Bonded-cell model for particle fracture

The mechanics of brittle granular materials with coevolving grain size and shape

The influence of particle shape on the mechanics of sand is widely recognized, especially in mineral processing and geomechanics. However, most existing continuum theories for engineering applications do not encompass the morphology of the grains and its evolution during comminution. Similarly, the relatively few engineering models accounting for grain-scale processes tend to idealize particles as spheres, with their diameters considered as the primary and sole geometric descriptor. This paper inspires a new generation of constitutive laws for crushable granular continua with arbitrary, yet evolving, particle morphology. We explore the idea of introducing multiple grain shape descriptors into Continuum Breakage Mechanics (CBM), a theory originally designed to track changes in particle size distributions during confined comminution. We incorporate the influence of these descriptors on the elastic strain energy potential and treat them as dissipative state variables. In analogy with the original CBM, and in light of evidence from extreme fragmentation in nature, the evolution of the additional shape descriptors is postulated to converge towards an attractor. Comparisons with laboratory experiments, discrete element analyses and particle-scale fracture models illustrate the encouraging performance of the theory. The theory provides insights into the feedback among particle shape, compressive yielding and inelastic deformation in crushable granular continua. These results inspire new questions that should guide future research into crushable granular systems using particle-scale imaging and computations.

Numerical Analysis of Shear and Particle Crushing Characteristics in Ring Shear System Using the PFC2D

The shear and particle crushing characteristics of the failure plane (or shear surface) in catastrophic mass movements are examined with a ring shear apparatus, which is generally employed owing to its suitability for large deformations. Based on results of previous experiments on waste materials from abandoned mine deposits, we employed a simple numerical model based on ring shear testing using the particle flow code (PFC^2D). We examined drainage, normal stress, and shear velocity dependent shear characteristics of landslide materials. For shear velocities of 0.1 and 100 mm/s and normal stress (NS) of 25 kPa, the numerical results are in good agreement with those obtained from experimental results. The difference between the experimental and numerical results of the residual shear stress was approximately 0.4 kPa for NS equal to 25 kPa and 0.9 kPa for NS equal to 100 kPa for both drained and undrained condition. In addition, we examined particle crushing effect during shearing using the frictional work concept in PFC. We calculated the work done by friction at both peak and residual shear stresses, and then used the results as crushing criteria in the numerical analysis. The frictional work at peak and the residual shear stresses was ranged from 303 kPa·s to 2579 kPa·s for given drainage and normal stress conditions. These results showed that clump particles were partially crushed at peak shear stress, and further particle crushing with respect to the production of finer in shearing was recorded at residual shear stress at the shearing plane.

Strength and energy consumption of inherently anisotropic rocks at failure

Using a discrete-element approach and a bonding interaction law, we model and test crushable inherently anisotropic structures reminiscent of the layering found in sedimentary and metamorphic rocks. By systematically modifying the level of inherent anisotropy, we characterize the evolution of the failure strength of circular rock samples discretized using a modified Voronoi tesselation under diametral point loading at different orientations relative to the sample’s layers. We characterize the failure strength, which can dramatically increase as the loading becomes orthogonal to the rock layers. We also describe the evolution of the macroscopic failure modes as a function of the loading orientation and the energy consumption at fissuring. Our simulation strategy let us conclude that the length of bonds between Voronoi cells controls the energy being consumed in fissuring the rock sample, although failure modes and strength are considerably changing. We end up this work showing that the microstructure is largely affected by the level of inherent anisotropy and loading orientation.

Effect of particle shape on particle breakage inside rotating cylinders

We study the influence of particle shape on the evolution of particle breakage process taking place inside rotating cylinders. Extensive particle dynamics simulations taking into account the dynamics of the granular flow, particle breakage, and polygonal particle shapes were carried out. We find that the rate of particle breakage is faster in samples composed of initially rounder particles. The analysis of the active flowing layer thickness suggests that for samples composed of rounder particles a relatively lower dilatancy and higher connectivity lead to a less curved free surface profile. As a result, rounder particles rolling down the free surface have a higher mobility and thus higher velocities. In consequence, the faster breakage observed for rounder initial particles is due to the larger particles kinetic energy at the toe of the flow.

Scaling behavior of particle breakage in granular flows inside rotating drums

We perform systematic particle dynamics simulations of granular flows composed of breakable particles in a 2D rotating drum to investigate the evolution of the mean particle size and specific surface as a function of system parameters such as drum size, rotation speed, filling degree, and particle shape and size. The specific surface increases at a nearly constant rate up to a point where particle breakage begins to slow down. The rates of particle breakage for all values of system parameters are found to collapse on a master curve when the times are scaled by the characteristic time defined in the linear regime. We determine the characteristic time as a function of all system parameters, and we show that the rate of particle breakage can be expressed as a linear function of a general scaling parameter that incorporates all our system parameters. This scaling behavior provides a general framework for the upscaling of drum grinding process from laboratory to industrial scale.

Evolution of fragment size distributions from the crushing of granular materials

We study fragment size distributions after crushing single and many particles under uniaxial compression inside a cylindrical container by means of numerical simulations. Under the assumption that breaking goes through the bulk of the particle we obtain the size distributions of fragments for both cases after large displacements. For the single-particle crushing, this fragmentation mechanism produces a log-normal size distribution, which deviates from the power-law distribution of fragment sizes for the packed bed. We show that as the breaking process evolves, a power-law dependency on the displacement is present for the single grain, while for the many-grains system, the distribution converges to a steady state. We further investigate the force networks and the average coordination number as a function of the particle size, which gives information about the origin of the power-law distributions for the granular assembly under uniaxial compression.

