Packing Densification Research Articles

Numerical investigation on the densification of granulated porous indium tin oxide powders before compaction

Dense and uniform initial packing structures of powders are of key significance in powder metallurgy process, which can provide the precondition for the fabrication of high-performance components with low cost and high efficiency. In this paper, the packing densification of indium tin oxide (ITO) granulated micro powders with continuous size distributions and internal porosity under three-dimensional vibrations was numerically investigated by discrete element method (DEM). Firstly, the DEM model was validated by physical experiments, and the contact parameters between particles and the porosity therein were determined. Then the effects of operating parameters on the macro/micro properties (e.g., packing density, coordination number (CN), pores, and forces) of the packing structures were analyzed. Results show that the mean CN cannot intuitively reflect the packing structure due to the complex and varied inter-particle contacts caused by the inhomogeneity of the particle size in a multi-sized granular system. Additionally, the excellent packing structure of porous ITO particles is always obtained from low amplitude when the vibration intensity is the same. Corresponding mechanism analyses reveal that higher amplitude normally causes strong convective diffusion, leading to more pores in the packing. This increases the probability of wedging effect occurring during settling, thereby reducing the packing density. However, optimal packing quality with low amplitude can only be achieved when coupled with high frequency. Therefore, applying vibration is an effective way to achieve dense packing of porous spherical particles, especially at low amplitude and high-frequency operating conditions.

Effect of vibration direction on the packing of sphero-cylinders

Particle packing is widely encountered when coping with granular materials, while mechanical vibration is usually used for packing densification. Vibration direction has been proven to be crucial for the ordered packing of spherical particles, but there are few reports for non-spherical ones in this regard. In this study, the effect of vibration direction on the macroscopic and microscopic packing parameters of sphero-cylinders are systematically examined using discrete element method (DEM). Due to the anisotropic shapes of sphero-cylinders, their packing characteristics are much richer and also more complex than those of spheres. It is found that vibration direction affects both the packing density and the packing structure of sphero-cylinders through tuning their orientation distributions and contact modes. Moreover, vibration direction plays a significant role in determining the optimal vibration intensities for dense packing. When the sphericity of Voronoi cell decreases and/or the density increases, the Nematic order parameter increases accordingly. Besides, no obvious relationship between the packing density and the average contact number is observed.

Effect of Horizontal Vibrations and Particle Size on the Packing Density of Multi-Sized Sphere Mixtures: Discrete Element Method Simulation

Abstract Particle packing densification due to vibrations is a common process that occurs in many industrial applications and is beneficial for achieving better mechanical properties in powder metallurgy. However, most of the research up to this point was focused on vibration compaction of uniform-sized or binary particle mixtures, while most actual commercial powders consist of particles of variable sizes. In this work, the packing of multi-sized sphere mixtures under horizontal vibrations is simulated with the help of the discrete element method (DEM). The variations of total and local packing density with vibrations and particle size were investigated. The simulation results suggest that there are optimal values for the two vibration parameters at which the closest packing is obtained. Further increase in the particle size decreases the density and slightly shifts these peaks to the lower values of vibrations. Local density values are quite uniform at the optimal vibration parameters, but the deviations become higher when frequency or amplitude is too low or high. With an increase in particle size, these trends become less profound and more deviated. The investigations of effects of size can help in predicting optimal parameters and density values for experimental studies. These developments are similar to those for uniform and binary particle assemblies and correlate with experimental and numerical studies from the literature. The results can be helpful in carefully choosing the particle mixture properties and vibration conditions for actual manufacturing.

CFD-DEM numerical study on air impacted packing densification of equiaxed cylindrical particles

A CFD-DEM model was developed to reproduce the packing densification process of mono-sized equiaxed cylindrical particles under air impact. The effects of operating parameters on packing density were firstly studied. Then various microscopic properties of packing structures such as coordination number (CN), contact types, particle orientations, pore features were characterized and compared. And corresponding densification mechanisms were analysed based on particle motion behaviour, local structure evolution, and forces. Results indicate that the air impact can realize the packing densification of cylindrical particles under appropriate conditions. The pore size distribution in the packing of cylindrical particles shows a tail at larger pore sizes compared with that in the packing of equal spheres. Both the size and the sphericity of the pores decrease in the final dense packing; also, more surface-surface and less surface-edge contacts between two particles therein can be formed. More cylindrical particles tend to be in parallel or perpendicular contact with each other to form more stable local structures during air impact. Most particles at higher position move down (direction of gravity/air impact) with about one particle length during the densification process and most particles exhibit translational motion to realize the local rearrangement for pore filling through air impact induced inter-particle forces.

