对薄层柱壳爆炸膨胀断裂过程的研究

 本文提出了一个用于描述动态破坏发展过程的损伤度函数。从这个损伤度函数出发,把材料特征性方程取为强化粘塑性本构方程形式,导出了薄层柱壳爆炸膨胀运动在两种近似下（恒定膨胀速度近似合恒定应变速率近似）断裂判据的解析表达式。结果分析表明,在上述条件下,存在着一个动态断裂“塑性峰”,在这个峰值条件的应变率下,柱壳出现贯穿断裂时刻的应变最大。以软钢为算例,本断裂判据可以比较好地解释Иванов和陈大年等给出的实验结果。这时,动态断裂“塑性峰”对应的应变率为4×10⁴ s^-1,相应的应变约为60%~80%。     

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。     

关於固体的现实应力空间(续)

前文[1]综合四理论[2],[3],[4],[5]构成固体现实应力空间之一初步理论,大体反映固态静力学性质,对金属较对非金属固体反映得当,后者受范形变曲面有异于弥氏圆柱。总起来看,前文仅涉及原则概念,未触及具体问题。为使此理论对金属压力加工及材料试验研究有所帮助,本文进一步研究几个问题:1)由应力空间图形比较不同金属的静力学性质;2)受范形变效率及其计算;3)形变过程之轨迹;并得到一定数量或质量上的结论。同时,附带对前文[1]中一个实验记录图的错误作修正,包括在附录内。     

Temperature dependence of development of slip bands and of strain hardening in AgCl crystals

The dependence of the flow stress and the slip band density on the plastic strain has been measured at 201 K, 293 K and 363 K. The growth of deformation concentrated in an average slip band has been stated. The types of obstacles acting against the rise and development of a slip band and the temperature dependence of the strain hardening in AgCl crystals are discussed. An equation stating the dependence of the flow stress on the slip band density is presented. The hardening in AgCl crystals is classified as the stage III — hardening.     

Dynamic strain of a longitudinally vibrating viscoelastic rod with an end mass

The dynamic strain of a viscoelastic rod excited into longitudinal simple harmonic vibration, a constant amplitude displacement being maintained by a shaker at one end and a mass terminating the other end, is theoretically investigated in this paper. The general equation of the strain distribution in the rod is derived by solving the one-dimensional wave equation. It is shown that the strain in the rod is the largest at the excited end, at the antiresonant frequencies. Simplified approximate equations are derived for the low loss case to calculate the largest strain in the rod with knowledge of the loss factor.     

高温高应变率下混凝土材料的损伤演化方程

采用?74 mm大口径分离式霍普金森压杆(SHPB)对不同温度(20、200、400℃)下的C45混凝土材料进行动态力学性能实验,得到了不同温度、不同应变率下混凝土材料的应力-应变曲线。实验结果表明:在20~400℃温度范围内,混凝土材料具有温度硬化和应变率硬化现象。基于上述实验数据给出了损伤变量关于塑性应变的关系式,并通过相关实验数据确定了不同温度、不同应变率下损伤演化方程的材料参数。将该损伤演化方程应用于混凝土材料的本构关系中,预测结果与实验数据具有较好的一致性,证明了所提出的高温、高应变率下混凝土材料损伤演化方程的合理性。     

Kinetics of Macrolocalization Patterns of Plastic Flow of Metals

The features of the macroscopic inhomogeneity of plastic deformation in the form of autowaves with a pulsating amplitude are analyzed, and data on the localization of sources of acoustic emission at different stages of plastic flow in the stretching of fcc mono- and polycrystals are presented. The relationship between the local components of the plastic distortion tensor in the strain localization zone is traced. The role of acoustic phenomena accompanying the localization of plastic strain in the development of the process of plastic deformation is considered.     

Dislocation dynamics and viscosity effects in a planar stress wave in a metal

Dislocation concepts are used in examining viscosity effects in planar stress waves. An equation is derived relating the viscous stress to the microdynamic parameters of the crystal. This is used to calculate the viscous stress in a stationary plastic wave for 6061-T6 polycrystalline aluminum. A method is given for estimating the rate of plastic strain for stationary stress waves.     

Discrete rearranging disordered patterns, part II: 2D plasticity, elasticity and flow of a foam

The plastic flow of a foam results from bubble rearrangements. We study their occurrence in experiments where a foam is forced to flow in 2D: around an obstacle; through a narrow hole; or sheared between rotating disks. We describe their orientation and frequency using a topological matrix defined in the companion paper (F. Graner, B. Dollet, C. Raufaste, and P. Marmottant, this issue, 25 (2008) DOI 10.1140/epje/i2007-10298-8), which links them with continuous plasticity at large scale. We then suggest a phenomenological equation to predict the plastic strain rate: its orientation is determined from the foam's local elastic strain; and its rate is determined from the foam's local elongation rate. We obtain a good agreement with statistical measurements. This enables us to describe the foam as a continuous medium with fluid, elastic and plastic properties. We derive its constitutive equation, then test several of its terms and predictions.     

