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Shock-induced structural transformations in copper exhibit notable directional dependence and anisotropy, but the mechanisms that govern the responses of materials with different orientations are not yet well understood. In this study, we employ large-scale non-equilibrium molecular dynamics simulations to investigate the propagation of a shock wave through monocrystal copper and analyse the structural transformation dynamics in detail. Our results indicate that anisotropic structural evolution is determined by the thermodynamic pathway. A shock along the ⟨100⟩ orientation causes a rapid and instantaneous temperature spike, resulting in a solid–solid phase transition. Conversely, a liquid metastable state is observed along the ⟨111⟩ orientation due to thermodynamic supercooling. Notably, melting still occurs during the ⟨110⟩ -oriented shock, even if it falls below the supercooling line in the thermodynamic pathway. These results highlight the importance of considering anisotropy, the thermodynamic pathway and solid-state disordering when interpreting phase transitions induced by shock. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'. [ABSTRACT FROM AUTHOR]

This paper touches upon a question of whether the physical state of shock-compressed copper is equilibrium. Answering this question requires that experimental data on defective electrical resistance are used to estimate point defect concentration. Quantitative information on the concentration of defects can be obtained if the type of occurring defects is known. A dependence between defect concentration in copper and a shock wave pressure is obtained in an assumption of the predominant formation of vacancies. It is shown that the number of defects monotonically increases with increasing shock wave pressure. The vacancy concentration calculated in this study (≈0.8% at a pressure of 20 GPa) exceeds the corresponding equilibrium value by ten orders of magnitude. Thus, the state of copper under shock compression is highly defective and highly nonequilibrium. The general features of the state of copper and silver are described by comparing data for shock-compressed metals. As demonstrated by comparing the data obtained immediately after the passage of a shock wave through a sample (in situ) with the known results for samples recovered after the experiment, the number of recorded defect concentrations in the first case is larger (up to two orders of magnitude). Thus, the method of stored samples does not provide objective information on the state of substance directly behind the shock front. The problem of constructing the equation of state under conditions of a nonequilibrium physical state is briefly discussed. [ABSTRACT FROM AUTHOR]

Single crystals subjected to shock compression exhibit responses with distinct two-wave structures for certain crystal orientations. However, little is known to date regarding how the shock response depends on crystal orientation, and especially why the two-wave structure depends on the crystal orientation. In this work, molecular dynamics simulations of shock compressions in copper single crystals are performed to investigate the orientation dependence of shock responses and the corresponding deformation mechanisms. Four copper single crystals with [001], [011], [012], and [123] crystal orientations along the depth direction are investigated. The [011], [012], and [123] crystal orientations of copper single crystals show distinct two-wave structures in their shock responses, while such a two-wave structure in the shock response is not seen for those orientations having a [001] crystal orientation. The potential causes are analyzed by considering the propagation velocities of both elastic and plastic waves. We develop a technique for identifying twin structures in face-centered cubic crystals and this technique can effectively identify the twin structure. The morphology of shock-induced defects (e.g., dislocations and twins) shows the significant dependence of crystal orientation and the mechanisms behind these are discussed in detail. Finally, the Johnson-Cook constitutive model describing dynamic deformations at high temperatures and high strain rates is used to analyze the relationships between the shock responses and microscopic defects. The predictions of the Johnson-Cook constitutive model are consistent with the results of the molecular dynamics simulations. [ABSTRACT FROM AUTHOR]

Abstract—The dynamic properties of commercial copper (99.8 wt % purity) with a submicrocrystalline and nanocrystalline structure obtained by high-strain-rate deformation using the dynamic channel-angular pressing (DCAP) method have been studied in this work. The tests were carried out under conditions of shock compression at a pressure of 5.6−6.8 GPa at a strain-rate of (0.9−2.0) × 105 s–1. The analysis of the evolution of the structure and mechanical properties, namely, the dynamic elastic limit, dynamic yield stress, and the spall strength of copper before and after DCAP in different regimes, made it possible to evaluate the influence of the dispersity and imperfection of the crystal structure on its resistance to the high-strain-rate deformation and fracture. It has been shown that the grain refinement from 100 to 0.5−1.0 μm increased the dynamic elastic limit and the dynamic yield stress of copper by six times, but only slightly decreased the spall strength. The further refinement of the structure (up to 0.05−0.40 μm) increases the spall strength of copper by 1.4 times as compared to its value in the initial coarse-grained state. [ABSTRACT FROM AUTHOR]

