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.     

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.     

多孔脆性材料对高能量密度脉冲的吸收和抵抗能力

作用在脆性结构材料表面的高能量密度脉冲会以冲击波的形式传播进入材料内部, 导致压缩破坏和功能失效. 通过设计并引入微孔洞, 显著增强了脆性材料冲击下的塑性变形能力, 从而使脆性结构材料可以有效地吸收耗散冲击波能量, 并抑制冲击诱导裂纹的扩展贯通. 建立格点-弹簧模型并用于模拟研究致密和多孔脆性材料在高能量密度脉冲加载下的冲击塑性机理、能量吸收耗散过程和裂纹扩展过程. 冲击波压缩下孔洞塌缩, 导致体积收缩变形和滑移以及转动变形, 使得多孔脆性材料表现出显著的冲击塑性. 对致密样品、气孔率5%和10%的多孔样品吸能能力的计算表明, 多孔脆性材料吸收耗散高能量密度脉冲的能力远优于致密脆性材料. 在短脉冲加载下, 相较于遭受整体破坏的致密脆性材料, 多孔脆性材料以增加局部区域的损伤程度为代价, 阻止了严重的冲击破坏扩展贯通整个样品, 避免了材料的整体功能失效.     

On mechanical stability of molybdenum

Investigations of the strength properties of materials under different loading conditions are of practical importance in many engineering applications. The knowledge of elastic moduli as a function of strain is required for determination of strength properties. In the present work, we have determined the elastic moduli of molybdenum through first principles study of the energy changes under three different loading conditions namely ‘uni-axial tensile deformation’ along [0 0 1] direction, ‘uni-axial tensile loading’ along [0 0 1] direction and ‘hydrostatic tensile loading’. The stability conditions for the system are expressed in terms of the elastic moduli and analyzed along the deformation paths corresponding to these three loading modes. The theoretical spall strength (σ_S), tensile strength (σ_T) along [0 0 1] direction and hydrostatic tensile strength (σ_H), are evaluated as a stress at the first onset of the instability for three loading conditions, respectively. The calculated equilibrium volume and elastic moduli are compared with that reported from experimental and other theoretical works.     

多孔未极化Pb(Zr0.95Ti0.05)O3铁电陶瓷单轴压缩力学响应与相变

通过添加造孔剂的方法制备了四种不同孔隙率未极化PZT95/5铁电陶瓷. 采用非接触式的数字散斑相关性分析(digital image correltation, DIC)全场应变光学测量技术, 对多孔未极化PZT95/5 铁电陶瓷开展了单轴压缩实验研究, 讨论了孔隙率对未极化PZT95/5铁电陶瓷的力学响应与畴变、相变行为的影响. 多孔未极化PZT95/5铁电陶瓷的单轴压缩应力-应变关系呈现出类似于泡沫或蜂窝材料的三阶段变形特征, 其变形机理主要归因于畴变和相变的共同作用, 与微孔洞塌缩过程无关. 多孔未极化PZT95/5铁电陶瓷的弹性模量、压缩强度都随着孔隙率的增加而明显降低, 而孔隙率对断裂应变的影响较小. 预制的微孔洞没有改善未极化PZT95/5铁电陶瓷材料的韧性, 这是因为单轴压缩下未极化PZT95/5铁电陶瓷的断裂机理是轴向劈裂破坏, 微孔洞对劈裂裂纹传播没有起到阻碍和分叉作用. 准静态单轴压缩下多孔未极化PZT95/5铁电陶瓷畴变和相变开始的临界应力都随着孔隙率的增大而呈线性衰减, 但相变开始的临界体积应变却不依赖孔隙率.     

The non-Hooke’s behavior of porous zirconia subjected to high-rate compressive deformation

The deformation of partially stabilized zirconia ZrO₂(Y₂O₃) with various pore morphologies is studied. During the synthesis of bar and lamellar ceramic structures, an effect of mechanical instability is discovered. This effect, along with the purely elastic behavior of the ceramic and the accumulation of microdamages under high-rate compressive deformation, produces considerable strains in the porous structure without material failure and substantially extends the applications of porous ceramic materials.     

Microstructure and mechanical characteristics of nanodiamond-SiC compacts

Superhard nanodiamond-SiC ceramics are prepared by infiltrating liquid Si into porous nanodiamond compacts under pressure. Synthesized samples are 2.2 mm thick and 3–4 mm in diameter. The effect of particle size of dynamically synthesized nanodiamond powders on silicon infiltration and SiC phase formation is studied. It is established that silicon does not penetrate into the pores of nanodiamond powders if the original particle size is smaller than 0.5–1.0 μm. The critical pore size for infiltration is 100–200 nm. A study of the microstructure of the samples showed the presence of the nanometer-and submicron-scale SiC phase. The ultrasound velocities are measured in the prepared compacts, and the elastic moduli are calculated. __________ Translated from Fizika Tverdogo Tela, Vol. 46, No. 4, 2004, pp. 734–736. Original Russian Text Copyright ? 2004 by Ekimov, Gromnitskaya, Mazalov, Pal’, Pichugin, Gierlotka, Palosz, Kozubowski.     

