An official website of the United States government
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.
more »
« less
This content will become publicly available on June 29, 2027
Beyond Kinematic Strain Localization: Grain-Resolved Stress, Co-axiality, and Mechanical Work in 3D Triaxially-Compressed Sand
Strain localization in granular materials is commonly identified from kinematic signatures: intense shear strain, enhanced grain rotations, and local dilation or compaction. Yet failure in granular media is governed not only by grain kinematics, but also by how stress and mechanical work are distributed across localization zones and the surrounding material. Measuring these quantities in 3D, opaque granular materials has remained difficult, limiting experimental tests of localization theories based on constitutive softening and non-coaxiality. Here we combined X-ray computed tomography (XRCT) and 3D X-ray diffraction (3DXRD) to measure grain-scale kinematics, grain-resolved stress tensors, stress orientations, and local mechanical work during triaxial compression of sand-like quartz at 10 MPa confining pressure and natural sand at 15 MPa confining pressure. Analysis revealed (a) compactive shear bands that exhibited constitutive behavior similar to the surrounding bulk material, but approached critical state and accumulated plastic flow earlier, (b) minimal non-coaxiality between stress and strain rate, and (c) significantly elevated plastic work within shear bands, providing a signature of localization comparable to kinematics. This study provides critical new experimental constraints for constitutive models capturing localization in granular media and pushes our experimental understanding of localization zones beyond kinematics. It complements prior kinematic-only analysis of localization zones and prior studies of grain stresses in smaller samples containing only a few thousand grains with data from samples containing over 29,000 grains.
more »
« less
- Award ID(s):
- 1942096
- PAR ID:
- 10694195
- Publisher / Repository:
- SSRN
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Frictional sliding along grain boundaries in brittle shear zones can result in the fragmentation of individual grains, which ultimately can impact slip dynamics. During deformation at small scales, stick–slip motion can occur between grains when existing force chains break due to grain rearrangement or failure, resulting in frictional sliding of granular material. The rearrangement of the grains leads to dilation of the granular package, reducing the shear stress and subsequently leading to slip. Here, we conduct physical experiments employing HydroOrbs, an elasto-plastic material, to investigate grain comminution in granular media under simple shear conditions. Our findings demonstrate that the degree of grain comminution is dependent on both the normal force and the size of the grains. Using the experimental setup, we benchmark Discrete Element Method (DEM) numerical models, which are capable of simulating the movement, rotation, and fracturing of elasto-plastic grains subjected to simple shear. The DEM models successfully replicate both grain comminution patterns and horizontal force fluctuations observed in our physical experiments. They show that increasing normal forces correlate with higher horizontal forces and more fractured grains. The ability of our DEM models to accurately reproduce experimental results opens up new avenues for investigating various parameter spaces that may not be accessible through traditional laboratory experiments, for example, in assessing how internal friction or cohesion affect deformation in granular systems.more » « less
-
Plastic-bonded granular materials (PBM) are widely used in industrial sectors, including building construction, abrasive applications, and defense applications such as plastic-bonded explosives. The mechanical behavior of PBM is highly nonlinear, irreversible, rate dependent, and temperature sensitive governed by various micromechanical attributions such as grain crushing and binder damage. This paper presents a thermodynamically consistent, microstructure-informed constitutive model to capture these characteristic behaviors of PBM. Key features of the model include a breakage internal variable to upscale the grain-scale information to the continuum level and to predict grain size evolution under mechanical loading. In addition, a damage internal state variable is introduced to account for the damage, deterioration, and debonding of the binder matrix upon loading. Temperature is taken as a fundamental external state variable to handle non-isothermal loading paths. The proposed model is able to capture with good accuracy several important aspects of the mechanical properties of PBM, such as pressure-dependent elasticity, pressure-dependent yield strength, brittle-to-ductile transition, temperature dependency, and rate dependency in the post-yielding regime. The model is validated against multiple published datasets obtained from confined and unconfined compression tests, covering various PBM compositions, confining pressures, temperatures, and strain rates.more » « less
-
Concrete features significant microstructural heterogeneity which affects its mechanical behavior. Strain localization in the matrix phase of concrete has received significant attention due to its relation to microcracking and our ability to quantify it with X-ray computed tomography (XRCT). In contrast, stresses in sand and aggregates remain largely unmeasured but remain critical for micromechanics-based theories of failure. Here, we use a combination of in-situ XRCT, 3D X-ray diffraction (3DXRD), and scanning 3DXRD to directly measure strain and stress within sand grains in two samples of mortar containing different sand volume fractions. Our results reveal that, in contrast to inclusion theories from continuum micromechanics, aggregates feature a broad distribution of average stresses and significant gradients in their internal stress fields. Our work furnishes the first known dataset with these quantitative stress measurements and motivates improvements in micromechanics models for concrete which can capture stress heterogeneity.more » « less
-
Abstract The spatial organization of deformation may provide key information about the timing of catastrophic failure in the brittle regime. In an ideal homogenous system, deformation may continually localize toward macroscopic failure, and so increasing localization unambiguously signals approaching failure. However, recent analyses demonstrate that deformation, including low‐magnitude seismicity, and fractures and strain in triaxial compression experiments, experience temporary phases of delocalization superposed on an overall trend of localization toward large failure events. To constrain the conditions that promote delocalization, we perform a series of X‐ray tomography experiments at varying confining pressures (5–20 MPa) and fluid pressures (0–10 MPa) on Westerly granite cores with varying amounts of preexisting damage. We track the spatial distribution of the strain events with the highest magnitudes of the population within a given time step. The results show that larger confining pressure promotes more dilation, and promotes greater localization of the high strain events approaching macroscopic failure. In contrast, greater amounts of preexisting damage promote delocalization. Importantly, the dilative strain experiences more systematic localization than the shear strain, and so may provide more reliable information about the timing of catastrophic failure than the shear strain.more » « less
