大量椭球颗粒随机分布三维区域的模拟及其四面体网格快速生成算法

针对颗粒为椭球形状并且随机分布的多相复合材料给出了三维情形下的计算机模拟方法,并对此复杂区域提供了一种四面体网格快速生成算法。此方法的基本思想:首先是根据材料的要求,给出随机颗粒材料的计算机模拟,然后对模拟后的颗粒边界初始化,得到一些初始剖分点,并给出剖分区域的初始网格(正四面体),接着把颗粒的初始边界点投入到剖分区域中,替换区域中靠此点近的点,并且采用加点寻找边界的方法和修正初始点方法来解决四面体穿刺边界问题,从而得到整个区域的四面体网格。最后用实例说明了算法的有效性。     

Grain Shape Effects on Permeability,Formation Factor,and Capillary Pressure from Pore-Scale Modeling

We invoke pore-scale models to evaluate grain shape effects on petrophysical properties of three-dimensional (3D) images from micro-CT scans and consolidated grain packs. Four sets of grain-packs are constructed on the basis of a new sedimentary algorithm with the following shapes: exact angular grain shapes identified from micro-CT scans, ellipsoids fitted to angular grains, and spheres with volume and surface-to-volume ratio equal to original angular grains on a grain-by-grain basis. Subsequently, a geometry-based cementation algorithm implements pore space alteration due to diagenesis. Eight micro-CT scans and 144 grain-pack images with $500 \times 500 \times 500$ voxels (the resolution units of 3D images) are analyzed in this study. Absolute permeability, formation factor, and capillary pressure are calculated for each 3D image using numerical methods and compared to available core measurements. Angular grain packs give rise to the best agreement with experimental measurements. Cement volume and its spatial distribution in the pore space significantly affect all calculated petrophysical properties. Available empirical permeability correlations for non-spherical grains underestimate permeability between 30 and 70 % for the analyzed samples. Kozeny–Carman’s predictions agree with modeled permeability for spherical grain packs but overestimate permeability for micro-CT images and non-spherical grain packs when volume-based radii are used to calculate the average grain size in a pack. We identify surface-to-volume ratio and grain shape as fundamental physical parameters that control fluid distribution and flow in porous media for equivalent porosity samples.     

Propagation and scattering of ultrasonic waves in polycrystals with arbitrary crystallite and macroscopic texture symmetries

A general ultrasonic attenuation model for a polycrystal with arbitrary macroscopic texture and triclinic ellipsoidal grains is described with proper accounting for the anisotropic Green’s function for the reference medium. The texture and the ellipsoidal grain frames in the model are independent and the wave propagation direction is arbitrary. The attenuation coefficients are obtained in the Born approximation accompanied by the Rayleigh and stochastic asymptotes. The scattering model displays statistical anisotropy due to two independent factors: (1) shape of the oriented grains and (2) preferred crystallographic orientation of the grains leading to macroscopic anisotropy of the homogenized reference medium. The model is applicable to most single phase polycrystalline materials that may occur as a result of thermomechanical manufacturing processes leading to different macrotextures and elongated-shaped grains. It predicts the strength of ultrasonic scattering and its dependence on frequency and propagation direction as a function of grain shape, grain crystallographic symmetry and macroscopic texture parameters and provides the texture-induced dependence of macroscopic ultrasonic velocity on propagation angle. It considers proper wave polarizations due to macroscopic anisotropy and scattering-induced transformations of waves with different polarizations. Competing effects of grain shape and texture on the attenuation are observed. In contrast to the macroscopically isotropic case, where in the stochastic regime the attenuation is highest in the direction of the longest ellipsoidal axis of the grain, the wave attenuation in the elongation direction may be suppressed or amplified by the texture with different effects on the quasilongitudinal and quasitransverse waves. The frequency behavior is also interestingly affected by texture: a hump in the total attenuation coefficient is found for the fast quasitransverse wave which is purely the result of macroscopic anisotropy and the existence of two quasitransverse waves; this hump is not observed in the macroscopically isotropic case. Striking differences of the texture effect on the directional dependences of the attenuation coefficients are found at low versus high frequencies.     

