Haut PDF Evolution of particle size distributions in crushable granular materials

Evolution of particle size distributions in crushable granular materials

Evolution of particle size distributions in crushable granular materials

Emilien Az´ema, Farhang Radjai University Montpellier 2, CNRS LMGC, Place Eug`ene Bataillon, 34095 Montpellier Cedex 05, France. ABSTRACT: By means of the contact dynamics method together with a particle fracture model, in which the particles are cohesive aggregates of irreducible polygonal fragments, we investigate the evolution of particle size distribution in the process of uniaxial compaction of granular materials. The case of single particle breakup under compressive stress is used to test the method and the influence of discretization (number of irreducible fragments). We show that the breaking threshold of the granular assembly scales with the internal cohesion of the particles but it depends also on the initial size distribution and irregularity of polygonal particle shapes. The evolution of size distribution proceeds by consecutive periods of intense particle crushing, characterized by local shattering instability, and periods of little breaking activity. Starting with either monodisperse or power- law distribution of particle sizes, the latter evolves towards a broad distribution of the fragmented particles with a nearly power-law distribution in the range of intermediate particle sizes. Interestingly, a finite number of large particles survive despite ongoing crushing process due to the more homogeneous distribution of forces in the presence of small fragmented particles filling the pores between larger particles.
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Rheology of granular materials composed of crushable particles

Rheology of granular materials composed of crushable particles

2.2 Simulation setup For our simulations we used pentagon-shaped particles. Due to their 5-fold directional symmetry, the pentagons are less prone to local ordering than hexagons and squares, which may spontaneously organize into locally ordered structures. The size of a pentagonal particle is defined by the diameter d of its circumscribed circle. We used a uni- form distribution of particle volume fractions in a range [d min , d max = 3d min ]. Initially, we have 1000 particles, which may potentially fragment into 44249 fragments of diameter d 0 = 0.2d min using the BCM; see fig. 2. These particles are initially placed on a square lattice in a rect- angular box of dimensions l 0 ×h 0 and deposited under the action of the gravity g. Then, the gravity is set to 0 and the packings are subjected to isotropic compression. The friction coefficient between particles and with the walls is set to zero during compression in order to obtain dense and isotropic packings as shown in fig. 2(a). The coeffi- cient of friction between cells is set to μ c = 0.3.
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Cohesive granular materials composed of nonconvex particles

Cohesive granular materials composed of nonconvex particles

DOI: 10.1103/PhysRevE.87.052207 PACS number(s): 45.70.−n, 83.80.Fg, 61.43.Gt I. INTRODUCTION Cohesive granular materials are at the heart of a variety of engineering applications in particle processing, soil me- chanics, and powder technology. The shear strength of such materials can be split into an internal angle of friction, as in cohesionless materials, and a macroscopic cohesion, which reflects the aptitude of the material to sustain tensile stresses [ 1 , 2 ]. This cohesion in combination with granular disorder has drastic effects on the equilibrium states. The angle of repose increases with cohesion and the material can be molded into arbitrary shapes. The packing fraction may vary in a broader range and often long force chains build up despite locally loose structures [ 3 ]. The properties of compressibility and flowability are essential for the manufacture of homogeneous and resistant compacts in powder technology [ 4 ]. Cohesive granular materials have been investigated by experiments and numerical simulations for a better understanding of the scale-up of interactions between the particles. Very loose packings characterized by low connectivity and chainlike structures have been evidenced in assemblies of nano-sized particles governed by van der Waals forces [ 5 ]. Loose cohesive powders and the dynamics of pore collapse during the compaction process have been extensively studied by the discrete element method (DEM), which provides direct access to the particle-scale information and underlying physical mechanisms [ 3 , 6 – 9 ]. The compaction of ceramic and metallic powders have been modeled by DEM simulations [ 10 – 13 ]. The shear strength and force distributions of wet granular packings have been studied as a function of water content and the size polydispersity of the particles [ 14 – 16 ]. DEM simulations have also been used to investigate the flow properties of cohesive granular materials [ 17 – 22 ].
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Influence of grain size distribution on critical state of granular materials

