A novel spatio-temporal method for determining necking and fracture strains of sheet metals

Forming limit diagrams (FLDs) and fracture forming limit diagrams (FFLDs) have been widely used to evaluate formability of sheet metals. There are many existing methods for determining localised necking strain and fracture strain necessary to construct these diagrams, however, none has been widely accepted and applied to the range of available formability testing methods, e.g. Nakajima tests and biaxial tensile tests. In this study, a novel spatio-temporal method is proposed and developed for determining the localised necking strain and the fracture strain in deformed sheet metals. In the method, localised necking is assumed to appear at the beginning of an increasing difference between average thickness strain within two rectangular zones where localised necking occurs. The effects of dimensions of the two zones on determined localised necking strains were investigated using uniaxial tensile tests for three sheet metals: AA7075, boron steel and AA6082, and the optimal dimensions are recommended to ensure accurate determinations. In comparison with several widely used existing methods, it was concluded that the novel method has greater simplicity, stability and accuracy in determining the localised necking strains. The method was also successfully applied to determine the localised necking strain and the fracture strain for AA5754 in biaxial tensile tests and it was demonstrated to be unaffected by noise and the Portevin–Le Châtelier (PLC) effect.