Influence of particle breakage on the dynamic compression responses of brittle granular materials

The dynamic compression responses of dry quartz sand are tested with a modified spilt Hopkinson pressure bar (MSHPB), and the quasi-static compression responses are tested for comparison with a material testing system. In the experiments, the axial stress–strain responses and the confining pressure of the jacket are both measured. Comparison of the dynamic and the quasi-static axial stress–strain curves indicate that dry quartz sand exhibits obvious strain-rate effects. The grain size distributions of the samples after dynamic and quasi-static loading are obtained with the laser diffractometry technique to interpret the rate effects. Quantitative analyses of the grain size distributions show that at the same stress level, the particle breakage extent under quasi-static loading is larger than that under dynamic loading. Moreover, the experimental and the theoretical relationships of the particle breakage extent versus the plastic work show that the energy efficiency in particle breakage is higher under quasi-static loading, which is the intrinsic cause of the strain-rate effects of brittle granular materials. Using the discrete element method (DEM), the energy distributions in the brittle granular material under confined compression are discussed. It is observed that the input work is mainly transformed into the frictional dissipation, and the frictional dissipation under dynamic loading is higher than that under quasi-static loading corresponding to the same breakage extent. The reason is that more fragmentation debris is produced during dynamic breakage of single grains, which promotes particle rearrangement and the corresponding frictional dissipation significantly.     

Grain breakage under uniaxial compression using a three-dimensional discrete element method

Grain breakage in rockfill in civil engineering structures is the major cause responsible for settlement and collapse. It is inherently due to large grain size and angular shape of the grains. To model these features, a three-dimensional discrete element model of a breakable grain is presented hereafter. The model is able to reproduce grain breakage into rigid irregular fragments with conservation of the mass of the initial grain. Polyhedral shapes are chosen to represent the grains, and are divided into irregular tetrahedral fragments joined together by a cohesive law to enable breakage. This model is implemented in a Non-Smooth Contact Dynamics code. Single grain crushing tests are first conducted to capture the influence of mechanical and geometrical parameters of the model. The intra-granular cohesion defines the grain strength. The grain size and the size and geometrical disposition of subgrains can act in a competitive way, thus contributing to the definition of the grain strength, and in the validation of the scale of effect observed in this type of material: the bigger the grain, the lower its strength. The same grain model is then used to generate multi granular samples subjected to oedometric compression, where grains interact via contact and friction processes, with a uniform initial grain size distribution. The effects of grain breakage are investigated through the analysis on the macroscopic and microscopic scales, with a comparison with unbreakable grains samples. The ability of the model to reproduce physical laboratory tests is confirmed through the simulations.     

DEM simulations of stiff and soft materials with crushable particles: an application of expanded perlite as a soft granular material

The mechanical behavior of granular materials is largely affected by particle breakage. Physical and mechanical properties of granular materials, such as grain size distribution, deviatoric and volumetric behavior, compressibility and mobilized friction angle are affected by particle crushing. This paper focuses on the evolution of the above mentioned characteristics using the Discrete Element Method (DEM). Behaviors of stiff and soft materials are studied using well established crushing criteria. Results from simulations indicate that stiff materials, have a typical fractal distribution of particle size, which is dominant when confining pressure increases. The fractal characteristic parameter of grain size effect is discussed. Evolution of shear stresses and volumetric strains during shearing are also predicted and analyzed. Expanded perlite, selected as a soft material, is investigated in terms of shear and volumetric behavior. For perlite, triaxial compression tests and corresponding DEM simulations are also performed. Results show good agreement between experiments and simulations and support the fact that the DEM can be considered as a useful tool to predict the behavior of crushable granular materials.     

DEM simulation on the one-dimensional compression behavior of various shaped crushable granular materials

In order to investigate the effects of particle shape on the compression behavior of granular materials, a series of simulations was conducted using a two-dimensional discrete element method employing moment springs. Fracturable granular assemblies were constructed from particles of the same shape and size. The range of possible particle shapes includes disk, ellipse and hexagon, with different aspect ratios. Simulations of single particle crushing tests on elliptical particles showed that crushing could be classified into three types: cleavage destruction, bending fracture and edge abrasion, depending on the manner of compression. A series of simulations of one-dimensional compression tests was then conducted on six types of crushable particle assemblies; the three types of crushing mentioned above were also observed, but their rates of occurrence depended on the particle shape. Cleavage destruction was mainly observed with circular and elliptical particles; bending fracture was observed only with elongated particles; edge abrasion was frequently observed with angular particles. Despite the difference in crushing type, all samples, when subjected to intense compression, converged to a critical grading with unique void ratio, grain size distribution and aspect ratio, with a similar distribution of number of contact points.     