Influence of grain size distribution on critical state of granular materials

Since the pioneering work of Roscoe and Schofield (1958), the critical state concept has been developed and largely regarded as a fundamental framework for the devel- opment of constitutive models for soils. Based on this concept, lots of studies have been conducted on crushable soils (see for example Daouadji and Hicher, 1997), which have shown that the GSD of the soil changes during its lifetime by crushing of particles, leading to an increase of the coefficient of uniformity Cu. These changes influence the basic constitutive properties of the material, in particular the properties such as the critical state which is dependent on the particle size distribu- tion at a given point of the loading history. As the fine content increases and the soil becomes better graded, it has been experimentally shown that the critical state line moves downwards (Biarez and Hicher 1994). Based on these new findings, some new models for crushable soils have been developed (Daouadji et al. 2001). Also, by means of discrete element method (DEM), Wood and Maeda (2007) showed the de- pendence of the critical state of granular materials on their initial GSD. However, so far, no detailed experimental data confirm these findings obtained by DEM.
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Effect of size polydispersity versus particle shape in dense granular media

Effect of size polydispersity versus particle shape in dense granular media

FIG. 13. (Color online) Linear correlation between the coordina- tion number Z and reduced particle size d r . In the analysis of the connectivity and coordination only the force-bearing contacts are considered. The purely “geo- metrical contacts,” where the normal force is strictly zero, and the “floating particles,” that have no force-bearing contacts, are thus excluded from the statistics. The proportion P f of floating particles is, however, an interesting fabric property as it provides an indication of the degree of arching in a granular material. In polydisperse materials, the arching effect is enhanced by size dispersion and we thus expect an increasing number of particles to be excluded from the force network. Figure 14 shows P f as a function of s in our packings for all values of δ. We see that P f is quite small for s < 0.4 but increases up to nearly 0.25 for s varying from 0.4 to 0.9. It is also remarkable that P f is practically independent of δ. Note that most floating particles are small particles representing a small volume fraction of the packing, as can be observed in Fig. 9(b) .
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Effects of shape and size polydispersity on strength properties of granular materials

Effects of shape and size polydispersity on strength properties of granular materials

I. INTRODUCTION Most granular materials in their natural state or processed industrially are characterized by a broad range of particle shapes and sizes. For example, it is often a tedious task to describe in a simple way various shapes and size distributions of the fragments found in a coarse material generated by progressive fracturing of a rock or those of aggregates formed in a sintered powder. Although this polydispersity in the composition of granular materials is an obvious aspect of gran- ular rheology, recent theoretical and experimental research has mainly focused on monodisperse systems composed of spherical particles. Hence, the effects of increasing departure from spherical shape and increasing size span on the structure and strength of granular materials are still largely open issues in granular research.
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Stress transmission in cemented bidisperse granular materials

Stress transmission in cemented bidisperse granular materials

3 LMGC, Université de Montpellier, CNRS, Montpellier, France (Received 25 October 2019; revised manuscript received 20 February 2020; accepted 8 April 2020; published 4 May 2020) We analyze stress distributions in a two-dimensional bidisperse cemented granular packing for a broad range of the values of particle-size ratio, the volumes of large and small particles, and the amount of cementing matrix. In such textured porous materials, the stress concentration, which controls the fracture and fragmentation of the material under tensile loading or in grinding processes, reflects not only the porosity but also the contact network of the particle phase and the resulting stress chains. By means of peridynamic simulations under tensile loading, we show how both the texture and stress distribution depend on size ratio, volume ratio, and the amount of the cementing matrix. In particular, the volume fraction of the class of small particles plays a key role in homogenizing stresses across the system by reducing porosity. Interestingly, the texture controls not only the porosity but also the distribution of pores inside the system with its statistical variability, found to be strongly correlated with the homogeneity of stresses inside the large particles. The most homogeneous stress distribution occurs for the largest size ratio and largest volume fraction of small particles, corresponding to the lowest pore size dispersion and the cushioning effect of small particles and its similar role to the binding matrix for stress redistribution across the packing. At higher porosity, the tensile stresses above the mean stress fall off exponentially in all phases with an exponent that strongly depends on the texture. The exponential part broadens with decreasing matrix volume fraction and particle-size ratio. These correlations reveal the strong interplay between size polydispersity and the cohesive action of the binding matrix for stress distribution, which is significant for the behavior of textured materials in grinding operations.
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Experimental framework for evaluating the mechanical behavior of dry and wet crushable granular materials based on the particle breakage ratio

