Limit strains of sheet metal forming under broken-line strain paths (Ⅰ) ——proposing and analyzing on the limit strains for sheet metal forming

Abstract

The current studies of strain paths' effect on the forming limit diagram(FLD) are briefly summed up from 4 aspects, moreover, the concepts that complex, simple stain paths are axplained, and the geometric relationship of varians strains is illustrated which is based on Hill'48 yield criterion, are illustrated. In order to calculate limit strains of sheet metal during it's forming with any complex strain path, the three assumptions for sheet metal forming are proposed, viz. Any complex strain path might be transformed to the broken-line strain paths combined with a number of linear strain paths by simplifying; The limit thickness strain might be equal to sheet metal formability; The formability of sheet metal under the broken-line strain path might be dependent on the final strain ratio in forming process, and the line of reasoning on them is annotated. At the same time, on the basis of these assumptions, the theoretical formulas for calculating limit strains in sheet metal forming are deduced under the broken-line strain path with strains' principle axes turning during alternating from prior strain path to subsequent one, in terms of which the forming limit diagrams could be drawn for sheet metal forming with any complex strain path.