High strain rate deformation and fracture of the magnesium alloy Ma2-1 under shock wave loading

This paper presents the results of measurements of the dynamic elastic limit and spall strength under shock wave loading of specimens of the magnesium alloy Ma2-1 with a thickness ranging from 0.25 to 10 mm at normal and elevated (to 550°C) temperatures. From the results of measurements of the decay of the elastic precursor of a shock compression wave, it has been found that the plastic strain rate behind the front of the elastic precursor decreases from 2 × 10⁵ s^?1 at a distance of 0.25 mm to 10³ s^?1 at a distance of 10 mm. The plastic strain rate in a shock wave is one order of magnitude higher than that in the elastic precursor at the same value of the shear stress. The spall strength of the alloy decreases as the solidus temperature is approached.     

Deformation resistance and fracture of iron over a wide strain rate range

The results of measurements of the decay of an elastic precursor in iron at the distances from 0.13 to 10 mm and the spall strength of the samples with such thicknesses have been compared with similar data for the nanometer-scale samples. The decay has been described by a unique dependence whose differentiation gives the relationship between the initial plastic strain rate in the range from 10³ to 10⁹ s^?1 and the compression stress in the elastic shock wave from 1.5 to 27.5 GPa. The dynamic breaking strength (spall strength) varies in this range of shock-wave load time from 1.5 to 20 GPa.     

Two-wave structure of plastic relaxation waves in crystals under intense shock loading

The mechanism of formation of a two-wave structure of plastic relaxation waves at shock wave stresses σ > 1 GPa (plastic strain rates $\dot \varepsilon $ > 10⁶ s^?1) has been theoretically considered using the dislocation kinetic equations and relationships. It has been shown that, under intense shock loading, two plastic relaxation waves are generated in the crystal. Initially, there arises the first wave (in the traditional terminology, it is an elastic precursor) associated with the generation of geometrically necessary dislocations at the boundary between the compressed and uncompressed parts of the crystal. Then, there arises the second wave due to the dislocation multiplication on geometrically necessary dislocations of the first wave in the form of forest dislocations. The dependences of the stresses on the plastic strain rate σ ～ $\dot \varepsilon ^{1/4} $ in the first wave and σ ～ $\dot \varepsilon ^{2/5} $ in the second wave, as well as the dependences of the stresses on the thickness of the target D, i.e., σ ～ D ^?1/3 and σ ～ D ^?2/3, respectively, have been determined by solving the relaxation equations. The obtained relationships have been confirmed by the experimental data available in the literature.     

Behavior of aluminum near an ultimate theoretical strength in experiments with femtosecond laser pulses

The dynamics of the motion of the free surface of micron and submicron films under the action of a compression pulse excited in the process of femtosecond laser heating of the surface layer of a target has been investigated by femtosecond interferometric microscopy. The relation between the velocity of the shock wave and the particle velocity behind its front indicates the shock compression to 9–13 GPa is elastic in this duration range. This is also confirmed by the small (≤1 ps) time of an increase in the parameters in the shock wave. Shear stresses reached in this process are close to their estimated ultimate values for aluminum. The spall strength determined at a strain rate of 10⁹ s⁻¹ and a spall thickness of 250–300 nm is larger than half the ultimate strength of aluminum.     

On the homogeneous nucleation and propagation of dislocations under shock compression

The dynamic response of crystalline materials subjected to extreme shock compression is not well understood. The interaction between the propagating shock wave and the material’s defect occurs at the sub-nanosecond timescale which makes in situ experimental measurements very challenging. Therefore, computer simulation coupled with theoretical modelling and available experimental data is useful to determine the underlying physics behind shock-induced plasticity. In this work, multiscale dislocation dynamics plasticity (MDDP) calculations are carried out to simulate the mechanical response of copper reported at ultra-high strain rates shock loading. We compare the value of threshold stress for homogeneous nucleation obtained from elastodynamic solution and standard nucleation theory with MDDP predictions for copper single crystals oriented in the [0 0 1]. MDDP homogeneous nucleation simulations are then carried out to investigate several aspects of shock-induced deformation such as; stress profile characteristics, plastic relaxation, dislocation microstructure evolution and temperature rise behind the wave front. The computation results show that the stresses exhibit an elastic overshoot followed by rapid relaxation such that the 1D state of strain is transformed into a 3D state of strain due to plastic flow. We demonstrate that MDDP computations of the dislocation density, peak pressure, dynamics yielding and flow stress are in good agreement with recent experimental findings and compare well with the predictions of several dislocation-based continuum models. MDDP-based models for dislocation density evolution, saturation dislocation density, temperature rise due to plastic work and strain rate hardening are proposed. Additionally, we demonstrated using MDDP computations along with recent experimental reports the breakdown of the fourth power law of Swegle and Grady in the homogeneous nucleation regime.     

