Prediction of Forming Limits under Complex Strain Paths

"Padwal and Chaturvedi have developed the model based on M-K theory, considering Hosford's yield criterion and critical thickness strain criterion"" to predict the sheet metal forming limits under simple (constant) strain ratio paths. This analysis has been extended in this paper to predict the sheet metal forming limits under complex strain paths. The effects of exponent ""a"" in Hosford's yield criterion and strain paths on the forming limits under complex strain paths are studied using this analysis. The predictions of the present analysis are compared, both for simple and complex strain paths, with experimental results of Ishigaki for A.K. steel and also with the predictions of Rao and Chaturvedi's model. The quantitative analysis of the error in predicting the forming limits has also been carried out using a method suggested by the authors earlier.1. INTRODUCTIONThe constant strain ratio condition has been assumed in the theories developed for prediction of forming limit diagrams (FLO). In actual forming operation, this condition is seldom satisfied. Even in the case of simple single stage press formed components, the strain path becomes curved and non-linear. In the case of pressings with complex shapes, or multiple stages of forming, the changes in strain path are more pronounced and even abrupt.Experimental study of the forming limits, under two stage strain paths, by Ishigaki [1], has shown that the forming limits are path dependent. It has been observed that the forming limits lower than that under simple strain paths, may be obtained under certain strain paths (when the first stage strain path is either equibiaxial tension or uniaxial tension, followed by the second stage strain path as plane strain). Rasmussen's work [2J, on the theoretical study of forming limits under curvilinear strains paths, has shown that a large drop in formability can result from very small changes in strain path. Thus if a deformation process gives rise to failures due to plastic instability, the failure is not necessarily due to insufficient formability of the material. In such cases, FLOs based on constant strain ratio path should not be used directly in predicting the success or failure of the forming operation. Thus the knowledge of forming limits under complex strain paths is of great importance to the interpretation of press-shop problems."