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.

     

Breakage of an artificial crushable material under loading

The mechanical behaviour of granular materials depends on their grading. Crushing of particles under compression or shear modifies the grain size distribution, with a tendency for the percentage of fine material to increase. It follows that the frictional properties of the material and the critical states are modified as a consequence of the changes in grain size distribution and the available range of packing densities. This paper illustrates an extended experimental investigation of the evolution of the grading of an artificial granular material, consisting of crushed expanded clay pellets under different loading conditions. The changes of grading of the material after isotropic, one-dimensional and constant mean effective stress triaxial compression were described using a single parameter based on the ratio of the areas under the current and an ultimate cumulative particle size distribution, which were both assumed to be consistent with self similar grading with varying fractal dimension. Relative breakage was related to the total work input for unit of volume. For poorly graded samples, the observed maximum rate of breakage is practically independent of initial uniformity. Further experiments at higher confining stress are required to investigate the mechanics of breakage of better graded samples.     

Discrete element modelling of cyclic loading of crushable aggreates

This paper examines the discrete element modelling of cyclic loading of an aggregate of crushable sand grains. Each grain of sand is modelled as an agglomerate of balls bonded together. The aggregate is subjected to compaction followed by isotropic normal (plastic) compression, and then unloaded to half the maximum applied stress. The aggregate is then subjected to cyclic loading to a maximum stress ratio of 0.8. The aim of the paper is to examine the reduction of the rate of axial strain with number of cycles, and to determine the relative influences of volumetric strain and shear strain rates on the axial strain rate. In particular, the paper aims to show whether particle breakage is mainly related to the accumulation of volumetric strain. This is found to be the case, which is consistent with proposals by other authors that plastic hardening under monotonic loading is due to particle fracture.     

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.     

中低应变率下砂岩动力特性试验研究

为研究岩石在中低速冲击下的动力特性,利用MTS和落锤冲击试验系统进行了红砂岩准静态和动态单轴压缩试验,获得了10-2-101.7 s-1应变率范围砂岩全应力-应变曲线。结果表明,中低应变率加载条件下,砂岩经历典型压密、弹性变形、非稳定裂纹发展至脆性破裂后阶段。随着加载应变率的提高,砂岩峰值应力及其对应应变、残余应变均逐步增加,破坏模式则由X状共轭剪切破坏转变为劈裂破坏;动态强度增长遵循热活化和宏观黏性机制联合作用规律;中低应变率下岩石的吸收总能量和弹性应变能随变形演化规律基本一致,且弹性应变能和较耗散应变能的应变率效应更为显著。     

Investigation of the influence of frictional viscosity regularization on quasi-static gas-solid flow predictions in a conical spouted bed with non-porous draft tube

The stress in the quasi-static particle flow is often modeled through the Mohr-Coulomb failure criterion. In the extension to complex three-dimensional flows, a granular viscosity is introduced through a tensorial rheology and the deviatoric frictional stress tensor is assumed aligned with the strain rate tensor. This granular viscosity is singular as the shear rate approaches zero, regardless of the local rheology. We discuss the influence of regularizing such a frictional viscosity on the particle circulation rate and other measured characteristics in a laboratory scale draft tube spouted bed. The friction between particles is modeled either with a constant Coulomb rheology or using a local particle pressure and strain-rate based friction known as $\mu \left(I\right)$-rheology. The predictions appear very dependent on the regularization parameter introduced by the method. The mean properties of the flow (e.g. circulation and pressure drop) monotonically converge towards the measurements when the regularization parameter tends to zero. In other respects, the two regularization models regarded in this study induced similar hydrodynamics within the spouted bed of interest. But the analysis of the conditional averages of the inertial number and the fraction of the solids in the quasi-static regime shows that the extent and staticity of the quasi-static region is sensitive to changes to the regularization parameter or regularization function.     

Rate dependent behavior and modeling of concrete based on SHPB experiments

The dynamic behavior of concrete is studied experimentally by testing annular and solid concrete specimens using split Hopkinson pressure bar (SHPB). The dynamic increase factor (DIF) of annular samples is relatively lower than the DIF of solid samples. The dynamic behavior of concrete seems to be independent of the quasi-static strength of concrete. The mode of failure of concrete was a typical ductile failure at high strain-rates and brittle at low strain-rates. No significant influence of strain-rate on the initial elastic modulus of concrete was observed. An empirical equation is proposed for the estimation of DIF of concrete based on the experiments. A model is developed for the prediction of stress–strain curve of concrete under dynamic loading which shows good agreement with the experiments.     