Temperature–rate dependences of the flow stress and the resistance to fracture of a VT6 titanium alloy under shock loading at a temperature of 20 and 600°C

The evolution of elastic-plastic shock compression waves in a VT6 titanium alloy is measured at a distance of 0.16–17 mm at room temperature and 600°C. The results of measuring the decay of an elastic precursors and the compression rate in a plastic shock wave are used to determine the temperature–rate dependences of the flow stress in the strain-rate range 10³–10^7s–1. New data for the spall strength of the alloy at normal and elevated temperatures are obtained.     

On the power-law pressure dependence of the plastic strain rate of crystals under intense shock wave loading

The plastic deformation of metallic crystals under intense shock wave loading has been theoretically investigated. It has been experimentally found that the plastic strain rate $\dot \varepsilon $ and the pressure in the wave P are related by the empirical expression $\dot \varepsilon $ ～ P ⁴ (the Swegle-Grady law). The performed dislocation-kinetic analysis of the mechanism of the origin of this relationship has revealed that its power-law character is determined by the power-law pressure dependence of the density of geometrically necessary dislocations generated at the shock wave front ρ ～ P ³. In combination with the rate of viscous motion of dislocations, which varies linearly with pressure (u ～ P), this leads to the experimentally observed relationship $\dot \varepsilon $ ～ P ⁴ for a wide variety of materials with different types of crystal lattices in accordance with the Orowan relationship for the plastic strain rate $\dot \varepsilon $ = bρu (where b is the Burgers vector). In the framework of the unified dislocation-kinetic approach, it has been theoretically demonstrated that the dependence of the pressure (flow stress) on the plastic strain rate over a wide range from 10^?4 to 10¹⁰ s^?1 reflects three successively developing processes: the thermally activated motion of dislocations, the viscous drag of dislocations, and the generation of geometrically necessary dislocations at the shock wave front.     

Ultrahigh-strain-rate plastic deformation of a stainless-steel sheet with TiN coatings driven by laser shock waves

In this paper, a novel dynamic ultrahigh-strain-rate forming method driven by laser impact is reported. The technique is based on a mechanical, not thermal, effect. It is found that the ultrahigh-strain-rate is the most important feature for laser shock forming. Usually it is about 10⁷–10⁹ s^-1, two or more orders of magnitude higher than that of explosive forming, a method with the largest strain rate previously. Studies on the hardness and residual stress of the surfaces indicate that laser shock forming has some peculiarities other forming methods lack. It introduces strain hardening and compressive residual stresses on both surfaces of the metal sheet, resulting in an obvious improvement in fatigue and corrosion resistance. We also discover some non-linear plastic deformation characteristics in laser shock forming. PACS 42.62.Cf; 81.70.C; 62.20.-x; 81.40.Vw; 62.50.+p; 81.65.-b     

Effect of Small Preliminary Deformation on the Evolution of Elastoplastic Waves of Shock Compression in Annealed VT1-0 Titanium

The evolution of an elastoplastic waves of shock compression in VT1-0 titanium in the as-annealed state and after preliminary compression is measured. A preliminary strain of 0.6% and the related increase in the dislocation density are found to change the deformation kinetics radically and to decrease the Hugoniot elastic limit. An increase in the preliminary strain from 0.6% to 5.2% only weakly changes the Hugoniot elastic limit and the compression rate in the plastic shock wave. The measurement results are used to plot the strain rate versus the stress at the initial stage of high-rate deformation, and the experimental results are interpreted in terms of dislocation dynamics.     

冲击加载下Zr51Ti5Ni10Cu25Al9金属玻璃的塑性行为

进行了10—27 GPa应力范围内Zr₅₁Ti₅Ni₁₀Cu₂₅Al₉金属玻璃的平面冲击实验以研究其高压-高应变率加载下的塑性行为.由样品自由面粒子速度剖面的分析获得了冲击加载过程的轴向应力,并通过轴向应力与静水压线的比较获得剪应力.实验结果表明,尽管存在明显的松弛效应,但Zr基金属玻璃的Hugoniot弹性极限随着冲击应力的增加而增加.然而,塑性波阵面上的剪应力则显示先硬化而后软化现象,而且软化的幅度随冲击应力的增加而增加.冲击加载下Zr基金属玻璃的上述剪应力变化特征与分子动力学模拟结果比较一致,但与压剪实验结果和一维应力冲击实验结果明显不同.     

