Finite element analysis of superplastic metal forming processes

Abstract

The commercial development of superplastic materials has provided opportunities for producing complex components using new forming techniques. The available analyses are restricted to specific shapes and other simplified assumptions. There is a great need for a generalized analytical technique which will be independent of material characteristics and geometry, and also flexible enough to accommodate more rigor in the analyses. Finite element displacement method has been used in this research to meet such a strong industrial need. The finite element method involves finite deformations with large rotations of material particles, contact conditions with or without frictional effects, and non-conservative pressure loadings. The contact problem is solved using a new method which is very attractive to metal forming problems. The algorithm imposes geometric constraints on the pseudo equilibrium configuration, defined as a configuration at which the compatibility conditions are violated. The frictional conditions of sticking, slipping, rolling or tension release are determined from the relative magnitudes of the normal and tangential global nodal forces. For problems involving superplastic materials, a finite element equation has been developed based on the principle of virtual work, and is solved using an updated Lagrangian method with velocity as the primary solution variable. Since the sheet metal forming processes feature finite strain accompanied by considerable spin of the principal axes, a rotation-invariant rate of deformation tensor is used in the constitutive equation. The incompressibility condition is imposed through the use of a penalty parameter with integration on the appropriate integrals. The non-conservative pressure loading is evaluated by continually updating the load bearing surface within each load step. Example problems to demonstrate the applicability of the contact algorithm to a range of boundary value problems for a variety of material models, have been solved. A typical superplastic sheet metal forming, involving the pressure forming of a rectangular pan is solved. The research provides a finite element method of solution to the analyses of materially- and geometrically-nonlinear forming problems with contact and friction between the components. The method can be eventually integrated with a CAD/CAM environment as an effective design and analysis tool.