考虑尺寸效应的多晶金属循环塑性分析

本文采用多晶塑性分析方法,设材料点包含一定数量的各向异性单晶晶粒并考虑晶粒尺寸的影响,计算材料点的应力和应变时利用了Taylor假设。模型引入考虑尺寸效应的晶体滑移硬化函数,同时针对晶体滑移引入背应力及其方向性硬化的描述,以反映不同晶粒尺寸材料在循环加载条件下的力学行为。利用该模型,本文第一作者采用显式格式编制了与ABAQUS商用有限元软件接口的用户材料子程序（VUMAT）,实例计算证实该模型可以反映和描述多晶金属材料在材料反复加载条件下的循环塑性行为与尺寸效应。     

Lithium Diffusion and Stress in a Polycrystalline Film Electrode

In the present work, the two-dimensional analytical solution for Li diffusion in grains and grain boundaries of a polycrystalline film electrode is established with consideration of Li-segregation at the grain boundary. The stress field induced by the inhomogeneity of Li concentration, called chemical stress here for brevity, is analyzed via the finite element simulation.The effects of the grain boundary including its size, its diffusion coefficient as well as the segregation phenomenon on the solute concentration and the chemical stress are examined. It shows that grain boundaries can assist fast diffusion and significantly affect the stress profile in the whole film. It proves that tailoring the grain boundary size or other grain boundary-related parameters may provide an alternative strategy for improving the overall diffusivity and mechanical stability of battery electrodes.     

Particle shape consideration in numerical simulation of assemblies of irregularly shaped particles

The mechanical behavior of granular materials depends much on the shape of the constituent particles. Therefore appropriate modeling of particle, or grain, shape is quite important. This study employed the method of direct modeling of grain shape (Matsushima & Saomto, 2002), in which, the real shape of a grain is modeled by combining arbitrary number of overlapping circular elements which are connected to each other in a rigid way. Then, accordingly, a discrete-element program is used to simulate the assembly of grains. In order to measure the effects of grain shape on mechanical properties of assembly of grains, three types of grains—high angular grains, medium angular grains and round grains are considered where several biaxial tests are conducted on assemblies with different grain types. The results show that the angularity of grains greatly affects the behavior of granular soil.     

Recoverable creep deformation and transient local stress concentration due to heterogeneous grain-boundary diffusion and sliding in polycrystalline solids

Numerical simulations are used to investigate the influence of heterogeneity in grain-boundary diffusivity and sliding resistance on the creep response of a polycrystal. We model a polycrystal as a two-dimensional assembly of elastic grains, separated by sharp grain boundaries. The crystal deforms plastically by stress driven mass transport along the grain boundaries, together with grain-boundary sliding. Heterogeneity is idealized by assigning each grain boundary one of two possible values of diffusivity and sliding viscosity. We compute steady state and transient creep rates as functions of the diffusivity mismatch and relative fractions of grain boundaries with fast and slow diffusion. In addition, our results show that under transient conditions, flux divergences develop at the intersection between grain boundaries with fast and slow diffusivity, which generate high local stress concentrations. The stress concentrations develop at a rate determined by the fast diffusion coefficient, and subsequently relax at a rate determined by the slow diffusion coefficient. The influence of the mismatch in diffusion coefficient, loading conditions, and material properties on the magnitude of this stress concentration is investigated in detail using a simple model problem with a planar grain boundary. The strain energy associated with these stress concentrations also makes a small fraction of the plastic strain due to diffusion and sliding recoverable on unloading. We discuss the implications of these results for conventional polycrystalline solids at high temperatures and for nanostructured materials where grain-boundary diffusion becomes one of the primary inelastic deformation mechanisms even at room temperature.     

