Analyses of Axisymmetric Sheet Forming Processes by Rigid-Viscoplastic Finite Element Method

Two types of sheet forming processes are analyzed by rigid-viscoplastic FEM (Finite Element Method): axisymmetric punch stretching and hydrostatic bulge forming. The present formulations, based on the membrane theory and the Hill’s anisotropic flow rule, include the rate sensitivity which is a key factor in controlling the forming of superplastic materials. Normal anisotropy is taken into account and Coulomb friction is assumed at the interface between punch and sheet. Nonsteady-state deformation processes, investigated in this study, were quasi-statically and incrementally analyzed. An FEM code was developed, using two-node linear elements with two degrees of freedom at each node, and applied to solve four categories of problems: (1) A.K. steel punch stretching, (2) hydrostatic bulging of a rate-insensitive material, (3) hydrostatic bulging of rate-sensitive materials, and (4) hydrostatic bulging of a superplastic material (Ti-6-4). Strain distributions and shape changes predicted in the first two problems were compared with experiments and results of other analyses. The results of the third problem could not be compared with experiments; however, the results showed that the rate sensitivity affects the deformation as expected. The fourth problem is the main theme of this paper. To maintain the superplasticity in forming processes and to produce sound products, the control of the strain-rate is a key factor. A hydrostatic bulge forming process, which is often used for manufacturing structural aerospace parts, was analyzed and discussed. Further, an optimum pressure curve (pressure versus time), which maintains the desired strain-rate in the deformed material, was obtained and compared with the results of an analytical prediction, available in the literature.