A theoretical and experimental investigation of limit strains in sheet metal forming

The paper deals with an analytical technique for predicting FLDs based on linear, bilinear and trilinear straining paths—although any general curvilinear strain path can be handled by the method. The analytical procedure was based on the work of Marciniak and Kuczynski (known as the M-K model). The influence of material properties, such as anisotropy, strain hardening and strain rate sensitivity, as well as the effect of strain path, on the shape and level of the FLD were investigated. Material property data were determined from tests on Interstitial Free (IF) steel sheet. An experimental FLD was constructed for the IF steel sheet in the as-received condition. Additional FLDs were also produced following pre-straining of the as-received sheet. Comparison between the experimentally determined FLDs and those predicted from the theoretical model was favourable. Conventional FLDs are constructed in strain space with the principal surface strains as coordinate axes. However, they can be plotted in principal stress space, and some investigators have claimed this is a better representation. By knowing the strain path the stress state at the limit strain can be determined, and these limit stresses were plotted in principal stress space in order to construct a Forming Limit Stress Diagram (FLSD). It turned out that regardless of the shape of the FLD and the type of pre-strain imposed, all the FLSDs were almost identical. In contrast when plotted in strain space the FLD was very sensitive to the type of straining path.