Initial Packing Structure Research Articles

Micromechanical modeling of hollow cylinder torsional shear test on sand using discrete element method

Previous studies on the hollow cylinder torsional shear test (HCTST) have mainly focused on the macroscopic behavior, while the micromechanical responses in soil specimens with shaped particles have rarely been investigated. This paper develops a numerical model of the HCTST using the discrete element method (DEM). The method of bonded spheres in a hexagonal arrangement is proposed to generate flexible boundaries that can achieve real-time adjustment of the internal and external cell pressures and capture the inhomogeneous deformation in the radial direction during shearing. Representative angular particles are selected from Toyoura sand and reproduced in this model to approximate real sand particles. The model is then validated by comparing numerical and experimental results of HCTSTs on Toyoura sand with different major principal stress directions. Next, a series of HCTSTs with different combinations of major principal stress direction (α) and intermediate principal stress ratio (b) is simulated to quantitatively characterize the sand behavior under different shear conditions. The results show that the shaped particles are horizontally distributed before shearing, and the initial anisotropic packing structure further results in different stress–strain curves in cases with different α and b values. The distribution of force chains is affected by both α and b during the shear process, together with the formation of the shear bands in different patterns. The contact normal anisotropy and contact force anisotropy show different evolution patterns when either α or b varies, resulting in the differences in the non-coaxiality and other macroscopic responses. This study improves the understanding of the macroscopic response of sand from a microscopic perspective and provides valuable insights for the constitutive modeling of sand.

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.

Preparing high strength cementitious materials with high proportion of steel slag through reverse filling approach

Steel slag is an industrial solid waste with latent hydration nature, possessing a high potential use in cement and concrete but has not been fully utilized yet. This study reveals an implication approach based on dense packing to achieve high utilization efficiency of both steel slag and cement. Steel slag-based reverse filling approach utilizes higher volume of relatively coarser steel slag particles as micro fillers and a smaller quantity of fine cement grains as the major binding component. Thus, giving an initial compact packing structure and an enhanced strength of the resulting materials. Based on the packing density of various mixes, steel slag-based reverse filling cementitious materials are formulated. Early age hydration kinetics, fluidity of fresh pastes, and properties including mechanical strength and water absorption are further investigated on paste specimens. Results indicated that a maximum packing density of 0.6956 was attained for the blend containing 85 % steel slag with 15 % superfine Portland cement. The compressive strength of formulated mixes reached 96.4 MPa, 105.6 MPa and 123.8 MPa at 180 days for pastes containing 15 %, 25 % and 35 % of superfine Portland cement, respectively. The addition of appropriate amount of gypsum can enhance long-term strength by 8 ∼ 18 MPa through improving the early-age hydration kinetics of the steel slag based cementitious systems. The findings of this research help to valorize steel slag utilization in cement-based materials without sacrificing mechanical property and durability.

A Study of Compaction Densification Behavior of Composite Particles by Multiparticle Finite Element Method

In this paper, 3D particulate scale modelling on the die compaction of DEM generated initial packings of both soft and hard particles was conducted by employing the multiparticle finite element method (MPFEM). The effects of initial packing structures as well as the compaction pressure on the macroscopic and microscopic properties of the whole powder mass and local structures were investigated. In addition, corresponding physical experiments were carried out for model validation. The results show that the compact obtained from the initial dense packing under vibration undergoes yielding stage earlier than that with natural initial packing (without vibration), and the relative density is much higher. Pores that are significantly smaller and with more uniform size and homogenous stress distribution are observed in the former case. Highest stress regions occur in most cases at a grain boundary with large curvature after deformation. Moreover, the high stress in the central part of both soft and hard particles during compaction is significantly reduced after pressure unloading, reaching a new force balance. In this case, the stress is concentrated mainly at the corners of the deformed particles, which creates the risk of cracking during subsequent sintering at either the contact region between particles or the corners. The numerical results are found to be in good agreement with those from physical experiments, confirming the robustness and reliability of the numerical model used in the simulations.