Experimental and numerical determination of representative elementary volume for granular plant materials

A series of physical and numerical tests were conducted to determine representative elementary volume of granular plant material. The load response of pea grain assembly poured into a cuboid test chamber and subjected to uniaxial confined compression was studied. The apparatus was equipped with adjustable side walls that allowed measurement of boundary stresses in samples of varying thickness. It was found that load distribution varied considerably in samples of thickness smaller than three times the size of the particle. Less pressure variation was observed in grain assemblies of thickness equaled to three, five and seven times the particle size. Comparison between experimental data and numerical DEM results have shown qualitative agreement. It was found that the specimen of dimension not smaller than five times the particle size can be used as a representative elementary volume in confined uniaxial compression test of granular plant materials.     

Numerical analysis of compression mechanics of highly polydisperse granular mixtures with different PSD-s

The deformation of three-dimensional highly polydisperse packings of frictional spheres with continuous unimodal and discrete uniform particle size distributions (PSDs) under uniaxial compression was investigated, using the discrete element method. The stress transmission and elasticity parameters, i.e., the effective elastic modulus and the Poisson’s ratio of the granular assemblies were examined; these parameters are important in many engineering disciplines. The influence of the shape of the PSD on the porosity and the transmission of pressures in samples was observed; however, the shape of the PSD did not affect the stiffness and the Poisson’s ratio of polydisperse granular packings. The results revealed that, in some cases, knowledge of the grain size distribution is not a critical issue for modeling granular packings composed of non-uniformly sized spheres.     

A discrete model for simulating shear strength and deformation behaviour of rockfill material, considering the particle breakage phenomenon

This study focuses on numerical modelling of rockfill material with the discrete element method (DEM). This method was used due to the special features of rockfill material, such as intense particle breakage and high contracting behaviour, which are inherently due to large particle size. Because the DEM models the interaction of separate elements, it is capable of modelling discrete structures of granular materials and particle breakage. The model used in this study uses PFC^2D and considers breakable clumps. To validate the presented model for rockfill material, numerical single crushing tests and triaxial tests on the Purulia dam’s material were simulated. Due to the size-dependant crushing strength being involved in the breakage criterion, and also considering particle confinement, size-dependant and stress level-dependant behaviour was successfully simulated on modelled rockfill material. The variation of the sample’s particle grading from before the biaxial tests and after shear failure occurred was reported. The obtained results demonstrate the accuracy of the adopted model and the model’s capability for considering a rockfill material’s strength, deformation and crushing behaviour.     

Effects of various loading stress paths on the stress-strain properties and on crushability of an industrial soft granular material

Mechanical characteristics (i.e., stiffness, internal friction angle, peak strength) and crushability of a soft granular material were evaluated by performing a comprehensive series of laboratory tests using the following devices: standard and non-standard triaxial apparatus, direct and annular shear box, oedometer and hydrostatic devices. The initial tested specimens differ by initial void ratio, grading characteristics and particle hardness. The air-dried specimen of soft particles were then subjected to monotonic loadings for various stress paths (direct and annular shear stress paths, oedometer stress paths until different upper normal pressures, triaxial stress paths including different confining pressures). After each homogeneous test, sieving has been performed in order to characterize the evolution of grading characteristics of the granular packing. Experimental results on mechanical properties show that maximum internal friction angle is rather independent of the particle stiffness even though small differences may exist before peak stress-state. As highlighted by recent studies (Arslan in Granul Matter 11(2): 87–97, 2009), the volumetric response of the specimen indicates that classical critical state is no more a relevant framework when particle crushability is too high compared with the applied stress-state. Crushability related to loading paths has been evaluated through the relative breakage ratio (B_r). The first results pointed out the effects of initial geometrical configuration (i.e., void ratio, grading) and particle stiffness. Analysis of the stress paths effects on the amount of breakage revealed that stress-state is not sufficient to describe properly breakage undergone by the material which is confirmed by an obvious link between volumetric strain and total breakage. Finally, the present study showed that the percentage of fine particles content during breakage may be seen as a function of the “level” of deviatoric loading paths.     

A large deformation breakage model of granular materials including porosity and inelastic distortional deformation rate

A general constitutive model of crushable granular materials is developed within the context of large deformations. The time evolution equations for breakage, inelastic porous compaction and dilation, and distortional deformations are coupled by a yield surface and restrictions are imposed to ensure that these inelastic processes are dissipative. Some of the most salient mechanisms of such materials are described, including: (1) stiffness dependent on the breakage (a variable index of grading), porosity, and pressure; (2) critical comminution pressure and isotropic hardening, also dependent on the breakage and porosity; (3) jamming transition between solid and gaseous states; (4) a dilation law that embodies competition between porous compaction (due to the rate of breakage) and bulking (porous dilation at positive pressure due to the rate of inelastic distortional deformation); and finally, (5) the non-unique critical state relation between stress and porosity, in terms of the loading history and grading changes.     

