Analytical Modeling of Axi-Symmetric Sheet Metal Forming

The cup drawing is a basic deep drawing process. Thus, understanding the mechanics ofthe cup drawing process helps in determining the general parameters that affect the deep drawingprocess. There are mainly two methods of analysis; experimental and analytical/numerical.Experimental analysis can be useful in analyzing the process to determine the process parameters thatproduce a defect free product. However, experimental work is usually very expensive and timeconsuming to perform. On the other hand, the Analytical/Numerical modeling can be used to modeland analyze the process through all stages of deformation. This approach is less time consuming andmore economical than experimental analysis. There have been several efforts to solve and analyze thedeep drawing problem. Among these are the attempts to analyze the cup drawing process, by fewresearches who developed analytical models for the cup drawing process to solve for stresses andstrains over the deforming sheet metal. However, they did not explain how to determine the movingboundaries in the deforming sheet. This paper deals with the analysis of deep drawing of circularblanks into axi-symmetric cylindrical cups forming using numerical modeling. A rigid plasticmaterial model with the variational approach is used for this analysis. The amount of draw obtainablein the drawing process has been related both theoretically and experimentally with the initial diameterof the blank. The strains in the radial and circumferential directions have been measured. Acorrelation on the flange thickness variation by taking into account the work hardening with theanalytical and experimental values also has been arrived at.