Toward the use of small size bulge tests: Numerical and experimental study at small bulge diameter to sheet thickness ratios

For calibrating sheet metal hardening and anisotmpic constitutive models, the bulge test has proven to be an invaluable tool. In recent studies, the analysis of the test has been considerably improved by using Digital Image Correlation. Despite the progress achieved in the analysis of the measured data, based on membrane hypotheses it is still necessary to use large bulge diameter to sheet thickness ratios of more than 100 in order to ensure the validity of the standard equations. In order to overcome this constraint, a numerical study of a wide range of specimen material behaviors and various bulge geometries is performed. The numerical results obtained are used to draw up new estimates for the bending strain, the radii of curvature and the average bulge stress. The numerical and experimental data show that the inner and the outer radii of curvature do not share the same center. This means that the difference between outer and inner radii of curvature is not equal to the thickness of the apex. The accuracy of the approach presented here is assessed on the basis of numerical simulations and experiments. Numerical simulations involve six different types of Swift and Voce behavior. Experimental validation is performed from original bending and curvature measurements on aluminum and steel bulges. Lastly, a hardening law identification algorithm is presented and compared with experimental results obtained for bulge diameters as small as 50 mm and bulge size ratios ranging from 42 to 150.

Automated summary

The bulge test is a vital tool for calibrating sheet metal hardening and anisotropic constitutive models, and has been significantly improved through the use of Digital Image Correlation in recent studies. A numerical study covering a wide range of specimen material behaviors and bulge geometries was conducted to overcome the need for large bulge diameter to sheet thickness ratios.