DEM simulation of vibrated packing densification of mono-sized regular octahedral particles

The densification of mono-sized regular octahedral particles under vibration is simulated by a DEM model. The model is validated by physical experiments. The effects of operating parameters including vibration amplitude and frequency are investigated. The obtained packing structures are characterized, and corresponding densification mechanisms are identified. The results indicate that vibration amplitude is more critical for densification compared to frequency, where a wide range of suitable amplitudes exists to realize the dense packing structures. Ordered packing structure exists in boundary region. The central region possesses good particle position randomness and orientation randomness, and the packing density for poured packing (initial loose packing) and vibrated packing (dense packing) in the central region are 0.670 and 0.684, respectively. During densification, contacts and constraints between particles decrease, and the stress within the structure becomes larger. The typical arrangement of neighboring particles is close to but not perfect face to face (F–F) contact. Particles in the boundary region experience more rotations and can form local ordered structures. These structures prevent the relative movement of individual particles but favor their movement as a whole. Particles in the central region have relatively little movement and rotation. The ordered structures formed at boundary is difficult to extend to the central region due to the restricted change of particle contact conditions.

Experimental and Numerical Study on the Packing Densification of Metal Powder with Gaussian Distribution

In the additive manufacturing of metal materials, powder bed fusion 3D laser printing is the most widely used processing method. The density of the packed bed is another important parameter that can affect the part quality; however, it is the least understood parameter and needs further study. Aiming at addressing the problem of the powder packing density in the powder tank before powder spreading, which is neglected in the existing research, a combination of numerical simulation and experimental research was used to analyze the powder particle size distribution, powder stiffness coefficient, and vibration condition. Considering the van der Waals forces between the powders, a discrete element model suitable for fine metal powders for 3D printing is proposed. At the same time, a mathematical model that takes into account the vibration state is proposed, and the factors affecting the density of the powder were analyzed. A self-designed and manufactured three-dimensional vibration test rig was used to conduct physical experiments on spherical metal powders with approximately Gaussian distributions to obtain the maximum densities. The results obtained by the numerical simulation analysis method proposed in this paper are in good agreement with the experimental results. The influence of the amplitude and vibration frequency on the powder packing density is the same; that is, it increases with an increase in amplitude or frequency, and then decreases with a further increase in amplitude or frequency after reaching the maximum. It is unreasonable to discuss the packing densification only relying on the vibration intensity. Therefore, it is necessary to combine the amplitude and frequency to analyze the factors that affect the packing density of powders.

Study the densification behavior and cold compaction mechanisms of solid particles-based powder and spongy particles-based powder using a multi-particle finite element method

Powders could be based on solid particles or spongy particles depending on the powder manufacturing procedures. In this article, the numerical study of the cold compaction process for copper solid particles-based powder (i.e. Cu solid powder) and spongy particles-based powder (i.e. Cu sponge powder) has been carried out by using a two-dimensional multi-particle finite element method (2D-MPFEM) based on single action die compaction. The effects of internal pores content, external pressure, initial packing structure on the packing densification were systematically presented. Relative density, stress distribution, internal pore deformations, and force chain movements, particle rearrangement, and interfacial behavior within spongy particles were characterized and analyzed. The results reveal that the densification behavior of the sponge powder depends basically on the internal pore’s content. Moreover, at low and medium relative density (ρ < 0.95), the densification behavior of the sponge powder is faster than solid particles-based powder. However, at higher relative density near unity, the force required to cause further compaction is significantly larger in the sponge powder. In addition, from the microscopic analysis, the deformation behavior of the particles and the internal pores and the force chain development rely mostly on the structure configuration, internal pore content and its position.

Experimental study on 3D vibrated packing densification of mono-sized dodecahedral particles

Packing densification of mono-sized regular dodecahedral particles subjected to 3D vibrations was studied through systematical physical experiments. The influences of various vibration conditions and container size on the packing density were analyzed and the operating parameters were optimized. The obtained microstructures of different packings were characterized through 3D CT non-destructive inspection. The results show that by properly controlling the vibration conditions, the transition from initial loose to final dense packing structure of mono-sized regular dodecahedral particles can be reproduced. A maximum packing density of 0.709, which is the currently obtainable densest random packing structure of mono-sized regular dodecahedral particles in physical experiments, can be realized by extrapolating the packing densities obtained in different sized containers. Microscopic analyses on the 3D computer re-constructed packing structures from experiments clearly demonstrate the specific characteristics of the generated initial loose and final dense packings. The obtained results can enhance the deep understanding of packing behavior of dodecahedral particles and provide researchers with valuable reference to the design and fabrication of some new materials.