Rheology of granular materials composed of crushable particles

We investigate sheared granular materials composed of crushable particles by means of contact dynamics simulations and the bonded-cell model for particle breakage. Each particle is paved by irregular cells interacting via cohesive forces. In each simulation, the ratio of the internal cohesion of particles to the confining pressure, the relative cohesion, is kept constant and the packing is subjected to biaxial shearing. The particles can break into two or more fragments when the internal cohesive forces are overcome by the action of compressive force chains between particles. The particle size distribution evolves during shear as the particles continue to break. We find that the breakage process is highly inhomogeneous both in the fragment sizes and their locations inside the packing. In particular, a number of large particles never break whereas a large number of particles are fully shattered. As a result, the packing keeps the memory of its initial particle size distribution, whereas a power-law distribution is observed for particles of intermediate size due to consecutive fragmentation events whereby the memory of the initial state is lost. Due to growing polydispersity, dense shear bands are formed inside the packings and the usual dilatant behavior is reduced or cancelled. Hence, the stress-strain curve no longer passes through a peak stress, and a progressive monotonic evolution towards a pseudo-steady state is observed instead. We find that the crushing rate is controlled by the confining pressure. We also show that the shear strength of the packing is well expressed in terms of contact anisotropies and force anisotropies. The force anisotropy increases while the contact orientation anisotropy declines for increasing internal cohesion of the particles. These two effects compensate each other so that the shear strength is nearly independent of the internal cohesion of particles.

Shear strength and microstructure of polydisperse packings: The effect of size span and shape of particle size distribution

By means of extensive contact dynamics simulations, we analyzed the effect of particle size distribution (PSD) on the strength and microstructure of sheared granular materials composed of frictional disks. The PSDs are built by means of a normalized β function, which allows the systematic investigation of the effects of both, the size span (from almost monodisperse to highly polydisperse) and the shape of the PSD (from linear to pronouncedly curved). We show that the shear strength is independent of the size span, which substantiates previous results obtained for uniform distributions by packing fraction. Notably, the shear strength is also independent of the shape of the PSD, as shown previously for systems composed of frictionless disks. In contrast, the packing fraction increases with the size span, but decreases with more pronounced PSD curvature. At the microscale, we analyzed the connectivity and anisotropies of the contacts and forces networks. We show that the invariance of the shear strength with the PSD is due to a compensation mechanism which involves both geometrical sources of anisotropy. In particular, contact orientation anisotropy decreases with the size span and increases with PSD curvature, while the branch length anisotropy behaves inversely.

Stress Transmission and Failure in Disordered Porous Media

By means of extensive lattice-element simulations, we investigate stress transmission and its relation with failure properties in increasingly disordered porous systems. We observe a non-Gaussian broadening of stress probability density functions under tensile loading with increasing porosity and disorder, revealing a gradual transition from a state governed by single-pore stress concentration to a state controlled by multipore interactions and metric disorder. This effect is captured by the excess kurtosis of stress distributions and shown to be nicely correlated with the second moment of local porosity fluctuations, which appears thus as a (dis)order parameter for the system. By generating statistical ensembles of porous textures with varying porosity and disorder, we derive a general expression for the fracture stress as a decreasing function of porosity and disorder. Focusing on critical sites where the local stress is above the global fracture threshold, we also analyze the transition to failure in terms of a coarse-graining length. These findings provide a general framework which can also be more generally applied to multiphase and structural heterogeneous materials.

Identification of the fragmentation of brittle particles during compaction process by the acoustic emission technique

Some nuclear fuels are currently manufactured by a powder metallurgy process that consists of three main steps, namely preparation of the powders, powder compaction, and sintering of the compact. An optimum between size, shape and cohesion of the particles of the nuclear fuels must be sought in order to obtain a compact with a sufficient mechanical strength, and to facilitate the release of helium and fission gases during irradiation through pores connected to the outside of the pellet after sintering. Being simple to adapt to nuclear-oriented purposes, the Acoustic Emission (AE) technique is used to control the microstructure of the compact by monitoring the compaction of brittle Uranium Dioxide (UO2) particles of a few hundred micrometers. The objective is to identify in situ the mechanisms that occur during the UO2 compaction, and more specifically the particle fragmentation that is linked to the open porosity of the nuclear matter. Three zones of acoustic activity, strongly related to the applied stress, can be clearly defined from analysis of the continuous signals recorded during the compaction process. They correspond to particle rearrangement and/or fragmentation. The end of the noteworthy fragmentation process is clearly defined as the end of the significant process that increases the compactness of the material. Despite the fact that the wave propagation strongly evolves during the compaction process, the acoustic signature of the fragmentation of a single UO2 particle and a bed of UO2 particles under compaction is well identified. The waveform, with a short rise time and an exponential-like decay of the signal envelope, is the most reliable descriptor. The impact of the particle size and cohesion on the AE activity, and then on the fragmentation domain, is analyzed through the discrete AE signals. The maximum amplitude of the burst signals, as well as the mean stress corresponding to the end of the recorded AE, increase with increasing mean diameter of the particles. Moreover, the maximum burst amplitude increases with increasing particle cohesion.