Effect of grain size on brittle and semibrittle strength: Implications for micromechanical modelling of failure in compression

Triaxial experiments were performed at room temperature and confining pressures up to 450 MPa on four pure, dense calcite rocks whose average grain sizes range over four orders of magnitude. Volumetric strain was measured during some of the experiments and microstructural studies were conducted to identify the active deformation mechanisms. The brittle fracture strength and macroscopic initial “plastic” yield stress in the semibrittle field follow empirical Hall‐Petch relations. The confining pressure at the brittle‐ductile transition depends inversely on grain size, but the stress ratio σ 3 /σ 1 at the transition is nearly the same for the different rocks. We assume that the initial flaw size scales with grain size and compare our experimental data to the fracture mechanics models of Ashby and Hallam (1986) for brittle fracture and Horii and Nemat‐Nasser (1986) for the brittle‐plastic transition in compression. The first model predicts that small confining pressures are sufficient to inhibit work softening behavior; however, our data indicate that localization occurs for significantly higher values of confining pressure than predicted. Furthermore, we find that localization is inhibited with increased confining pressure because of the increased activity of plastic flow mechanisms, rather than because of the increased difficulty of crack propagation alone. With certain assumptions, the model predicts the experimentally determined slope of the Hall‐Petch relation in the brittle field, although it underestimates the compressive strength of the rocks. The second model predicts that the stress ratio σ 3 /σ 1 at the brittle‐plastic transition scales with the, square root of the grain size; however, the experimental data do not corroborate the model unless the square of the ratio of the mode I fracture toughness to the plastic yield stress in shear scales with the grain size. The stress ratio at the brittle‐ductile transition is apparently a constant for many different rock types; we suggest that the physical basis for this relationship is that the ductility of most mineral aggregates falls within a small range.