Influence of the reversible α–ε phase transition and preliminary shock compression on the spall strength of armco iron

Full wave profiles are used to determine the Hugoniot elastic limit and the spall strength of armco iron samples with an as-received structure and the samples recovered after preliminary loading by plane shock waves with an amplitude of 8, 17, and 35 GPa. The measurements are performed at a shock compression pressure below and above the polymorphic a–e transition pressure. Metallographic analysis of the structure of armco iron shows that a developed twinned structure forms inside grains in the samples subjected to preliminary compression and recovered and that the twin concentration and size increase with the shock compression pressure. The spall strength of armco iron under shock loading below the phase transition pressure increases by approximately 10% due to its preliminary deformation twinning at the maximum shock compression pressure. The spallation of samples with various structures at a shock compression pressure above the phase transition proceeds at almost the same tensile stresses. The polymorphic transition in armco iron weakly affects its strength characteristics.     

Deformation and Spallation of Explosive Welded Steels under Gas Gun Shock Loading

We investigate deformation and spallation of explosive welded bi-steel plates under gas gun shock loading. Free surface histories are measured to obtain the Hugoniot elastic limit and spall strengths at different impact velocities.Pre-and post-shock microstructures are characterized with optical metallography, scanning electron microscopy,and electron backscatter diffraction. In addition, the Vickers hardness test is conducted. Explosive welding can result in a wavy steel/steel interface, an ultrafine grain region centered at the interface, and a neighboring high deformation region, accompanied by a hardness with the highest value at the interface. Additional shock compression induces a further increase in hardness, and shock-induced deformation occurs in the form of twinning and dislocation slip and depends on the local substructure. Spall damage nucleates and propagates along the ultrafine grain region, due to the initial cracks or weak interface bonding. Spall strengths of bimetal plates can be higher than its constituents. Plate impact offers a promising method for improving explosive welding.     

Critical measurements for validation of constitutive equations under shock and impact loading conditions

Interpretation of the data often requires numerical simulations of the experiments and comparisons with the data. However, determination of an appropriate set of values for parameters in constitutive equations valid under shock and high strain rate loading remains one of the most difficult tasks for material model developers. Most researchers employ experimental data obtained under idealized stress/strain states in the model parameter calibration scheme. Since the dynamic response of materials is very complex, especially the failure response, the generality of the model parameters is highly questionable. For example, the fracturing of ceramic materials involves nucleation, propagation, and coalescence of microcracks under shock and impact. The dynamic deformation processes in ceramics include dynamic pore collapse, dislocation generation, twinning, and microcracking. When shocked above the Hugoniot elastic limit, the ceramic deformation becomes inelastic; therefore, the constitutive model formulation should consider modeling the effects of these various processes on the degradation of strength and stiffness of ceramic. This paper presents a brief summary of diagnostic measurements and modeling techniques associated with validation and verification of ceramic constitutive/damage models under high strain rate, shock, and penetration loading applications.     

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.     

Effect of a fullerene C60 addition on the strength properties of nanocrystalline copper and aluminum under shock-wave loading

The Hugoniot elastic limit and the spall strength of aluminum and copper samples pressed from a mixture of a metallic powder and 2–5 wt % C₆₀ fullerene powder are measured under a shock loading pressure up to 6 GPa and a strain rate of 10⁵ s^?1 by recording and analyzing full wave profiles using a VISAR laser interferometer. It is shown that a 5% C₆₀ fullerene addition to an initial aluminum sample leads to an increase in its Hugoniot elastic limit by an order of magnitude. Mixture copper samples with 2% fullerene also exhibit a multiple increase in the elastic limit as compared to commercial-grade copper. The elastic limits calculated from the wave profiles are 0.82–1.56 GPa for aluminum samples and 1.35–3.46 GPa for copper samples depending on the sample porosity. The spall strength of both aluminum and copper samples with fullerene additions decreases approximately threefold because of the effect of high-hardness fullerene particles, which serve as tensile stress concentrators in a material under dynamic fracture.     

