Session C1: ME.4 Strength II

Shock structures at ultrahigh strain rates: what can they tell us about material behavior on very fast time scales?

In recent years, techniques based on table-top laser systems have shown promise for investigating dynamic material behavior at high rates of both compressive and tensile strain. Common to these techniques is a laser pulse that is used in some manner to rapidly deliver energy to the sample; while the energy itself is often comparatively very small, the intensity can be made high by tightly focusing the pump light. In this way pressures or stresses can be obtained that are sufficiently large to have relevance to a wide range of basic and applied fields. Also, when combined with established ultrafast diagnostics these experiments provide very high time resolution which is particularly desirable when studying, for example shock waves, in which the time for the material to pass from undisturbed to fully compressed (the ``rise time'') can be extremely short (order 10 ps or less) even at fairly small peak stresses. Since much of the most interesting physics comes into play during this process it is important to be able to adequately resolve the shock rise. In this context I will discuss our measurements on aluminum and iron thin films and compare the results with known behavior observed at lower strain rates. Specifically, for aluminum, I will compare our assumed steady wave data at strain rates of up to 10$^{10}$ s$^{-1}$ to literature data up to $\sim$10$^{7}$ s$^{-1}$ and show that the well-known fourth power scaling relation of strain rate to shock stress is maintained even at these very high strain rates. For iron, I will show how we have used our nonsteady data (up to $\sim$10$^{9}$ s$^{-1})$ to infer a number of important properties of the alpha to epsilon polymorphic transition: 1. The transition can occur on the tens of ps time scale at sufficiently high strain rates and corresponding very large deviatoric stresses, and 2, most of the material appears to transform at a substantially higher stress than the nominal value usually inferred from shock wave experiments of about 13 GPa. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344 with Laboratory directed Research and Development funding (12ERD042), as well as being based on work supported as part of the EFree, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award No. DESC0001057.   

On the weak shock limit (WSL) in condensed matter

The response of materials under shock encompass a range of pressure levels that span a region from the elastic limit up to the \textit{finis extremis} at which the material enters the warm dense matter regime. Between these bounds the material spans two distinct regimes characterized by different wave profiles and responses. These are general known as the strong shock and weak shock regimes. The boundary between these is simply described by the overtake of the shock over the elastic wave to form a single rather than a two-wave structure. However this threshold corresponds to a change from an unsteady region to a single zone that corresponds to a series of physical thresholds being exceeded. This paper describes some of these and explores their consequences upon observed response with emphasis on steady and unsteady regions at relevant length scales.   

Dynamic Strength of Tantalum under impact

Plane impact experiments of double shock and shock-rarefaction in Tantalum were carried out in a gas gun. VISAR diagnostics has been implemented to measure the particle velocity and the free surface velocity. The VISAR information was utilized to study the dynamic strength of Tantalum under compression and tension. The pressure in the experiments was below 35GPa. In this pressure range the dominant mechanism is expected to be dislocation motion. A 1-d hydrodynamic code was used in order to match various strength models. As expected, both the Johnson-Cook and the Guinan-Steinberg models do not reproduce the experimental results. Therefore in this paper we compare the Zerilli-Armstrong model which has been recently calibrated at strain rate of 6x10$^{3}$ s$^{-1}$ using the split Kowalsky-Hopkinson bar to our experimental results at strain rate of 10$^{6}$ s$^{-1}$.   

Laser Compression of Nanocrystalline Tantalum

Nanocrystalline tantalum (g.s. $\sim$70 nm) prepared by severe plastic deformation (HPT) from monocrystalline [100] stock was subjected to high energy laser driven shock compression (up to $\sim$850 J), generating a pressure pulse with initial duration of ? 3 ns and amplitude of up to $\sim$145 GPa. TEM revealed few dislocations within the grains and an absence of twins at the highest shock strengths, in contrast with monocrystalline tantalum, which exhibited twinning at P \textgreater\ $\sim$45 GPa. Hardness measurements were conducted and show a rise as the energy deposition surface is approached, evidence of shock-induced defects. The grain size was found to increase at a distance of 100 $\mu$m from the energy deposition surface as a result of thermally induced grain growth. Calculations using the Hu-Rath analysis are consistent with the experimental results. The experimentally measured dislocation densities and threshold stress for twinning are compared with predictions using analyses based on physically-based constitutive models. The predicted threshold stress for twinning increases from $\sim$45 GPa for the monocrystalline to $\sim$165 GPa for the nanocrystalline tantalum.   

On the residual yield stress of shocked metals

The measurement of the free-surface velocity is commonly employed in planar shock-compression experiments. It is known that the peak free-surface velocity of a shocked elastic-plastic material should be slightly less than twice the particle velocity behind shock front; this difference being proportional to the yield stress. Precise measurement of the free-surface velocity can be a rich source of information on the effects of time and strain on material hardening or softening. With this objective, we performed comparative measurements of the free-surface velocity of shock loaded aluminium AD1 and magnesium alloy Ma2 samples of various thicknesses in the range 0.2mm to 5mm. We observed the expected hysteresis in the elastic-plastic compression-unloading cycle for both AD1 and Ma2; where qualitatively the peak free-surface velocity increased with increasing specimen thickness. However, the relative change in magnitude of hysteresis as function of specimen thickness observed for the Ma2 alloy was smaller than expected given the large observed change in precursor magnitude. We propose that softening due to multiplication of dislocations is relatively large in Ma2 and results in a smaller hysteresis in the elastic-plastic cycle.