Nigel Park

The role of cold work on the shock response of tantalum

The effect of prior cold work on the shock response of tantalum has been investigated via plate impact. As-received and 50% cold-rolled material has been studied to determine the Hugoniot Elastic Limit (HEL), shear strength evolution behind the shock front, and spall strength. Results show that there is a significant drop in both HEL and shear strength due to cold-rolling, but as the thickness of the target (or time) increases, results converge between the two states. Results suggest that this is due to the cold-rolling process moving dislocations away from the surrounding interstitial solute atoms that collect there, thus reducing the initial stress to initiate yield. In other words, the main contribution of cold-rolling is to increase the population of mobile dislocations within the microstructure rather that just increase the dislocation density as a whole. In contrast, the spall strength in both states appears almost identical. It is suggested that the high Peierls stress prevents a large increase in dislocation density during rolling and hence reduces any post rolling strengthening that might be observed in the spallation response. Finally, we observe a significant change in spall response below a pulse width of 150 ns. We believe that this represents a change from a nucleation and growth of ductile voids type mechanism to one based on ductile fracture of atomic planes. The fact that at these low pulse durations, results appear to trend towards the theoretical strength of tantalum would lend support to this hypothesis.

Nanosecond white-light Laue diffraction measurements of dislocation microstructure in shock-compressed single-crystal copper

Under uniaxial high-stress shock compression it is believed that crystalline materials undergo complex, rapid, micro-structural changes to relieve the large applied shear stresses. Diagnosing the underlying mechanisms involved remains a significant challenge in the field of shock physics, and is critical for furthering our understanding of the fundamental lattice-level physics, and for the validation of multi-scale models of shock compression. Here we employ white-light X-ray Laue diffraction on a nanosecond timescale to make the first in situ observations of the stress relaxation mechanism in a laser-shocked crystal. The measurements were made on single-crystal copper, shocked along the [001] axis to peak stresses of order 50 GPa. The results demonstrate the presence of stress-dependent lattice rotations along specific crystallographic directions. The orientation of the rotations suggests that there is double slip on conjugate systems. In this model, the rotation magnitudes are consistent with defect densities of order 10(12) cm(-2).

Nanosecond x-ray Laue diffraction apparatus suitable for laser shock compression experiments

We have used nanosecond bursts of x-rays emitted from a laser-produced plasma, comprised of a mixture of mid-Z elements, to produce a quasiwhite-light spectrum suitable for performing Laue diffraction from single crystals. The laser-produced plasma emits x-rays ranging in energy from 3 to in excess of 10 keV, and is sufficiently bright for single shot nanosecond diffraction patterns to be recorded. The geometry is suitable for the study of laser-shocked crystals, and single-shot diffraction patterns from both unshocked and shocked silicon crystals are presented.

Simulating picosecond x-ray diffraction from shocked crystals using post-processing molecular dynamics calculations

Calculations of the patterns of x-ray diffraction from shocked crystals derived from the results of non-equilibrium molecular dynamics (NEMD) simulations are presented. The atomic coordinates predicted from the NEMD simulations combined with atomic form factors are used to generate a discrete distribution of electron density. A fast Fourier transform (FFT) of this distribution provides an image of the crystal in reciprocal space, which can be further processed to produce quantitative simulated data for direct comparison with experiments that employ picosecond x-ray diffraction from laser-irradiated crystalline targets.

Simulations of copper single crystals subjected to rapid shear

We report on nonequilibrium molecular dynamics simulations of single crystals of copper experiencing rapid shear strain. A model system, with periodic boundary conditions, which includes a single dislocation dipole is subjected to a total shear strain of close to 10% on time-scales ranging from the instantaneous to 50 ps. When the system is strained on a time-scale short compared with a phonon period, the initial total applied shear is purely elastic, and the eventual temperature rise in the system due to the subsequent plastic work can be determined from the initial elastic strain energy. The rate at which this plastic work occurs, and heat is generated, depends on the dislocation velocity, which itself is a function of shear stress. A determination of the stress-dependence of the dislocation velocity allows us to construct a simple analytic model for the temperature rise in the system as a function of strain rate, and this model is found to be in good agreement with the simulations. For the effective dislocation density within the simulations, 7.8×1011cm−2, we find that applying the total shear strain on time-scales of a few tens of picoseconds greatly reduces the final temperature. We discuss these results in the context of the growing interest in producing high pressure, solid-state matter, by quasi-isentropic (rather than shock) compression.We report on nonequilibrium molecular dynamics simulations of single crystals of copper experiencing rapid shear strain. A model system, with periodic boundary conditions, which includes a single dislocation dipole is subjected to a total shear strain of close to 10% on time-scales ranging from the instantaneous to 50 ps. When the system is strained on a time-scale short compared with a phonon period, the initial total applied shear is purely elastic, and the eventual temperature rise in the system due to the subsequent plastic work can be determined from the initial elastic strain energy. The rate at which this plastic work occurs, and heat is generated, depends on the dislocation velocity, which itself is a function of shear stress. A determination of the stress-dependence of the dislocation velocity allows us to construct a simple analytic model for the temperature rise in the system as a function of strain rate, and this model is found to be in good agreement with the simulations. For the effective di...