多孔脆性介质冲击波压缩破坏的细观机理和图像

本文采用一种具有良好定量性质的离散元模型研究了带孔洞的各向同性脆性介质在细观尺度上的压缩破坏特征. 通过对孤立孔洞、三种简单的孔洞排布方式和大量孔洞随机排布等几种情况的模拟, 认识到了剪切破坏和局域拉伸破坏是冲击波压缩下多孔介质的基本破坏模式; 孔洞之间的损伤贯通会促进孔洞在较低应力下发生塌缩, 但损伤区的应力松弛过程却会对一定范围内的介质起到损伤屏蔽作用; 不同区域中损伤促进和损伤屏蔽的综合效果是在多孔脆性介质中形成一种高损伤区与低损伤区间错排布的奇特损伤分布. 本文的研究结果为深入理解脆性材料冲击波压缩破坏的演化过程和机理提供了细观尺度上的初步物理图像.     

Resonant ultrasound spectroscopy measurement of Young's modulus,shear modulus and Poisson's ratio as a function of porosity for alumina and hydroxyapatite

Modulus–porosity relationships are critical for engineered bone tissue scaffold materials such as hydroxyapatite (HA), where porosity is essential to biological function. Resonant ultrasound spectroscopy (RUS) measurements revealed that the Young's modulus, E, and shear modulus, G, of both alumina and HA decrease monotonically with increasing volume fraction porosity, P, for 0.06 < P < 0.39 (alumina) and 0.05 < P < 0.51 (HA). Although the elastic moduli of porous materials have been measured by a number of different ultrasonic resonance techniques (of which the RUS technique is one example) and over the last decade the elastic moduli of many solids have been measured by the RUS technique, this study is the first systematic RUS study of porous materials. Comparison of E versus P data for alumina (which has been studied extensively) with literature data from several measurement techniques indicates the RUS technique is effective for modulus–porosity measurements. Another key result is that although the HA specimens included in this study have a unimodal pore size distribution, the details of the decrease in E and G with increasing P agree well with literature data for HA with both unimodal and bimodal pore size distributions. In addition, Poisson's ratio exhibits a local minimum in the porosity range of 0.2 < P < 0.25 for both HA and alumina, which may be related to the pore morphology evolution during sintering.     

Temperature dependence of elastic moduli of submicrocrystalline copper

The possibility of applying the two-component model of single-phase hybrid materials to the explanation of the anomalous temperature dependence of elastic moduli of copper with a submicrocrystalline structure has been discussed. An analysis has been performed based on new experimental data. A twin mechanism of changes in the crystallite orientation has been proposed. These changes cause the anomalous behavior of the elastic moduli of copper during deformation and subsequent heatings.     

Ultrasonic waves in porous ceramics with non-spherical holes

Formulae describing the effective elastic moduli of a porous ceramic medium are derived using Eshelby's solution and Maxwell's approximation. The ceramic medium is considered as an infinite matrix, which has uniform elastic properties and encloses non-spherical pores. A numerical evaluation of the velocity of an ultrasonic wave in the ceramic, as function of the porosity and pore shape, is presented. The theoretical results were combined with those obtained experimentally for different firing temperatures of the ceramic.     

Simulations of X‐ray diffraction of shock‐compressed single‐crystal tantalum with synchrotron undulator sources

Polychromatic synchrotron undulator X‐ray sources are useful for ultrafast single‐crystal diffraction under shock compression. Here, simulations of X‐ray diffraction of shock‐compressed single‐crystal tantalum with realistic undulator sources are reported, based on large‐scale molecular dynamics simulations. Purely elastic deformation, elastic–plastic two‐wave structure, and severe plastic deformation under different impact velocities are explored, as well as an edge release case. Transmission‐mode diffraction simulations consider crystallographic orientation, loading direction, incident beam direction, X‐ray spectrum bandwidth and realistic detector size. Diffraction patterns and reciprocal space nodes are obtained from atomic configurations for different loading (elastic and plastic) and detection conditions, and interpretation of the diffraction patterns is discussed.     

