Identification of Post-necking Tensile Stress–Strain Behavior of Steel Sheet: An Experimental Investigation Using Digital Image Correlation Technique Surajit Kumar Paul, Satish Roy, S. Sivaprasad, H.N. Bar, and S. Tarafder (Submitted October 18, 2017; in revised form February 7, 2018) The stress–strain behavior of sheet metal is commonly evaluated by tensile test. However, the true stress– strain curve is restricted up to uniform elongation of the material. Usually, after the uniform elongation of the material the true stress–strain is obtained by extrapolation. The present work demonstrates a procedure to find out the true tensile stress–strain curve of the steel sheet after necking using digital image correlation (DIC) technique. HillÕs normal anisotropic yield criteria and local strains measured by DIC technique are used to correct the local stress and strain states at the diffuse necked area. The proposed procedure is shown to successfully determine the true tensile stress–strain curve of ferritic and dual-phase steel sheets after necking/uniform elongation. Keywords diffuse necking, digital image correlation, post-neck- ing tensile stress–strain curve, sheet metal, tensile test 1. Introduction Finite element method has been extensively used nowadays to optimize metal forming operations, simulation of crash events and other large deformation processes. Many metal forming operations lead to strains that are beyond the uniform elongation of the material. For a precise simulation of crash events and machining operations, information on stress–strain response of materials over a large range of strain is mandatory. Therefore, there is a requirement of generation of stress–strain response of a material beyond its uniform elongation. The classical methods of obtaining stress–strain behavior of a material such as conventional tensile tests are not sufficient to get the stress–strain response after necking (Ref 1). More expensive and cumbersome hydraulic bulge tests are normally used to obtain the required stress–strain information in such cases (Ref 2). Of late, few research groups (Ref 3-10) have worked on hybrid methods, employing a combination of experiment, analysis and finite element simulation, to construct post-necking tensile stress–strain curve. However, these meth- ods are not simple and straightforward to employ in an engineering scenario. Bridgman (Ref 11) was the first to propose a method for determining the post-necking hardening behavior of a round bar. Principally, the proposal was to correct the geometry of necking profile (i.e., local area correction). Zhang et al. (Ref 12) extended this concept for a tensile test specimen with cross section of rectangular geometry. However, this method is valid only up to a maximum aspect ratio of 8 for the rectangular cross section. Koc and Stok [13) proposed an inverse method based on the experimentally measured tensile forces. Kajberg and Lindkvist (Ref 14) combined the in-plane displacement fields measured by digital speckle photography (DSP) and inverse modeling, to describe the stress–strain response of a sheet metal at high plastic strains. Tao et al. (Ref 15) reported an iterative procedure to determine the stress–strain curve beyond necking using digital image correlation (DIC). Holmberg et al. (Ref 16) employed tensile tests using DIC to determine the formability of sheet metal. Merklein et al. (Ref 17) determined the thermo- mechanical material characteristics by measuring deformation of tensile specimens using DIC. Gre ´diac and Pierron (Ref 18) successfully determined the post-necking plastic material behavior through DIC and virtual field based inverse modeling. Marth et al. (Ref 10) used optical full-field displacement measurements to compute local strain fields and stress–strain curve of the material after necking. Coppieters et al. (Ref 5) presented an alternative technique without using a finite element (FE) model to identify the hardening behavior of sheet metal after necking. This method minimized the differ- ence between the internal and external work in the necking region in a tensile experiment. Tardif and Kyriakides (Ref 6) predicted post-necking true stress–strain curve of Al-6061-T6 sheet metal. They simulated the tensile test of Al-6061-T6 sheet metal numerically using a 3D finite element model, and the response of the sheet metal was iteratively extrapolated until the simulated and measured force-elongation matched. They also validated their method by measurement of strains in necking zone and geometry of the neck. Gerbig et al. (Ref 9) presented a general framework for coupling DIC with FE analysis to find out material parameters from measurements of non-uniform displacement fields in a tensile specimen. The aim was to reduce the discrepancy between measured and calculated force and displacement fields by continually correcting the material constants in a selected constitutive equation. Wang and Tang (Ref 7) predicted tensile true stress–strain curve after necking from standard flat coupon by numerical simulation with a Surajit Kumar Paul, Department of Mechanical Engineering, Indian Institute of Technology Patna, Patna, Bihar, India; Satish Roy, S. Sivaprasad, H.N. Bar, and S. Tarafder, Fatigue and Fracture Group, CSIR-National Metallurgical Laboratory, Jamshedpur 831007, India. Contact e-mails: paulsurajit@yahoo.co.in, surajit@iitp.ac.in. JMEPEG ÓASM International https://doi.org/10.1007/s11665-018-3701-3 1059-9495/$19.00 Journal of Materials Engineering and Performance