DEM investigations of two-dimensional granular vortex- and anti-vortex-structures during plane strain compression

The paper presents simulation results of a quasi-static plane strain compression test on cohesionless initially dense sand under constant lateral pressure using a three-dimensional discrete element method. Grains were modelled by means of spheres with contact moments imitating irregular particle shapes. The material behaviour was studied at both global and local levels. The stress–strain and volumetric-strain curves, distribution of void ratio, resultant grain rotation and contact forces were calculated. The main attention was paid to the appearance of plane strain granular micro-structures like vortex and anti-vortex structures in the granular specimen during deformation. In order to detect two-dimensional vortex and anti-vortex structures, a method based on orientation angles of displacement fluctuation vectors of neighbouring single spheres was used. The effect of the method parameters was also analyzed.     

Thermo elastic analysis of functionally graded rotating disks with temperature-dependent material properties: uniform and variable thickness

A thermo elastic analysis is presented for axisymmetric rotating disks made of functionally graded material (FGM) with variable thickness. Material properties are assumed to be temperature-dependent and graded in the radial direction according to a grading index power law distribution. The temperature field considered is assumed to be uniformly distributed over the disk surface and varied in the radial direction. Semi-analytical solutions for the displacement field are given for solid disk and annular disk under free-free and fixed-free boundary conditions. The effects of the thermal field, the material grading index and the geometry of the disk on the displacement and stress fields are investigated. Results of this study emphasize on the crucial role of the temperature-dependent properties in a high temperature environment. A comparison of these results with the reported ones in the literature that is temperature-dependent versus temperature-independent suggests that a functionally graded rotating disk with concave thickness profile can work more efficiently than the one with uniform thickness irrespective of whether the material properties are assumed to be temperature-dependent or temperature-independent.     

Breakage behaviour of single rice particles under compression and impact

Grain breakage is mainly caused by impact and compression load in harvest and processing. At present, the mechanism of grain breakage under loading, especially the statistics of breakage characteristics, is not clear. The analysis of breakage process of single particle provides a foundation for the understanding of breakage mechanisms. This paper aims to examine breakage behaviour of a single rice particle under compression and impact experiments. Firstly, the equivalent diameter (D_p) and moisture content (MC) of rice particles were regarded as important factors that may affect breakage. Then, by performing quasi-static compression and dynamic impact experiments under different values of D_p and MC, the detailed compression failure force, rice strength, breakage modes, breakage probability, and the breakage probability models were analyzed comprehensively. Furthermore, breakage processes of rice particles under these two breakage experiments were compared and discussed. Finally, the Weibull distribution of the compression breakage characteristics, the “non-size effect” of compression and impact breakage, the tensile failure forms, velocity threshold of impact breakage and the close relationship between the breakage characteristics under impact and compression were mainly found. The findings are useful for providing guidance for the revelation of breakage mechanism and optimizing related agricultural equipment design.     

FE Analysis of Contractant Shear Zones in Loose Granular Materials

The paper focuses on the formation of contractant shear zones in initially loose cohesionless granular materials subject usually to continuous densification. For a simulation of the mechanical behaviour of a granular material during monotonous deformation paths, a micro-polar hypoplastic constitutive model was used which takes into account particle rotations, curvatures, non-symmetric stresses, couple stresses and the mean grain diameter as a characteristic length. The FE investigations of shear localization were carried out with initially very loose quartz sand during four different rate boundary value problems: shearing of an infinite layer between two very rough walls, plane strain compression under constant lateral pressure, biaxial compression with rigid and deformable boundaries and passive earth pressure on a horizontally translating retaining wall. The calculations were carried out with a simple random distribution of the initial void ratio under conditions of large deformations and curvatures.     

Synthesis and Enhanced Superplasticity of the Zirconia-dispersed Alumina Nanocomposite

A series of alumina-zirconia composites with various grain sizes were prepared from the nano-sized powders with different agglomerations. Microstructural analysis of the sintered compacts indicates that the as-sintered material is a typical intra/inter granular nanocomposite with uniform distribution of the zirconia grains in the alumina matrix. Superplastic deep drawing test under different conditions demonstrates that dense Al2O3/ZrO2 samples with average grain size of 230 nm can be elongated to a dome height of at least 12 mm at the punch rate of 0.6 mm·min-1 at 1400℃. Further drawing tests show that for the composites with larger grain size, such elongation cannot be achieved at such a strain rate.     

