An iterative procedure for determining effective stress–strain curves of sheet metals

An iterative correction procedure using 3D finite element analysis (FEA) was carried out to determine more accurately the effective true stress–true strain curves of aluminum, copper, steel, and titanium sheet metals with various gage section geometries up to very large strains just prior to the final tearing fracture. Based on the local surface strain mapping measurements within the diffuse and localized necking region of a rectangular cross-section tension coupon in uniaxial tension using digital image correlation (DIC), both average axial true strain and the average axial stress without correction of the triaxiality of the stress state within the neck have been obtained experimentally. The measured stress–strain curve was then used as an initial guess of the effective true stress–strain curve in the finite element analysis. The input effective true stress–strain curve was corrected iteratively after each analysis session until the difference between the experimentally measured and FE-computed average axial true stress–true strain curves inside a neck becomes acceptably small. As each test coupon was analyzed by a full-scale finite element model and no specific analytical model of strain-hardening was assumed, the method used in this study is shown to be rather general and can be applied to sheet metals with various strain hardening behaviors and tension coupon geometries.