Shock-induced Plasticity Research Articles

Peierls Stress of Dislocations in Molecular Crystal Cyclotrimethylene Trinitramine

Dislocation mediated plasticity in the α phase of the energetic molecular crystal cyclotrimethylene trinitramine (RDX) was investigated using a combination of atomistic simulations and the Peierls-Nabarro (PN) model. A detailed investigation of core structures and dislocation Peierls stress was conducted using athermal atomistic simulations at atmospheric pressure to determine the active slip systems. Generalized stacking fault energy surfaces calculated using atomistic simulations were used in the PN model to also estimate the critical shear stress for dislocation motion. The primary slip plane is found to be (010) in agreement with experimental observations, with the (010)[100] slip systems having the lowest Peierls stress. In addition, atomistic simulations predict the (021)[01[overline]2], (021)[100], (011)[100], (001)[100], and (001)[010] slip systems to have Peierls stress values small enough to allow plastic activity. However, there are less than five independent slip systems in this material in all situations. The ranking of slip systems based on the Peierls stress values is provided, and implications are discussed in relation to experimental data from nanoindentation and shock-induced plastic deformation.

Shock response of nanotwinned copper from large-scale molecular dynamics simulations

A series of large-scale molecular dynamics simulations have been performed to investigate the shock response of nanotwinned (NT) Cu, including shock-induced plasticity, strength behind the shock front, and spall behaviors. In this study, two configurations were investigated at an impact velocity of 600m/s, i.e., the practical NT polycrystalline Cu with an average grain size of 10 nm and the simple NT single-crystalline Cu with an impact direction of [11 (2) over bar]. In the NT polycrystalline Cu, the average flow stress behind the shock front first increases with decreasing twin-boundary spacing (TBS), reaching a maximum at a critical TBS, and then decreases as the TBS become even smaller. This trend of the average flow stress with decreasing TBS is due to two competitive dislocation activities under shock loading, with one being inclined to the twin boundaries (the dislocation-twin boundary intersecting) and the other parallel to the twin boundaries (detwinning with twin-boundary migration). Since voids always nucleate near the grain boundary (GB) junctions and then grow along the GBs to create spallation, no apparent correlation between the spall strength and TBS is observed in the NT polycrystalline Cu. However, the spall strengths of the NT single-crystalline Cu are found to increase with decreasing TBS. Two partial dislocation slips initiated from each twin boundary create voids at the intersections between the partial dislocation slips and twin boundaries. The smaller TBSs result in a larger number of twin boundaries and provide more nucleation sites for voids, requiring a higher tensile stress to create spallation in the NT single-crystalline Cu. These findings should provide insights for understanding the deformation physics of the NT metals subjected to shock loading.

Multiscale dislocation dynamics simulations of shock-induced plasticity in small volumes

Multiscale dislocation dynamics plasticity (MDDP) was used to investigate shock-induced deformation in monocrystalline copper. In order to enhance the numerical simulations, a periodic boundary condition was implemented in the continuum finite element (FE) scale so that the uniaxial compression of shocks could be attained. Additionally, lattice rotation was accounted for by modifying the dislocation dynamics (DD) code to update the dislocations’ slip systems. The dislocation microstructures were examined in detail and a mechanism of microband formation is proposed for single- and multiple-slip deformation. The simulation results show that lattice rotation enhances microband formation in single slip by locally reorienting the slip plane. It is also illustrated that both confined and periodic boundary conditions can be used to achieve uniaxial compression; however, a periodic boundary condition yields a disturbed wave profile due to edge effects. Moreover, the boundary conditions and the loading rise time show no significant effects on shock–dislocations interaction and the resulting microstructures. MDDP results of high strain rate calculations are also compared with the predictions of the Armstrong–Zerilli model of dislocation generation and movement. This work confirms that the effect of resident dislocations on the strain rate can be neglected when a homogeneous nucleation mechanism is included.