Quantifying particle-scale 3D granular dynamics during rapid compaction from time-resolved in situ 2D x-ray images

Understanding the particle-scale dynamics of granular materials during rapid compaction and flow is of fundamental importance for manufacturing, planetary science, geology, and defense applications. Time-resolved 2D radiography and static 3D x-ray tomography are powerful in situ tools for studying particle-scale dynamics but provide detail only in 2D or with significant time-scale limitations, respectively. Here, we introduce a new method that uses 2D in situ x-ray imaging for determining time-resolved 3D particle-scale dynamics in rapidly compressed granular materials. The method employs initial particle packing structures obtained from x-ray tomography, a 2D x-ray image generation algorithm, and an optimization algorithm. We first describe and validate the method using finite element simulations. We then apply the technique to x-ray phase-contrast images obtained during rapid compaction of granular materials with varying particle morphology and sample thickness. The depth-resolved particle-scale dynamics reveal complex velocity and porosity fields evolving heterogeneously along and perpendicular to the compaction direction. We characterize these features, their fluctuations near the compaction front, and the compaction front thickness. Our technique can be applied to understanding granular dynamics during rapid compaction events, and rearrangements during slower, but non-quasi-static, flows.

Multi-particle FEM modeling on hot isostatic pressing of Ti6Al4V powders

The hot isostatic pressing (HIP) of Ti6Al4V powders was systematically simulated in two dimensions by using multi-particle finite element method (MPFEM) from particulate scale. Different initial packing structures formed by three kinds of powders (i.e. mono-sized powder, binary powder, and powder with normal size distribution) were firstly constructed. Subsequently, the effects of capsule shape, HIP procedure, temperature, pressure, as well as the powder type on the densification behavior of different Ti6Al4V compacts were investigated and discussed. The macroscopic property like relative density and various microscopic properties such as coordination number, stress/strain distributions of capsule and particles, deformation degree, pore filling behavior, densification mechanism and so on were quantitatively characterized. The results indicate that a larger aspect ratio (AR) is more likely to induce local order packing structure during particle rearrangement, and the proportion of powder particles with more regular deformation of Ti6Al4V compact increases after HIP. The total strain energy and deformation mechanisms of Ti6Al4V compacts are quite different with different HIP procedures. With the rise of temperature, the equivalent total strain of both the capsule and the particles became larger and the equivalent Von Mises stress decreased after HIP. In addition, Ti6Al4V powders with different size ratios will affect the performance of the compact in HIP process. The larger the particle size, the smaller the strain acting on the particle, the closer the roundness of the particle to 1. The Ti6Al4V compacts with different particle size distributions were found to exhibit different densification mechanisms. For packing of mono-sized powder, particle rearrangement destroyed bridging structure and large pores so as to accelerate the densification process. While for the Ti6Al4V compacts formed by binary powder or the powder with normal size distribution, the densification mechanism can be inferred to the extreme deformation of small particles promoting relative rigid motion of large particles.

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.

Particulate Scale Numerical Investigation on the Compaction of TiC-316L Composite Powders

This paper presents a numerical investigation on the 2D uniaxial die compaction of TiC-316L stainless steel (abbreviated by 316L) composite powders by the multiparticle finite element method (MPFEM). The effects of TiC-316L particle size ratios, TiC contents, and initial packing structures on the compaction process are systematically characterized and analyzed from macroscale and particulate scale. Numerical results show that different initial packing structures have significant impacts on the densification process of TiC-316L composite powders; a denser initial packing structure with the same composition can improve the compaction densification of TiC-316L composite powders. Smaller size ratio of 316L and TiC particles (R316L/RTiC = 1) will help achieve the green compact with higher relative density as the TiC content and compaction pressure are fixed. Meanwhile, increasing TiC content reduces the relative density of the green compact. In the dynamic compaction process, the void filling is mainly completed by particle rearrangement and plastic deformation of 316L particles. Furthermore, the contacted TiC particles will form the force chains impeding the densification process and cause the serious stress concentration within them. Increasing TiC content and R316L/RTiC can create larger stresses in the compact. The results provide valuable information for the formation of high-quality TiC-316L compacts in PM process.

