Modeling soft granular materials

Soft-grain materials such as clays and other colloidal pastes share the common feature of being composed of grains that can undergo large deformations without rupture. For the simulation of such materials, we present two alternative methods: (1) an implicit formulation of the material point method (MPM), in which each grain is discretized as a collection of material points, and (2) the bonded particle model (BPM), in which each soft grain is modeled as an aggregate of rigid particles using the contact dynamics method. In the MPM, a linear elastic behavior is used for the grains. In order to allow the aggregates in the BPM to deform without breaking, we use long-range center-to-center attraction forces between the primary particles belonging to each grain together with steric repulsion at their contact points. We show that these interactions lead to a plastic behavior of the grains. Using both methods, we analyze the uniaxial compaction of 2D soft granular packings. This process is nonlinear and involves both grain rearrangements and large deformations. High packing fractions beyond the jamming state are reached as a result of grain shape change for both methods. We discuss the stress-strain and volume change behavior as well as the evolution of the connectivity of the grains. Similar textures are observed at large deformations although the BPM requires higher stress than the MPM to reach the same level of packing fraction.     

颗粒形状、含量和基体特性对金属基复合材料压缩力学行为的影响

通过建立轴对称体胞模型,用数值分析手段研究了在变形速率范围10－4~105/s内,陶瓷颗粒增强铝合金复合材料的压缩塑性流变特征,讨论了不同颗粒形状(圆柱形和球形),不同颗粒体积含量(10％~50％)和不同铝合金基体(LC4、LY12CZ和7075)对金属基复合材料流动应力、应变率敏感性等的影响,构造了可以描述高应变率下金属基复合材料压缩行为的本构模型,并考虑了基体特性、颗粒形状、体积含量及应变率的影响,得出了与试验相吻合的结果。     

Micromechanics approach to the indentation hardness of glass matrix particulate composites

A theoretical analysis is made of the indentation hardness of glass matrix, particulate composites. It is hypothesized that glass is an elastic-plastic solid on a microscopic scale. Based upon the Marsh theory of indentation, expressions are formulated for indentation hardness of two-phase composites containing spherical particles. When hard particles are dispersed in a soft glass matrix, the overall hardness depends upon the matrix hardness, the volume-fraction of dispersed phase, the elastic properties of the two phases and also the matrix flow stress. On the other hand, when soft particles are dispersed in a hard glass matrix, the hardness and the elastic moduli vary in parallel with the volume-fraction of dispersed phase. Furthermore, the present analysis indicates that the hardness of a composite is independent of the particle size and interparticle spacing if the volume-fraction of the particles is kept constant. Experimental results of the Vickers hardness of phase-separated glasses as well as published hardness data for a glass-ceramic are used for the verification of the theory. The proposed theory explains well the hardness behaviour of such glass matrix composites in terms of the properties and amounts of the individual phases and the microstructural effects.     

The elastic properties, elastic models and elastic perspectives of metallic glasses

Bulk metallic glass (BMG) provides plentiful precise knowledge of fundamental parameters of elastic moduli, which offer a benchmark reference point for understanding and applications of the glassy materials. This paper comprehensively reviews the current state of the art of the study of elastic properties, the establishments of correlations between elastic moduli and properties/features, and the elastic models and elastic perspectives of metallic glasses. The goal is to show the key roles of elastic moduli in study, formation, and understanding of metallic glasses, and to present a comprehensive elastic perspectives on the major fundamental issues from processing to structure to properties in the rapidly moving field.A plentiful of data and results involving in acoustic velocities, elastic constants and their response to aging, relaxation, applied press, pressure and temperature of the metallic glasses have been compiled. The thermodynamic and kinetic parameters, stability, mechanical and physical properties of various available metallic glasses especially BMGs have also been collected. A survey based on the plentiful experimental data reveals that the linear elastic constants have striking systematic correlations with the microstructural features, glass transition temperature, melting temperature, relaxation behavior, boson peak, strength, hardness, plastic yielding of the glass, and even rheological properties of the glass forming liquids. The elastic constants of BMGs also show a correlation with a weighted average of the elastic constants of the constituent elements. We show that the elastic moduli correlations can assist in selecting alloying components with suitable elastic moduli for controlling the elastic properties and glass-forming ability of the metallic glasses, and thus the results would enable the design, control and tuning of the formation and properties of metallic glasses.We demonstrate that the glass transition, the primary and secondary relaxations, plastic deformation and yield can be attributed to the free volume increase induced flow, and the flow can be modeled as the activated hopping between the inherent states in the potential energy landscape. We then propose an extended elastic model to understand flow in metallic glass and glass-forming supercooled liquid, and the model presents a simple and quantitative mathematic expression for flow activation energy of various glasses. The elastic perspectives, which consider all metallic glasses exhibit universal behavior based on a small number of readily measurable parameters of elastic moduli, are presented for understanding the nature and diverse properties of the metallic glasses.     