Parameterization of a rate-dependent model of shock-induced plasticity for copper, nickel, and aluminum

A mechanistic model of shock-wave-induced viscoplasticity is parameterized for three polycrystalline metals: Cu, Ni, and Al. The model is also extended to higher stress wave amplitudes by incorporating homogeneous dislocation nucleation within the constitutive framework. Steady shock waves are simulated to demonstrate the model and compare results to experimental data. Stress wave amplitudes of up to 30GPa have been simulated in each metal; these stress waves generate strain rates of up to ∼1010s−1 in the shock front. Model results compare favorably with experimental velocity profiles, dynamic stress–strain curves, the Swegle-Grady scaling law, and non-invasive measurements of shear strength in the shocked state. Furthermore, simulated stress-strain-rate profiles exhibit points of self-intersection (loops) because the mobile and immobile dislocation densities have been assigned as internal state variables. Such loops, which have been observed in experiments, are not captured by flow functions that are based on a single monotonically-increasing internal state variable. Finally, the model of 6061-T6 Al alloy is revisited to ammend a prior conclusion regarding shear strength in the shocked state and the onset of homogeneous dislocation nucleation.

Role of interfaces in shock-induced plasticity in Cu/Nb nanolaminates

We investigate deformation of pure Cu, pure Nb and 30 nm Cu/30 nm Nb nanolaminates induced by high strain rate shock loading. Abundant dislocation activities are observed in shocked pure Cu and Nb. In addition, a few deformation twins are found in the shocked pure Cu. In contrast, in shocked Cu/Nb nanolaminates, abundant deformation twins are found in the Cu layers, but only dislocations in the Nb layers. High resolution transmission electron microscopy reveals that the deformation twins in the Cu layers preferentially nucleate from the Cu(112)//Nb(112) interface habit planes rather than the predominant Cu(111)//Nb(110) interface planes. Our comparative study on the shock-induced plastic deformation of the pure metals (Cu and Nb) and the Cu/Nb nanolaminates underscores the critical role of heterogeneous phase interfaces in the dynamic deformation of multilayer materials.

Modeling Shock Induced Plasticity in Copper Single Crystal: Numerical and Strain Localization Issues

Multiscale dislocation dynamics plasticity (MDDP) simulations are carried out to address the following issues in modeling shock-induced plasticity: 1- the effect of finite element (FE) boundary conditions on shock wave characteristics and wave-dislocation interaction, 2- the effect of the evolution of the dislocation microstructure on lattice rotation and strain localization. While uniaxial strain is achieved with high accuracy using confined boundary condition, periodic boundary condition yields a disturbed wave profile due the edge effect. Including lattice rotation in the analysis leads to higher dislocation density and more localized plastic strain.

Dynamic response ofCu46Zr54metallic glass to high-strain-rate shock loading: Plasticity, spall, and atomic-level structures

We investigate dynamic response of ${\text{Cu}}_{46}{\text{Zr}}_{54}$ metallic glass under adiabatic planar shock wave loading (one-dimensional strain) with molecular dynamics simulations, including Hugoniot (shock) states, shock-induced plasticity, and spallation. The Hugoniot states are obtained up to 60 GPa along with the von Mises shear flow strengths, and the dynamic spall strengths, at different strain rates and temperatures. The spall strengths likely represent the limiting values achievable in experiments such as laser ablation. For the steady shock states, a clear elastic-plastic transition is identified (e.g., in the shock velocity-particle velocity curve), and the shear strength shows strain softening. However, the elastic-plastic transition across the shock front displays transient stress overshoot (hardening) above the Hugoniot elastic limit followed by a relatively sluggish relaxation to the steady shock state, and the plastic shock front steepens with increasing shock strength. The local von Mises shear strain analysis is used to characterize local deformation, and the Voronoi tessellation analysis, the corresponding local structures at various stages of shock, release, tension and spallation. The plasticity in this glass, manifested as localized shear transformation zones, is of local structure rather than thermal origin, and void nucleation occurs preferentially at the highly shear-deformed regions. The Voronoi and shear strain analyses show that the atoms with different local structures are of different shear resistances that lead to shear localization (e.g., the atoms indexed with $⟨0,0,12,0⟩$ are most shear-resistant, and those with $⟨0,2,8,1⟩$ are highly prone to shear flow). The dynamic changes in local structures are consistent with the observed deformation dynamics.

