Rheology of granular materials composed of crushable particles

Particle fracture regimes from impact simulations

We introduce an approach to particle breakage, wherein the particle is modeled as an aggregate of polyhedral cells with their common surfaces governed by the Griffith criterion of fracture. This model is implemented within a discrete element code to simulate and analyze the breakage behavior of a single particle impacting a rigid plane. We find that fracture dynamics involves three distinct regimes as a function of the normalized impact energy ω. At low values of ω, the particle undergoes elastic rebound and no cracks occur inside the particle. In the intermediate range, the particle is damaged by nucleation and propagation of cracks, and the effective restitution coefficient declines without breakup of the particle. Finally, for values of ω beyond a well-defined threshold, the particle breaks into fragments and the restitution coefficient increases with ω due to kinetic energy carried away by the fragments. We show that particle damage, restitution coefficient, and fracture efficiency (the amount of energy input consumed for particle fracture) collapse well as a function of dimensionless scaling parameters. Our data are also sufficiently accurate to scale fragment size and shape distributions. It is found that fragment masses (volumes) follow a power-law distribution with an exponent decreasing with fracture energy. Interestingly, the average elongation and flatness of fragments are very close to those observed in experiments and lunar samples at the optimal fracture efficiency.

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.

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.