Forming limit diagrams of tubular materials by bulge tests

This study uses bulge tests to establish the forming limit diagram (FLD) of tubular material AA6011. A self-designed bulge forming apparatus of fixed bulge length and a hydraulic test machine with axial feeding are used to carry out the bulge tests. Loading paths corresponding to the strain paths with a constant strain ratio at the pole of the bulging tube are determined by FE simulations linked with a self-compiled subroutine and are used to control the internal pressure and axial feeding punch of the test machine. After bulge tests, the major and minor strains of the grids beside the bursting line on the tube surface are measured to construct the forming limit diagram of the tubes. Furthermore, Swiftʹs diffused necking criterion and Hillʹs localized necking criterion associated with Hillʹs non-quadratic yield function are adopted to derive the critical principal strains at the onset of plastic instability. The critical major and minor strains are plotted to construct the forming limit curve (FLC). The effects of the exponent in the Hillʹs non-quadratic yield function and the normal anisotropy of the material on the yield locus and FLC are discussed. Tensile tests are used to determine the anisotropic values in different directions with respect to the tube axis and the K and n values of the flow stress of the tubular material. The analytical FLCs using the n values obtained by tensile tests and bulge tests are compared with the forming limits from the forming limit experiments.