Abstract
Study of the superplastic bulging of metal sheet has great significance in theory and application. Researchers all over the world have attached great importance to it. The existing analytical theory is far from perfect and the results deduced from it do not describe the real situation very well. In this paper the mechanical analysis of the free bulging of metal sheet is established according to the basic theory of plastic mechanics for continuous media in combination with the viscoplastic constitutive equation and the superplastic constitutive equation with varying m. A differential equation for particle displacements was first obtained; then the analytical formulations of particle displacements which vary with change in the geometric coordinate and the bulging height or bulging time. The mechanical analysis for free bulging was obtained from the results. At the same time, the geometric relation between the bulging contour and particle path was obtained from the viewpoint of quantitative analysis. Comparing the experimental results with the theoretical analysis, we found that the analytical results deduced from the viscoplastic equation agrees with experimental results only within the hemisphere of bulging, and the results deduced from the constitutive equation with varying m agrees with experimental data over the whole process before rupture.
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