Gauss integration applied to a Green''s function formulation for cylindrical fiber composites

The stress in an elastic two phase material is formulated in terms of eigenstrains and Green's functions leading to a singular integral equation. The singularity is dealt with by a subtraction technique and contour integrations, one of which corresponds to the Eshelby solution. The remaining non-singular integration is evaluated numerically using a Gauss rule. The calculated local stresses are within 1% of the analytical solution for an isolated inclusion problem. Also, the effective properties as a function of volume fraction are in good agreement with Christensen's analytical result. The method is then used to study rectangular versus square packing. The volume averaged stiffness for rectangular packing may be either higher or lower than that for square packing, depending on the loading direction. The stress concentration factor is shown to increase with fiber volume fraction. The stress concentration factor also increases at a decreasing rate as the fiber to matrix stiffness ratio is increased. All changes examined that an increase in the stiffness, whether by increased fiber volume fraction, increased fiber stiffness or an alternate packing arrangement, also increase the fiber stress concentration factor.     

Structural properties of wet granular beds subjected to tapping

Based on a simple numerical model for wet granular beds, we study the structural properties of wet particles subjected to tapping in terms of the global anisotropy and angular distribution presented by their contacts. The model allows to generate 2-dimensional packings of disks that can form capillary bridges due to the presence of interstitial liquid. A pseudodynamic simulation of adhesive hard disks has been implemented. The bed is subjected to a tapping-like excitation and we study the evolution of structural anisotropy of the packing with the number of taps. We also analyse the behavior of the angular distribution of contacts and anisotropy as a function of tapping intensity and liquid content. Present results help to better understand the behavior found in a previous work for the packing fraction of these systems. They also demonstrate that anisotropy alone not always helps to completely understand the behavior of the structural properties of wet particles.     

Prediction of elastic moduli of angle-ply laminates from various rhombohedral unit cells

The elastic properties of angle-ply laminates are investigated by using the numerical homogenization based on a rhombohedral unit cell. A discussion of the influence of fiber packing geometry on the elastic moduli is included. The efficiency of various fiber distributions is validated by comparing the results of homogenization analyses with the available analytical solutions. The prediction is performed for various values of fiber orientation, fiber volume fraction and ply thickness.     

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。      

An empirical approach for the optimisation of aggregate combinations for self-compacting concrete

The fresh and hardened properties of self-compacting concrete (SCC) depend on number of factors such as paste composition, paste content, aggregate content, aggregate gradation etc. In the present investigation, the influence of the packing density of aggregates on the properties of SCC was evaluated. Experiments were conducted to measure the packing density for different combinations of aggregates precisely. A ternary packing diagram (TPD) was developed based on the packing density of measured and interpolated data. Considering the limitations in generalising the TPD and the difficulty involved in adopting mathematical models for aggregates, an attempt was made to establish a simple method for the selection of the combination of aggregates resulting in maximum packing density from the particle size distribution of aggregates (represented by the Coefficient of uniformity??C _u). Further, studies were extended to investigate the effect of aggregate packing density on fresh and hardened SCC properties. The results indicate that for a constant paste volume and paste composition, with increase in packing density of aggregates, the fresh properties and the compressive strength of SCC were improved positively. An attempt was also made to identify the influence of 10 different proportions of aggregates having the same packing density on the properties of SCC. The results indicate that at the same aggregate packing density, the fresh concrete properties were influenced significantly by the choice of the aggregate combination, while there was little or no influence on the hardened properties. Furthermore, the experimental data obtained was used for supplementary validation of the existing model (compressible packing model) for predicting the packing density and the fresh behaviour of SCC.     