Packing of different shaped tetrahedral particles: DEM simulation and experimental study

Packings of different mono-sized tetrahedral particles under 3D vibrations were studied by physical experiments and DEM simulations. The effects of vibration conditions and particle shape on the packing densification were comprehensively investigated and optimized. Corresponding characteristic microscopic properties such as coordination number (CN), particle contact type, radial distribution function (RDF), and particle orientations were numerically characterized and analyzed. The results show that the DEM model can be well validated by physical experiments. Microscopic analysis indicates that the minimum mean CN appears for tetrahedral particles with regular shape. The RDF shows that as the shape deviates from regular tetrahedral particles, the frequency of face-face, vertex-face and edge-edge contacts all decreases while that of edge-face contact increases. The cluster evolutions demonstrate that the reduction or disappearance of two important local clusters (dimer and wagon wheel structures) is one of the main reasons for the decrease of packing density of irregular tetrahedral particles.

Numerical realization and structure characterization on random close packings of cuboid particles with different aspect ratios

Packing processes of cuboid particles with different aspect ratios (h/b) under 3D vibrations were numerically reproduced by discrete element method using multi-sphere model. The influences of vibration conditions (e.g. vibration time, frequency, and amplitude) and particle shape on the packing densification were comprehensively analyzed. The macro property such as packing density (ρ) and micro properties such as coordinate number (CN), radial distribution function (RDF), contact types and force networks were systematically characterized and compared, and the densification mechanism was discussed. Meanwhile, the randomness of cuboid packing systems was evaluated by nematic order parameter (S2) and cubic order parameter (S4). The results show that dense packings of cuboids with different aspect ratios can be realized by properly controlling vibration conditions. In ρ ~ h/b curve, three peaks can be identified at h/b = 0.5, 1.0 and 1.5, corresponding to the packing densities of 0.700, 0.736 and 0.707, respectively. After vibration, the nematic order parameter S2 decreases in each case and cuboids with too high or too low aspect ratios are easier to form orientational order, while the cubic order parameter S4 increases but it is not positively correlated to the value of packing density. The formation of more face-to-face contacts leads to higher averaged CN and packing density. RDF indicates that special local structures can be formed during packing densification. Force networks indicate that the vibration energy transferred from the container enables cuboid particles near the bottom to generate orientation ordering, where more strong forces are observed, which can promote the rearrangement of cuboid particles for packing densification.

High density and high strength cement-based mortar by modification with epoxy resin emulsion

The HDHS (high dense and high strength) cement-based paste and mortar were designed based on the densest packing model determined by Dinger-Funk equation. The HDHS cement-based paste was modified by adding different contents of epoxy resin emulsion (ERE) and curing agent (CA). The influences of the degree of packing densification on the pore structure and mechanical strength of the HDHS cement-based paste were investigated. The hydration process of the modified HDHS cement-based paste, pore structure and mechanical properties of the modified HDHS cement-based mortar were researched. The results show that the compressive strength of the HDHS cement-based paste firstly increases and then decreases with the decrease of the Euclidean distance. The compressive strength reaches the maximum value of 123.4 MPa while the porosity is 10.15% at the Euclidean distance of 64.30. It is also found that the hydration of the modified HDHS cement-based paste can be divided into four stages based on the normalized heat flow. The influence of the polymer (ERE and CA) on the hydration is different at every stage. The adding of polymer reduces the compressive and flexural strength but increases the bonding strength of modified HDHS cement-based mortar. When the P/C (polymer/cement-based powders, wt.%) ratio is 12.5% and the CA/ERE ratio (wt.%) is 0.5, the compressive strength is still above 75 MPa and the bonding strength obtains the maximum of 2.65 MPa while the porosity is just 7.74%.

