Measurement and simulation of comminution rate in granular materials subjected to creep tests

Abstract

The subcritical growth of intra-particle cracks and their consequent rupture are often cited among the processes responsible for creep in granular solids. However, classical testing procedures do not involve measurements of grain size distribution, thus preventing a connection of creep strains to delayed breakage. Here, a rate-dependent Breakage Mechanics framework inspired by the physics of delayed crack growth is used to interpret creep measurements through continuum variables reflecting the release of elastic energy during comminution. Creep experiments were conducted on water-saturated materials with different particle size and shape. Each specimen was subjected to stages of oedometric compression and creep at stress levels sufficient to induce grain fracture. During each test, the evolution of the grain size distribution was monitored to quantify the progression of comminution. The experiments were finally interpreted and simulated with a breakage kinetics model characterized by a power law expression similar to those used in subcritical crack growth theories. The results show that the proposed model is able to replicate the phenomenology of delayed breakage. The power law coefficient linking the breakage growth rate to the elastic stored energy was found independent of the size of the grains and characterized by values within the range reported for the stress corrosion index of quartz. By contrast, the calibration of the breakage model revealed that the timescale of comminution was size-dependent, thus signaling an increase of elapsed creep time in materials with larger grains. This finding suggests that samples consisting of larger grains may require longer time until all particles contributing to creep strain attain failure, thus stressing the connection between the processes occurring at the grain scale and those measurable at the continuum scale.