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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property of material is important for fast dynamic loading design. Strain rate based constitutive models are essential in order to model structures subjected to high rates of loading. The high strain rate constitutive equation is widely used in reactor designing (Chellapandi et al. 2001). In the other engineering application such as analysis during impact loading, crash analysis of vehicle, impact testing of bullet proof armour, extrusion, rolling, high speed machining etc., the high strain rate constitute equation is required. High strain rate material data for SS316LN is scarce in literature. To evaluate the wide range strain rate based behavior of material, Split-Hopkinson Pressure Bar (SHPB) is commonly used for the testing due to its simplicity. For finite element analysis of material for high strain rate condition, rate dependent Johnson-Cook plasticity model is widely used. It is a closed form plasticity model associated with strain rate based hardening behavior of the material. Nomenclature Plastic strain F Ratio of force ̇ Plastic strain rate Design temperature ρ Density of bar Reference temperature σ Stress Melting temperature A cross section of bar ˜ Particle velocity C 0 velocity of wave in material Z Impedance 2. Split Hopkinson Pressure Bar (SHPB) Test The Split-Hopkinson Pressure Bar (SHPB) test setup is used for the dynamic fracture experiments of materials. The SHPB test setup consists a gas gun, a striker, an incident bar and a transmitted bar. The specimen is kept in between the ends of two straight long bars called incident bar and transmission bar. At the one end of incident bar a compressive wave is generated by the striker with the help of pressure gun. The high strength material, in order of yield strength of ~2000 MPa (Sharman et al. 2011), is used for striker, incident bar and transmission bar to keep them in elastic region during loading. Only specimen, which is sandwiched between incident and transmission bar, is subjected to large plastic deformation. The wave passes through the incident bar called incident wave is splits in two pars at the inter face of incident bar and specimen. One part reflect back through the incident bar called reflected wave and another part transmits through the specimen. The transmission wave through the specimen again splits in two parts at specimen- transmission bar interface, one of which reflect back to specimen and another transmit through the transmitted bar which is called the transmission wave. The strain gauges are provided the mid point in incident and mid-point in transmission bar which provide the incident and transmission signal respectively. The strain gauge at the incident bar also measure the reflection signal. These signals (reflection and transmission) are important to evaluate the high strain rate stress-strain data of material. The reflection signal is used for the evaluation of strain rate and strain in specimen and transmission signal is used to evaluate the load and stress in specimen with function of time. The working principle of Split-Hopkinson Pressure Bar is based on principle of one dimensional wave propagation proved in Eq. (1) where C 0 is the velocity of wave in material. 2 2 2 = 2 2 (1) The D’ Alembert solution for the wave equation is provided in Eq. 2. Function f and g are initial condition dependent arbitrary functions for wave propagation in positive xand negative x direction respectively. The str ain (ε) induced in bar due to wave propagation in positive xdirection is provided in Eq. 3. The particle velocity is provided in the Eq. 4. From Eq. 3 and Eq. 4, particle velocity is also written in strain form as in Eq. 5. ( , ) = ( − ) + ( + ) (2) ( , ) = = ′ ( − ) (3) ( , ) = =− ′ ( − ) (4)