• Shock compression of porous Cu with various gas concentrations, porosities and shock intensities is studied via MD. • The HEL of porous metals increases with higher gas concentration and decreases with larger porosity. • The back-and-forth propagation of elastic shockwave leads to the formation of the "surface cap" structure. • The presence of gas significantly inhibits the post-shock temperature rising. • A new model for predicting the Hugoniot of porous materials containing gas is proposed based on Wu-jing EOS. Shock compression of porous copper containing helium is studied via non-equilibrium molecular dynamic simulations. The results show that the shock propagation exhibits an elastic-plastic double-shockwave structure at low shock velocity. The shock Hugoniot elastic limit increases with higher gas concentration, and decreases with larger porosity, while almost independent of the shock velocity. The back-and-forth propagation of elastic shockwave between plastic shockwave and free surface leads to the occurrence of the special structure of "surface cap", which can protect the porous metal in the vicinity of the free surface from collapse. The plastic shock propagates faster with higher gas concentration and gradually catches up with the elastic shockwave as shock intensity increases. Compared with porous copper without gas, the presence of helium significantly inhibits the post-shock temperature rising and the shock melting behavior. A new theoretical model was proposed to quantify the shock Hugoniot of porous materials containing gas. The model's predictions align well with MD simulations across a wide pressure range up to 100 GPa with different gas concentrations and porosities. [ABSTRACT FROM AUTHOR]

A simple phenomenological model of electrical resistance of metals at high pressures and temperatures is considered on the basis of the Bloch-Griineisen equation of electrical resistance and Mie-Gruneisen equation of state. Two free parameters of the model for copper are found through comparisons of model predictions with experimental data on isothermal compression and isobaric heating. The dependence of the specific electrical resistance of copper on the shock pressure in the range up to 20 GPa is determined on the basis of experiments including measurements of electrical conductivity of foil samples. Comparisons of the experimental shock wave results with the formulated model reveal the difference in the specific electrical resistance values. It is proposed to attribute the observed difference between the model and experimental results to the nonequilibrium nature of the physical state under shock compression, leading to generation of defects of the crystal structure of the metal. The electrical resistance component caused by the crystal structure defects is identified, and its dependence on the shock pressure is determined. The concentration of point defects in shock-compressed copper is estimated. The contribution of defects to electrical resistance of the shock-compressed metal is found to increase with increasing pressure. This effect should be taken into account in determining the equilibrium specific electrical conductivity and the derivatives of the physical variables (e.g., thermal conductivity). [ABSTRACT FROM AUTHOR]

A few-parameter equation of state in the Mie-Grüneisen form is proposed to describe shock compression of condensed matter. The equation is based on a postulated dependence of the Grüneisen coefficient on the specific volume and temperature Γ(V, T), which provides a qualitative description of compression of metal samples in strong shock waves. The curve of cold compression is found on the basis of the dependence Γ(V, T) with the use of a generalized formula for the Grüneisen function. Heat-induced oscillations of the crystal lattice are described in the Debye approximation. The resultant Grüneisen function has two free parameters. The values of other coefficients of the equation of state are determined from the reference data for matter under normal conditions and also from limiting values under extreme conditions. The model is tested by an example of copper. The derived equation of state describes the cold compression curve, normal isotherm, shock compressibility, as well as the copper unloading curves in density, pressure, and internal energy ranges for which experimental data are available. The thermodynamic characteristics of copper (isentropic modulus of volume compression, velocity of sound, Debye temperature, specific heat, linear expansion coefficient, and melting temperature) are calculated. Comparisons with available experimental data show that the proposed model, despite its simplicity, ensures a consistent description of a large array of experimental data in the region of high energy densities. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulations of shock compression are carried out over a range of pressures (from 22 GPa to 75 GPa) to investigate the shock-induced defect microstructure in single crystal Cu. The results show that under increasing shock pressure, we can detect three distinct phases of the defect regimes for single crystal Cu: dislocations → stacking faults → twins. We show the evolution processes of different defect microstructures. According to the analyses of these evolution processes, the formation mechanisms of various defect microstructures are studied. When the shock pressure is less than 30 GPa, the motion of dislocations is a significant mechanism in single crystal Cu under the shock compression. The motion between various dislocations and loops widely exists on the (1 1 1) close-placed plane. The interesting dislocation loops are obtained at a relatively low pressure, and a new mechanism of nucleation and development of the dislocation loop is proposed. When the shock pressure is greater than 30 GPa, a large number of intersecting stacking faults are formed. On the (0 0 1) surface, stacking faults align along the [2 2 0] and [ 2 ¯ 2 0 ] directions at exactly 90 degrees, and they are present roughly in the same proportion. The stacking fault spacing decreases with the increase of shock pressure, and shock-induced plasticity increases as a function of shock strength. The structure of the simulation, based on the topology, matches extremely well with that found in recent transmission electron microscopy studies of single crystal Cu recovered from laser shock experiments. At a relatively high pressure (61 GPa), we find that the stacking faults and twins exist together in single crystal Cu. It is shown that two types of stacking faults with vertical directions are the competitive mechanism. When one of them dominates, twins will be formed from this type of stacking fault. Thus, the directions of twins are randomly distributed in the initial stage. Rotation and combination of twins are significant mechanisms, and these mechanisms lead to the final formation of twins. At 75 GPa, twins elongate along [ 1 2 ¯ 1 ] and [ 1 ¯ 2 ¯ 1 ¯ ] directions on the ( 1 ¯ 0 1 ) surface. The configuration and direction of the twins are in agreement with experimental results. [ABSTRACT FROM AUTHOR]

