Dislocation Mechanics of Shock-Induced Plasticity
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AN important upturn in the flow stress of oxygenfree electrolytic (OFE) copper at the high strain rate end of the split Hopkinson pressure bar (SHPB) test results was reported in a pioneering study by Follansbee et al.[1] The upturn, which initially was accounted for by a dislocation drag explanation, was in fact later, more likely, attributed to additional strain hardening caused by the sudden onset of a new mechanism of dislocation generation.[2] Figure 1 shows the referred-to experimental test results and also includes comparison with a computed Zerilli–Armstrong (Z-A) constitutive equation curve for the strain rate dependence of the flow stress. The equation parameters were determined from other experiments and were applied separately to computational mechanics modeling of a number of dynamic deformation results, especially including the complete shapes of Taylor-type solid cylinder impact test specimens.[3] Of special interest in Figure 1 are the two heavy lines drawn to show limiting values for the flow stress dependence on strain rate when evaluated in terms of an activation volume parameter defined from the thermal activation-strain rate analysis (TASRA) as R.W. ARMSTRONG, Professor Emeritus, is with the Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA. Contact e-mail: [email protected] W. ARNOLD, Project Manager for Studies, is with the MBDA-TDW, 86523, Schrobenhausen, Germany. F.J. ZERILLI, Senior Research Scientist, is with the Research and Technology Department, Naval Surface Warfare Center, Indian Head Division, Indian Head, MD 20640, USA. This article is based on a presentation made in the symposium entitled ‘‘Dynamic Behavior of Materials,’’ which occurred during the TMS Annual Meeting and Exhibition, February 25–March 1, 2007 in Orlando, Florida, under the auspices of The Minerals, Metals and Materials Society, TMS Structural Materials Division, and TMS/ASM Mechanical Behavior of Materials Committee. Article published online June 6, 2007. METALLURGICAL AND MATERIALS TRANSACTIONS A
V ¼ kB T½@ ln ðdc=dtÞ=@s T
½1
in which equation kB is Boltzmann’s constant equal to 1.38 · 10)23 J/K, T is the absolute temperature, (dc/dt) is the plastic shear strain rate, and s* is the thermal component of shear stress. Although V* has volumetric dimensions, the TASRA-based model description leads to V* = bA*, where both b, the dislocation Burgers vector, and A*, the activation area that a dislocation encounters in surmounting the barrier to movement, are in the plane of shear. The two lines in Figure 1 were obtained for copper with b = 0.256 nm at 300 K and with selected reference values of A* = 1000 b2, as an upper limiting value typical of conventional tests at ambient temperature, and A* = b2, for a theoretical lower limiting value for slip.[4] In the present investigation, the top-ended SHPB copper test results shown in Figure 1 are further connected with even higher strain rate results reported in another pioneering research investigation of shockinduced plasticity
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