Micromechanics of contact-bound cohesive granular materials in confined compression.

The mechanical behavior of granular materials results from interparticle interactions, which are predominantly frictional. With the presence of even very small amounts of cohesion this frictional interparticle behavior significantly changes. In this study, we introduce trace amounts of cohesive binder between the intergranular contacts in a sample of quartz particles and apply one-dimensional (1D) compression loading. X-ray computed tomography is performed in situ during 1D compression. We make observations at three different length scales. At the macroscopic or ensemble scale, we track the evolution of the porosity, particle size and the stress-strain response during this compression. At the microstructure or interparticle scale, we compute the directional distribution of contacts and the particles. We also track the evolution of the fabric chains with continued compression. We also evaluate particle rotations, displacements, contact twist, rotation, and sliding. We show through our experiments that even a small amount of cohesion (as low as 1% by weight) significantly changes the response at multiple length scales. This interparticle cohesion suppresses the fragmentation of grains, alters force transmission and changes the structure of the ensemble.

Assessing continuum plasticity postulates with grain stress and local strain measurements in triaxially compressed sand.

Critical state and continuum plasticity theories have been used in research and engineering practice in soil and rock mechanics for decades. These theories rely on postulated relationships between material stresses and strains. Some classical postulates include coaxiality between stress and strain rates, stress-dilatancy relationships, and kinematic assumptions in shear bands. Although numerical and experimental data have quantified the strains and grain kinematics in such experiments, little data quantifying grain stresses are available. Here, we report the first-known grain stress and local strain measurements in triaxial compression tests on synthetic quartz sands using synchrotron X-ray tomography and 3D X-ray diffraction. We use these data to examine the micromechanics of shear banding, with a focus on coaxiality, stress-dilatancy, and kinematics within bands. Our results indicate the following: 1) elevated deviatoric stress, strain, and stress ratios in shear bands throughout experiments; 2) coaxial principal compressive stresses and strains throughout samples; 3) significant contraction along shear bands; 4) vanishing volumetric strain but nonvanishing stress fluctuations throughout samples at all stages of deformation. Our results provide some of the first-known in situ stress and strain measurements able to aid in critically evaluating postulates employed in continuum plasticity and strain localization theories for sands.

Force inference in granular materials: Uncertainty analysis and application to three-dimensional experiment design.

Interparticle forces are known to influence mechanical and physical properties of granular materials. A method for inferring forces in two-dimensional and three-dimensional experiments has recently been developed and applied to the problem of examining force statistics, energy dissipation, fracture mechanics, and force-property relations. However, a systematic analysis of uncertainties in the forces inferred through this method has not been undertaken. In this paper, our goal is therefore to perform such a systematic analysis. We first review and modify the force inference technique to eliminate its sensitivity to the choice of units and coordinate system origin. We then use discrete-element method simulations to perform a systematic study of how experimental uncertainties and data-processing errors lead to errors in inferred forces. For the considered experiments and simulations, we find that (1) errors in inferred force magnitudes and orientations increase as the ratio between particle stress uncertainties and a measure of stress imposed on the system increases, but remain small in the largest forces in a material; (2) the absence of a moderate number of particle stress tensors in the force inference procedure leads to negligible errors in inferred force magnitudes and orientations; and (3) particle stress tensors that cannot be directly measured during experiments can be "recovered" through the force inference procedure. Based on our results, we make recommendations for future experiment design to reduce uncertainties in inferred forces.

Quantifying local rearrangements in three-dimensional granular materials: Rearrangement measures, correlations, and relationship to stresses.

Quantifying the ways in which local particle rearrangements contribute to macroscopic plasticity is one of the fundamental pursuits of granular mechanics and soft matter physics. Here we examine local rearrangements that occur naturally during the deformation of three samples of 3D granular materials subjected to distinct boundary conditions by employing in situ x-ray measurements of particle-resolved structure and stress. We focus on five distinct rearrangement measures, their statistics, interrelationships, contributions to macroscopic deformation, repeatability, and dependence on local structure and stress. Our most significant findings are that local rearrangements (1) are correlated on a scale of three to four particle diameters, (2) exhibit volumetric strain-shear strain and nonaffine displacement-rotation coupling, (3) exhibit correlations that suggest either rearrangement repeatability or that rearrangements span multiple steps of incremental sample strain, and (4) show little dependence on local stress but correlate with quantities describing local structure, such as porosity. Our results are presented in the context of relevant plasticity theories and are consistent with recent findings suggesting that local structure may play at least as important of a role as local stress in determining the nature of local rearrangements.

The influence of packing structure and interparticle forces on ultrasound transmission in granular media.

Ultrasound propagation through externally stressed, disordered granular materials was experimentally and numerically investigated. Experiments employed piezoelectric transducers to excite and detect longitudinal ultrasound waves of various frequencies traveling through randomly packed sapphire spheres subjected to uniaxial compression. The experiments featured in situ X-ray tomography and diffraction measurements of contact fabric, particle kinematics, average per-particle stress tensors, and interparticle forces. The experimentally measured packing configuration and inferred interparticle forces at different sample stresses were used to construct spring networks characterized by Hessian and damping matrices. The ultrasound responses of these network were simulated to investigate the origins of wave velocity, acoustic paths, dispersion, and attenuation. Results revealed that both packing structure and interparticle force heterogeneity played an important role in controlling wave velocity and dispersion, while packing structure alone quantitatively explained most of the observed wave attenuation. This research provides insight into time- and frequency-domain features of wave propagation in randomly packed granular materials, shedding light on the fundamental mechanisms controlling wave velocities, dispersion, and attenuation in such systems.

Characterization of the crystal structure, kinematics, stresses and rotations in angular granular quartz during compaction.

Three-dimensional X-ray diffraction (3DXRD), a method for quantifying the position, orientation and elastic strain of large ensembles of single crystals, has recently emerged as an important tool for studying the mechanical response of granular materials during compaction. Applications have demonstrated the utility of 3DXRD and X-ray computed tomography (XRCT) for assessing strains, particle stresses and orientations, inter-particle contacts and forces, particle fracture mechanics, and porosity evolution in situ. Although past studies employing 3DXRD and XRCT have elucidated the mechanics of spherical particle packings and angular particle packings with a small number of particles, there has been limited effort to date in studying angular particle packings with a large number of particles and in comparing the mechanics of these packings with those composed of a large number of spherical particles. Therefore, the focus of the present paper is on the mechanics of several hundred angular particles during compaction using in situ 3DXRD to study the crystal structure, kinematics, stresses and rotations of angular quartz grains. Comparisons are also made between the compaction response of angular grains and that of spherical grains, and stress-induced twinning within individual grains is discussed.