Triaxial behavior of granular material under complex loading path by a new numerical true triaxial engine

A new numerical true triaxial engine based on discrete element method accounting for rolling resistance contact is developed. By this engine, we have simulated mechanical behavior of granular materials under complex stress loading path in this study. Stress-strain responses of a kind of typical granular sand under several stress loading path in meridian and deviatoric stress space are provided. The results show that the three dimensional effects like the intermediate principal stress play an important role in the modeling processes. Theoretical analysis in strength characteristic implies the strength criteria with three parameters such as unified strength criterion and van Eekelen strength criterion are capable of describing cohesionless granular material behaviors in three dimensional stress states. Moreover, the case study for Chende sand further demonstrates the numerical true triaxial engine, is a potential tool. As compared to conventional triaxial compression test, this new developed apparatus could be widely used to “measure” elastic-plastic behavior in three dimensional stress space for finite element analysis in geotechnical problems.     

Cyclic loading and fatigue in ice

Isotropic polycrystalline ice was subjected to cyclic loading in uniaxial compression at ?5°C, with stress limits 0–2 and 0–3 MPa, and frequencies in the range 0.043 to 0.5 Hz. Stress-strain records showed hysteresis loops progressing along the strain axis at non-uniform rates. The effective secant modulus, which was about half the true Young's modulus, decreased during the course of a test. The elastic strain amplitude and the energy dissipated during a loading cycle both increased with increase of time and plastic strain. Strain-time records gave mean curves which were identical in form to classical constant-stress creep curves, with a small cyclic alternation of recoverable strain about the mean curve. The inflection point of the “creep curve”, marking the transition from strain hardening to strain softening, occurred at a plastic strain of 1% (±0.1%), which is about the same as the “ductile failure strain” found in constant stress creep tests and in constant strain-rate tests on ice of the same type at the same temperature. The dissipation of strain energy up to this “failure point” was much higher for the cyclic tests than for corresponding quasi-static tests ? 100 to 600 kPa (or kN-m/m³) in comparison to about 30 kPa. The number of cycles taken to reach the “failure point” was of no direct significance, varying greatly with stress amplitude and with frequency. The results of the tests suggest that maximum resistance under compressive cyclic loading occurs at an axial plastic strain of about 1%, which is essentially the same as the failure strain for ductile yielding under constant stress and under constant strain-rate.     

Creep of granular materials

This paper examines the creep of brittle granular materials subjected to one-dimensional compression. One-dimensional creep tests were performed on aggregates of brittle pasta and compared with the behaviour of sand at much higher stress levels. It was found that for both materials, creep strain is proportional to the logarithm of time. One possible mechanism for creep is particle crushing. However, it is usually difficult to measure changes in the particle size distribution during creep because the fines produced are so small, and the mass of fines is too small to measure accurately unless creep is permitted for a very long time. However, for pasta, the particle fragments produced are large, and it is found that particle crushing does occur during creep for 24 hours. This is consistent with the proposition that the behaviour of all brittle granular materials is essentially the same. A micro mechanical argument is then summarised which predicts that creep strain should be proportional to log time.     

DEM simulation of the shear behaviour of breakable granular materials with various angularities

Particle shape is an important factor that affects particle breakage and the mechanical behaviour of granular materials. This report explored the effect of angularity on the mechanical behaviour of breakable granular materials under triaxial tests. Various angular particles are generated using the quasi-spherical polyhedron method. The angularity α is defined as the mean exterior angle of touching faces in a particle model. A breakable particle is constructed as an aggregate composed of coplanar and glued Voronoi polyhedra. After being prepared under the densest conditions, all assemblies were subjected to triaxial compression until a critical state was reached. The macroscopic characteristics, including the shear strength and dilatancy response, were investigated. Then, particle breakage characteristics, including the extent of particle breakage, breakage pattern and correlation between the particle breakage and energy input, were evaluated. Furthermore, the microscopic characteristics, including the contact force and fabric anisotropy, were examined to probe the microscopic origins of the shear strength. As α increases, the peak shear strength increases first and then remains constant, while the critical shear strength generally increases. Assemblies with larger angularity tend to cause more serious particle breakage. The relative breakage is linearly correlated with α under shear loading. Compared with unbreakable particles, the peak shear strength and the critical volumetric strain decline, and the degree of decline linearly increases with increasing α.     