Simulation and Physical Experiment Study on Powder Metallurgy Preparation of Silicon Composite Powder

The compaction and sintering processes of multi-component silicon powders, including single-action die compaction, uniaxial hot pressing and bidirectional hot compaction, were numerically performed by FEM (finite element method) modelling. The relationships of initial packing structure, compaction method, pressing pressure and sintering temperature between overall relative densities of multi-component silicon components were systematically discussed and studied. Meanwhile, various macro- and microscopic properties of silicon composite powders were carefully characterized, such as overall and local relative density, local stress distributions and void filling behaviour. The results show that fully compacted silicon composite targets with low internal stress can be obtained by using uniaxial hot pressing or bidirectional hot compaction method. And the physical experiments were carried out to verify the accuracy of the simulation results.

Three-dimensional MPFEM modelling on isostatic pressing and solid phase sintering of tungsten powders

Particulate scale three-dimensional CIP and solid phase sintering of tungsten powder in powder metallurgy process was numerically reproduced using MPFEM method. The effects of initial packing structures on the densification behavior of the tungsten powders during CIP and sintering were systematically investigated. Various macroscopic and microscopic properties including relative density, overall/local stress distributions, deformation status, pore filling behavior as well as densification mechanisms were characterized and analyzed. The results indicate that the initial packing structure before CIP plays an important role in determining the properties of both green compact and sintered part after compaction and sintering. Detailed analyses of individual particles revealed that the particles with larger deformation tend to generate greater stress concentration during CIP and sintering; meanwhile, the stress distribution in different location of each particle also demonstrated that a close relationship exists between the stress concentration/release process of individual particles and their initial packing structure before CIP.

Cohesive zone method based multi particle finite element simulation of compaction densification process of Al and NaCl laminar composite powders

Multi particle finite element method (MPFEM) has been extensively used to numerically model the compaction process of powder materials. However, MPFEM is not able to simulate the fracture phenomenon for brittle powder materials. In this study, cohesive zone method (CZM) based MPFEM is developed to simulate the compaction densification process of Al and NaCl laminar composite powders. Cohesive zone layer and initial crack are used in modeling the NaCl particle to reproduce its fracture process. A simulation of gravity effect is first conducted to arrange the powders randomly, and then top punch moves downwards to compact the laminar composite powders. Different initial random packing structures, size ratios of NaCl/Al powders and contents of NaCl powders are constructed for compaction with different pressures. Macro and micro analysis of the numerical modeling results is carried out to identify the densification process. Physical experiments and data fitting are used to validate the accuracy and robustness of the numerical simulation. Results demonstrate that the developed CZM-based MPFEM has successfully simulated the fracture phenomenon of NaCl powders and the compaction process of Al and NaCl laminar powders.

Particulate Scale Multiparticle Finite Element Method Modeling on the 2D Compaction and Release of Copper Powder

Herein, two‐dimensional (2D) single‐action die compaction process of copper (Cu) powder was simulated by the multiparticle finite element method (MPFEM) at particulate scale. The initial packing structure, generated by the discrete element method (DEM), was used as an input for the FEM model, where the mesh division of each particle was discretized. The evolution of macro‐ and microscopic properties, such as relative density, stress distribution, particle deformation, void filling behavior, and force transmission, during compaction and pressure release processes have been systematically studied. The results revealed that the force is mainly concentrated on largely deformed regions of the particles during compaction and formed a contact force network, which hindered the densification process. In the compact, the shorter side of the large void edges rendered higher stress than the longer side. On the other hand, the stress distribution of small void edges remained uniform. After pressure release, large residual stress was observed at the contact area of the adjacent particles and the maximum stress was observed at the particles’ edges. Moreover, the residual stress did not proceed to the interior of the particles. Meanwhile, the stress of large void edges has been completely released but exhibited a nonuniform distribution. The smaller fraction of void filling resulted in a larger reduction of the released stress after pressure removal. Also, the particles closer to the upper die exhibited higher average equivalent von Mises stress inside the particles during compaction and pressure release processes.