The behaviour of niobium and molybdenum during uni-axial strain loading

The mechanical response of niobium and molybdenum during one dimensional shock loading in the weak shock regime is investigated in terms of the Hugoniot elastic limit (dynamic yield) and spall (tensile) strengths. Results indicate that although both metals have high elastic limits of ca. 2 GPa, their responses are very different. Deformation in the weak shock regime in niobium is controlled by both the motion and generation of dislocations, resulting in high spall (dynamic tensile) strengths and ductility. In contrast, molybdenum has low spall strength and ductility, which suggests lower dislocation mobility in this metal. We have also shown that the strain-rate in the rising part of the shock front is related to the stress amplitude by the fourth power, as first shown by Swegle and Grady. Although we have not been able to elucidate further on the power relation, we believe that the scaling factor A is related to a materials ability to accommodate shock imposed plasticity via slip and dislocation generation. Overall, we have used arguments about the Peierls stress in body centred cubic metals to explain these results, with niobium (low Peierls stress) having a high dislocation mobility, resulting in behaviour showing some similarities to face centred cubic metals. Molybdenum, with its much higher Peierls stress has a much lower dislocation mobility, and hence lower spall strengths and ductility.

IN‐SITU PROBING OF LATTICE RESPONSE IN SHOCK COMPRESSED MATERIALS USING X‐RAY DIFFRACTION

Lattice level measurements of material response under extreme conditions are required to build a phenomenological understanding of the shock response of solids. We have successfully used laser produced plasma x‐ray sources coincident with laser driven shock waves to make in‐situ measurements of the lattice response during shock compression for both single crystal and polycrystalline materials. Using a detailed analysis of shocked single crystal iron which has undergone the α‐e phase transition we can constrain the transition mechanism to be consistent with a compression and shuffle of alternate lattice planes.

Shock response of body centered cubic metals

Over the past few years, a research programme has been in place to examine the shock response of body centred cubic metals such as tantalum and tungsten. Examination of the development of shear strength behind the shock front has shown common behaviour in that a marked decrease has been noted, both in the pure metals and their simple alloys. This has been ascribed to the low generation of new dislocation line length due to the high Peierls stresses found in these metals. However more recent work in niobium and molybdenum has shown a more constant response in shear strength due to either a much lower Peierls stress (niobium) or the possibility of twin formation (molybdenum). Examination of the rise times in rear surface velocity traces in these materials has also shown a degree of agreement with changes in lateral stress behind the shock front.

Spall strength of niobium and molybdenum

The shock responses of niobium and molybdenum have been investigated as part of a wider program on bcc metals. Previous work has studied shear strength development behind the shock front and related the observed behaviour to known deformation mechanisms. We now turn our attention to the dynamic tensile (spall) response of these materials. Although both metals are bcc in nature, and both are also adjacent to each other in the periodic table, they nevertheless display markedly different behaviors. Niobium has been shown to be highly ductile, with a high spall strength. In contrast, molybdenum is brittle, with a low spall strength that reduces to near zero as stress amplitude increases. Results are discussed in terms of the deformation mechanisms.

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

We report experiments in which powder-diffraction data were recorded from polycrystalline vanadium foils, shock-compressed to pressures in the range of 10–70 GPa. Anisotropic strain in the compressed material is inferred from the asymmetry of Debye-Scherrer diffraction images and used to infer residual strain and yield strength (residual von Mises stress) of the vanadium sample material. We find residual anisotropic strain corresponding to yield strength in the range of 1.2 GPa–1.8 GPa for shock pressures below 30 GPa, but significantly less anisotropy of strain in the range of shock pressures above this. This is in contrast to our simulations of the experimental data using a multi-scale crystal plasticity strength model, where a significant yield strength persists up to the highest pressures we access in the experiment. Possible mechanisms that could contribute to the dynamic response of vanadium that we observe for shock pressures ≥30 GPa are discussed.