DEM simulation of binary sphere packing densification under vertical vibration

The densification of random binary sphere packings subjected to vertical vibration was modeled by using the discrete element method (DEM). The influences of operating parameters such as the vibration conditions, sphere size ratio (diameter ratio of larger versus small spheres), and composition (volume fraction of large spheres) of the binary mixture on the fractional packing density φ (defined as the volume of spheres divided by the volume of container) were studied. Two packing states, i.e., random loose packing (RLP) and random close packing (RCP), were reproduced and their micro properties such as the coordination number (CN), radial distribution function (RDF), and force structure were characterized and compared. The results indicate that properly controlling vibration conditions can realize the transition of binary packing structure from the RLP to RCP state when the sphere size ratio and composition are fixed, and the fractional packing density for RCP after vibration can reach φ_RCP?≈?0.86. Different packing characteristics from RLP and RCP identify that RCP shows much denser and more uniform structure than RLP. The current modeling results are in good agreement with those obtained from both the physical experiments and the proposed empirical models in the literature.     

Micromechanics of interfacial thermal stresses in fiber reinforced composites

This paper develops a generic 2D micromechanical model that deal with the interfacial thermal stresses in fiber reinforced composites with randomly packed fibers of different sizes and thermoelastic properties by successive superposition of the solution of a single fiber embedded in a matrix. This approach reduces the complicated micromechanical model to a system of linear algebraic equations using the perturbation technique. The accuracy of current approach is verified by comparing it with the existing analytical solution. The micromechanics model is then applied to analyze periodically and randomly packing fiber reinforced composites. Analysis results show that the effect of a single fiber is localized and there is an optimal elastic mismatch of fiber and matrix where the interfacial hoop stress is insensitive to the fiber packing arrangement and the fiber volume fraction.     

An analytical model for the longitudinal permeability of aligned fibrous media

This paper presents an analytical series solution of the longitudinal fluid flow in porous media consisting of aligned rigid fibers, which, in turn, is used to establish a relationship for the longitudinal permeability as a function of the fiber packing geometry, fiber volume fraction and the fiber radius. The analytical series solution is developed for rectangular and staggered packing arrangements of the fibers using the boundary collocation method where the constants in the series solution are solved for numerically. As the number of boundary collocation points is increased, the analytical solution is shown to converge with a finite element solution of the identical flow situation for all fiber volume fractions and packing arrangements. In addition, the permeability results are presented in a dimensionless form as a function of the fiber volume fraction and fiber packing arrangement for a general applicability and easy use of the results for predicting the longitudinal permeability of fiber tows consisting of aligned rigid fibers.     

Packing Densities and Glass Forming Ability of Alloys

The random closed packing fraction of hard balls of three different sizes were measured by use of the Archimedes method. This packing fraction increases as the kind of balls with different sizes increases. The packing fraction is related to the mixing entropy of an ideal solution in respect to the holes among the hard balls. The composition zone of La-Al-Ni amorphous alloy made by cooling the alloy melt with a cooling rate of 90 Ks-1 is located at same zone of the largest values of packing fraction and mixing entropy of hard balls in the ternary system. where the proportion of atom sizes of La, Al and Ni is similar to that of hard balls. The packing fraction and the mixing entropy are qualitatively considered as one of the criteria of the glass forming ability of alloys     

粉体堆积密度的理论计算

考察了紧密堆积时多级理想球形颗粒混合粉体的堆积密度的理论值与粒级组分数的关系,紧密堆积时颗粒的粒度分布特征,以及堆积密度的理论值与单一粒径粉体空隙体积分数、颗粒干扰宽度的相关关系。研究表明,原始堆积密度越大,多粒级理想球形颗粒混合粉体达到相同的堆积密度所需的粒级数越少,各粒级的体积含量随着粒级的增加呈指数下降,且原始堆积密度越大,下降速度越快;其粒度分布符合对数正态分布;堆积密度的理论值与单一粉体空隙体积分数、颗粒干扰宽度的符合二元二次非线性关系。     

Vapor-liquid equilibrium and volumetric properties calculations for solutions in the supercritical carbon dioxide

The calculations of gas solubilities in supercritical solvents require equations of state remaining accurate in the critical range, which are difficult to obtain with classical models. In this work, the Helmholtz energy of a mixture is considered as the sum of the Helmholtz energies of pure components taken at a constant packing fraction and of a residual term which may have the form of a RedlichKister, Van Laar, NRTL, UNIQUAC, or UNIFAC function. Thus it is possible to assign to a given component an equation of state whose form is different from that of the others. This model has been applied to binary systems containing supercritical carbon dioxide. The results are improved with respect to those obtained with the classical model for vapor-liquid equilibria and for volumetric properties.     

