains refer to improving the sheet forming. However, in researches the effects of through-thickness shear stresses, also known as out-of-plane shear, has been studied less. The generalized forming limit diagram is a great curve that includes all six components of the stress tensor. In this paper, the effect of normal comprehensive and through-thickness shear stresses on the limit strain AA6011 aluminum sheet using a modified M-K and the anisotropic Yield function, Hill 48 and by using numerical solutions of nonlinear equations, Newton-Raphson method. The first the forming limit diagram was drawn with the assumption that the through-thickness shear stresses and then the effects of normal comprehensive stress and through-thickness shear stress on the limit strains were proved and the generalized forming limit curves were obtained. The results show that forming limits can be increased significantly by both normal compressive stress and through-thickness shear stresses. Also, the effects of normal stress on increasing the formability of sheet compared with the effects of through-thickness shear stress is greater.