The role of contact friction in the dynamic breakage behavior of granular materials

Based on the discrete element method, a multi-scale model is employed to investigate the role of contact friction in the dynamic compression responses of brittle granular materials. Four numerical granular samples with different particle friction coefficients ranging from 0.0 to 2.0 are tested and the particle breakage extent is quantified with the Einav breakage index. It is observed that the relationship of the breakage extent with the axial stress is apparently non-monotonic concerning the particle friction coefficient. At the same stress level, the breakage extent exhibits a minimum when the particle friction coefficient is around 0.1 but increases significantly with the particle friction coefficient to both sides. The micro physical origin of this non-monotonic behavior is a distinct transition in dominant particle-breakage modes from tension to shear. Moreover, energy analyses also show non-monotonic evolution of the frictional and damping dissipation with the particle friction coefficient. The joint effect of these two dissipation terms contributes to the non-monotonic behavior of particle breakage. In addition, the accuracy and competence of two frequently-used micro quantities, fraction of sliding contacts and average coordination number, are discussed.

     

Analysis of the influence of crushing on the behavior of granular materials under shear

The behavior of granular materials mainly depends on the mechanical and engineering properties of particles in its structural matrix. Crushing or breakage of granular materials under compression or shear occurs when the energy available is sufficient to overcome the resistance of the material. Relatively little systematic research has been conducted regarding how to evaluate or quantify particle crushing and how it effects the engineering properties of the granular materials. The aim of this study is to investigate the effect of crushing on the bulk behavior of granular materials by using manufactured granular materials (MGM) rather than using a naturally occurring cohesionless granular material. MGM allow changing only one particle parameter, namely the “crushing strength”. Four different categories of MGM (with different crushing strength) are used to study the effect on the bulk shear strength, stiffness modulus, friction and dilatancy angle “engineering properties”. A substantial influence on the stress–strain behavior and engineering properties of granular materials is observed. Higher confining stress causes some non-uniformity (strong variations/jumps) in volumetric strain and a constant volumetric strain is not always observed under large shear deformations due to crushing, i.e. there is no critical state with flow regime (with constant volumetric strain).     

Elastic behavior of glass-like functionally graded infinite hollow cylinder under hydrostatic loads using finite element method

A glass-like (viscoelastic) functionally graded cylinder is studied by using finite element method to investigate the mechanical responses. A subroutine is developed by using ANSYS parametric design language (APDL) to simulate two nonlinearities, which are the variation of material properties with respect to time and position. The cylinder is made of two different viscoelastic materials, namely, pure material one at inner and pure material two at outer surfaces. The material properties are assumed to be presented by simple power law distribution and moreover, bulk and shear moduli are varying with respect to time using the kernel functions depicted regarding Prony series. It is shown that the hoop stresses take the same values at the mean radius (middle of the thickness) for different values of time and grading index. It is found that the radial stress decreases to certain values for specific grading index and then by increasing the grading index it increases to maximum value that related to pure material cylinder. It is shown that unlike the zero axial stress in pure material cylinders, it varies along the thickness from minimum to maximum at inner and outer surfaces, respectively. It is concluded that the viscoelastic functionally graded (VFG) materials play an important role in steady and transient response of hollow cylinder under hydrostatic load.     

Stress-chain based micromechanics of sand with grain shape effect

The mechanical behaviors of granular media are controlled by grain properties and microstructure. The primary property of granular media is denoted by its grain shape, grain size distribution, stiffness, and interparticle friction. The grain shape itself is of particular importance. Microstructures are formed in the connection paths of contact points between grains. In this paper, the deformation of granular materials with different grain shapes was simulated using two-dimensional DEM under different stress-levels and densities. After analyzing the results, the authors investigated fabric changes. The evolution rule of stress-induced anisotropy and its limitation as well as the existence of a critical state of fabric are revealed.     

直眼掏槽破岩过程模拟与空孔效应分析

基于空孔直眼掏槽的基本形式,运用三维有限元软件LS-DYNA,模拟了槽孔与3种不同直径空孔的动态破碎贯通过程,得到了直眼掏槽爆破应力分布规律.模拟结果表明:空孔在掏槽爆破中提供初始自由面,对槽腔岩石破碎具有导向作用;通过3组模型破岩过程的对比,可以清晰的看出空孔直径越大,破岩过程的拉伸破坏区域和压缩破坏区域越明显.进一...