Automatic generation of 2D micromechanical finite element model of silicon–carbide/aluminum metal matrix composites: Effects of the boundary conditions

Two-dimensional finite element (FE) simulations of the deformation and damage evolution of Silicon–Carbide (SiC) particle reinforced aluminum alloy composite including interphase are carried out for different microstructures and particle volume fractions of the composites. A program is developed for the automatic generation of 2D micromechanical FE-models with randomly distributed SiC particles. In order to simulate the damage process in aluminum alloy matrix and SiC particles, a damage parameter based on the stress triaxial indicator and the maximum principal stress criterion based elastic brittle damage model are developed within Abaqus/Standard Subroutine USDFLD, respectively. An Abaqus/Standard Subroutine MPC, which allows defining multi-point constraints, is developed to realize the symmetric boundary condition (SBC) and periodic boundary condition (PBC). A series of computational experiments are performed to study the influence of boundary condition, particle number and volume fraction of the representative volume element (RVE) on composite stiffness and strength properties.     

Particle Size Distribution of Limestone Fillers: Granulometry and Specific Surface Area Investigations

Mineral fillers can be defined as “inert materials included in a mix design for some useful purpose” (NF P18-508 Janvier 2012). They can be added to compounds in order to complete a large variety of final properties without increasing costs or to improve specific characteristics like hardness, brittleness, impact strength, compressive strength, softening point, fire resistance, surface texture, electrical conductivity, and so on. In Belgium, locally available limestone fillers are specifically very well adapted for the optimization of particle packing and flow behavior of cementitious pastes in concrete mixes. Limestone fillers may be easily characterized in terms of chemical and mineralogical properties. These properties are fundamental for the study of the behavior of concrete mixes in fresh state and for understanding interactions existing at the level of the interfacial transition zone between aggregates and cement paste. These properties are however insufficiently discriminant and particle size, as well as shape distribution, seem to have a potential influence on physical phenomena which happen during the setting process. The aim of this article is to compare five major techniques used to quantify the size and the shape of limestone fillers particles: laser diffraction scattering, wet sieving, and image analysis for particle size measurement; and BET adsorption and Blaine permeability methods for specific surface area.     

Effect of volume fraction and wall thickness on the elastic properties of hollow particle filled composites

Hollow particle filled composites, called syntactic foams, are widely used in applications requiring high damage tolerance and low density. The understanding of the mechanics of these materials is largely based on experimental studies. Predictive models that are capable of estimating the elastic properties of these materials over wide variation of particle wall thickness, size, and volume fraction are not yet fully developed. The present study is focused on developing a modeling scheme to estimate the elastic constants for such materials. The elastic properties of an infinitely dilute dispersion of microballoons in a matrix material are first computed by solving a dilatation and a shear problem. A differential scheme is then used to extrapolate the elastic properties of composites with high volume fractions of microballoons. The results show that the model is successful in predicting the Young’s modulus for syntactic foams containing microballoons of a wide range of wall thickness and volume fraction.     

高体积含量颗粒增强复合材料的一个细观力学模型Ⅰ: 弹性分析与等效模量

提出了一种高体积含量颗粒增强复合材料的细观力学模型。该模型将颗粒简化为同质、同尺寸的弹性圆球, 两颗粒之间的粘接材料(基体) 简化为连接颗粒的一段圆柱体, 假设了圆柱形基体中的细观位移分布形式, 在此基础上分析了一对颗粒之间弹性的细观应力场和细观弹性系数, 将颗粒对的细观弹性系数在空间各个方向上平均, 得到材料的宏观弹性常数, 并建立了宏、细观分析之间的联系。最后用本模型分析了一种实际材料(两种体积含量) , 弹性常数的预测与实验吻合良好, 研究还发现颗粒的空间分布方式对材料宏观弹性常数的影响不大, 而对细观应力的影响显著。      

Bulk Metallic Glasses with Functional Physical Properties

In this review, we report on the formation of a variety of novel, metallic, glassy materials that might well have applications as functional materials. The metallic glasses, with excellent glass‐forming ability, display many fascinating properties and features such as excellent wave‐absorption ability, exceptionally low glass‐transition temperatures (～35–60 °C) approaching room temperature, ultralow elastic moduli comparable to that of human bone, high elasticity and high strength, superplasticity and polymer‐like thermoplastic formability near room temperature, an excellent magnetocaloric effect, hard magnetism and tunable magnetic properties, heavy‐fermion behavior, superhydrophobicity and superoleophobicity, and polyamorphism, all of which are of interest not only for basic research but also for technological applications. A strategy based on elastic‐moduli correlations for fabrication of bulk metallic glasses (BMGs) with controllable properties is presented. The work has implications in the search for novel metallic glasses with unique functional properties, for advancing our understanding of the nature and formation of glasses, and for extending the applications of the materials.     