Experimental framework for evaluating the mechanical behavior of dry and wet crushable granular materials based on the particle breakage ratio

Abstract: It has been widely shown that particle crushing increases the compressibility of granular materials. For a particular crushable material and given test conditions, an empirical relation can be established between the breakage ratio and the plastic work. Along these lines, constitutive models have been developed based on the effect of grading evolution during crushing. In parallel, due to corrosive attacks of the humid environment at the tip of microcracks within solid grains, the mechanical behavior of crushable granular materials depends also on the water content: the higher the material humidity, the higher the particle crushing. However, the experimental data on the relation between loading–wetting conditions and the breakage ratio are still quite scarce. In this paper, we present experimental results on crushable sand to study the effect of flooding under isotropic, oedometric, and triaxial stress paths. The main objective of this study is to obtain a consistent framework for the effect of water based on the breakage ratio. Our results have shown that, for a given initial density and stress path, the dry material after flooding reaches the equivalent behavior of the initially wetted material in terms of compression curve, particle crushing, and creep compressibility index, regardless of the point of flooding. Moreover, the relation between the breakage ratio and the final void ratio is unique and depends neither on the stress path, the water content, the point of flooding, nor the loading condition (time of creep or relaxation), but exclusively on the initial density and on intrinsic parameters. These findings could improve the prediction of the effect of water and time on the mechanical response of crushable granular materials through constitutive models based on grading evolution.
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Numerical study of crushable granular materials

Numerical study of crushable granular materials

Keywords: Granular materials; grain breakage; elasto-plasticity; critical state; grain size distribution. 1. INTRODUCTION Particle crushing occurred along both compression and shearing stress paths, especially under high confining stress (e.g. within earth dams, deep well shafts). This phenomenon is however more intense during shearing. The influence of particle crushing on the mechanical behavior of granular materials has been widely investigated in the past decades.

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Evolution of wet agglomerates inside inertial shear flow of dry granular materials

Evolution of wet agglomerates inside inertial shear flow of dry granular materials

The top and bottom walls were made rough by gluing an array of spherical particles of diameter d w = 2.23d min to them. In the second step, we removed the lateral walls along the x and y directions and replaced them by periodic boundary conditions. A spherical probe was introduced in the granular bed and its diameter was increased until reaching exactly 300 particles inside the probe; see Fig. 4(a) . Then, the capillary attraction forces and viscous forces were activated between neighboring particles inside the probe, creating thus a wet agglomerate of 300 particles inside a bed of dry particles. In the steady flow state, the height h of the simulation box is ∼35 mean particle diameters. The size of the agglomerate was chosen based on the size of the simulation box (the particle size needs to be small compared to the box size in order to avoid wall effects)
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Pressure dependence of the electrical transport in granular materials