Instantaneous work hardening behaviour of two-phase tungsten heavy alloys: a phenomenological approach

ABSTRACT

The present work describes a phenomenological approach to explain the instantaneous behaviour of tungsten heavy alloys (WHAs) in heat-treated and swaged conditions. The strengths and elongation values of heat-treated materials are lower and higher than those of the swaged samples respectively. The heat-treated materials exhibit two slopes in true stress–true plastic strain curves and follow the Ludwigson constitutive equation. On the other hand, swaged materials display a single slope and adhere to typical Swift constitutive equation. The latter reflect the presence of pre-strain in the materials due to swaging deformation. The fracture surfaces in heat-treated materials consist of W-W decohesion along with matrix rupture and W-cleavage, while swaged samples consist of mainly W-cleavage. Both the materials display three typical stages (I, II and III) of work hardening. The second derivatives of true stress–true plastic strain curves of these alloys exhibit a perfect parabola although the nature of true stress–true strain as well as true stress–true plastic strain curves is quite different in heat-treated and swaged materials. This has been observed for the first time in WHAs consisting of matrix and W-grains. The shape of the parabola is simple and easy to fit. The fitting parameters of parabolas have been successfully employed to explain the flow behaviour of a large number of tungsten heavy alloys having two-phase microstructure in different processing conditions.     

Ultrasonic study on the change in elastic anisotropy with plastic compressive deformation

The macroscopic elasticity of a polycrystalline material is more or less anisotropic due to the presence of texture. In this Paper, the change in such elastic anisotropy with plastic deformation was studied ultrasonically. Test specimens prepared from a rolled plate of mild steel were deformed plastically by uni-axial compression, and the relative retardation and polarization directions of two independent transverse waves were measured by analysing frequency spectra of ultrasonic waves. It was confirmed from the results that the plastic deformation changes not only the degree of the elastic anisotropy but also its principal axes towards those of the plastic strain. A preliminary consideration was presented concerning the relation between the elastic stiffness and small plastic strain.     

Softening and hardening of yield stress by hydrogen–solute interactions

Abstract

Hydrogen atoms have a wide variety of effects on the mechanical performance of metals, and the underlying mechanisms associated with effects on plastic flow and embrittlement remain to be discovered or validated. Here, the reduction in the plastic flow stress (softening) due to hydrogen atoms in solute-strengthened metals, previously proposed by Sofronis et al. is demonstrated at the atomistic level. Glide of an edge dislocation through a field of solutes in a nickel matrix, both in the absence of hydrogen and in the presence of H bound to the solutes, is modelled. The ‘solutes’ here are represented by vacancies, enabling use of accurate binary Ni–H interatomic potentials. Since vacancies have a misfit strain tensor in the Ni matrix and also bind hydrogen atoms, they are excellent surrogates for study of the general phenomenon. The binding of H to the solute (vacancy) reduces the misfit volume to nearly zero but also creates a non-zero tetragonal distortion. Solute strengthening theory is used to establish the connection between strength and solute/hydrogen concentration and misfit strain tensor. Simulations show that when a dislocation moves through a field of random vacancy ‘solutes’, the glide stress is reduced (softening) when H is bound to the solutes. Trends in the simulations are consistent with theory predictions. Trends of softening or hardening by H in metal alloys can thus be made by computing the misfit strain tensor for a desired solute in the chosen matrix with and without bound hydrogen atoms. Pursuing this, density functional theory calculations of the interaction of H with carbon and sulphur solutes in a Ni matrix are presented. These solutes/impurities do not bind with H and the complexes have larger misfit strains, indicative of H-induced strengthening rather than softening for these cases. Nonetheless, H/solute interactions are the only mechanism, to date, that shows nanoscale evidence of plastic softening due to hydrogen associated with the hydrogen-enhanced localised plasticity concept in fcc metals.     

Structure factors that influence the stability of plastic strain of bcc metals under tensile load

The effect of the Peierls stress on the ultimate tensile stress and uniform strain prior to the formation of a neck during stretching of metals and alloys with bcc structure is theoretically analyzed. The analysis is based on the equation for the variation of the dislocation density with deformation; this equation determines the shape of the work-hardening curve for a bcc material and the effect of the Peierls stress on the parameters of this equation (the annihilation coefficient for screw dislocations). Using the Considére condition for plastic instability of the neck type, the ultimate tensile stress and the magnitude of uniform strain are found theoretically as a function of the Peierls stress at different temperatures below 0.15T _m , where T _m is the melting temperature of the bcc metal. Theoretical results are illustrated with experimental data on the temperature dependences of the annihilation coefficients for screw dislocations and of the magnitude of uniform strain in molybdenum and Armco iron.     

