| Summary: | 碩士 === 國立中央大學 === 機械工程學系 === 85 === As for the upper-bound method on the theoretical analysis of
metal forming, the most research interests concentrate on the
kinematically admissible velocity field for a lower upper-
bound solution of energy dissipation. The analysis result
could provide some important reference for the metal
forming process. However, a large gap exists between the
theoretical prediction on deformation behavior and the
experimental results (normally, the metal deformation could
directly affect the mechanical behavior and also the
metallurgical properties of the final product). Therefore, in
this research work, a variational upper-bound (VUB) method
is proposed. It is the method that determines an upper-
bound solution using variational calculus.Specifically, the
upper-bound equation on energy dissipation, expressed in
terms of the rigid/plastic boundary function, is derived as a
functional and can be optimized by using a variational
approach. Consequeotly, in addition to the kinematically
boundary condition, a set of natural boundary conditions (NBCs)
can be derived theoretically and can be applied to approximate
the solution. These NBCs were found to affect the upper-
bound solution of energy dissipation as well as the pattern of
metal deformation significantly. In order to verify the
suitability and applicability of VUB method, the plane strain
problems of tube ironing and tube extrusion are analyzed.
Experimentaltests are designed and carried out to verify the
validity ofthe VUB method. The results show that the
prediction of metal deformation has been greatly improved
while comparing to the conventional upper-bound (CUB) method and
the slipline field theory, although that only 2% - 8%
improvemnet of energy dissipation has been achieved
(comparing with CUB method). Therefore, by applying VUB
method, the effective strain distribution for the deformed
material can be easily accessed. In addition, as for the metal
deformation of tube ironing and tube extrusion, experiments
show that the shear strain distribution on both internal tube
walls exist in opposite directions. This trends cannot be
predicted by applying CUB method and/or slipline field
theory. However, it can be well defined by the current proposed
VUB method.
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