The electrical resistance of copper foil under shock compression is measured. The electrical resistance and electrical conductivity are plotted as functions of the shock pressure in the interval up to 20 GPa. These dependences are monotonic and have no visible inflections or singularities. A qualitative dependence of the electrical resistance of the metal on the shock impedance of the material of the block containing the sample is found. A comparison of the data obtained in this study with results of other authors shows that it is important to take into account the block material, the shape and thickness of the sample, and the procedure of determining the state of the sample. [ABSTRACT FROM AUTHOR]

The electrical conductivity of some compositions based on the copper powder under shock compression is measured. The commercial copper powder, mixtures of copper with glass microspheres, and copper-aluminum mixtures are studied. The electrical conductivity is measured by the author's electrocontact technique, which allows the insulator-metal transition to be measured. Dependences of the electrical conductivity of powders on the shock wave pressure are obtained. As for aluminum powders examined previously, this dependence for the copper powder has a nonmonotonic character. The maximum electrical conductivity is ≈ 9·10 Ω · cm. With a further increase in the shock pressure, the electrical conductivity decreases approximately by an order of magnitude, which is explained by intense temperature heating. The results for the electrical conductivity at high shock pressures is qualitatively consistent with known broad-range models of conductivity proposed by Garanin and Bakulin. [ABSTRACT FROM AUTHOR]

We utilize non-equilibrium molecular dynamics simulations to reveal the dislocation processes underlying the recently observed pronounced effect of bimetal interface structures on the plastic response of Cu/Nb nanolayered composites to shock compression. Critical shock pressures to nucleate and transmit dislocations across an atomically flat interface are shown to be substantially higher than those from a faceted interface, due to atomic-level interface characteristics that cause these two types of interfaces to nucleate, absorb and transmit dislocations by significantly different mechanisms. [ABSTRACT FROM AUTHOR]

While shock loading has long been used to investigate dynamic damage evolution in materials, the role of interface structure in the response of shock-loaded polycrystalline materials has largely been ignored. In this work, a specially fabricated multicrystalline Cu specimen is used to interrogate the role of interface structure on microstructural and substructural evolution in shock-loaded materials. Results show that, under shock, grain boundaries respond differently as a function of structure. [ABSTRACT FROM AUTHOR]

Abstract: Monocrystalline copper samples with [001] and [221] orientations were subjected to shock/recovery experiments at 30 and 57GPa and 90K. The slip system activity and the microstructural evolution were investigated. Different defect structures, including dislocations, stacking faults, twins, microbands, and recrystallized grains were observed in the specimens. The residual microstructures were dependent on crystalline orientation and pressure. The differences with crystalline orientations are most likely due to different resolved shear stresses on specific crystalline planes. The geometric relationships between the shock propagation direction and crystalline orientation are presented under uniaxial strain. It is shown that the [221] orientation, by virtue of having fewer highly activated slip systems, exhibits greater concentration of deformation with more intense shear on the primary system. This, in turn leads to greater local temperature rise and full recrystallization, in spite of the thermodynamic residual temperature of ∼500K and rapid cooling (within 20s) to ambient temperature. The profuse observation of microbands is interpreted in terms of the mechanism proposed by Huang and Gray [J.C. Huang, G.T. Gray III, Acta Metallurgica 37 (1989) 3335–3347]. [Copyright &y& Elsevier]

