Breakage Mechanics Modeling of the Brittle-ductile Transition in Granular Materials
Abstract
During comminution, several energy dissipation processes operate simultaneously, including plastic
work due to internal friction, fracture energy release due to particle breakage, and plastic work due to the
rearrangement of fragments. Recent studies show that the plastic work due to particle rearrangement amounts to an
important part in the total dissipated energy, which is much larger than the fracture energy released to create new
surfaces, especially at high stress. This evolution of energy distribution between breakage dissipation and plastic work
during the comminution of granular material manifests as a transition from brittleness to ductility. However, there is
still no micromechanical model that can capture this transition. Breakage mechanics is a continuum mechanics theory
that allows to analyzing the behavior of granular materials based on statistical and thermodynamic principles. We use
this theory to propose a model that couples the energy dissipation caused by breakage and frictional plastic work. A
friction plasticity parameter is coupled to the breakage parameter. Physically, the relationship between plasticity and
breakage translates: (1) the increase of the dissipation induced by breakage in front of that induced by plastic
deformation when fragments produced by breakage have rougher surfaces with higher friction angles than the non
broken particles; and reversely; (2) the increase of the dissipation induced by plastic deformation in front of that
induced by breakage when the multiplication of fragments results in higher particle coordination numbers, shielding
effects and higher particle strength. Our modeling hypothesis is supported by experimental observations reported in the
literature, and simulations show that our coupled breakage-plasticity model better captures the brittle-ductile transition
observed in granular materials. The proposed modeling approach is expected to improve the fundamental
understanding of quasi-static confined comminution, which is a major issue in civil engineering, powder technology
and the mineral industry.