The Influence of Multiple Inclusions on the Cauchy Stress of a Spherical Particle-Reinforced Composite Under Uniaxial Loading

2014 ◽  
Author(s):  
Ke Niu ◽  
Armin Abedini ◽  
Zengtao Chen
Keyword(s):  
Spherical Particle ◽  
Single Particle ◽  
Volume Fraction ◽  
Unit Cell ◽  
Spherical Particles ◽  
Uniaxial Tensile ◽  
Cauchy Stress ◽  
Particle Volume ◽  
Volume Fractions ◽  
Unit Cells

This paper investigates the influence of multiple inclusions on the Cauchy stress of a spherical particle-reinforced metal matrix composite (MMC) under uniaxial tensile loading condition. The approach of three-dimensional cubic multi-particle unit cell is used to investigate the 15 non-overlapping identical spherical particles which are randomly distributed in the unit cell. The coordinates of the center of each particle are calculated by using the Random Sequential Adsorption algorithm (RSA) to ensure its periodicity. The models with reinforcement volume fractions of 10%, 15%, 20% and 25% are evaluated by using the finite element method. The behaviour of Cauchy stress for each model is analyzed at a far-field strain of 5%. For each reinforcement volume fraction, four models with different particle spatial distributions are evaluated and averaged to achieve a more accurate result. At the same time, single-particle unit cell and analytical model were developed. The stress-strain curves of multi-particle unit cells are compared with single-particle unit cells and the tangent homogenization model coupled with the Mori-Tanaka method. Only little scatters were found between unit cells with the same particle volume fractions. Multi-particle unit cells predict higher response than single particle unit cells. As the volume fraction of reinforcements increases, the Cauchy stress of MMCs increases.

Shock-Induced Multiphase Instability in a High Volume Fraction Finite-Thickness Particle Layer

2021 ◽  
Author(s):  
Bertrand Rollin ◽  
Frederick Ouellet ◽  
Bradford Durant ◽  
Rahul Babu Koneru ◽  
S. Balachandar
Keyword(s):  
Shock Tube ◽  
Volume Fraction ◽  
Solid Phase ◽  
Particle Volume Fraction ◽  
Finite Thickness ◽  
Spherical Particles ◽  
Shock Strength ◽  
Particle Volume ◽  
Particle Cloud ◽  
Particle Layer

Abstract We study the interaction of a planar air shock with a perturbed, monodispersed, particle curtain using point-particle simulations. In this Eulerian-Lagrangian approach, equations of motion are solved to track the position, momentum, and energy of the computational particles while the carrier fluid flow is computed in the Eulerian frame of reference. In contrast with many Shock-Driven Multiphase Instability (SDMI) studies, we investigate a configuration with an initially high particle volume fraction, which produces a strongly two-way coupled flow in the early moments following the shock-solid phase interaction. In the present study, the curtain is about 4 mm in thickness and has a peak volume fraction of about 26%. It is composed of spherical particles of d = 115μm in diameter and a density of 2500 kg.m−3, thus replicating glass particles commonly used in multiphase shock tube experiments or multiphase explosive experiments. We characterize both the evolution of the perturbed particle curtain and the gas initially trapped inside the particle curtain in our planar three-dimensional numerical shock tube. Control parameters such as the shock strength, the particle curtain perturbation wavelength and particle volume fraction peak-to-trough amplitude are varied to quantify their influence on the evolution of the particle cloud and the initially trapped gas. We also analyze the vortical motion in the flow field. Our results indicate that the shock strength is the primary contributor to the cloud particle width. Also, a classic Richtmyer-Meshkov instability mixes the gas initially trapped in the particle curtain and the surrounding gas. Finally, we observe that the particle cloud contribute to the formation of longitudinal vortices in the downstream flow.

