Experimental and theoretical investigations of the forming limit of 5754O aluminum alloy sheet under different combined loading paths

The forming limit experiments of 5754O aluminum alloy under combined loading paths are carried out and the forming limit diagrams made up of strains under four combined loading paths are obtained. The effects of the loading path on the forming limit under four combined loading paths are analyzed. The corresponding stress path is solved for each experimental strain path based on Yld2000-2d yield function and Chaboche hardening law. Then the theoretical FLDs-strain under the above combined loading paths are obtained based on Yld2000-2d yield function and Chaboche hardening law using M-K theory and validated with the experimental results. The effect of the angle of the groove in M-K theory on the prediction of forming limit is analyzed. The forming limit diagrams made up of the first and second principal stresses and forming limit diagrams made up of equivalent plastic strains are obtained from the experimental FLDs-strain under combined loading paths based on Yld2000-2d yield function and Chaboche type hardening model. The calculated FLDs-stress and FLDs-EP from experimental FLDs-strains are compared with the theoretical ones calculated with M-K theory. It is found that the loading path-dependence of FLD-stress and FLD-EP are much less than that of FLD-strain. The final thickness of 5754O aluminum alloy sheet under different loading paths is obtained from the FLD-strain. Then the thickness reduction rate of sheet metal are adopted to construct the forming limit diagram, which is named FLD-tr for abbreviation. It is found that the effect of strain path on FLD-tr is similar to those on FLD-stress and FLD-EP and is much less than that on FLD-strain. Since the thickness reduction rate can be easily obtained from FLD-strain without yield function and hardening model, FLD-tr is convenient for engineering application. The forming limits under the combined loading paths where the pre-strains are larger than that obtained in experiments are calculated and analyzed. It is found that, besides FLD-strain, the FLD-stress, FLD-EP and FLD-tr are also affected by loading paths when the pre-strain achieves some value and the reason is analyzed in detail. The prediction of forming limit under such combined loading paths with large pre-strains is discussed.