冲击加载下20钢中弹性前驱波衰减与应力松弛行为实验研究

 通过改变样品厚度，对平面冲击加载下20钢的弹性前驱波的波幅衰减和应力松弛进行了实验研究。采用激光速度干涉测速仪（VISAR）实测了样品后自由面速度历史，采样频率达到1 ns，保证了实验结果的准确性。实验结果显示：Hugoniot弹性极限随着传播距离呈指数衰减，在所研究的样品厚度范围内，Hugoniot弹性极限减小了44%；应力松弛行为和弹性前驱波的上升沿时间也依赖于传播距离；冲击加载的强度对材料动态屈服行为的影响很小。     

Influence of meso-scale structure on the Hugoniot elastic limit of constructional ceramics

A model of high strain rates of ceramic materials in shock waves is suggested. It is shown that the Hugoniot elastic limit of constructional ceramic materials based on boron carbide, silicon carbide, and aluminum oxide essentially depends on their meso-scale structure. The increase of porosity and the concentration and sizes of microcracks may reduce the Hugoniot elastic limit. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 75–83, March, 1999.     

Strength and failure of LK7 borosilicate glass under shock compression

The Hugoniot elastic limit (HEL), the spall strength, the failure threshold, and the failure wave velocity in LK7 glass during shock compression are measured. The HEL estimated from the profiles of compression waves of various intensities is 7.1 ± 0.1 GPa. The spall strength exceeds 7 GPa during shock compression in the elastic range and remains high when passing through the HEL. Failure waves form in the stress range from 5.7 to 10.3 ± 0.5 GPa.     

Elastic-plastic deformation and fracture of shock-compressed single-crystal and polycrystalline copper near melting

The Hugoniot elastic limit, the yield strength, and the spall strength of polycrystalline M1 copper and single-crystal (110) and (111) copper are determined during shock compression up to 8 GPa in the temperature range 20–1080°C from an analysis of the free-surface velocity profiles recorded with VISAR laser velocimeter. The measurements show that all copper samples exhibit strong athermal hardening (increase in the Hugoniot elastic limit) near the melting temperature. Copper single crystals have a very low elastic limit in the temperature range up to 600°C, this limit increases sharply as the temperature increases to 1000°C, and it depends on the crystallographic orientation of a single crystal. The temperature dependence of the spall strength has a threshold character for all copper samples. Copper single crystals demonstrate higher resistance to spall fracture; however, near the melting temperature, the difference between the spall strengths of the copper single crystals and M1 copper becomes insignificant, 50% of the initial level.     

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.     

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.     

Change of the kinetics of shock-wave deformation and fracture of VT1-0 titanium as a result of annealing

The paper presents the results of measurements of shock-wave compression profiles of VT1-0 titanium samples after rolling and in the annealed state. In the experiments, the pressure of shock compression and distance passed by the wave before emerging to the sample surface were varied. From measurements of the elastic precursor decay and compression rate in a plastic shock wave of different amplitudes, the plastic strain and the corresponding shear stresses in the initial and subsequent stages of high-rate deformation in an elastoplastic shock wave are determined. It is found that the reduction in the dislocation density as a result of annealing reduces the hardness of the material but significantly increases its dynamic yield strengh, corresponding to the strain rate above 10⁴ s^–1. With a reduction in the strain rate, this anomalous difference in the flow stresses is leveled off.     

Evolution of shock waves in SiC ceramic

The evolution of a shock compression wave in SiC ceramic is measured for determining the possible contribution of relaxation processes to the high-rate straining. No appreciable decay of the elastic precursor and other features of stress relaxation are revealed when the sample thickness changes from 0.5 to 8.3 mm, and the evolution of the compression wave corresponds to a simple wave. The measured values of the Hugoniot elastic limit (σ_HEL = 8.72 ± 0.17 GPa) and spall strength (σ_sp = 0.50–0.62 GPa) with allowance for the density of the ceramic are in conformity with the available data.     

Molecular dynamics simulation of the plastic behavior anisotropy of shock-compressed monocrystal nickel

Molecular dynamics simulations were used to study the plastic behavior of monocrystalline nickel under shock compression along the [100] and [110] orientations. The shock Hugoniot relation, local stress curve, and process of microstructure development were determined. Results showed the apparent anisotropic behavior of monocrystalline nickel under shock compression. The separation of elastic and plastic waves was also obvious. Plastic deformation was more severely altered along the [110] direction than the [100] direction. The main microstructure phase transformed from face-centered cubic to body-centered cubic and generated a large-scale and low-density stacking fault along the family of { 111 } crystal planes under shock compression along the [100] direction. By contrast, the main mechanism of plastic deformation in the [110] direction was the nucleation of the hexagonal, close-packed phase, which generated a high density of stacking faults along the [110] and[1?10] directions.     

