Finite strain and springback analysis of forming processes with finite element and experimental verifications

In sheet material forming processes, it is often found that bending and stretching around sharp corners of dies produce undesirable results such as shape deviation, necking or even fracture. Insight into effects associated with the strain distribution and shape deviation is needed to improve modeling of forming processes.; In this thesis, an efficient analytical method is described that simulates sheet metal forming processes under plane strain conditions. Bending and unbending effects are considered in the analysis by using thin shell theory. The bending strain is derived for combined stretching and bending conditions in an explicit form in terms of membrane strain and the ratio of sheet thickness to tool radius. Finite strain distributions with bending effects are obtained by incorporating Hill's non-quadratic yield function and normal anisotropy.; The shape deviation arises from the internal stress re-distribution during unloading. Its springback measures are analyzed under coupled stretching and bending conditions. The springback parameters are derived in terms of membrane strain, edge strain and material parameters. It is determined that large membrane strain restricts the bending strain and springback.; Stretching and deep drawing experiments were conducted to verify the theory. Strain distributions were measured for both stretching and deep drawing using an automated strain measuring system and compared with theory. The springback parameter and curvature were measured for the deep draw forming. It was found that the stretching will largely restrain the springback as long as the stretching force is larger than the yield strength. The shape deviation is more severe with smaller blank holder force, friction coefficient and membrane strain. The finite element simulations were carried out to validate the theory and the experiment. The theoretical predictions correlate well with the experimental data and finite element simulations. This confines the validity and effectiveness of the proposed analytical approach.; An outstanding advantage of the proposed analytical method is its efficiency over other methods such as finite element simulations. For theoretical forming analysis, the analytical method takes less than 1 minute on a low end PC (386SX, 16 MHz), where the same task takes as much as 3000 seconds of CPU on a mainframe UNIX system. Therefore, it is the efficiency as well as effectiveness of the analytical approach that distinguish the analytical method from others as a preferable forming analysis tool.; The thesis concludes that the larger membrane strain results in the smaller bending and unbending contributions. The efficiency and reliability of the proposed analytical method may make such an approach a useful design and control tool for sheet forming processes.