D. L. Tonks

Model of plastic deformation for extreme loading conditions

We present a model of metallic plastic flow suitable for numerical simulations of explosive loading and high velocity impacts. The dependence of the plastic strain rate on applied stress at low strain rates is of the Arrhenius form but with an activation energy that is singular at zero stress so that the deformation rate vanishes in that limit. Work hardening is modeled as a generalized Voce law. At strain rates exceeding 109 s−1, work hardening is neglected, and the rate dependence of the flow stress is calculated using Wallace’s theory of overdriven shocks in metals [D.C. Wallace, Phys. Rev. B 24, 5597 (1981); 24, 5607 (1981)]. The thermal-activation regime is continuously merged into the strong shock limit, yielding a model applicable over the 15 decades in strain rate from 10−3 to 1012 s−1. The model represents all aspects of constitutive behavior seen in Hopkinson bar and low-rate data, including a rapid increase in the constant-strain rate sensitivity, with 10% accuracy. High-pressure behavior is co...

Effects of grain size and boundary structure on the dynamic tensile response of copper

Plate impact experiments have been carried out to examine the influence of grain boundary characteristics on the dynamic tensile response of Cu samples with grain sizes of 30, 60, 100, and 200 μm. The peak compressive stress is ∼1.50 GPa for all experiments, low enough to cause an early stage of incipient spall damage that is correlated to the surrounding microstructure in metallographic analysis. The experimental configuration used in this work permits real-time measurements of the sample free surface velocity histories, soft-recovery, and postimpact examination of the damaged microstructure. The resulting tensile damage in the recovered samples is examined using optical and electron microscopy along with micro x-ray tomography. The free surface velocity measurements are used to calculate spall strength values and show no significant effect of the grain size. However, differences are observed in the free surface velocity behavior after the pull-back minima, when reacceleration occurs. The magnitude of th...

Micromechanics of spall and damage in tantalum

The authors conducted a series of plate impact experiments using an 80-mm launcher to study dynamic void initiation, linkup, and spall in tantalum. The tests ranged in peak shock pressures so that the effect of peak pressure on the transition from void initiation, incipient spall, and full spall could be studied. Wave profiles were measured using a velocity interferometry system (VISAR), and targets were recovered using {open_quotes}soft{close_quotes} recovery techniques. The authors utilized scanning electron microscopy, metallographic cross-sections, and plateau etching techniques to obtain quantitative information concerning damage evolution in tantalum under spall conditions. The data (wave profiles and micrographs) are analyzed in terms of a new theory and model of dynamic damage cluster growth.

Anisotropic shock response of columnar nanocrystalline Cu

We perform molecular dynamics simulations to investigate the shock response of idealized hexagonal columnar nanocrystalline Cu, including plasticity, local shear, and spall damage during dynamic compression, release, and tension. Shock loading (one-dimensional strain) is applied along three principal directions of the columnar Cu sample, one longitudinal (along the column axis) and two transverse directions, exhibiting a strong anisotropy in the response to shock loading and release. Grain boundaries (GBs) serve as the nucleation sites for crystal plasticity and voids, due to the GB weakening effect as well as stress and shear concentrations. Stress gradients induce GB sliding which is pronounced for the transverse loading. The flow stress and GB sliding are the lowest but the spall strength is the highest, for longitudinal loading. For the grain size and loading conditions explored, void nucleation occurs at the peak shear deformation sites (GBs, and particularly triple junctions); spall damage is entirely intergranular for the transverse loading, while it may extend into grain interiors for the longitudinal loading. Crystal plasticity assists the void growth at the early stage but the growth is mainly achieved via GB separation at later stages for the transverse loading. Our simulations reveal such deformation mechanisms as GB sliding, stress, and shear concentration, GB-initiated crystal plasticity, and GB separation in nanocrystalline solids under shock wave loading.