增强颗粒含量和尺寸对SiCp/Fe复合材料性能的影响

利用电流直加热动态热压烧结工艺,分别制备了增强颗粒体积含量从5%到15%,尺寸从3 μm到45 μm的SiCp/Fe复合材料,研究了粒子含量与尺寸对复合材料硬度、强度、延伸率和耐磨性能的影响.研究表明:增强颗粒的体积含量从5%提高到10%,可以明显提高材料的性能;随着增强颗粒含量进一步提高,颗粒团聚将导致材料性能降低;...     

Effect of molecular architecture of polycarboxylate ethers on plasticizing performance in alkali-activated slag paste

A range of anionic and cationic polycarboxylate ether (PCE) plasticizers with different molecular architectures (molecular weights, side chain lengths, and ratios of side chain density to backbone charge) are synthesized and tested to determine their effects on the rheological properties of fresh alkali-activated slag (AAS) pastes. A higher density of long side chains in the lower molecular weight polymers can provide a noticeable yield stress reduction, indicating a mild increase in workability compared to that of an unmodified AAS paste. It is hypothesized that side chains may have two important roles, i.e., providing steric hindrance to disperse particles after PCE adsorption on a particle surface, and also providing partial protection of the backbone charges against attachment of one PCE molecule to two or more slag particles, which is called bridging. This enhances the likelihood of adsorption on single particles, and thus increases the plasticizing action. A very similar plasticizing mechanism is observed for PCEs with similar structures but differing charge signs (cationic/anionic), which indicates that both anionic and cationic adsorption sites are available on AAS particle surfaces. The measured flow curves of all pastes are well described by the Herschel–Bulkley model with shear thinning behavior.     

Multi-length scale micromorphic process zone model

The prediction of fracture toughness for hierarchical materials remains a challenging research issue because it involves different physical phenomena at multiple length scales. In this work, we propose a multiscale process zone model based on linear elastic fracture mechanics and a multiscale micromorphic theory. By computing the stress intensity factor in a K-dominant region while maintaining the mechanism of failure in the process zone, this model allows the evaluation of the fracture toughness of hierarchical materials as a function of their microstructural properties. After introducing a multi-length scale finite element formulation, an application is presented for high strength alloys, whose microstructure typically contains two populations of particles at different length scales. For this material, the design parameters comprise of the strength of the matrix–particle interface, the particle volume fraction and the strain-hardening of the matrix. Using the proposed framework, trends in the fracture toughness are computed as a function of design parameters, showing potential applications in computational materials design.     

Pseudo-percolation: Critical volume fractions and mechanical percolation in polymer nanocomposites

Polymer nanocomposites offer a basis for the design and manufacture composite materials with greatly enhanced properties at relatively low volume fractions of the included phase. One underlying mechanism, thought to contribute to these properties is the presence of an interfacial region, ∼15 nm thick, between the polymer matrix and included particles. The size of the interface makes relatively little contribution to the effective properties of composites with micro-sized particles but, because its thickness is comparable to the size of the nanoscaled included phase, its potential impact within nanocomposites is much greater. In particular, percolated nano-microstructures may result at volume fractions below theoretical thresholds, due to connectivity achieved through rod-interface-rod, or ‘pseudo-percolation’, contact. In this work the influence of the interface layer is incorporated into estimates of critical volume fraction through an excluded volume model. Results show a significant reduction in the range of critical volume fractions. These values are incorporated into a mean-field micromechanics model to illustrate mechanical percolation through changes in predicted effective elastic composite properties.     

The influence of powder packing on the rheology of fibre-loaded pastes

The effects of fibre addition on the extrusion rheology of ceramic particulate pastes has been investigated using model pastes containing chopped glass fibre and alumina powders. In these pastes where the fibre diameter was much larger than the alumina particle diameter, there was a decrease in the pressure required to extrude the paste as the powder component was replaced by fibre, up to a ratio of 0.4 powder to 0.6 fibre by volume. When the pastes were characterized using physically based models this behaviour was reflected in lower values of the derived rheological parameters. It is shown that this behaviour can largely be attributed to the packing behaviour of the fibre and powder-phase components. The results also suggest that the presence of fibres increases the die entry pressure drop relative to the die land pressure drop. It is shown that while the models proposed by Milewski in combination with the rheological models can be used to illustrate the expected behaviour of composite pastes, the observed behaviour was better predicted by using modified models proposed by Karlsson and Spring. At high fibre loadings (>60 vol%), extrudable materials could not be formed; this was attributed to packing and mixing problems leading to increased fibre-fibre interaction preventing flow. This is highlighted by materials in which the ratio of powder to fibre was 1 to 4 by volume, where the paste-like body was compressible and exhibited some elastic springback. For pastes where the solid phase contains <50 vol% fibre the rheological behaviour is predictable if the packing behaviour of the fibre and the rheological behaviour of the pastes containing only the powder are known. This can be used as a tool to aid the design of composite pastes and for the development of suitable process equipment.     