A coupled CFD-DEM simulation of upward seepage flow in coarse sands

The suction anchor becomes more popular for offshore oil and gas industry in deeper water. For suction anchor–soil interaction, the prediction of hydraulic conductivity of porous materials is a long-standing problem in offshore engineering. To investigate the hydraulic characteristics, an upward seepage flow through saturated sands is considered in this study. A numerical approach, which is able to describe the fluid–particle interaction at particle scale, has been employed to analyse fluid flow in sands. This approach is constructed by adopting a coupled discrete element method and computational fluid dynamic approach (CFD-DEM numerical model). The coupled CFD-DEM approach is first benchmarked by a classic geomechanics problem where analytical solutions are available, and then employed to investigate the characteristics of upward seepage flow in coarse sand columns. Through numerical modelling, the predicted relation between hydraulic gradient and flow velocity is obtained and it is compared with the classical analytical correlation. The effect of several bulk and micromechanical parameters including packing porosity, particle size combination and inter-particle rolling resistance on the flow characteristics is numerically examined. The results show that the particle polydispersity and packing porosity have significant effect on the hydraulic conductivity in the seepage flow. The introduction of inter-particle rolling resistance can change initial packing structure of particle assembly in some extent rather than the hydraulic conductivity from the particle shape effect perspective. A further development of numerical model, in which the effect of non-spherical particles on the seepage flow, will be carried out later.

Numerical Simulation of Densification of Cu–Al Mixed Metal Powder during Axial Compaction

The densification mechanism of Cu–Al mixed metal powder during a double-action die compaction was investigated by numerical simulation. The finite element method and experiment were performed to compare the effect of the forming method, such as single-action die compaction and double-action die compaction, on the properties of compact. The results showed that the latter could significantly raise the densification rate and were in good agreement with Van Der Zwan–Siskens compaction equation. The effects of the different initial packing structures on the properties of the compact were studied. The results showed that a high-performance compact could be obtained using a dense initial packing structure at a given compaction pressure. Additionally, the effects of the Al content and compaction pressure on the relative density and stress distribution were analyzed. It was observed that, with an increase in the Al content at a given compaction pressure, the relative density of the compact increased, whereas the stress decreased. Furthermore, when the Al content was fixed, the relative density and stress increased with increasing compaction pressure. The relationship between the relative density and the compaction pressure under different friction conditions was characterized and fitted according to the Van Der Zwan–Siskens compaction equation. The influence mechanisms of die wall friction on the compaction behavior were investigated. It was revealed that friction is a key factor that causes the inhomogeneity of the powder flow and stress distribution. Finally, the effects of the dwell time and height–diameter ratio on the densification behavior were analyzed, and it was found that an increase in the dwell time promoted the densification process, whereas an increase of the height–diameter ratio could hinder the process.

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.

Compaction and solid-state sintering of tungsten powders: MPFEM simulation and experimental verification

The uniaxial die compaction and solid-state sintering of different sized tungsten powders in powder metallurgy (PM) process was numerically reproduced in multi-particle FEM (MPFEM) modeling from particulate scale. The effects of particle size, initial packing structure, compaction pressure and sintering temperature on the relative density of the tungsten powder component were systematically studied and discussed. Various macroscopic and microscopic properties of the powder mass with different initial packing structures during compaction and sintering were characterized and analyzed. These properties include the overall relative density, local stress distributions, force structure and transmission, particle rearrangement and deformation, void filling behavior, as well as the densification dynamics and mechanism. The results show that by properly controlling the operating conditions such as initial packing structure, compaction pressure and sintering temperature, high performance PM component with high relative density, uniform density, stress, and void distributions can be obtained. Meanwhile, physical experiments were implemented to verify the simulation results. It is indicated that MPFEM modeling used in current work can provide the researchers with an effective method to simulate the whole PM process for refractory tungsten powders from particulate scale, especially the coupling of different stages can reduce the assumptions in the modeling and make the simulation results more accurate and much closer to the actual process.