Shock wave loading and spallation of copper bicrystals with asymmetric Σ3〈110〉tilt grain boundaries

We investigate the effect of asymmetric grain boundaries (GBs) on the shock response of Cu bicrystals with molecular dynamics simulations. We choose a representative Σ3〈110〉tilt GB type, (110)_1/(114)_2, and a grain size of about 15 nm. The shock loading directions lie on the GB plane and are along [001] and [221] for the two constituent crystals. The bicrystal is characterized in terms of local structure, shear strain, displacement, stress and temperature during shock compression, and subsequent release and tension. The shock response of the bicrystal manifests pronounced deviation from planar loading as well as strong stress and strain concentrations, due to GBs and the strong anisotropy in elasticity and plasticity. We explore incipient to full spallation. Voids nucleate either at GBs or on GB-initiated shear planes, and the spall damage also depends on grain orientation.

Spall damage of copper under supported and decaying shock loading

We investigate spall damage of single crystal Cu under supported (square) and decaying (Taylor wave) shock wave loading with molecular dynamics simulations. Varying the target-to-flyer plate thickness ratio R (with target thickness fixed) as well as the impact velocity induces square and Taylor waves with different pulse shapes, durations and strengths, which are well correlated with prespall damage, spall strength, and spall damage. Taylor wave loading results in higher spall strength than the supported shock loading at the same impact velocities, and the spall strength can be similar for both loadings with the same peak free surface velocities, while Taylor wave loading induces less spall damage than square wave loading. Void nucleation is preceded by plasticity and solid-state disordering. Multiple spall events appear to be independent of each other at the early stage of spallation. In applying the acoustic method for deducing the spall strength from the free surface velocity histories, one should cons...

Dynamic response of phenolic resin and its carbon-nanotube composites to shock wave loading

We investigate with nonreactive molecular dynamics simulations the dynamic response of phenolic resin and its carbon-nanotube CNT composites to shock wave compression. For phenolic resin, our simulations yield shock states in agreement with experiments on similar polymers except the “phase change” observed in experiments, indicating that such phase change is chemical in nature. The elastic–plastic transition is characterized by shear stress relaxation and atomic-level slip, and phenolic resin shows strong strain hardening. Shock loading of the CNT-resin composites is applied parallel or perpendicular to the CNT axis, and the composites demonstrate anisotropy in wave propagation, yield and CNT deformation. The CNTs induce stress concentrations in the composites and may increase the yield strength. Our simulations suggest that the bulk shock response of the composites depends on the volume fraction, length ratio, impact cross-section, and geometry of the CNT components; the short CNTs in current simulations have insignificant effect on the bulk response of resin polymer.

The effect of vacancies on dynamic response of single crystal Cu to shock waves

Using molecular dynamics (MD) simulations, we investigate the effect of vacancies on the dynamic response of single crystal Cu to [100] shock loading, including plasticity and spallation, for an initial vacancy concentration (cv) ranging from 0% to 2%. A fixed impact velocity is adopted, for which plasticity and spall do not occur in the defect-free Cu during compression or tension. We show that shear flow strength (compressional or tensile) and spall strength decrease with increasing cv. At the MD scales, the vacancy effect becomes pronounced for cv>0.25%, where heterogeneous nucleation of plasticity prevails. Tensile plasticity may play a key role in inducing local heating and the power-law reduction in spall strength. Void nucleation occurs preferentially at highly sheared (plastically deformed) sites.

Void Coalescence Model for Ductile Damage

A model for void coalescence for high strain rate ductile damage in metals is presented. The basic mechanism is void linking through an instability in the intervoid ligament. The formation probability of void clusters is calculated, as a function of cluster size, imposed stress, and strain. A wave speed limiting is applied to the cluster size enhancement of cluster growth. Due to lack of space, model formulas are merely described and not derived.

Shock compression and spallation of single crystal tantalum

We present molecular dynamics simulations of shock-induced plasticity and spall damage in single crystal Ta described by a recently developed embedded-atom-method (EAM) potential and a volumedependent qEAM potential. We use impact or Hugoniotstat simulations to investigate the Hugoniots, deformation and spallation. Both EAM and qEAM are accurate in predicting, e.g., the Hugoniots and γ - surfaces. Deformation and spall damage are anisotropic for Ta single crystals. Our preliminary results show that twinning is dominant for [100] and [110] shock loading, and dislocation, for [111]. Spallation initiates with void nucleation at defective sites from remnant compressional deformation or tensile plasticity. Spall strength decreases with increasing shock strength, while its rate dependence remains to be explored.