Characterization of flow stress at ultra-high strain rates by proper extrapolation with Taylor impact tests

• A systematic procedure has been suggested to obtain the dynamic flow stress of a material at ultra-high strain rates.
• A hybrid experimental–numerical approach has been investigated by using the Taylor impact test.
• The uniaxial tensile tests have been performed at strain rates ranging from 10−3 s−1 to 103 s−1.
• The thermal softening effect at different strain rates is considered in the numerical simulations.
• The proposed hardening curves proposed well describe the deformation behavior up to the strain rate of 106 s−1.

This paper is to provide a novel systematic procedure to obtain the dynamic flow stress of a material at ultra-high strain rates ranging from 104 s−1 to 106 s−1 where hardening behaviors are difficult to acquire from conventional experiments. Uniaxial material tests with AISI 4340 steel are performed at a wide range of strain rates from 10−3 s−1 to 103 s−1 by using the INSTRON 5583, a high-speed material testing machine (HSMTM), and a tension split Hopkinson pressure bar (SHPB) testing machine. From the uniaxial tests above, stress–strain curves are obtained at the strain rates ranging from 10−3 s−1 to 103 s−1. However, stress–strain curves cannot be obtained at the strain rates higher than 104 s−1 due to the lack in experimental techniques. In order to characterize hardening behaviors at strain rates ranging from 104 s−1 to 106 s−1, Taylor impact tests are performed when the speed of a projectile is 200 m/s, 253 m/s, and 305 m/s, which entail ultra-high strain rates, high temperature, and large plastic deformation. Flow stresses at the ultra-high strain rates are characterized through an inverse optimization process by comparing the numerical simulation results with the experimental results of the sequentially deformed shapes of a projectile during the Taylor impact test. The thermal softening effect at different strain rates is also considered due to the elevated temperature caused by large plastic deformation. The flow stresses calibrated by the comparison are implemented to numerical simulation resulting in a good coincidence with the Taylor impact tests at different impact velocities. It is noted from the comparison that the yield stress and the comprehensive hardening curves proposed well describe the deformation behavior up to the strain rate of 106 s−1 beyond the strain rate range for conventional material testing.