Determination of the Forming-Limit Diagram from Deformations within Necking Instability: A Digital Image Correlation-Based Approach

It is now possible using digital-image correlation techniques to precisely measure deformation within a developing necking instability, during forming-limit experiments. However, the current standards for measuring limit strains rely only on data outside of the instability. We propose exactly the opposite, to use just those deformations from the material where the instability will develop. Marciniak and Kuczynski experiments were performed on a drawing-quality steel and the entire deformation history recorded with a high-resolution photographic camera. The strain fields from these image were analyzed with the digital-image correlation program NCORR, concentrating on where the necking instability would form. The Merklein et al. (CIRP Ann Manuf Technol 59:295-298, 2010) and Hotz et al. (Key Eng Mater 549:397-404, 2013) temporal analyses were modified through an original smoothing technique to uniquely identify, through a correspondence of results, when the deformation acceleration rate begins to rapidly increase within the developing instability. This defines a limit strain. These results were compared to the standard Bragard-type determination specified in the norm International Standard ISO 12004-2:2008 (Metallic materials—sheet and strip: determination of forming-limit curves. Part 2—determination of forming-limit curves in the laboratory, International Organization for Standardization, Geneva, 2008). We found a close agreement in balanced-biaxial tension between our proposed technique and the standard Bragard-type analysis. However, in plane-strain and uniaxial deformation the standard analysis appeared to be excessively conservative, by as much as 40% for our steel.