Pressure dependence of the electrical transport in granular materials

is moved by a stepper motor and then its displacement is controlled by a computer. Hence, moving the piston, the force can be easily changed and adjusted to the chosen value. Besides, the piston can be moved backward far from the first bead in order to have the possibility to roll the beads and to change the contacts between the beads. Note that a very small clearance of 2/100 mm is provided in the channel, so that the beads can move freely along the chain axis but not laterally. Hence, contrary to the powder, for the chain of beads, the same force is applied to each bead since the channel is straight and lateral displacements of the beads are negligible compared to axial displacements of the beads. Besides, [19] measured the total displacement of the chain and showed that the deformation of the beads is in the elastic regime [Hertz’s law, Eq. (1)] whatever the force applied to the chain (see Fig. 2 in [19]). Unlike the experiments with powders for which a new sample is sys- tematically used for each experimental run, the beads are not changed. But, to obtain reproducible measurements, the piston is moved backward and the beads are system- atically rolled so that the contacts between the beads are thus systematically changed before each measurement.
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Discrete numerical analysis of failure modes in granular materials

Discrete numerical analysis of failure modes in granular materials

the principle is the same, but stress probes describe a sphere instead of a circle (Fig- ure 5a). 3.2.2 Discrete Element Model In the same way as with the phenomenological constitutive relations, stress probes have been performed with the DEM along drained triaxial compressions, in axisym- metric conditions only [18]. Two samples are considered here, the dense and dilatant sample E1 (already used for proportional strain loading paths in Section 2.2), and a looser and essentially contractant sample E3 (see characteristics in Table 1). Fig- ure 6 presents circular diagrams of the normalized second-order work w 2n computed
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Continuum Modeling of Secondary Rheology in Dense Granular Materials

Continuum Modeling of Secondary Rheology in Dense Granular Materials

Next, we apply our nonlocal model to the problem of secondary rheology, by using finite-element calculations in the commercial package A BAQUS /S TANDARD [26] . For computational efficiency, we consider a two-dimensional analogue of the experiments of Reddy, Forterre, and Pouliquen [9] , pictured in Fig. 1 . The geometry is a planar annular shear cell with rough walls at an inner radius R i and outer radius R o . The inner wall is specified to rotate at a fixed rate Ω, and the outer wall does not rotate but may move radially so as to impart a confining pressure P a . A circular intruder with diameter D, which we specify to be rigid and frictionless, is located at a distance L away from the inner wall. Following Ref. [9] , we take R i =d ¼ 60, R o =d ¼ 180, and D=d ¼ 2, throughout, and consider different values of L=d. The value of outer radius is sufficiently large so as not to affect the calculation results, consistent with experiments. Finally, in our calculations, either the speed of the intruder V or the force applied to the intruder F is specified. We then calculate the steady flow fields predicted by the nonlocal rheology using A BAQUS . The governing partial differential equations are the equi- librium equations ∂σ ij = ∂x j ¼ 0 i , where inertia is neglected, since we are considering a quasistatic process and there is no gravitational body force since we are in two dimensions, and the differential relation for the granular fluidity (3) . These are solved in conjunction with the constitutive equations (1) and (2) by means of a user element subroutine in A BAQUS . The mechanical boundary conditions are as described above, and, for the fluidity boundary conditions, we specify that n i ð∂g=∂x i Þ ¼ 0 at the inner and outer walls, where n i is the outward surface normal. A detailed dis- cussion of the intruder boundary conditions is given in Supplemental Material [27] . The necessary material param- eters are fμ s ; b; Ag. Following previous work involving glass beads [13,17,28] , we take μ s ¼ 0.3819 and b ¼ 0.9377. For the two-dimensional problem, we take A ¼ 1.8 (see Supplemental Material [27] for a justification of this selection).
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Modeling soft granular materials