Influence of elastic strains on the adsorption process in porous materials. Thermodynamics and experiment

If we disregard the shape of the boundary hysteresis loop, H1 for SBA-15, MCM-41 and KIT-6, H2 for p⁺-type porous silicon and porous glass, the hysteretic features inside the loop are qualitatively the same for all these systems and show that none of them are composed of independent pores whether the pores are interconnected or not. We hence believe that the physical parameter which couples the pores is not the interconnectivity but the elastic deformation of the porous matrix. The thermodynamic approach we develop includes the elastic energy of the solid. We show that the variation of the surface free energy, which is proportional to the deformation of the porous matrix, is an important component of the total free energy. With porous silicon, we experimentally show that a stress external to the porous matrix exerted by the substrate on which it is supported significantly increases the total free energy and the adsorbed amount and decreases the condensation pressure compared to that of the same porous matrix detached from its substrate which is the relaxed state of the supported layer. This stress can be partly relaxed by making thicker porous layers due to the breaking of Si-Si bonds. This results in the shift of the isotherms towards that of the membrane. We propose a new interaction mechanism occurring through the pore wall elastic deformation in which the external mechanical stress is imposed on a given pore by its neighbours.     

晶界对纳米多晶铝中冲击波阵面结构影响的分子动力学研究

用分子动力学方法研究了纳米多晶铝在冲击加载下的冲击波阵面结构及塑性变形机理.模拟研究结果表明:在弹性先驱波之后,是晶界间滑移和变形主导了前期的塑性变形机理;然后是不全位错在界面上成核和向晶粒内传播,然后在晶粒内形成堆垛层错、孪晶和全位错的过程主导了后期的塑性变形机理.冲击波阵面扫过之后留下的结构特征是堆垛层错和孪晶留在晶粒内,大部分全位错则湮灭于对面晶界.这个由两阶段塑性变形过程导致的时序性塑性波阵面结构是过去未见报道过的. 关键词： 晶界 塑性变形 冲击波阵面 分子动力学     

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.     

Relaxation processes in metals at high strain rates

Mathematical modeling is used for experiments involving the loading of plates by plane shock waves to study the relaxation of shear stresses during the high-rate deformation of metallic materials. It is established that the characteristic relaxation times vary broadly — from fractions of a nanosecond to several microseconds. Such variation is indicative of a change in the mechanism responsible for relaxation. As a result, there is a difference between the quasi-equilibrium shear stresses in the elastic precursor and the same stresses behind the shock front. Metallic materials remain capable of resisting plastic deformation behind the front. Structural irregularities created by high-rate deformation result in localization of plastic flow at the microscopic level, which in turn causes the parameters of the stress-strain state at this level to differ from the corresponding parameters on the macroscopic scale.Siberian Physico-Technical Institute, affiliated with Tomsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 82–90, August, 1995.     

On the influence of frequency-dependent elastic properties in vibro-acoustic modelling of porous materials under structural excitation

The aspects related to modelling the frequency dependence of the elastic properties of air-saturated porous materials have been largely neglected in the past for several reasons. For acoustic excitation of porous materials, the material behaviour can be quite well represented by models where the properties of the solid frame have little influence. Only recently has the importance of the dynamic moduli of the frame come into focus. This is related to a growing interest in the material behaviour due to structural excitation. Two aspects stand out in connection with the elastic-dynamic behaviour. The first is related to methods for the characterisation of the dynamic moduli of porous materials. The second is a perceived lack of numerical methods able to model the complex material behaviour under structural excitation, in particular at higher frequencies. In the current paper, experimental data from a panel under structural excitation, coated with a porous material, are presented. In an attempt to correlate the experimental data to numerical predictions, it is found that the measured quasi-static material parameters do not suffice for an accurate prediction of the measured results. The elastic material parameters are then estimated by correlating the numerical prediction to the experimental data, following the physical behaviour predicted by the augmented Hooke?s law. The change in material behaviour due to the frequency-dependent properties is illustrated in terms of the propagation of the slow wave and the shear wave in the porous material.     

Pore size assessment based on wall collision broadening of spectral lines of confined gas: experiments on strongly scattering nanoporous ceramics with fine-tuned pore sizes

Wall collision broadening of absorption lines of gases confined in porous media is a recently opened domain of high-resolution spectroscopy. Here, we present an experimental investigation of its application for pore size assessment. We report on the manufacturing of nanoporous zirconia ceramics with well-defined pore sizes fine-tuned from 50 to 150 nm. The resulting pore structure is characterized using mercury intrusion porosimetry, and the optical properties of these strongly scattering materials are measured using femtosecond photon time-of-flight spectroscopy (transport mean free paths found to be tuned from 2.3 to 1.2 μm as the pore size increase). Wall collision line broadening is studied by performing near-infrared (760 nm) high-resolution diode laser spectroscopy of confined oxygen molecules. A simple method for quantitative estimation of the pore size is outlined and shown to produce results in agreement with mercury intrusion porosimetry. At the same time, the need for improved understanding of wall collision broadening is emphasized.