Characterizing the intrinsic properties of powder – A combined discrete element analysis and Hall flowmeter testing study

Discrete element modelling (DEM) and experimental characterization were carried out for Hall flowmeter tests, in which Inconel718 powders were poured down through a funnel into a density cup to form a heap. By measuring the flow rate, angle of repose and packing fraction from the experiments, and combining with DEM simulations, we were able to extract the coefficients of friction for the powder-powder and powder-wall interactions. We further studied the effect of powder-powder adhesion and found that the adhesion could greatly affect the flow rate and flow pattern. In particular, by increasing the adhesion, we observed a transition from a continuous to discontinuous discharging flow, and revealed an underlying mechanism for the transition. We also studied the effects of powder size and density cup diameter, and found that at their application size scale, the influences of these parameters on the measured results are negligible. The present work presents a simple approach to study the intrinsic properties of powders, and their influences on flowability and packing property.     

A hierarchical approach to simulate the packing density of particle mixtures on a computer

In many fields of materials science it is important to know how densely a particle mixture can be packed. The “packing density” is the ratio of the particle volume and the volume of the surrounding container needed for a random close packing of the particles. We present a method for estimating the packing density for spherical particles based on computer simulations only, i.e. without the need for additional experiments. Our method is particularly suited for particle mixtures with an extremely wide range of particle diameters as they occur e.g. in modern concrete mixtures. A single representative sample from such mixtures would be much larger than can be handled on present standard computers. In our hierarchical approach the diameter range is therefore divided into smaller intervals. Samples from these limited diameter intervals are drawn and their packing density is estimated from a simulated packing. The results are used to “fill” the interstices in the sample from the next larger particle interval. To account for the interaction between particles of different sizes we include larger particles into the sample of smaller ones. The larger ones act as part of the boundary during the packing. Thus we obtain more realistic estimates of how dense a fraction of particles can be packed within the whole mixture. The focus of this paper is on the divide-and-conquer approach and on how the simulation results from the fractions can be collected into an overall estimate of the packing density. We do not go into details of the simulation technique for the single packing. We compare our results to some experimental data to show that our method works at least as good as the classical analytical models like CPM without the need for any experiments.     

Inclusion interaction and effective material properties in a particle-filled composite material system

This work presents a methodology implementing random packing of spheres combined with commercial finite element method (FEM) software to optimize the material properties, such as Young’s modulus, Poisson’s ratio, and coefficient of thermal expansion (CTE) of two-phase materials used in electronic packaging. The methodology includes an implementation of a numerical algorithm of random packing of spheres and a technique for creating conformal FEM mesh of a large aggregate of particles embedded in a medium. We explored the random packing of spheres with different diameters using particle generation algorithms coded in MATLAB. The FEM meshes were generated using software MATLAB and TETGEN. After importing the databases of the nodes and elements into commercial FEM software ANSYS, the composite materials with spherical fillers and the polymer matrix were modeled using ANSYS. The effective Young’s modulus, Poisson’s ratio, and CTE along different axes were calculated using ANSYS by applying proper loading and boundary conditions. It was found that the composite material was virtually isotropic. The Young’s modulus and Poisson’s ratio calculated by FEM models were compared to a number of analytical solutions in the literature. For low volume fraction of filler content, the FEM results and analytical solutions agree well. However, for high volume fraction of filler content, there is some discrepancy between FEM and analytical models and also among the analytical models themselves. The discrepancy is attributed to the multi-body interaction effect of the filler particles when they are getting close.     