Shock-wave compression of x-cut quartz as determined by electrical response measurements

The mechanical response of x-cut quartz in the vicinity of the Hugoniot elastic limit is determined from measurements of the piezoelectric current from samples impact loaded from 26 to 130 kbar. The Hugoniot elastic limit is determined to be 60_?1·5⁺³ kbar at a compression of 0·066_?0·002^+0·004 This Hugoniot elastic limit corresponds to a shear strength of 5·5 per cent of the C₄₄ shear modulus. For stresses well above the Hugoniot elastic limit the electrical current measurements show that the material exhibits a substantial reduction of shear strength. The pressure derivative of the bulk modulus is determined to be 4·5, substantially less than the ultrasonic value. The experimental records show evidence for a time delay for reduction of shear strength which varies from about 10^?7 sec immediately above the 60 kbar Hugoniot elastic limit to about 10^?8 sec for stresses well above the Hugoniot elastic limit. The measurements also show stress relaxation below the Hugoniot elastic limit between 40 and 60 kbar.     

Modelling the dynamic deformation and patterning in fcc single crystals at high strain rates: dislocation dynamics plasticity analysis

The deformation process in copper and aluminium single crystals under shock loading is investigated using a multiscale model of plasticity that couples discrete dislocation dynamics and finite element analyses. Computer simulations are carried out to mimic loading condition of high strain rates ranging from 10⁵ to 10⁷?s^?1, and short pulse durations of few nanoseconds involved in recent laser based experiments. The effects of strain rate, shock pulse duration and the nonlinear elastic properties are investigated. Relaxed configurations using dislocation dynamics show formation of dislocation micro bands and weak dislocation cells. Statistical analyses of the dislocation microstructures are preformed to study the characteristics of the local dislocation densities and the distribution of the instantaneous dislocations velocities.     

无氧铜的准等熵压缩性

 利用递变冲击阻抗材料叠合而成的组合飞片，在二级轻气炮上对无氧铜进行了准等熵压缩性测量，加载时间约达1 μs。用激光速度干涉仪连续记录了不同厚度处无氧铜样品自由面速度随时间的变化过程，并通过拉格朗日波分析技术计算得到40 GPa下的准等熵的应力-应变曲线。结果表明：在低应力区，无氧铜的准等熵压缩线位于冲击绝热线之上；到32 GPa以上，准等熵压缩线才回落到冲击绝热线之下。这个现象与Barker、Chhabildas等对铝与钨的实测现象是一致的，它表明：在低应力区，材料的冲击强化效应与加载速率密切相关。     

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.     

无钴合金钢的冲击响应实验研究

 利用一级轻气炮作为加载手段,研究了无钴合金钢在3~20 GPa压力区间的冲击响应特性。用激光干涉测速——VISAR记录了双波结构的自由面速度剖面,并利用常压下的弹性纵波速度近似替代低压冲击下的弹性先驱波速度,确定了无钴合金钢的Hugoniot关系。根据自由面速度反映的层裂信息,给出了无钴合金钢的Hugoniot弹性极限、层裂强度以及层裂片厚度等动态力学参数。     

含微孔洞脆性材料的冲击响应特性与介观演化机制

微孔洞显著地影响着脆性材料的冲击响应,理解其介观演化机制和宏观响应规律将使微孔洞有利于而无害于脆性材料的工程应用.通过建立能够准确表现材料弹性性质和断裂演化的格点-弹簧模型,本文揭示了孔洞的演化对于脆性材料的影响.冲击下孔洞导致的塌缩变形和从孔洞发射的剪切裂纹所导致的滑移变形产生了显著的应力松弛,并调制了冲击波的传播.在多孔脆性材料中,冲击波逐渐展宽为弹性波和变形波.变形波在宏观上类似于延性金属材料的塑性波,在介观上对应于塌缩变形和滑移变形过程.样品中的气孔率决定了脆性材料的弹性极限,气孔率和冲击应力共同影响着变形波的传播速度和冲击终态的应力幅值.含微孔洞脆性材料在冲击波复杂加载实验、功能材料失效的预防、建筑物防护等方面具有潜在的应用价值.所获得的冲击响应规律有助于针对特定应用优化设计脆性材料的冲击响应和动态力学性能.