MPFEM simulation of compaction densification behavior of Fe-Al composite powders with different size ratios

In this paper, 2D single-action die compaction process of Fe-Al composite powders with different size ratios was simulated via the multi-particle finite element method (MPFEM) from particulate scale. Different initial packing structures generated by discrete element method (DEM) were imported into FEM model (where each particle was discretized for mesh division) for compaction. The compaction process was reproduced and the densification dynamics and mechanisms were analyzed and identified based on the evolution of macro and micro properties of the compact. The results indicate that, when the Al contents in the composite powder and the compaction pressure are fixed, higher relative densities can be obtained at smaller Fe/Al size ratios. During compaction, large stresses are mainly concentrated within those contacted Fe particles (near the surface region), forming the contact force network which impedes the compaction densification. Upon unloading, the contact force network is broken, and most internal stresses are released while only small amount of residual stresses are remained within Fe particles, which is susceptible to cracking or even failure during further processing. The smaller the Fe/Al size ratio is, the more complete is the release of the residual stress. During compaction, large voids (or pores) formed in the initial packing are filled by particle rearrangement (especially the rearrangement of small Fe particles) and plastic deformation of Al particles. However, there are still some small enclosed pores left in the final compact, which will lead to non-uniform deformation of adjacent particles and stress concentration during the subsequent sintering process.

Multi-particle FEM simulation of 2D compaction on binary Al/SiC composite powders

Multi-particle finite element method (MPFEM) is utilized to numerically study the 2D compaction of binary Al/SiC composite powders. Different initial packing structures with various Al/SiC particle size ratios and compositions are constructed and imported into FEM model for compaction. In the whole process, the macro and micro properties of the compacts are monitored and characterized, and the densification mechanism is identified. The results show that the densification process and the properties of the compacts are determined by initial powder packing structures. In the compaction of ordered initial packings, the force chains in the compacts are ordered with uniform distributions and the deformation of Al particles is regular. While in the compaction of random initial packings, the force chains in the compacts are disordered and the deformation of Al particles is irregular; in this case, the force chain structure is mainly determined by the contacted SiC particles. The compaction densification of the composite powder and corresponding properties of the compacts are influenced by the packing state, size and number of SiC particles in the initial packing structure.

Particulate scale MPFEM modeling on compaction of Fe and Al composite powders

In this paper, 2D single action die compaction of Fe and Al composite powders was simulated by multi-particle finite element method (MPFEM) from particulate scale. The initial packing structure generated by discrete element method (DEM) was input into FEM model where the mesh division of each particle was discretized. The effects of Al powder content on relative density and distribution, stress and distribution, particle deformation, void filling behavior, and force transmission in the compact during compaction, pressure holding and pressure releasing were systematically studied and analyzed. The results indicate that with the increase of Al content, high relative density can be obtained under the same compaction pressure, and the force chain structure becomes loose. When the Al content is fixed, the force is mainly concentrated on the Fe particles forming the contact force network which impedes the compaction densification. During compaction, void is mainly filled by the deformation of adjacent Al particles. It is difficult to deform those Al particles underneath the bridge or arching structure of Fe particles. Therefore, some small enclosed pores still left in the final compact. The internal stress in a particle is mainly concentrated near the surface region, and decreases rapidly after pressure releasing, while some residual stresses still exist inside Fe particles, leading to the possibility of cracking in the compact after unloading. Normally, the larger the compaction pressure is, the higher is the average residual stresses in Fe particles after releasing, and the largest local residual stresses occur in Fe particles close to the upper punch and die wall.

Constrained Sintering in Fabrication of Solid Oxide Fuel Cells.

Solid oxide fuel cells (SOFCs) are inevitably affected by the tensile stress field imposed by the rigid substrate during constrained sintering, which strongly affects microstructural evolution and flaw generation in the fabrication process and subsequent operation. In the case of sintering a composite cathode, one component acts as a continuous matrix phase while the other acts as a dispersed phase depending upon the initial composition and packing structure. The clustering of dispersed particles in the matrix has significant effects on the final microstructure, and strong rigidity of the clusters covering the entire cathode volume is desirable to obtain stable pore structure. The local constraints developed around the dispersed particles and their clusters effectively suppress generation of major process flaws, and microstructural features such as triple phase boundary and porosity could be readily controlled by adjusting the content and size of the dispersed particles. However, in the fabrication of the dense electrolyte layer via the chemical solution deposition route using slow-sintering nanoparticles dispersed in a sol matrix, the rigidity of the cluster should be minimized for the fine matrix to continuously densify, and special care should be taken in selecting the size of the dispersed particles to optimize the thermodynamic stability criteria of the grain size and film thickness. The principles of constrained sintering presented in this paper could be used as basic guidelines for realizing the ideal microstructure of SOFCs.