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 10 9 s Ϫ1 , 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 ͑1981͒; 24, 5607 ͑1981͔͒. 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 Ϫ3 to 10 12 s Ϫ1. 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 controlled by the shear modulus, G(,T), and the melting temperature, T m

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 lm. 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 the spall peak and its acceleration rate are dependent upon the grain size. The quantitative, postimpact, metallographic analyses of recovered samples show that for the materials with grain sizes larger than 30 lm, the void volume fraction and the average void size increase with increasing grain size. In the 30 and 200 lm samples, void coalescence is observed to dominate the void growth behavior, whereas in 60 and 100 lm samples, void growth is dominated by the growth of isolated voids. Electron backscatter diffraction (EBSD) observations show that voids preferentially nucleate and grow at grain boundaries with high angle misorientation. However, special boundaries corresponding to Rl (low angle, < 5) and R3 ($60 <111> misorientation) types are more resistant to void formation. Finally, micro x-ray tomography results show three dimensional (3D) views of the damage fields consistent with the two dimensional (2D) surface observations. Based on these findings, mechanisms for the void growth and coalescence are proposed. V

A detailed study is carried out of the separation of resonance Raman scattering into orders within the time-correlator formulation of Hizhnyakov and Tehver (HT). This formulation is exact for a multimode system at all temperatures and for all electron–phonon coupling strengths within well-defined ’’standard assumptions.’’ As in any Raman theory, the full m-phonon Raman scattering involves the electron–phonon coupling to infinite order, owing to virtual phonon transitions accompanying the m real final state phonon transitions. The HT separation into orders is seen to correspond to a particularly convenient grouping of the contributions, such that the full m-phonon scattering is expressed as a power series in explicit orders of the electron–phonon coupling, but with each term of the series also containing factors involving the electron–phonon coupling implicitly to infinite order. Each term of this series except the first vanishes for T→ 0, with the result that the (explicitly) mth order scattering and the full m-phonon scattering are identical at T = 0. Most importantly, at any temperature the contributions from each order to the resonance Raman excitation profile line shapes are obtainable from the optical absorption in a direct and simple way. We have previously stressed the usefulness of the first-order version of this feature for the analysis of experimental data, and here that work is contrasted with recent work of Hassing and Mortensen, who expressed the full one-phonon series for a single-mode system in a different form. For completeness, a detailed derivation of the entire theory is given, including proofs via phonon many-body techniques of the two fundamental identities upon which the HT approach rests and which were not proven in HT’s rather condensed presentation of their time-correlator formulation.

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 strain͒ is applied along three principal directions of the columnar Cu sample, one longitudinal ͑along the column axis͒ and two transverse directions, exhibiting a strong anisotropy in the response to shock loading and release. Grain boundaries ͑GBs͒ 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 junctions͒; 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.

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