High strain rate response of an elastomer

Abstract

Plate impact experiments have been performed to examine the high strain rate response of an elastomer (explosive binder) shocked to 8 kbar stress. Particle velocity data have been obtained using in-material electromagnetic velocity gauges. Normal impact experiments have provided compression and release wave velocities and stress-strain results; ramp wave experiments indicate that the elastomer response is independent of loading rate; inclined plate impact measurements show that the material does not support any shear even at these strain rates. Additionally, numerical simulations have been performed to show that shock propagation in viscous fluids canbe simulated without artificial viscosity but by using the material viscosity in the constitutive relations. Such simulations will be useful in obtaining material viscosities from the measured wave profiles.     

高压、高应变率与低压、高应变率实验的本构关联性

 指出Johnson-Cook（J-C）、Zerilli-Armstrong（Z-A）、Bodner-Parton（B-P）本构方程在一定条件下的适用性,表明对于低压、高应变率实验,单一曲线假定似乎可以采用。通过等效应力、等效应变,可以将不同应力状态下的流动应力函数采用统一的方程描述。然而,这些本构方程的确立,并不包括平面冲击波实验。对适合于平面冲击波实验的Steinberg-Cochran-Guinan（SCG）本构方程,讨论了其方程中所包含的高压与高应变率耦合效应。指出,以剪切模量度量的流动应力具有应变率相关性。基于温度效应的新发现以及直接测量平面冲击波流动应力的新进展,分别用J-C本构及SCG本构方程估算了钨材料在高压、高应变率加载下的流动应力。结果表明,采用J-C本构估算的流动应力仅在压力为10 GPa以下才能与实验数据相近,当压力高于10 GPa时,流动应力只能采用SCG本构估算。也指出了高压、高应变率本构方程与低压、高应变率本构方程所对应的不同物理背景。     

Influence of plastic deformation on fracture of an aluminum single crystal under shock-wave loading

The plastic deformation and the onset of fracture of single-crystal metals under shock-wave loading have been studied using aluminum as an example by the molecular dynamics method. The mechanisms of plastic deformation under compression in a shock wave and under tension in rarefaction waves have been investigated. The influence of the defect structure formed in the compression wave on the spall strength and the fracture mechanism has been analyzed. The dependence of the spall strength on the strain rate has been obtained.     

冲击波极端条件下玻璃的细观结构破坏

 研究了冲击波极端条件下玻璃介质的细观结构破坏问题，指出在低于Hugoniot弹性极限的应力区内，按照细观结构损伤程度的不同，在受压玻璃介质中可以划分出两个区域，即压缩区和破坏区。以K9和ZF1玻璃为例，通过双层结构样品实验，确认了玻璃样品的表面效应（即表面原生微裂纹的扩展）是破坏区形成的第一位原因。其次，基于对破坏区内细观结构损伤和破坏特性的分析，进一步提出：由于玻璃内部散布的不均匀相与其基体介质之间的压缩率不同，冲击波压缩造成了众多的局域变形点，当表面裂纹扩展到不均匀相与基体的边界处，会出现裂纹扩展路径拐折或分叉，造成介质的分割甚至粉碎，这是破坏区生成的第二位原因。     

Elastoplastic behavior of marble, granite, and quartzite under shock compression

Profiles of elastoplastic shock waves were experimentally revealed in three rocks, namely, in marble (ρ₀=2.68 g/cm³), quartzite (ρ₀=2.65 g/cm³), and granite (ρ₀=2.63 g/cm³). In all these substances, the splittingof the shock-wave front into a leading elastic precursor and a following plastic compression wave wererevealed. A diffusion of the front of the elastic precursor and a decrease in its amplitude were found to occur asthe front propagates through the samples of the substances studied. No sharp decrease in the amplitude of elasticwaves (yielding “tooth”) was fixed. Pressures in the elastic and plastic compression waves, as well as the waveand mass velocities and the magnitudes of the relative compression were determined.     

A dislocation kinetic model of the formation and propagation of intense shock waves in crystals

Analytical expressions for the front of a shock plastic wave and the plastic relaxation region behind the front have been obtained and a relation of the wave parameters to the pressure in the wave has been determined in the framework of the dislocation kinetic approach based on kinetic relationships and equations for the density of dislocations. Within this approach, the physical mechanism of the origin and the universality of the Swegle-Grady empirical relationship for crystals in the form of a power-law dependence of the plastic strain rate $\dot \varepsilon $ on the pressure in the wave P, that is, $\dot \varepsilon $ ～ P ⁴, have been discussed. The principal contribution to this dependence comes from the power-law (cubic) dependence of the density of dislocations generated in the wave front on the pressure. The universality of the Swegle-Grady relationship is based on the invariance of the dissipative action A. An explicit expression for the dissipative action has been derived: A = SBV ₀/3β. As follows from this expression, the dissipative action is determined by fundamental parameters for shock wave loading of crystals, such as the dislocation viscous drag coefficient B and the adiabaticity factor S (here, V ₀ is the specific volume and β is a coefficient of the order of 10^?3–10^?2). In light of the revealed circumstances, such phenomenological notions as the Hugoniot elastic limit and the elastic precursor have been critically examined.     

