Breakage Mechanics Modeling of the Brittle-ductile Transition in Granular Materials
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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.