Limit Strains of Sheet Metal Forming under Broken-line Strain Paths (Ⅱ)——Calculating and Testing on the Limit Strains for Sheet Metal Forming

Abstract

In part (Ⅰ) of this paper published,three assumptions for sheet metal forming are proposed,i.e.any complex swain path can be simplified to the broken-line strain paths combined with a number of linear strain paths;the limit thickness strain is also the sheet metal formability;the formability of sheet metal under the broken-line strain path depends on the final strain ratio in forming process, and 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 strain principle axes turning during alternating from the prior linear strain path to the subsequent one. The forming limit diagrams (FLDs) are firstly calculated by means of these assumptions and formulas in sheet metal forming under three two-step linear strain paths with strain principle axes turning,whose initial deformation are uniaxial tensile,plane strain and equibiaxial tensile strain respectively.Then these FLDs are discussed and verified through forming limit test.The obtained FLDs tally with the test results mentioned in this paper and those reported by some literature.Moreover,most past researches explained the influence of broken-line strain paths on FLDs from the viewpoint of plastic mechanics or plastic physics,here we on the basis of the ■equivalent curves describe the phenomenon of FLD state changed by broken-line strain paths from the viewpoint of plastic geometry.