Yield stress strengthening in ultrafine-grained metals: A two-dimensional simulation of dislocation dynamics

The effect of grain size on the tensile plastic deformation of ultrafine-grained copper polycrystals is investigated using a two-dimensional simulation of dislocation dynamics. Emphasis is put on the elementary mechanisms governing the yield stress in multislip conditions. Whatever the grain size, the yield stress is found to follow a Hall-Petch law. However, the elementary mechanism controlling slip transmission through the grain boundaries at yield is observed to change with the grain size. For the larger grain sizes, the stress concentrations due to dislocations piled-up at grain boundaries are responsible for the activation of plastic activity in the poorly stressed grains. For the smaller grain sizes, the pile-ups contain less dislocations and are less numerous, but the strain incompatibilities between grains become significant. They induce high internal stresses and favor multislip conditions in all grains. Based on these results, simple interpretations are proposed for the strengthening of the yield stress in ultrafine grained metals.     

Effects of lattice misorientations on strain heterogeneities in FCC polycrystals

It is well documented that the highly heterogeneous deformation behaviour and lattice rotation typically observed within grains in a polycrystal are attributed to microstructural features such as grain structure, topology, size, etc. In this work, the effects of low- and high-angle grain boundaries on the mechanical behaviour of FCC polycrystals are investigated using a micro-mechanical model based on crystal plasticity theory. The constitutive framework relies on dislocation mechanics concepts to describe the plastic deformation behaviour of FCC metallic crystals and is validated by comparing the measured and predicted local and macroscopic deformation behaviour in a thin Al-0.5% Mg polycrystal tensile specimen containing a relatively small number of surface grains. Comparisons at the microscopic (e.g. local slip distribution) and macroscopic (e.g. average stress-strain response) levels elucidate the role of low-angle grain boundaries, which are found to have a profound effect on both the local and average deformation behaviour of FCC polycrystals with a small number of grains. However, this effect diminishes when the number of grains increases and becomes negligible in bulk polycrystals. In light of the widely accepted view that high-angle grain boundaries strongly influence the mechanical behaviour of very fine-grained metals, this work has shown that low-angle grain boundaries can also play an equally important role in the deformation behaviour of polycrystals with a relatively small number of grains.     

Correlation of elastic wave attenuation and scattering with volumetric grain size distribution for polycrystals of statistically equiaxed grains

This study establishes an explicit relation between spatial two-point correlation function (TPCF) and volumetric (or three-dimensional) grain size distribution for aggregates of statistically equiaxed grains by extending a prior study (Sha, JASA, 2018). This relation is further validated by applying it to available TPCF and volumetric grain size distribution in the literature. Based on this relation, analytical attenuation coefficients for longitudinal and transverse waves, accounting for volumetric grain size distribution, are derived under Born approximation for macroscopically isotropic polycrystals of equiaxed triclinic grains. These attenuation models are applicable for whole frequency range except geometric region. Moreover, scattering coefficients for a polycrystal of equiaxed triclinic grains with a volumetric grain size distribution are obtained. Finally, the analytical attenuation model for the longitudinal wave is verified by comparison with existing 3D finite element simulation results in the literature. This theoretic study has practical applications to the inverse determination of volumetric grain size distribution from ultrasonic measurements.     

Grain size effects in multiphase steels assisted by transformation-induced plasticity

The influence of the austenitic grain size on the overall stress–strain behavior in a multiphase carbon steel is analyzed through three-dimensional finite element simulations. A recently developed multiscale martensitic transformation model is combined with a plasticity model to simulate the transformation-induced plasticity effects of a grain of retained austenite embedded in a ferrite-based matrix. Grain size effects are included via a surface energy term in the Helmholtz energy. Tensile simulations for representative orientations of the grain of retained austenite show that the initial stability of the austenite increases as the grain size decreases. Consequently, the effective strength is initially higher for smaller grains. The influence of the grain size on the evolution of the transformation process strongly depends on the grain orientation. For “hard” orientations, the transformation rate is higher for larger grains. In addition, the phase transformation is partially suppressed as the grain size decreases. In contrast, for “soft” orientations, the transformation rate is lower for larger grains. The phase transformation is more homogeneous for smaller grains and, consequently, the effective transformation strain is larger. Nevertheless, in multiphase carbon steels with a relatively low percentage of retained austenite, the influence of the austenitic grain size on the overall constitutive response is smaller than the influence of the austenitic grain orientation.     

