Superplastic forming is widely accepted as an advanced manufacturing method in the aerospace industry to produce complex components. However, in order to successfully design a superplastic forming process, it is necessary to predict the pressure loading cycle to maintain optimum superplastic conditions during deformation. In this dissertation a three dimensional finite element formulation for the design and analysis of thin sheet superplastic forming is presented. A non-Newtonian viscous model is used to describe the material behavior while principles of shell mechanics are used to model the sheet deformation. The sheet is discretized using a simple 6 noded Kirchhoff shell element which is capable of carrying constant membrane stress and constant moments. Based on the principle of rate of virtual work, the finite element equations have been developed with magnitudes referred to a convective coordinate system. The convective system changes with time and conforms to the shape of the midsurface of the shell. An explicit time stepping scheme is implemented to integrate the motion of the sheet from velocities which are the primary solution variables. The nonlinear equilibrium equations are solved using a Newton-Raphson iterative method. A new pressure prediction scheme, based on the power law constitutive model and membrane kinematic assumptions, has been developed and implemented into the formulation. The contact conditions are imposed by the method of pseudo-equilibrium coupled with a compatibility load step. Simple efficient techniques are employed in determining the occurrence and location of contact. A frictional contact procedure, which introduces the effect of friction through the application of tangential forces at the contact node, is presented. Finally, example problems to demonstrate the applicability of the model to simulate superplastic forming are solved. Simple shapes such as long rectangular pans and cones are superplastically formed and successfully verified with experimental results. The superplastic forming of a realistic industrial component is also presented.
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