Modeling soft granular materials

Farhang Radjai 1,4 Received: 15 January 2016 © Springer-Verlag Berlin Heidelberg 2016 Abstract Soft-grain materials such as clays and other col- loidal pastes share the common feature of being composed of grains that can undergo large deformations without rup- ture. For the simulation of such materials, we present two alternative methods: (1) an implicit formulation of the mate- rial point method (MPM), in which each grain is discretized as a collection of material points, and (2) the bonded par- ticle model (BPM), in which each soft grain is modeled as an aggregate of rigid particles using the contact dynamics method. In the MPM, a linear elastic behavior is used for the grains. In order to allow the aggregates in the BPM to deform without breaking, we use long-range center-to-center attrac- tion forces between the primary particles belonging to each grain together with steric repulsion at their contact points. We show that these interactions lead to a plastic behavior of the grains. Using both methods, we analyze the uniaxial compaction of 2D soft granular packings. This process is nonlinear and involves both grain rearrangements and large deformations. High packing fractions beyond the jamming state are reached as a result of grain shape change for both
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Numerical modeling of the tensile strength of a biological granular aggregate: Effect of the particle size distribution

Numerical modeling of the tensile strength of a biological granular aggregate: Effect of the particle size distribution

In the first step, a square box of the area A box =900∗(πrA 2 ) and length L = √ A box was filled with A-type discs using a Fast Poisson Disc Sampling (FPDS) method [14]. The first disc with a random radius within the normal distri- bution around rA was placed at a random position within the box. Then a high number of preliminary discs with random radii within the distribution around rA were ran- domly placed in the periphery of the already existing disc. All preliminary discs were tested consecutively for over- lap with the existing discs within a limited distance. If no such overlap exists, the preliminary disc was permanently placed into the sample volume. Additionally, a minimum distance dmin between the discs was required. The steps of randomly selecting a disc from the sample box, creating preliminary discs and checking for overlap were repeated. If after a finite number of iterations, no more discs could be permanently placed, the box was regarded as being filled. In the second step, smaller discs with a random radius fol- lowing the distribution around radius rB were placed into the free spaces remaining in-between the bigger discs. The same FPDS approach as for the A-type discs was used, only that no minimum distance between discs was required and which therefore enabled a dense packing of discs. Samples with fixed radius rA and different radii rB were created to investigate the effect of varying B-type disc ra- dius on the mechanical properties. The radius rB was var- ied from rB = 0.2rA to rB = rA in steps of 0.1rA . The resulting nine different radius ratios R = rB/rA were there- fore [0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]. For every radius ratio R five independent samples were created. An increase in r B inevitably resulted in a di fferent disc packing, including a significant change in the number of A- and B-type discs and the total number of discs. There- fore, the sole parameter that was chosen to be kept con- stant between samples was the ratio of total area occupied by A-type discs to total area occupied by B-type discs:
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Effect of the particle size and the liquid content on the shear behaviour of wet granular material

Effect of the particle size and the liquid content on the shear behaviour of wet granular material

sured using a measuring tube (see Table 1 ). The X-ray tomography is a potential technique for the analysis of the bulk properties of a granular material, in particular the voidage fraction. This technique allows by image analysis not only to estimate the voidage fraction but also to get information about the distribution of the voids in the granular bed, in particular for cohesive powder. The analysis of the glass beads of 70–110 μm was performed using Phoenix Nanotom® X-ray tomography. A sample of glass beads was putted in a small transparent gelatine capsule of 6 mm in diameter and manually slightly packed to avoid large gaps due to the filling process. We per- formed analysis of the glass beads 70–110 μm, dry and wet with differ- ent liquid fractions. The use of the PEG 400 as a liquid to wet the glass beads has been an advantage since it is detected in this analysis. The technique allows to achieve a large number of radiography in different angle of the sample and to combine them in order to obtain a 3D con- struction of the sample. This requires the use of software capable of pro- cessing such a large number of images in a reasonable time. In this study, the voidage fraction was analysed from the 2D radiography and the images were treated using Matlab®. Different images, representing different sections of the sample, were treated to estimate an average value of the voidage fraction. Further information about the image anal- ysis will be given next.
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Agglomeration of wet granular materials in rotating drum

