A Variational Upper-Bound Method - Its Application and Experimental Verification for Plane strain Problems

• Main Authors: Yang, Yeon-Sheng, 楊永盛
• Other Authors: Yeh, Wei-Ching, Lee, Sheng-Long
• Format: Others
• Language: zh-TW
• Published: 1997
• Online Access: http://ndltd.ncl.edu.tw/handle/32084006910971564725

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.