A hierarchical model for rate-dependent polycrystals

A hierarchical model of a polycrystalline aggregate of rigid viscoplastic grains is formulated, and a robust and efficient computational algorithm for its solution is proposed. The polycrystalline aggregate is modeled as a binary tree. The leaves of the binary tree represent grains, and higher tree nodes represent increasingly larger sub-aggregates of grains. The root of the tree represents the entire polycrystalline aggregate. Velocity and traction continuity are enforced across the interface between the children of each non-leaf node in the binary tree. The hierarchical model explicitly models intergranular interactions but is nevertheless comparable in computational effort to the mean field models of polycrystal plasticity. Simulations of tensile, compressive, torsional, and plane strain deformation of copper lead to predictions in good agreement with experiments, and highlight the interconnection between grain deformations and intergranular constraints. It is inferred from the results that a hybrid mean field/hierarchical model represents a computationally efficient methodology to simulate polycrystal deformation while accounting for intergranular interactions.     

The role of intergranular constraint on the stress-induced martensitic transformation in textured polycrystalline NiTi

The influences of grain boundaries and relative grain misorientations on stress-induced martensitic transformations in NiTi are studied using unique experiments and finite element modeling. Tensile and compressive mechanical tests reveal that polycrystalline NiTi with a dominant <111> fiber texture and single crystal NiTi oriented along the [111] direction exhibit nearly identical stress–strain curves during a stress-induced martensitic transformation. Micro-mechanical finite element simulations of fiber textured polycrystals and single crystals undergoing a multi-variant martensitic transformation confirm the relative indifference of the macroscopic transformation attributes to the presence of grain boundaries. On the microscale, the finite element simulations further reveal that the insensitivity of the transformation to intergranular constraint is linked to the local stress disturbance created by transforming grains. The transformation of grains that are favorably oriented with respect to the loading axis creates local stresses that invariably assist the transformation in neighboring grains, effectively lowering the influence of grain misorientations and boundaries on the macroscopic transformation behavior.     

Numerical evaluation of overestimation of the interface thickness around ellipsoidal particle

When interfacial layers are viewed as a separate phase, the interface thickness plays an essential role in assessing physico-mechanical properties of particulate materials. However, the interface thickness from sectional analysis is often overestimated, due to the irregularity of surface textures of grains in opaque materials that gives rise to the normal of a cross-sectional plane non-perpendicular to the surface of grains. Hence, the determination of the overestimation degree is very critical to precisely obtain the interface thickness. This article develops a numerical model for the overestimation degree of the interface thickness around an ellipsoidal grain with an arbitrary aspect ratio, by applying an accurate sectional analysis algorithm, and quantitative stereology and geometrical probability theories. Furthermore, on the basis of the developed numerical model, the influence of ellipsoidal particle shape on the overestimation degree is quantitatively characterized.     

Attrition and particle breakage under monotonic and cyclic loadingAttrition et rupture de particules sous chargements monotones et cycliques

The morphological evolution of gravel grains under monotonic and cyclic loading, typically present in road structures, is presented. Two types of mineralogy are considered: a limestone and a sandstone. Loading in uniaxial strain conditions are applied, with a maximum mean pressure of 5 MPa and a maximum number of cycles of 250?000. Variations in grain size distribution and grain shape, measured with image analysis techniques, are discussed in detail. In the case of uniform grain size distribution, particle breakage does appear for stresses around 500 kPa for the limestone grains and 100 kPa for the sandstone grains. For well-graded materials under low cyclic pressures (<1 MPa), changes in grain size distribution can hardly be detected. To cite this article: F. Mayoraz et al., C. R. Mecanique 334 (2006).     