Mechanical response of a soft rubber compound compressed at various strain rates

Rate-dependent material constitutive behavior models are needed in numerical simulations of shock-mitigation structures. In this research, compressive stress–strain response of a soft rubber compound is obtained experimentally at quasi-static, intermediate and high strain rates under uniaxial-stress and uniaxial-strain loading states. Kolsky bars with modifications for characterizing soft materials and a long Kolsky bar are used to conduct the dynamic experiments, while an MTS load frame is used for conducting experiments at quasi-static rates. Compression experiments are conducted at each decade in the strain-rate scale without any gap typically seen in the intermediate range. The experimental results show significant strain-rate effects on the mechanical behavior of this soft material, which are summarized via a rate-dependent constitutive model.     

A hybrid approach for modeling of breakable granular materials using combined finite-discrete element method

It is well known that particle breakage plays a critical role in the mechanical behavior of granular materials and has been a topic subject to intensive studies. This paper presents a three dimensional fracture model in the context of combined finite-discrete element method (FDEM) to simulate the breakage of irregular shaped granular materials, e.g., sands, gravels, and rockfills. In this method, each particle is discretized into a finite element mesh. The potential fracture paths are represented by pre-inserted non-thickness cohesive interface elements with a progressive damage model. The Mohr–Coulomb model with tension cut-off is employed as the damage initiation criterion to rupture the predominant failure mode at the particle scale. The particle breakage modeling using combined FDEM is validated by the qualitative agreement between the results of simulated single particle crushing tests and those obtained from laboratory tests and prior DEM simulations. A comprehensive numerical triaxial tests are carried out on both the unbreakable and breakable particle assemblies with varied confining pressure and particle crushability. The simulated stress–strain–dilation responses of breakable granular assembly are qualitatively in good agreement with the experimental observations. The effects of particle breakage on the compressibility, shear strength, volumetric response of the fairly dense breakable granular assembly are thoroughly investigated through a variety of mechanism demonstrations and micromechanical analysis. This paper also reports the energy input and dissipation behavior and its relation to the mechanical response.     

高轴压比配筋PVA纤维增强混凝土柱抗震性能试验研究

为提高钢筋混凝土柱在高轴压比下的抗震性能,采用聚乙烯醇（PVA）纤维增强混凝土代替普通混凝土是可选择的措施之一。设计6个剪跨比为4的钢筋混凝土柱试件,其中4个试件采用PVA纤维增强混凝土,另外2个对比试件采用普通混凝土,进行拟静力试验以研究高轴压比下的抗震性能。通过改变轴压比和纤维掺量,在水平循环往复荷载作用下,观测试件裂缝开展及破坏过程,研究滞回性能、骨架曲线、延性性能及耗能能力。试验结果表明:高轴压比下,PVA纤维增强钢筋混凝土柱破坏时,裂缝开展缓慢,纤维的桥接作用有效地抑制了裂缝的开展;纤维增强混凝土柱主要表现为延性破坏模式,极限位移角约为普通混凝土柱的1.47倍~1.53倍,表明其具有良好的塑性变形能力和损伤容限;PVA纤维增强钢筋混凝土柱的耗能比约为普通混凝土柱的1.82倍~1.95倍,表明其耗能能力显著提高,抗震性能优越。     

泡孔尺寸对开孔泡沫铝合金力学性能的影响

在分离式霍普金森压杆(SHPB)和MTS810材料试验机上对多组孔径、多组密度的开孔泡沫铝合金(AA6101)材料进行了准静态与动态压缩实验研究。泡孔尺寸不仅影响着材料的屈服强度和塑性模量等,还影响着材料的应变率敏感性。另外,不同孔径的泡沫铝合金有不同的理想吸能效率。     

Calculation of fracture work of short-glass-fibre reinforced polythylene for static and dynamic loading rates

The fracture work of ductile thermoplastics reinforced with short fibres differs in its dependence on fibre content for static and dynamic loading conditions. It is suggested that this is due to strain-rate dependence of matrix behaviour which affects energy dissipation. For composites with fibres of sub-critical length several mechanisms contribute to the work of fracture, viz. debonding, sliding, pull-out, brittle matrix fracture and plastic matrix deformation. SEM investigations show that for short-glass-fibre reinforced polyethylene the pull-out contribution can be neglected under static load conditions, whereas at high loading rates the plastic deformation of the matrix bridges loses its dominant role. With these assumptions the work of fracture is calculated and the influence of loading rate is discussed.     

