Mechanical analysis for superplastic free bulging based on ellipsoidal surface

The real profile of superplastic free bulging is axisymmetric rotating surface, and therefore the theory of spherical assumption can not reflect the actual superplastic free bulging process. Experimental results show that the shape of superplastic free bulging is ellipsoidal surface. Starting from the fundamental theory of plastic mechanics for continuous media, combined with the geometric equation, mechanical equilibrium equation and the anisotropic incremental theory of Hill, the mechanics analysis for superplastic free bulging process based on the assumption of ellipsoidal surface is accomplished. The self regulation on thickness uniformity is presented. The radial and tangential stress at different positions for free bulging is given, and then the spatial distribution of the stress, strain and strain rate fields is established. The analytical formula of the m value is given by utilizing its definition, and the optimal loading path of the superplastic free bulging is got. Ellipsoidal surface hypothesis is verified by experiment, and elliptic function fits up to more than 0.996.