Flipping the sign of refractive index changes in ultrafast and temporally shaped laser-irradiated borosilicate crown optical glass at high repetition rates

Ultrafast subpicosecond laser exposure usually induces negative refractive index changes in optical glasses with strong thermal expansion such as borosilicate BK7 due to volume expansion and mechanical rarefaction. We show that temporally shaped laser excitation on picosecond scales and at high repetition rates can invert the regular material response resulting in a significant refractive index increase. Simulations of pulse propagation and evolution of heat and strain waves in BK7 glass exposed to different pulse durations were performed to understand mechanisms of refractive index increase. Narrow spatial distribution of energy for optimized picosecond pulses determines shock-induced plastic deformations accompanied by partial healing of the lateral strain due to preferential heat flow. The matter momentum relaxation produces directional on-axis material compaction.

Shock Compression of Monocrystalline Copper: Atomistic Simulations

Molecular dynamics (MD) simulations were used to model the effects of shock compression on [001] and [221] monocrystals. We obtained the Hugoniot for both directions, and analyzed the formation of a two-wave structure for the [221] monocrystal. We also analyzed the dislocation structure induced by the shock compression along these two crystal orientations. The topology of this structure compares extremely well with that observed in recent transmission electron microscopy (TEM) studies of shock-induced plasticity in samples recovered from flyer plate and laser shock experiments. However, the density of stacking faults in our simulations is 102 to 104 times larger than in the experimental observations of recovered samples. The difference between experimentally observed TEM and calculated MD results is attributed to two effects: (1) the annihilation of dislocations during post-shock relaxation (including unloading) and recovery processes and (2) a much shorter stress rise time at the front in MD (<1 ps) in comparison with flyer-plate shock compression (∼1 ns).

Dislocation Mechanics of Shock-Induced Plasticity

The constitutive deformation behavior of copper, Armco iron, and tantalum materials is described over a range of strain rates from conventional compressive/tensile testing, through split Hopkinson pressure bar (SHPB) test results, to shock-determined Hugoniot elastic limit (HEL) stresses and the follow-on shock-induced plasticity. A mismatch between the so-called Zerilli–Armstrong (Z-A) constitutive equation description of pioneering SHPB measurements for copper provided initial evidence of a transition from the plastic strain rate being controlled by movement of the resident dislocation population to the strain rate being controlled by dislocation generation at the shock front, not by a retarding effect of dislocation drag. The transition is experimentally confirmed by connection with Swegle–Grady-type shock vs plastic strain rate measurements reported for all three materials but with an important role for twinning in the case of Armco iron and tantalum. A model description of the shock-induced plasticity results leads to a pronounced linear dependence of effective stress on the logarithm of the plastic strain rate. Taking into account the Hall–Petch grain size dependence is important in specifying the slip vs twinning transition for Armco iron at increasing strain rates.

Simulation of shock-induced plasticity including homogeneous and heterogeneous dislocation nucleations

A model of plasticity that couples discrete dislocation dynamics and finite element analysis is used to investigate shock-induced dislocation nucleation in copper single crystals. Homogeneous nucleation of dislocations is included based on large-scale atomistic shock simulations. The resulting prodigious rate of dislocation production takes the uniaxialy compressed material to a hydrostatically compressed state after a few tens of picoseconds. The density of dislocations produced in a sample with preexisting dislocation sources decreases slightly as shock rise time increases, implying that relatively lower densities would be expected for isentropic loading using extremely long rise times as suggested experimentally.

Shock-Induced Structural Phase Transition, Plasticity, and Brittle Cracks in Aluminum Nitride Ceramic

Atomistic mechanisms of fracture accompanying structural phase transformation (SPT) in AlN ceramic under hypervelocity impact are investigated using a 209 x 10(6) atom molecular-dynamics simulation. The shock wave generated by the impact splits into an elastic wave and a slower SPT wave that transforms the wurtzite structure into the rocksalt phase. The interaction between the reflected elastic wave and the SPT wave front generates nanovoids and dislocations into the wurtzite phase. Nanovoids coalesce into mode I cracks while dislocations give rise to kink bands and mode II cracking.