Announcements

 This paper examines the yielding of brittle granular materials subjected to one-dimensional compression. For an aggregate of uniform grains, at low stresses there is negligible reduction in voids ratio, and at high stresses voids ratio reduces approximately logarithmically with stress as a distribution of particle sizes evolves. A suitable definition of yield would appear to be the point of maximum curvature on a plot of voids ratio against the logarithm of stress, corresponding to the onset of grain fracture. It is proposed that the yield stress is approximately proportional to the average or Weibull 37% tensile strength of the particles in the aggregate. One-dimensional compression tests were performed on aggregates of brittle breakfast cereals, (cornflakes, rice krispies) and pasta and compared with the results for a typical one-dimensional compression test on dense silica sand at much higher stress levels. In addition, the tensile strengths of 30 particles for each material were determined by compression between flat platens, and found to satisfy the Weibull distribution. It is found that if voids ratio is plotted against the logarithm of stress, then yield occurs at much lower stresses for the cereals and pasta than for the dense silica sand, typically by two orders of magnitude. However, if voids ratio is plotted against the logarithm of stress normalised by the Weibull 37% tensile strength of the constituent grains, then the yielding region for each material is approximately the same. This confirms the proposed definition of yield as suitable, and that the yield stress determined in this way is approximately proportional to the tensile strength of the grains. The constant of proportionality is in the range 0.1–0.3, and this is consistent with observed heterogeneous stress distributions in discrete element simulations. Received: 12 June 2001     

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.     

Analysis of the evolution of granular stress-strain and voidage states based on DEM simulations

We review and discuss the results of our granular-dynamics simulations of the time evolution of the microstructure of compact granular beds as found in pouring, in hopper filling and discharge, and in a shear cell. These systems are mainly quasi-static. However, it is also common to encounter localized 'shear zones' with significant velocity/voidage fluctuations and high bulk-strain gradients. These narrow-banded zones are separated from near-static regions by sharp, discontinuous changes of bulk stress and voidage. Within these bands the granular assembly undergoes a transition from the quasi-static to the inertial state, where enduring particle contacts are increasingly replaced by collisional ones. We focus on the discrete particle origins of this inhomogeneous yield/flow behaviour. We show the usefulness of analysing the local evolution in terms of relative rotation of the grains which is observed to cause rapid local bulk dilation responsible for setting off avalanches near free-surface boundaries and protracted bulk-failure planes in confined static assemblies. We also present some evidence to suggest that allowing for effective continuous particle-particle interactions could approximate observed effects attributable to particle shape and surface roughness. Wavelet analyses have been applied successfully to generate the variations in periodicity and the relative sequence of evolution of the stress, strain-rate and voidage states in avalanching granular heaps and in the wall region of axially symmetric hopper flows.     

3D printing of tuneable agglomerates: Strain distribution and effect of internal flaws

The current study presents a novel and reliable method for producing 3D printed agglomerates with different colour distributions and material properties with 2-fold aims: providing feasible and accurate control on compression of agglomerates under different compression angles, and better tracking of individual particle position after agglomerate breakage. Multi-coloured agglomerates in cubic tetrahedral and random sphere shapes were printed with both rigid and soft bonds. The printed agglomerates were analysed thoroughly of their surface and structural properties including surface roughness and printing accuracy. The agglomerate breakage behaviours under static compression were analysed as a function of bond strength, loading rate and loading directions, with strain distribution plotted over the random sphere agglomerate structure. In addition, agglomerate structures with designed internal macro-voids in different positions and sizes were also created for breakage study, in an effort to better understand parameters governing the mechanical properties of agglomerates with cavities and voids which is inevitable in particle industry but poorly understood at present.