Grain fragmentation in sheared granular flow: weakening effects, energy dissipation, and strain localization

Abstract

We describe the shear flow of a disordered granular material in the presence of grain fracture using the shear-transformation-zone (STZ) theory of amorphous plasticity adapted to systems with a hard-core inter-particle interaction. To this end, we develop the equations of motion for this system within a statistical-thermodynamic framework analogous to that used in the analysis of molecular glasses. For hard-core systems, the amount of internal, configurational disorder is characterized by the compactivity $X=\partial V/\partial S_C$, where $V$ and $S_C$ are respectively the volume and configurational entropy. Grain breakage is described by a constitutive equation for the temporal evolution of a characteristic grain size $a$, based on fracture mechanics. We show that grain breakage is a weakening mechanism, significantly lowering the flow stress at large strain rates, if the material is rate-strengthening in character. We show in addition that if the granular material is sufficiently aged, spatial inhomogeneity in configurational disorder results in strain localization. We also show that grain splitting contributes significantly to comminution at small shear strains, while grain abrasion becomes dominant at large shear displacements.

16 pages, 10 figures

References in corpus (10)

• Shear-transformation-zone theory of plastic deformation near the glass transition
• Strain localization in a shear transformation zone model for amorphous solids
• Hysteresis and competition between disorder and crystallization in sheared and vibrated granular flow
• Rate dependent shear bands in a shear transformation zone model of amorphous solids
• Steady-state, effective-temperature dynamics in a glassy material
• Linear Response Theory for Hard and Soft Glassy Materials
• Shear-Transformation-Zone Theory of Linear Glassy Dynamics
• Universal Jamming Phase Diagram in the Hard-Sphere Limit
• Non-equilibrium thermodynamics in sheared hard-sphere materials
• Ratio of effective temperature to pressure controls the mobility of sheared hard spheres

Cited by in corpus (6)

• Local and global avalanches in a 2D sheared granular medium
• Stick-slip instabilities in sheared granular flow: the role of friction and acoustic vibrations
• Shear flow of angular grains: acoustic effects and non-monotonic rate dependence of volume
• A two-scale model for sheared fault gouge: Competition between macroscopic disorder and local viscoplasticity
• Localization and instability in sheared granular materials: Role of friction and vibration
• A Model for Athermal Strain Localization in Dry Sheared Fault Gouge