Discrete element method dynamic simulation of icosahedral particle packing under three-dimensional mechanical vibration

Packing densification of monosized regular icosahedral particles under three-dimensional mechanical vibration has been simulated by the discrete element method (DEM). The effects of the vibration conditions and container size on packing densification were systematically investigated. In addition to the macroscale properties (packing density and porosity), the microscale properties, such as the coordination number (CN), radial distribution function (RDF), particle contact type, particle orientation distribution, and stresses/forces, in random loose packing (RLP) and random close packing (RCP) were also characterized and analyzed. The results show that transformation of icosahedral particle packing from RLP to RCP can be realized by properly controlling the vibration conditions. The maximum random packing density without the wall effect reaches 0.7078. Microscale property analysis shows that the average CN increases after vibration. The RDF curves contain two clear peaks for RLP and three for RCP. From RLP to RCP, the probability of face to face contact between two particles increases, while the probabilities of edge to edge, edge to face, and face to vertex contact decrease. The orientation correlation functions indicate the randomness of the vibrated packing structure. In addition, more uniform force and stress distributions are observed within the dense packing structure.

Two-Dimensional Multiparticle Finite Element Modeling on the Cold Isostatic Pressing of Al Powder

In this article, the cold isostatic pressing (CIP) of Al powders with different initial packing structures was numerically simulated in two dimensions using the multiparticle finite element method from particulate scale. The effects of external pressure and initial packing structures on the packing densification and performance of the compacts were systematically studied. Various macro/micro properties (such as relative density and distribution, local stress and distribution, and particle deformation behavior) and the densification dynamics/mechanisms were characterized and analyzed. Corresponding modeling on die compaction was also conducted for comparison. The results show that the relative displacement of particles is much less and the particle shape is more regular for CIP of ordered initial packing structure than those for CIP of random initial packing structure, and the distributions of relative density and local stress in the compact for the former case are more homogeneous. Compared with die compaction, the formability of CIP is much better; also, the compact has higher relative density and more uniform density and stress distributions. The normal stresses are transmitted in all directions in the compact during CIP because the external load is applied uniformly to the outer surface of the rubber mold from all directions in the entire process, while the normal stresses are directional along the loading path during die compaction.

Dynamic characteristics of binary sphere mixtures under air impact

This paper presents a numerical study on the packing densification process of binary sphere mixtures under air impact using a combined computational fluid dynamics and discrete element method (CFD-DEM) scheme. The effects of particle size ratio (PSR) on the force and stress characteristics including the depth-averaged normal force, probability density function (PDF) of normal forces, distributions of strong forces, mean stress distribution in the axial cross-section, and depth-averaged mean stress for various contact types, are comprehensively analyzed. In addition, the distribution of fluid-particle interaction forces is also discussed to explain the densification mechanism during air impact. The results reveal that the force and stress characteristics are significantly affected by both PSR and air impact. For each PSR, the packing density increases with the gas inlet velocity to a maximum and then decreases. Meanwhile, both the depth-averaged normal force and the mean stress in initial packing increase linearly with the depth, while the relationship between the depth-averaged normal force or mean stress and the depth is in power law growth in the final packing after air impact. The contact type of L-S (L-large sphere, S-small sphere) plays a leading role in the PDF of normal forces, while the effects of S-S contact type on the packing system is weak. Furthermore, apart from the L-L contact, the strong force percentage of other contacts increases after air impact densification. The air impact can effectively improve the uniformity of the normalized mean stress distribution for the packing of binary mixtures. Finally, the distribution of fluid-particle interaction forces demonstrates that the packing can be densified by obvious rearrangement of small particles for adjacent pore filling, and this trend will become more apparent with the increase of PSR.

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

ABSTRACTTo 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 XL (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.

DEM simulation on the vibrated packing densification of mono-sized equilateral cylindrical particles

The packing densification of mono-sized equilateral cylindrical particles under mechanical vibration is numerically reproduced using discrete element method (DEM). The influences of vibration frequency, amplitude and container size on the macro property (e.g. packing density) of each packing are studied. Meanwhile, various micro-properties including coordination number (CN), radial distribution function (RDF), local structures, contact types, particle position/orientation distributions, forces/stresses of the vibrated dense packing are characterized and compared with those of the loose initial poured packing. The results show that properly controlling vibration conditions can realize the transition of equilateral cylindrical particles from random loose packing (RLP) to random close packing (RCP). The maximum packing density without wall effects can reach about 0.7166, which agrees with experimental and numerical results in literature. Micro property analyses demonstrate that the average CN increases slightly after vibration. The RDF curves indicate three obvious peaks for both poured and vibrated packings. The distributions of intersection angles imply that the perpendicular arrangements of the cylindrical particles are common in both packing structures. From RLP to RCP, the probability of side-edge, bottom-edge and edge-edge contacts between two particles decreases, while that of side-side, side-bottom and bottom-bottom contacts increases. Both particle position and orientation distributions illustrate that the structure in the center of the vibrated packing is disordered. The distribution of strong forces follows the exponential law, while that of weak forces follows the power law. The static vertical stresses in both packings can be predicted by Janssen model. After vibration, a much denser and more stable structure with a larger saturation stress is obtained due to the reducing inter-particle friction effects.