Abstract: Copper and copper aluminum (2 and 6wt% Al) with orientations [001] and [134] were subjected to high intensity laser shocks (energy levels of 40–300J; energy densities of 15–70MJ/m2 and durations below 10ns). In situ X-ray diffraction and VISAR wave profile measurements were used to study the response of the lattice to the shock. Recovered samples were characterized by transmission electron microscopy in order to study the defects within the lattice. The results are rationalized in terms of a criterion in which slip and twinning are considered as competing mechanisms. The slip-twinning transition is determined quantitatively and predicted as a function of orientation, temperature, and stacking fault energy (determined by the Al content of the alloy). A constitutive description is applied to the two orientations and differing compositions, incorporating both slip and twinning in terms of orientation, stacking fault energy, temperature, and strain rate. The threshold stress is calculated, considering the effect of shock heating. The constitutive description provides calculated thresholds in pure copper: 18GPa for [001] and 25GPa for [134]. The experimentally determined threshold twinning stress for pure copper in the [001] orientation is 25GPa, whereas the one for the [134] orientation is between 40 and 60GPa. The predictions are in agreement with experiments. It also provides thresholds for the Cu–Al alloys. The growth of voids in incipient spalling is modeled by dislocation loop emission from the void surface. The first dislocation-based void growth mechanism, proposed by Lubarda et al. [Acta Mat 2004; 52: 1397] is reviewed and extended to three dimensions. It has a generality rendering it applicable to a broad range of strain rates. [Copyright &y& Elsevier]

Radiation from shock-compressed water at pressures of 10.0-39.5 GPa loaded through targets made of various metals (Al, Mg, and Cu) is studied. It is shown that the radiation intensity depends on both shock pressure and the nature of the metal. At pressures below 25 GPa in the region of water transparency, the radiation intensity considerably exceeds the presumed level of thermal radiation. This effect can partly be explained by the interaction of the target material with water and by nonthermal radiation from shock-compressed water. For comparison, some experimental data on shock-induced radiation from a number of transparent materials (Kron-8 optical glass, glycerin, and sodium salt) are given. [ABSTRACT FROM AUTHOR]

For understanding material performance under dynamic loading, there is significant interest in the strain rate dependence of material response and in the degree to which high-rate response depends on initial material state. Experimental tests at high strain rates (> 10 3 / s) often use measurement of shape change to infer flow strength behavior. Given stress and strain heterogeneities, inferences about flow strength behavior from those observations are facilitated by comparisons with advanced simulations. A new plate impact-based experimental test is described, consisting of in situ X-ray imaging to observe the closure of a cylindrical hole during the passage of a pressure pulse of controlled amplitude and duration. With the goal of providing unique data regarding plastic response at high strain rates, the closure of the hole is measured through time using multi-frame imaging. A first set of experiments on copper examines the role of starting microstructure on material flow behavior. The experimental observations are compared with predictions from direct numerical simulations using the Preston-Tonks-Wallace (PTW) and the Mechanical Threshold Stress (MTS) flow strength models. The quantitative utility of the overall approach is demonstrated in that the results provide information about MTS model parameters associated with high-rate hardening behavior, with the parameters having been unconstrained by quasi-static experimental data. [ABSTRACT FROM AUTHOR]

• The compression ratios of nanoporous Cu with He doping are lower than that without He. • The shock wave propagates fast in the nanoporous Cu with high content of He doping. • It forms internal helium jets in the nanoporous Cu with He doping under high impact velocities. • The surface damage of nanoporous Cu is affected by impact velocity and concentration of helium. We have investigated the effects of helium (He) doping on the shock responses including shock Hugoniot, collapse mechanism of voids and the evolvement of microstructure in nanoporous copper (Cu) under shock wave loading using molecular dynamics method. We show that the compression ratios of nanoporous Cu with He doping are lower than that without He. The compression ratio reduces with the helium content increasing. The U s – u p relations shows that the shock wave propagates faster in the nanoporous Cu with 10% and 20% He doping than that without He. We further show that internal helium jets form in the nanoporous Cu with He doping under high impact velocities and a shock wave in He forms during the collapse process of helium-doped voids. We reveal that the critical impact velocity to form surface fragment in nanoporous Cu without He is about 2.0 km/s. The surface damage of the nanoporous Cu is affected by He doping when the atomic ratio of He–vacancy >5%. The results show that it is more difficult to form ejecta for nanoporous Cu with He doping under high speed impact. [ABSTRACT FROM AUTHOR]