玻璃纤维/聚乳酸复合包装薄膜的制备及表征

目的添加适量的玻璃纤维(GF)改善聚乳酸(PLA)的力学性能以适应产品的包装。方法聚乳酸与玻璃纤维共混制备复合包装材料,为了增加2种物质的相容性,加入KH550改性玻璃纤维以增强材料的力学性能。测试该复合材料力学性能、透光率、红外谱图,并用扫描电子显微镜观察复合包装材料的断面形貌。结果聚乳酸中添加一定量的玻璃纤维后,复合薄膜的力学性能增强。添加质量分数为15%的玻璃纤维,薄膜的拉伸强度最大;添加质量分数为25%的玻璃纤维时,冲击强度最大;用质量分数为1%的KH550偶联剂改性玻璃纤维,明显增强了GF和PLA的相容性,拉伸强度明显提高;GF所占比例愈大,GF/PLA复合薄膜材料的透光率越低,雾度越高,对包装材料的可视性有一定的影响。结论玻璃纤维具有超强的增强效果,其在改善聚乳酸脆性方面具有显著的意义和广阔的发展前景。     

Experimental study on the packing densification of mixtures of spherical and cylindrical particles subjected to 3D vibrations

To identify the dense packing of cylinder–sphere binary mixtures (spheres as filling objects), the densification process of such binary mixtures subjected to three-dimensional (3D) mechanical vibrations was experimentally studied. Various influential factors including vibration parameters (such as vibration time t, vibration amplitude A, frequency ω, vibration acceleration Γ) as well as particle size ratio r (small sphere vs. large cylinder), composition of the binary mixtures X_L (volume fraction of cylinders), and container size D (container diameter) on the packing density ρ were systematically investigated. The results show that the optimal vibration parameters for different binary cylinder–sphere mixtures are different. The smaller the size ratio, the less vibration acceleration is needed to form a stable dense packing. For each binary mixture, high packing density can be obtained when the volume fraction of large cylindrical particles is dominant. Meanwhile, increasing the container size can decrease the container wall effect and get higher packing density. The proposed analytical model has been proved to be valid in predicting the packing densification of current cylinder–sphere binary mixtures.     

膜法海水吸收烟气中二氧化碳的试验研究

采用自制聚丙烯中空纤维膜接触器,以海水作为吸收剂,对模拟烟气中CO2进行吸收试验研究,主要考察烟气流量、CO2浓度、海水流量、海水pH值及膜填充率对CO2脱除率及膜接触器传质性能的影响.研究结果表明:(1)提高烟气流量或CO2浓度能提高膜接触器对CO2的处理量,导致脱碳率下降;(2)提高海水流量能明显提高脱碳率和传质速率;(3)提高海水pH可增大海水对CO2的吸收能力,直接决定了海水对CO2的吸收机制;(4)增大膜接触器填充率所对应的脱碳率并非最高,有效气液接触面积是影响脱碳率和过程传质的重要因素.     

纳米纤维素/聚乳酸复合包装薄膜的制备及表征

目的添加适量的纳米纤维素改善聚乳酸的脆性,以适应产品的包装。方法将聚乳酸(PLA)与纳米纤维素(CNFs)共混制备复合包装材料,测试该复合材料的力学性能、透光率、红外谱图,并用扫描电子显微镜(SEM)观察了复合包装材料的表面形貌。结果纳米纤维素添加到聚乳酸中增加了其力学性能,当纳米纤维素质量分数为2%时,拉伸强度和冲击强度都达到最大;随着添加CNFS比例的增大,CNFs/PLA复合薄膜材料的透光率随之降低,雾度随之升高,但是该薄膜作为包装材料对商品的可视性影响不大。结论纳米纤维素(CNFs)是具有一定长径比的纳米级线状材料,对材料的拉伸强度具有增强作用。