Computer Simulation Model for Spherical Particle Filled Composite Materials

2011 ◽  
Vol 474-476 ◽  
pp. 7-10 ◽  
Author(s):  
Zhuo Chen ◽  
Zhi Xiong Huang ◽  
Ming Zhang ◽  
Min Xian Shi ◽  
Yan Qin ◽  
...  
Keyword(s):  
Computer Simulation ◽  
Composite Materials ◽  
Simulation Model ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Spherical Particles ◽  
Computer Simulation Model ◽  
Particle Volume ◽  
Minimal Sphere ◽  
Center Density

This paper introduced a computer simulation model for composite materials which was reinforced by spherical particles. We introduced its algorithm and visualize the model with different particle volume fraction. In order to evaluate the uniformity of the particle distribution, we estimated Particle Center Density and standard deviation of minimal sphere distance.

Comparative Evaluation of Algorithms for Achieving Ultrapacked Thermal Greases: Microstructural Models and Effective Behavior

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Sukshitha Achar P. L ◽  
Huanyu Liao ◽  
Ganesh Subbarayan
Keyword(s):  
Heuristic Algorithms ◽  
Volume Fraction ◽  
Augmented Lagrangian Method ◽  
Random Network ◽  
Optimization Algorithms ◽  
Particle Packing ◽  
Computational Time ◽  
Particle Volume ◽  
Volume Fractions ◽  
Number Of Particles

Abstract In this work, we develop and evaluate algorithms for generating ultrapacked microstructures of particles. Simulated microstructures reported in the literature rarely contain particle volume fractions greater than 60%. However, commercially available thermal greases appear to achieve volume fractions in the range of 60–80%. Therefore, to analyze the effectiveness of commercially available particle-filled thermal interface materials (TIM), there is a need to develop algorithms capable of generating ultrapacked microstructures. The particle packing problem is initially posed as a nonlinear programming problem, and formal optimization algorithms are applied to generate microstructures that are maximally packed. The packing efficiency in the simulated microstructure is dependent on the number of particles in the simulation cell; however, as the number of particles increases, the packing simulation is computationally expensive. Here, the computational time to generate microstructures with large number of particles is systematically evaluated first using optimization algorithms. The algorithms include the penalty function methods, best-in-class sequential quadratic programming method, matrix-less conjugate gradient method as well as the augmented Lagrangian method. Heuristic algorithms are next evaluated to achieve computationally efficient packing. The evaluated heuristic algorithms are mainly based on the drop-fall-shake (DFS) method, but modified to more effectively simulate the mixing process in commercial planetary mixers. With the developed procedures, representative volume elements (RVE) with volume fraction as high as 74% are demonstrated. The simulated microstructures are analyzed using our previously developed random network model to estimate the effective thermal and mechanical behavior given a particle arrangement.

Effects of Particle Concentration on the Partitioning of Suspensions at Small Divergent Bifurcations

1996 ◽  
Vol 118 (3) ◽  
pp. 287-294 ◽  
Author(s):  
R. Ditchfield ◽  
W. L. Olbricht
Keyword(s):  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Particle Diameter ◽  
Circular Cross Section ◽  
Experimental Results ◽  
Hydrodynamic Interactions ◽  
Spherical Particles ◽  
Straight Tube ◽  
Particle Volume ◽  
Reynolds Number Flow

Experimental results are reported for the low Reynolds number flow of a suspension of spherical particles through a divergent capillary bifurcation consisting of a straight tube of circular cross-section that splits to form two tubes of equal diameter. The partitioning of particles between the downstream branches of the bifurcation is measured as a function of the partitioning of total volume (particles + suspending fluid) between the branches. Two bifurcation geometries are examined: a symmetric Y-shaped bifurcation and a nonsymmetric T-shaped bifurcation. This experiment focuses on the role of hydrodynamic interactions between particles on the partitioning of particles at the bifurcation. The particle diameter, made dimensionless with respect to the diameter of the branch tubes, ranges from 0.4 to 0.8. Results show that hydrodynamic interactions among the particles are significant at the bifurcation, even for conditions where interactions are unimportant in the straight branches away from the bifurcation. As a result of hydrodynamic interactions among particles at the bifurcation, the partitioning of particles between the branches is affected for particle volume fractions as small as 2 percent. The experimental results show that the effect of particle volume fraction is to diminish the inhomogeneity of particle partitioning at the bifurcation. However, the magnitude of this effect depends strongly on the overall shape of the bifurcation geometry, and, in particular on the angles between the branches.