Agglomeration of wet granular materials in rotating drum

OBJECTIVES & METHODOLOGY AGGLOMERATION OF WET GRANULAR MATERIAL IN ROTATING DRUM THANH-TRUNG VO , SAEID NEZAMABADI , JEAN-YVES DELENNE , FARHANG RADJAI 1 1 2 1,3 Laboratoire de Mécanique et Génie Civil (LMGC), Université de Montpellier, CNRS, Montpellier, France IATE, UMR1208 INRA - CIRAD - Université de Montpellier - SupAgro, 34060 Montpellier, France

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Acoustics and frictional sliding in granular materials

Acoustics and frictional sliding in granular materials

When interpreting the simulations, it is necessary to take these differences into account. This can be done by comparing various dimensionless parameters that char- acterize both the experiments and the simulations. To make our comparison concrete, we will consider two rel- atively small acoustic transmission experiments [1; 3] where the experimental parameters are clearly docu- mented.. The principal dimensionless parameters and their values are shown in Tab. 1. As one can see certain parameters are quite close while others are different. The first two parameters describing the system size are roughly similar, but those describing the grain stiffness and the strain rate are very different. Accordingly, the effect of these last two parameters will be carefully ex- amined in the paper.
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Evolution of particle structure during water sorption observed on different size fractions of durum wheat semolina

Evolution of particle structure during water sorption observed on different size fractions of durum wheat semolina

Fig. 1 at 50× show that the powders conserved the same structure up to 85% RH, then agglomeration takes place at 97% RH. This agglomera- tion was clearest in finest particles. At 800×, the morphology of surfaces at 75% RH is not really affected in comparison with initial powders. Some modifications on the protein matrix could be observed at 85%RH and became clear at 97% RH. Indeed, the hard structure of protein changed into a softer matter, and then bridges were formed among par- ticles producing agglomeration. The gluten–starch bond is really strong, but can be easily separated with water [17] . Consequently the modifica- tion of the protein matrix caused the exposure of starch grains, interacting directly with humidity. The starch texture did not change, but starch grains swelled. Pure wheat starch swelled to 17% of its initial volume due to humidity [18] . The percentage value of this swelling de- pends on the complexity of the protein–starch matrix; however an in- crease of the grain size is clear. This evolution of the microstructure becomes more evident at high RH. As specific surface is inversely pro- portional to the particle size, a greater water uptake is seen in small par- ticles, which have a smaller particle volume, consequently the same quantity of water wets the particle deeper; thus the formation of brid- ges between particles is observed. On the other hand, big particles uptake a smaller quantity of water, consequently the formation of brid- ges leading to obtaining granulates is more difficult. Another interesting observation is the number of broken starch grains that can be easily observed at 97% RH. This provides evidence that the finest particles (0–160 μm) suffered a rupture at the gluten–starch bond edge. These particles are naturally detached from the bigger particles during milling, whereas bigger particles present fractures at the starch grains. These fractures are the result of a difficult breaking of the gluten–starch bond, produced by blades during milling of the wheat kernel [6] . The re- sistance to the separation of the starch–protein binding is characteristic of hard flours [17] . This evolution of the structure can be related to the heterogeneity of the kernel texture. Another possibility is the milling conditions applied to the grain kernel. Saad et al. proposed that milling conditions could apply different forces throughout the grain and pro- duce two kinds of ruptures: grains broken at the edge and grains broken through the starch particle [15] .
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Determination of Particle Size, Surface Area, and Shape of Supplementary Cementitious Materials by Using Different Techniques

Determination of Particle Size, Surface Area, and Shape of Supplementary Cementitious Materials by Using Different Techniques

Abstract The particle size distribution, surface area and shape are fundamental characteristics of supple- mentary cementitious materials (SCMs). Accurate measurement of these properties is required in com- putational efforts to model the hydration process, and the characterization of these parameters is also an important practical issue during the production and use of blended cements. Since there are no standard procedures specifically for the determination of phys- ical properties of SCMs, the techniques that are currently used for characterizing Portland cement are applied to SCMs. Based on the fact that most of the techniques have been developed to measure cements, limitations occur when these methods are used for other materials than cement, particularly when these have lower fineness and different particle shape and
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