Occurrence of gradual resonance in a finite-length granular chain driven by harmonic vibration

This study presents numerical simulations of the resonance of a finite-length granular chain of dissipative grains driven by a harmonically vibrated tube. Multiple gradual resonant modes, namely non-resonance mode, partial-resonance mode, and complete-resonance mode, are identified. With a fixed vibration frequency, increasing vibration acceleration leads to a one-one-one increase in the number of grains participating in resonance, which is equal to the number of grain-wall collisions in a vibration period. Compared with the characteristic time of the grain–grain and the grain–wall collisions, the time of free flight plays a dominant role in grain motion. This situation results in the occurrence of large opening separation gaps between the grains and independent grain–grain and grain–wall collisions. A general master equation that describes the dependence of the system energy on the length of the granular chain and the number of grain–wall collisions is established, and it is in good agreement with the simulation results. We observe a gradual step-jump increase in system energy when the vibration acceleration is continuously increased, which is dedicated to an individual energy injection. The phase diagrams in the spaces of packing density and vibration acceleration, chain length and vibration acceleration show that shorter granular chain and larger packing density favor the occurrence of complete-resonance mode.

     

On the Generation of Discrete Isotropic Orientation Distributions for Linear Elastic Cubic Crystals

We consider a model for the elastic behavior of a polycrystalline material based on volume averages. In this case the effective elastic properties depend only on the distribution of the grain orientations. The aggregate is assumed to consist of a finite number of grains each of which behaves elastically like a cubic single crystal. The material parameters are fixed over the grains. An important problem is to find discrete orientation distributions (DODs) which are isotropic, i.e., whose Voigt and Reuss averages of the grain stiffness tensors are isotropic. We succeed in finding isotropic DODs for any even number of grains N≥4 and uniform volume fractions of the grains. Also, N=4 is shown to be the minimum number of grains for an isotropic DOD. This revised version was published online in August 2006 with corrections to the Cover Date.     

Effect of the grain elongation on the behaviour of granular materials in biaxial compression

In this article we study the effect of the grain elongation on the shearing behaviour of dense granular materials by means of 2D numerical simulations of biaxial compression tests, using the Contact Dynamics method. The case of grains with hexagonal shapes (and four possible different elongations) is studied in comparison to the case of a sample with circular grains. For the shapes studied, samples with polygonal grains exhibit initial densities higher than the sample with discs, and the initial density decreases when the grain elongation increases. The friction angle at the residual state increases linearly with the particle elongation ratio. The cumulative rotations of discs are higher than those of polygons. Finally, in the case of elongated hexagons, the grains with highest rotations are located along thin bands because the shear bands are thinner and more persistent for these shapes.     

Effect of Particle Morphology,Compaction, and Confinement on the High Strain Rate Behavior of Sand

The effect of grain shape, size distribution, intergranular friction, confinement, and initial compaction state on the high strain rate compressive mechanical response of sand is quantified using Long Split Hopkinson Pressure Bar (LSHPB) experiments, generating up to 1.1 ms long load pulses. This allowed the dynamic characterisation of different types of sand until full compaction (lowest initial void ratio) at different strain rates. The effect of the grain morphology and size on the dynamic compressive mechanical response of sand is assessed by conducting experiments on three types of sand: Ottawa Sand with quasi-spherical grains, Euroquartz Siligran with subangular grains and Q-Rok with polyhedral grain shape are considered in this study. The adoption of rigid (Ti64) and deformable (Latex) sand containers allowed for quasi-uniaxial strain and quasi-uniaxial stress conditions to be achieved respectively. Additionally, the effect of intergranular friction was studied, for the first time in literature, by employing polymer coated Euroquartz sand. Appropriate procedures for the preparation of samples at different representative initial consolidation states are utilized to achieve realistic range of naturally occurring formations of granular assembly from loose to dense state. The results identify material and confining sample state parameters which have significant effect on the mechanical response of sand at high strain rates and their interdependency for future integration into rate dependent constitutive models.