Effect of plastic straining on magnetostriction of ferromagnetic polycrystals—experiments and multiscale modeling

The influence of plastic deformations on magnetostriction of NO–3% Si–Fe alloy is studied. Experimental measurements are presented. The magnetostriction is strongly anisotropic before deformation and plastic strain tends to homogenize this behavior. The modeling consists in the calculation of a specific residual stresses field and its introduction in the magnetic model. Experiments and modeling are in good agreement.     

Modeling of macroscopic strain localization in alloys with the <Emphasis Type="Italic">L</Emphasis>1<Subscript>2</Subscript> structure

Results of mathematical modeling of plastic strain superlocalization are presented with allowance for dislocation redistribution into dislocation walls. The model based on the concept of hardening and rest is used to construct equations describing kinetics of dislocations and substructure transformations. It is demonstrated that depending on the scenario of the strain model evolution in the microvolume of a deformable body, different types of localization are possible under the influence of stress concentrators.     

Determination of elastic and plastic strain of samples tested with the high frequency fatigue method

Two methods are presented which calculate the plastic strain and the total strain amplitude in a sample, subjected to high frequency fatigue, with the aid of temperature distribution measurements. The applicability of both methods is illustrated on polycrystalline copper.     

Digital image correlation using iterative least squares and pointwise least squares for displacement field and strain field measurements

Digital image correlation (DIC) method using iterative least squares algorithm (ILS) for displacement field measurement and pointwise least squares algorithm (PLS) for strain field measurement is proposed in this paper. A more general and practical intensity change model is employed with consideration of the linear intensity change of the deformed image, followed by an iterative least squares algorithm for calculating displacement field with sub-pixel accuracy. The concept of correlation function is not used in the ILS method, even though we prove that the algorithm is actually equivalent to the optimization of the sum of squared difference correlation function using improved Newton–Raphson method. Besides, different from the conventional strain estimation approaches based on smoothing the displacement fields first and followed by differentiation of the smoothed displacement fields, a simple yet effective PLS algorithm is proposed for extracting strain fields from the computed displacement fields. The effectiveness and accuracy of the proposed techniques is verified through numerical simulation experiments. A practical application of the algorithms to residual plastic deformation field measurement of GH4169 alloy subjected to tensile fatigue is also presented.     

微扩张管道内幂律流体非定常电渗流动

研究了电渗驱动下幂律流体在有限长微扩张管道内非稳态流动特性.基于Ostwald-de Wael幂律模型,采用高精度紧致差分离散二维Poisson-Nernst-Planck方程及修正的Cauchy动量方程,数值模拟了初始及稳态时刻微扩张管道内幂律流体电渗流流场分布情况,研究了管道截面改变对幂律流体无量纲剪切应变率及无量纲表观黏度的影响,以及无量纲表观黏度对拟塑性流体与胀流型流体流速分布的影响.数值模拟结果显示,当扩张角和无量纲电动宽度一定时,电场驱动下的幂律流体在近壁区域速度响应都很快;初始时刻,近壁处表观黏度的变化受到剪切应变率变化的影响,从而影响了三种幂律流体速度峰值的分布,出现拟塑性流体流速在扩张段上游及扩张段近壁处速度峰值均为幂律流体中最大、而在扩张段下游三种幂律流体速度峰值相近的现象;稳态时刻,幂律流体速度剖面呈现塞型分布,且满足连续性条件下,幂律流体流速随扩张管半径增大而减小,牛顿流体流动规律与宏观尺度下流动规律相同;初始时刻,在相同电动宽度、不同壁面电势作用下,幂律流体在扩张管近壁处剪切应变率分布的差异导致表观黏度分布的差异,并最终导致拟塑性流体与胀流型流体流速分布的差异.     

Three-dimensional phase field microelasticity theory of a multivoid multicrack system in an elastically anisotropic body: Model and computer simulations

The phase field microelasticity theory of a three-dimensional, elastically anisotropic system of voids and cracks is proposed. The theory is based on the equation for the strain energy of the continuous elastically homogeneous body presented as a functional of the phase field, which is the effective stress-free strain. It is proved that the stress-free strain minimizing the strain energy of this homogeneous modulus body fully determines the elastic strain and displacement of the body with voids and/or cracks. The proposed phase field integral equation describing the elasticity of an arbitrary system of voids and cracks is exact. The geometry and evolution of multiple voids and/or cracks are described by the phase field, which is the solution of the time-dependent Ginzburg-Landau equation. Other defects, such as dislocations and precipitates, are trivially integrated into this theory. The proposed model does not impose a priori constraints on possible void and crack configurations or their evolution paths. Examples of computations of elastic equilibrium of systems with voids and/or cracks and the evolution of cracks under applied stress are considered.