Abstract
Two criteria of instability are required to predict the failure in rolled sheet metal when bulged by lateral pressure through elliptical dies. The attainment of a pressure maximum is observed when the ratio of the lengths of the ellipse axes approaches unity. In nearly circular bulges this marks the onset of failure by diffuse necking under a falling pressure in the polar region. Dies with sharper elliptical apertures produce plane strain failures under a rising pressure in the region of the rim. In stretching flat sheet a local instability occurs when the rim force attains its maximum. The influence of sheet curvature upon plane strain fracture alters the limiting strain. Predictions of the critical pressure are derived for each failure and applied to an automotive aluminium alloy sheet (Alusuisse AC 120). The theory confirms experiments that show plane strain failure as a cut-off point in the plot of pressure versus height. A maximum pressure marks the start of a failure by diffuse pole thinning. In contrast, edge failures occur with uniform thinning from pole to rim along the minor axis of the ellipsoid bulge. A generalized theoretical approach accounts for each failure with an r variation in the plane of the sheet and orientation of the ellipse axes to the rolling direction. The tests reported refer to alignments between the roll direction and both axes of five elliptical dies with different aspect ratios. Pole failures provide positive forming limit strains for biaxial stress ratios between 0.5 and 1. Rim failures supply the limiting plane strains.
Published Version
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