Evaluating hardening laws at large tensile strains in sheet specimens

In the finite element modeling of sheet metal formability, the strains in the sheet are calculated from a hardening law which is normally derived from a tensile test. These laws are known to be accurate only up to the maximum uniform strain in tension. However, they are extrapolated during modeling to strains three to five times greater than the uniform strain. In assessing the applicability of these hardening laws at large strains, tensile specimens of 1008 AK steel and commercial purity titanium and zinc were gridded with a fine mesh and slowly pulled to failure. During the test, photographs were taken of the deforming grid in order to develop a complete strain and strain-rate history for each element across the minimum cross section. These data were combined with a hardening law for each material to calculate the total axial load on the specimen. Good agreement between the calculated and measured loads suggests that hardening laws for these materials can be extrapolated to large strains.