CFD-DEM modeling on air impact densification of equal spheres: Structure evolution, dynamics, and mechanism

This paper presents a numerical modeling on the packing densification of uniform spheres under air impact using a combined Computational Fluid Dynamics (CFD) and Discrete Element Method (DEM). In the whole process, the packing structure evolution, corresponding dynamics and densification mechanism are comprehensively studied. Macro and micro properties such as packing density, coordination number, radial distribution function, as well as forces in the packings at different stages are characterized and compared. The results show that air impact can realize the transition of particle packing from random loose to random close state at appropriate conditions. In this duration, the depth-averaged normal force increases linearly with the height. Meanwhile, numerous normal forces are close to the horizontal at the final packing stage due to the effect of air impact, and their distributions indicate exponential decay law. While the distribution of the fluid-particle interaction forces increases with the height. Local packing structure evolution demonstrates that the dominating densification mechanism under the air impact is ‘pushing filling’.

DEM dynamic simulation of tetrahedral particle packing under 3D mechanical vibration

The transition from random loose packing (RLP) to random close packing (RCP) of mono-sized regular tetrahedral particles under 3D mechanical vibration was modeled by using discrete element method. The effects of vibration conditions and container size on the packing densification were systematically studied, and the macro and micro properties such as packing density, coordination number (CN), particle contact type, radial distribution function (RDF), particle orientation correlation, and forces between particles were characterized and analyzed. The randomness of the obtained dense packings and corresponding densification mechanisms were also investigated. The results show that RCP of the tetrahedral particles can be realized by properly controlling the vibration conditions. And the obtained maximum random packing density can reach about 0.7402 by extrapolating the packing densities in different sized containers. The average CN for RLP and RCP are 7 and 6.3, and the CN distribution for RCP is higher and narrower than that for RLP. From RLP to RCP, the frequency of face to face (F-F) contact between two particles increases, while that of vertex to face (V-F) contact and edge to face (E-F) contact decreases, and edge to edge (E-E) contact does not change much. RDF characterization shows four obvious peaks on the curves of RLP and RCP, where the height of the first peak (F-F contact) increases while that of other peaks decreases from RLP to RCP. The densification mechanism can be ascribed to the formation of wagon wheel local dense structures through rearrangement by ‘pushing filling’ and ‘jumping filling’.

Experimental study on the packing of cubic particles under three-dimensional vibration

Densification of cubic particles under three-dimensional (3D) mechanical vibration was studied experimentally. Effects of vibration time (t), frequency (f), vibration amplitude (A), vibration acceleration (Г), container size (D) and particle sphericity (φ) on packing density (ρ) were comprehensively analyzed. To identify the effects of particle shape, the packing densification of cuboid 1 (12mm×12mm×28mm) and cuboid 2 (4mm×8mm×16mm) were systematically studied under the same conditions. The results show that the structure of cubic particles can be first densified from random loose packing (RLP) to random close packing (RCP) and then to ordered packing (OP) gradually. In comparison, cuboid 1 and cuboid 2 particles can only form RCP structure, but cannot achieve OP even under further vibration. Vibration parameters (t, f, A and Г) are shown to be important to the packing densification. Based on the results of varying f and A, A - f phase diagrams are established for choosing the optimal vibration parameters to achieve the desired dense packing structures. Besides, it is shown the size of container (wall effect) has monotonic influence on packing density, i.e., the larger container size corresponds to the less wall effect and higher packing density. Cubic particles can form ordered packing because of the geometrical symmetry with aspect ratio of 1. After eliminating the wall effect by extrapolating the packing densities in different sized containers, typical packing densities of the three types of particles are obtained with ρRLP=0.658, ρRCP=0.830 and ρOP=0.965 for cubic particles; ρRLP=0.625 and ρRCP=0.740 for cuboid 1 particles; ρRLP=0.591 and ρRCP=0.731 for cuboid 2 particles. These findings indicate cubic particles are efficient in densification which can be readily realized through proper 3D mechanical vibration.

DEM simulation of binary sphere packing densification under vertical vibration

ABSTRACTThe 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 φRCP ≈ 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.