Vol.:(0123456789) 1 3 Metals and Materials International https://doi.org/10.1007/s12540-020-00895-3 Determination of Johnson–Cook Material Parameters for Armour Plate Using DIC and FEM Sangeeta Khare 1  · Krishna Kumar 1  · Shashank Choudhary 2  · Pundan Kumar Singh 2  · Rahul Kumar Verma 2  · Puneet Mahajan 1 Received: 7 September 2020 / Accepted: 29 September 2020 © The Korean Institute of Metals and Materials 2020 Abstract Understanding of material behavior of armour steel under large deformations and high strains during loading is very crucial in designing steel structures for various applications. Johnson–Cook fow stress and Johnson–Cook failure models were adopted for modeling and predicting the material fow behavior of armour plate. The material parameters of Johnson–Cook fow stress have been determined experimentally from tests performed at diferent strain rates (10 −4 –1550 s −1 ) and temperatures (25–600 °C). The damage parameters of Johnson–Cook failure model were determined through experiments on fat tensile specimens in combination with fnite element simulation. Using these materials parameters, fnite element simulations were performed on notch specimens of diferent radii between 2 mm and 20 mm loaded under tension. Load-strain curves were in good agreement with the experimentally obtained data. Triaxiality obtained from simulation were matched against the reported values from the literature. Keywords Armour steel · Johnson–Cook fow stress and failure models · Flat specimen · Finite element simulation · Digital image correlation · Triaxiality 1 Introduction Armor steels are very promising materials which combine high strength and high ductility with excellent load carrying capability and formability [1] and are extensively used to construct armoured vehicles to protect against an external threat. These materials when subjected to dynamic loading conditions such as ballistic impact may experience a wide range of strains, strain-rates, temperatures and pressure [2]. In order to predict their behavior under these varying factors, it is crucial to study their fow stress and failure initiation behavior experimentally and incorporate these in a constitu- tive law. Johnson–Cook (JC) [3] model is one of the widely used constitutive models to predict the dynamic behavior of armour steels [4–7]. Flow stress model proposed by Johnson–Cook depends on the strain state, strain rate and temperature. At large strains, damage initiates in ductile materials due to nucleation of voids. These voids grow and coalesce leading ultimately to the failure of the material. The strain at which failure initiates is predicted by a separate JC failure model which relates this strain to triaxiality, strain rate and temperature in the material. JC failure model has an exponential dependence on stress triaxiality as derived by McClintock [8] and Rice and Tracey [9] who analyzed the void growth under hydrostatic loading in materials. This dependence is often investigated experimentally by perform- ing tensile tests on round bar specimens with diferent notch radii. The strain distribution is almost uniform across the neck while the stress state is triaxial at the center of the notch and the failure initiation always occurs there [10]. The stress analysis of these specimens was carried out by Bridg- man [11] who provided an equation for triaxiality at center of these specimens as where R is curvature radius of the neck and a is radius of the necking cross section. The initial stress triaxiality for round (1)  = 1 3 + ln ( 1 + a 2R ) * Sangeeta Khare sckhare@gmail.com 1 Department of Applied Mechanics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India 2 Research and Development, Tata Steel Limited Jamshedpur, Jamshedpur 831007, India