PSI - Issue 60

S.K. Pandey et al. / Procedia Structural Integrity 60 (2024) 665–677 S. K. Pandey/ Structural Integrity Procedia 00 (2023) 000 – 000 = ∫

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3. Johnson-cook Plasticity model Johnson-Cook plasticity model (Johnson and cook 1983) is a type of Mises plasticity model which include hardening law and rate dependence. It is basically best suited for metal with high-strain-rate deformation. The technique of simulation is based on adiabatic transient dynamic due to the fast loading condition. Johnson-Cook plasticity can be used with Johnson-Cook damage model. It uses Mises yield surface for associated flow rule and isotropic hardening is used. The Johnson-Cook plasticity equation is provided in eq. 17. The equivalent Von-Mises stress ( σ ) depends upon plastic strain ( ) , strain rate ( ̇ ) and the temperature of material. Here , , , and are the five parameters. The parameter implies the initial yield strength of material. The parameters and represents the flow stress on strain hardening behaviour at quasi-static strain rate. Parameters represent strain rate effect and m represent thermal softening effect. ̂ can be represented as [( − ) ( − ) ⁄ ] . Here, , and are design temperature, reference temperature and melting temperature respectively. In this analysis where temperature effect is not considered the value of ̂ is considered as 0. = [ + ( ) ] [1 + ∗ ( ̇ ̇ )] (1− ̂ ) (17) 4. Finite Element Analysis of SHPB The finite element analysis of the Split-Hopkinson Pressure Bar prior to the experiment can help to finalised the velocity and size of striker for a given material of specimen. It may also help to understand the overall behaviour of pulse signal. The Finite element analysis of Split-Hopkinson Pressure Bar is carried out using ABAQUES/Explicit 2017 finite element code (ABAQUS manual). The striker, incident bar, specimen and transmission bar are modelled using 3D brick element. The material property for striker, incident bar and transmission bar is linear elastic whereas elasto-plastic material models such as rate independent plasticity model, Johnson-Cook plasticity model with/without rate effect has been adopted for specimen. The dynamic explicit analysis duration is considered for 700 micoseconds which is sufficient to travel the wave pulse from incident to transmitted bar. Since dynamic explicit is conditionally stable numerical simulation hence the time step in the order of 10e-8 is taken which is sufficiently lower than time required to travel the wave in an element. The various types of analysis has been carried out to understand the FEA model behaviour. The specimen arrangement in Split-Hopkinson Pressure Bar test Setup is provided in Fig. 1. The length of striker, incident bar, specimen and transmission bar are taken as 0.5 m, 1.3 m, 5 mm and 1.3 m respectively. The diameter of striker, incident bar, specimen and transmission bar are taken as 13 mm, 13 mm, 5 mm and 13 mm respectively.

Fig. 1. Specimen arrangement in Split-Hopkinson Pressure Bar test Setup