1-D and 2-D modeling of U-Ti alloy response in impact experiments

Dynamic response of a U-0.75wt%Ti alloy has been studied in planar (disk-on-disk), reverse (disk-on-rod) and symmetric (rod-on-rod) ballistic impact experiments performed with a 25 mm light-gas gun. The impact velocities ranged between 100 and 500 m/sec and the samples were softly recovered for further examination, revealing different degrees of spall fracture (planar impact) and of adiabatic shear bands (ballistic experiments). The back (planar experiments) and the lateral (ballistic experiments) surface velocities were continuously monitored by VISAR. The velocity profiles and the damage maps were simulated using a 2-D AUTODYN Lagrangian finite differences code. Simulations of the planar experiments were performed with special attention to the compressive path of the loading cycle in order to calibrate a modified Steinberg-Cochran-Guinan (SCG) constitutive model. The Bauschinger effect and a single-parameter spall model were added to describe the unloading and tensile paths. The calibrated SCG model was then employed to simulate the ballistic experiments. An erosion AUTODYN built-in subroutine with a threshold value of plastic strain was chosen to describe the failure in the ballistic impact experiments. The results of the suggested experimental-numerical technique can be taken into account in estimating the different contributions to the shock-induced plastic deformation and failure.

Metals far from equilibrium: From shocks to radiation damage

Shock waves and high-energy particle radiation can each drive materials far from thermodynamic equilibrium and enable novel scenarios in the processing of materials. A large number of theoretical and experimental studies of shock deformation have been performed on polycrystalline materials, but shock deformation in single crystals has only recently been studied in some detail. We present molecular dynamics (MD) simulations of the shock response of single crystal copper, modeled using an embedded atom potential that reproduces both defect formation and high pressure behavior. Shock-induced plasticity will also be discussed. Predicting the in-service response of ferritic alloys in future fusion energy environments requires a detailed understanding of the mechanisms of defect accumulation and microstructure evolution in harsh radiation environments, which include a high level of He generation concurrent with primary damage production. The second half of this paper describes results of atomistic MD and kinetic Monte Carlo simulations to investigate the role of He on point defect cluster behaviour and damage accumulation in bcc Fe. The goal of these simulations is to study the mechanisms responsible for the formation of vacancy-He clusters which serve as He bubble and void nuclei in fusion reactor materials.

Subnanosecond x-ray diffraction from laser-shocked crystals.

We have used single-shot sub-nanosecond x-ray diffraction to directly measure lattice parameters of crystals during the passage of laser-driven shock waves. Changes in the interatomic spacings can be measured with a temporal resolution better than 50 ps. We have studied shock-launching in single crystals and have directly measured dynamic tension during shock-breakout from a rear surface. In separate experiments we have directly observed the onset of shock-induced plasticity by diffracting from planes running perpendicular to the shock front. In addition to the single crystal work we have recently demonstrated that we can record x-ray powder patterns with sub-nanosecond exposure times; and are now in a position to laser-shock polycrystalline material simultaneously with the x-ray flash. The technique promises to be useful in the study of many fundamental problems in shock wave physics, including the behaviour of materials at the lattice level during plastic deformation and shock-induced polymorphic phase transitions.

X-ray diffraction analysis of plastic deformation in the Salmon Event

X-ray diffraction rocking curve studies were combined with X-ray topography of halite crystals taken from the Tatum salt dome before and after the 5-kT Salmon nuclear explosion. The results of these measurements indicated that beyond a radial distance of 126 meters from the shot point the halite had experienced no detectable shock-induced plastic deformation. At distances less than 126 meters the strain accommodation consisted of intragranular gliding on multiple slip systems and localized rotation of substructural lattice regions with respect to each other. This turbulent plastic deformation led to pronounced lattice kinking and eventually to a general fragmentation of the halite crystals. The breakup of the halite lattice into small subgrain blocks and the misorientation between subgrain blocks increased with approach toward the shot point. Because of the relatively low values of the angular range of reflection of the subgrain blocks in comparison with the large induced misorientation between the blocks, it was inferred that excessive accumulation of long-range stresses was absent and that the shocked structure tended to assume a configuration of low lattice strain.