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Numerical simulation of superplastic forming with pressure control using a membrane finite element method (초소성 재료의 압력제어성형에 관한 박막유한요소해석)
Superplastic sheet forming process undergoes very large tensile elongation of the order of 200 percent and the accompanying large bending deformation, which results in severe geometrical nonlinearity. The analysis of superplastic sheet forming process, therefore, is generally carried out by the finite element method with large deformation. In this paper, the analysis of superplastic sheet forming process, especially free bulging process and constrained bulging process, is studied by the use of the finite element method using a convected coordinate system and a skew boundary condition. The finite element formulation is derived from equilibrium equations by the principle of virtual work of large deformation for incremental analysis. In the formulation, the large inelastic behavior of the superplastic material is described as incompressible, nonlinear, viscous flow. The formulation is then approximated to the finite dimensional space with the use of membrane elements, which results in algebraic linear equations. In addition to the finite element formulation, a pressure cycle control algorithm is combined in the analysis for optimization of the forming time, which deals with the maximization of the strain rate sensitivity, the protection of thickness reduction, the consistency of the desired strain rate and improvement of formability. The developed finite element code is applied to the free bulging process and the constrained bulging process to predict the optimal forming pressure and the pole height with the forming time, the deformed shape with the variation of time, and the distribution of the thickness.