Nonequilibrium processes in condensed media: Part 1. Experimental studies in light of nonlocal transport theory

Based on experimental research in shock loading of solid-state materials it is shown that among the important dynamic characteristics of the process, like spatial-temporal mass velocity profiles of shock waves, are the mass velocity variation, velocity defect, and structural instability threshold recorded in real time. Analysis of these characteristics depending on the strain rate, target thickness, and structural state of material demonstrates that conventional approaches of continuum mechanics fail to provide their adequate interpretation and simulation of shock wave processes. A new concept of shock wave processes in condensed media is proposed. The concept, being based on nonlocal nonequilibrium transport theory, allows describing the transition from elastic to hydrodynamic response of a medium depending on the loading rate and time. A nonstationary elastoplastic wave model is proposed for describing the relaxation of an elastic precursor and formation of a retarded plastic front during the wave propagation in a medium with regard to structural evolution. Analysis of the experimental data shows that the division of stresses and strains into elastic and plastic components is incorrect for shock loading.     

Semiconductor-metal transition in selenium under shock compression

Phase transitions in selenium are studied by time-resolved measurements of the electrical conductivity under shock compression at a pressure of up to 32 GPa. The pressure dependence of the electrical conductivity (σ(P)) has two portions: a sharp increase at P < 21 GPa and a plateau at P > 21 GPa. The experimental data and the temperature estimates indicate that, at P < 21 GPa, selenium is in the semiconductor state. The energy gap of semiconducting selenium decreases substantially under compression. At P > 21 GPa, the electrical conductivity saturates at ～10⁴ Ω^?1 cm^?1. Such a high value of the electrical conductivity shows the effective semiconductor-metal transition taking place in shock-compressed selenium. Experiments with samples having different initial densities demonstrate the effect of temperature on the phase transition. For example, powdered selenium experiences the transition at a lower shock pressure than solid selenium. Comparison of the temperature estimates with the phase diagram of selenium shows that powdered selenium metallizes in a shock wave as a result of melting. The most plausible mechanism behind the shock-induced semiconductor-metal transition in solid selenium is melting or the transition in the solid phase. Under shock compression, the metallic phase arises without a noticeable time delay. After relief, the metallic phase persists for a time, delaying the reverse transition.     

纳米多晶铜中冲击波阵面的分子动力学研究

冲击波阵面反映材料在冲击压缩下的弹塑性变形行为以及屈服强度、应变率条件等宏观量, 还与冲击压缩后的强度变化联系. 本文使用分子动力学方法, 模拟研究了冲击压缩下纳米多晶铜中的动态塑性变形过程, 考察了冲击波阵面和弹塑性机理对晶界存在的依赖, 并与纳米多晶铝的冲击压缩进行了比较. 研究发现: 相比晶界对纳米多晶铝的贡献而言, 纳米多晶铜中晶界对冲击波阵面宽度的影响较小; 并且其塑性变形机理主要以不全位错的发射和传播为主, 很少观察到全位错和形变孪晶的出现. 模拟还发现纳米多晶铜的冲击波阵面宽度随着冲击应力的增加而减小, 并得到了冲击波阵面宽度与冲击应力之间的定量反比关系, 该定量关系与他人纳米多晶铜模拟结果相近, 而与粗晶铜的冲击压缩实验结果相差较大.     

Shock-wave studies of anomalous compressibility of glassy carbon

The physico-mechanical properties of amorphous glassy carbon are investigated under shock compression up to 10 GPa. Experiments are carried out on the continuous recording of the mass velocity of compression pulses propagating in glassy carbon samples with initial densities of 1.502(5) g/cm³ and 1.55(2) g/cm³. It is shown that, in both cases, a compression wave in glassy carbon contains a leading precursor with amplitude of 0.135(5) GPa. It is established that, in the range of pressures up to 2 GPa, a shock discontinuity in glassy carbon is transformed into a broadened compression wave, and shock waves are formed in the release wave, which generally means the anomalous compressibility of the material in both the compression and release waves. It is shown that, at pressure higher than 3 GPa, anomalous behavior turns into normal behavior, accompanied by the formation of a shock compression wave. In the investigated area of pressure, possible structural changes in glassy carbon under shock compression have a reversible character. A physico-mechanical model of glassy carbon is proposed that involves the equation of state and a constitutive relation for Poisson’s ratio and allows the numerical simulation of physico-mechanical and thermophysical properties of glassy carbon of different densities in the region of its anomalous compressibility.