A constitutive model for strain rates from 10−4 to 106 s−1

Abstract

We have developed an addition to the Steinberg–Guinan high strain-rate constitutive model that extends its validity to strain rates as low as 10−4 s−1. With this new model, we have successfully reproduced a number of rate-dependent, shock-induced phenomena in tantalum, such as precursor on reshock, precursor decay, and shock smearing. We have also successfully calculated a plate-impact experiment at a loading stress of 230 GPa as well as extensive data for yield strength versus strain rate at room temperature and yield strength versus temperature at a strain rate of 10−4 s−1.

Orientation and rate dependence in high strain-rate compression of single-crystal silicon

“…31 The algorithm used for its implementation is due to Wilkins 32 and is described in Steinberg and Lund. 33 A full description of the model and input parameters may be found in Appendix B. The Gilman model was established in the late sixties and has been widely used in the intervening years to interpret time-dependent deformation data over a range of experimental platforms, materials and deformation timescales 11 12 34 35 36 .…”

X-ray diffraction measurements of plasticity in shock-compressed vanadium in the region of 10–70 GPa

“…Of these, that due to Steinberg and Guinan 20 does not depend on strain rate, whereas those due to Steinberg and Lund 21 and Preston, Tonks, and Wallace 22 include ratedependent effects and transition to phonon drag at the highest strain rates. The more-recent multiscale strength model due to Barton et al 23 includes a detailed treatment of the evolution of the dislocation density and dislocation velocity.…”

The use of the direct impact Hopkinson pressure bar technique to describe thermally activated and viscous regimes of metallic materials

“…Again for nickel, with a grain size down to 130 nm, the threshold strain rate was found to be invariant. There are several material models describing the upturn of the strength in the 10 3 -10 4 s −1 regimes [11][12][13][14][15][16]. For example, a modification of the strain-rate term in the Johnson-Cook model has been used which includes a power strain-rate component added to the logarithm strainrate term of the classic Johnson-Cook formulation, D(έ/έ 1 ) k , with D and k two constants [11].…”