Radiative Transfer With Dependent Scattering by Particles: Part 1—Theoretical Investigation

1986 ◽  
Vol 108 (3) ◽  
pp. 608-613 ◽  
Author(s):  
J. D. Cartigny ◽  
Y. Yamada ◽  
C. L. Tien
Keyword(s):  
Radiative Transfer ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Spherical Particles ◽  
Sphere Model ◽  
Radiation Scattering ◽  
Particle Volume ◽  
Scattering Approximation ◽  
Regime Map ◽  
Packed Sphere

Dependent radiation scattering for which the independent scattering theory fails to predict the scattering properties is important in analyzing radiative transfer in packed and fluidized beds. In this paper the dependent scattering properties have been derived assuming the Rayleigh–Debye scattering approximation for two cases: two identical spheres and a cloud of spherical particles. The two-sphere calculated results compare well with the exact solutions in the literature, giving confidence in the present analytical approach. The gas model and packed-sphere model have been employed to calculate dependent scattering properties for a cloud of particles of small and large particle volume fraction, respectively. The calculated dependent scattering efficiencies for a cloud of particles are smaller than the independent scattering efficiencies and decrease with increasing particle volume fraction. A regime map for independent and dependent scattering has been constructed and compared with existing empirical criteria.

VISCOSITY METHOD FOR THE DETERMINATION OF THE THICKNESS OF SOLVATION LAYERS NEAR PARTICLES DISPERSED IN A LIQUID

2005 ◽  
Vol 12 (03) ◽  
pp. 457-462 ◽  
Author(s):  
SHAOXIAN SONG ◽  
YIMIN ZHANG ◽  
TOMLINSON FORT
Keyword(s):  
Size Distribution ◽  
Spherical Particle ◽  
Volume Fraction ◽  
Spherical Particles ◽  
Viscosity Method ◽  
Theoretical Derivation ◽  
Solid Spheres

In this paper, we present a method for determining the thickness of solvation layers near spherical particles dispersed in a liquid through measurements of the viscosity of the dispersion as a function of the volume fraction of the dry particles in the dispersion and the size distribution of the particles. It is termed viscosity method. The theoretical derivation for the method is based on Einstein's theory of viscosity of dispersions, while two assumptions are made: 1. Solvation layers contribute to increasing the viscosity of the dispersion in c times as the same volume of rigid solid spheres. 2. The thickness of solvation layers is the same near every chemically similar spherical particle in a given dispersion.

Numerical Study of Forced Convection of Nanofluids in a Microchannel Heat Sink

2008 ◽  
Author(s):  
Parisa Vaziee ◽  
Omid Abouali
Keyword(s):  
Heat Transfer ◽  
Pressure Drop ◽  
Heat Sink ◽  
Volume Fraction ◽  
Numerical Study ◽  
Heat Removal ◽  
Al2o3 Nanoparticles ◽  
Microchannel Heat Sink ◽  
Particle Volume ◽  
Volume Fractions

Effectiveness of the microchannel heat sink cooled by nanofluids with various particle volume fractions is investigated numerically using the latest theoretical models for conductivity and viscosity of the nanofluids. Both laminar and turbulent flows are considered in this research. The model of conductivity used in this research accounts for the fundamental role of Brownian motion of the nanoparticles which is in good agreement with the experimental data. The changes in viscosity of the nanofluid due to temperature variation are considered also. Final results are compared with the experimental measurements for heat transfer coefficient and pressure drop in microchannel. Enhancement in heat transfer is achieved for laminar flow with increasing of volume fraction of Al2O3 nanoparticles. But for turbulent flow an enhancement of heat removal was not seen and using higher volume fractions of nanoparticles increases the maximum substrate temperature. Pressure drop is increased with using nanofluids because of the augmentation in the viscosity and this increase is more noticeable in higher Reynolds numbers.