Experimental verification of the theory of elastic properties usingscattering approximations in (0-3) connectivity composite materials

New methods of estimating effective macroscopic elastic constants for inhomogeneous materials have recently been proposed using elastic-wave scattering theory. However, there are few experimental measurements which allow the validation of these models. The purpose of this paper is to verify if the scattering approximation theories allow prediction of the acoustic properties of epoxy composites containing tungsten powder for various particle sizes and various volume fractions of filler. The theoretical predictions are compared with the experimental results and the different models are discussed     

The effect of particle distribution on damage formation in particulate reinforced metal matrix composites deformed in compression

Image analysis results are reported on the generation of damage in particulate reinforced metal matrix composites during compressive deformation. The technique allows the automated collection of data on the incidence of particle fracture and void formation in the matrix as a function of important microstructural parameters such as local particle volume fraction and particle size. There is a strong relationship between damage and the local volume fraction of the reinforcement proving that damage formation is accentuated in regions of particle clustering. With the SiC reinforced materials examined, there was observed to be a change in dominance of damage mechanism from particle fracture at low local volume fractions to void formation in the matrix within strongly clustered regions. The results are compared with finite element (FE) modelling of the compressive deformation of clustered particles using a simple cluster of equi-spaced particles. The FE results suggest that plastic flow is generally inhibited in clustered regions. In certain highly clustered configurations shielding is such that flow does not occur in the heart of the cluster even at high levels of average plastic strain. The modelling suggests that the change in dominance of damage mechanism is related to the dramatic increase in tensile hydrostatic stresses in the matrix with higher levels of particle clustering.     

Identification of effective properties of particle reinforced composite materials

For the determination of effective elastic properties an energy averaging procedure has been used for particle reinforced composite materials. This procedure is based on finite element calculations of the deformation energy of a characteristic volume element. The proposed approach allows the determination of effective properties of particle reinforced composite with acceptable precision. The calculated effective properties of the composite are found in range between upper and lower Hashin-Shtrikman bounds. The averaging elastic properties of the composite depend on the properties of the particles, matrix volume fraction of the particles and some parameters taking into account the influence of the interphase between matrix and particles. These dependencies can be presented by simple analytical functions approximatically. An identification procedure basing on numerical experiments allows the estimation of the unknown approximation parameters. The obtained functions describe precisely the numerical data for any relationship between material constituents.     

B_4C增强铝基复合材料力学性能有限元模拟

建立了颗粒增强铝基复合材料的轴对称单胞模型,并通过有限元方法模拟了B_4C颗粒增强5083铝基复合材料的力学性能和微观应力分布。结果表明,模拟结果与实验结果吻合较好,模拟椭球体颗粒增强复合材料的抗拉强度为485 MPa,而实验值为477 MPa,相对误差仅为1.7%。颗粒形状对复合材料微观应力场有很大影响:圆柱体颗粒的尖角处容易造成应力集中,而球体颗粒界面处应力分布较为均匀。在一定范围内,复合材料的弹性模量和抗拉强度随着B_4C颗粒体积分数的增加而增加。在颗粒体积分数不变的情况下,不同长径比的颗粒沿复合材料受力方向定向排列时,颗粒的长径比越大,复合材料的弹性模量、强度等力学性能也越高。     

Magnetostrictive properties of epoxy resins modified with Terfenol-D particles for detection of internal stress in CFRP. Part 1: Materials and processes

Magnetostrictive particles like Terfenol-D are investigated with respect to their ability to detect internal stress, generated in carbon fibre-reinforced polymers (CFRP) in a non-destructive way. The results are presented in two parts. The first part elucidates the ideas for the preparation of dispersions based on these particles with high density in epoxy resins. There is particular focus on the effects of particle size and concentration. Different particle sizes in a range of 0–300?μm are selected by special separation techniques. The particle size distribution is controlled in dry state by laser diffraction method. Changing of the chemical composition, particularly by the oxidation of particles, is analysed by EDX. Use of a magnetic field is identified as a suitable means for the stabilisation of these high-weighted particle fractions dispersed in epoxy resins. The particle size distribution, as well as the alignment of particles, in the cured epoxy resins is investigated by SEM and light microscopy. The second part of the study covers the magnetostrictive properties of the modified epoxy resins which are quantified by the detection of internal stress in CFRP.