A New Unit Cell Concerned Realistic Geometry Structure of 3D Four Directional Braided Composite

2016 ◽  
Vol 860 ◽  
pp. 65-68
Author(s):  
Hai Jun Zhang ◽  
Chu Wei Zhou
Keyword(s):  
Volume Fraction ◽  
Unit Cell ◽  
Fiber Volume ◽  
The Real ◽  
Braided Composite ◽  
Packing Factor ◽  
Geometry Structure ◽  
Element Simulation ◽  
Unit Cells ◽  
Realistic Geometry

This paper represented a new unit cell of 3D four directional braided composite for mechanical properties calculation. There are three disadvantages of unit cells in most previous works such as the fiber volume fraction hard to touch the reality despite the packing factor is maximum 1, the yarns are curved subjectively which is far away from realistic geometry structure, a quantity of connected surfaces are neglected as the yarns are not match the real appearance. A new unit cell established based on the real manufacturing process and structure could improve these aspects in this work. The yarn in the unit cell was similar to the real one which was constructed by photos. The details at the conjoined position were also expressed thoroughly. The result of finite element simulation was in good agreement with the available experimental data.

scholarly journals Rheology of mobile sediment beds in laminar shear flow: effects of creep and polydispersity

2021 ◽  
Vol 932 ◽  
Author(s):  
Christoph Rettinger ◽  
Sebastian Eibl ◽  
Ulrich Rüde ◽  
Bernhard Vowinckel
Keyword(s):  
Friction Coefficient ◽  
Shear Flow ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Rheological Behaviour ◽  
Spherical Particles ◽  
Particle Volume ◽  
Two Phase ◽  
Transport Modelling ◽  
Static State

Classical scaling relationships for rheological quantities such as the $\mu (J)$ -rheology have become increasingly popular for closures of two-phase flow modelling. However, these frameworks have been derived for monodisperse particles. We aim to extend these considerations to sediment transport modelling by using a more realistic sediment composition. We investigate the rheological behaviour of sheared sediment beds composed of polydisperse spherical particles in a laminar Couette-type shear flow. The sediment beds consist of particles with a diameter size ratio of up to 10, which corresponds to grains ranging from fine to coarse sand. The data was generated using fully coupled, grain resolved direct numerical simulations using a combined lattice Boltzmann–discrete element method. These highly resolved data yield detailed depth-resolved profiles of the relevant physical quantities that determine the rheology, i.e. the local shear rate of the fluid, particle volume fraction, total shear and granular pressure. A comparison against experimental data shows excellent agreement for the monodisperse case. We improve upon the parameterization of the $\mu (J)$ -rheology by expressing its empirically derived parameters as a function of the maximum particle volume fraction. Furthermore, we extend these considerations by exploring the creeping regime for viscous numbers much lower than used by previous studies to calibrate these correlations. Considering the low viscous numbers of our data, we found that the friction coefficient governing the quasi-static state in the creeping regime tends to a finite value for vanishing shear, which decreases the critical friction coefficient by a factor of three for all cases investigated.

Multi-Scale Approach for Nonhomogeneous Microstructural Effects on Damage in Particulate Composites

2003 ◽  
Author(s):  
W. M. Cho ◽  
Y. W. Kwon ◽  
C. T. Liu
Keyword(s):  
Volume Fraction ◽  
Global Analysis ◽  
Particle Volume Fraction ◽  
Crack Tip ◽  
Particulate Composites ◽  
Local Analysis ◽  
Particle Volume ◽  
Damage Initiation ◽  
Volume Fractions ◽  
Multi Scale

This study investigated the effects of random and non-uniform particle distributions on the damage initiation and growth in particulate composites. Numerical specimens with either no crack or an existing crack were examined. For the cases with no crack, the effect of sizes of the representative area for non-uniform particle volume fractions was studied on the overall stress-strain curves and the results were compared with that of the specimen with uniform particle volume fractions. Other studies considered cracked specimens, either single edge crack or a center crack. The global-local approach was used along with multi-scale technique. The global analysis determined the deformations around the crack tip. Then, the local analysis evaluated the damage progress at the crack tip using the solution of the global analysis as boundary conditions. The results showed non-uniformed particle volume fractions in particulate composites caused the crack growth at lower applied loads than the uniform particle volume fraction. Statistical data were also plotted for the non-uniform particle volume fraction cases.

Sign in / Sign up

Export Citation Format

Share Document