Fracture toughness and surface energies of covalent minerals: theoretical estimates

Abstract

Theoretical estimates of the ideal brittle fracture toughness and surface energies of 16 covalent minerals and materials have been obtained, based on a Morse-type bonding model. The materials range from ice to diamond, and include polymorphs of C, SiC, Si3N4, and SiO2, together with B4C, BN (borazone) and MoS2 (molybdenite). The toughness model utilised enthalpy data, plus elastic compliance and stiffness constants. The resulting stress intensity, KIC, for propagation of randomly planar transgranular cracks ranged from ∼0.11 (ice) to ∼3.3 MPam1/2 (diamond). The corresponding critical energy release rates, GIC, ranged from ∼1.27 to ∼9.95 Jm−2. Estimates of the critical stress intensity for cleavage (KIC)hkl, of monocrystals on commonly observed (hkl) cleavage planes indicated (KIC)hkl<KIC, consistent with expectations. Our analysis shows that the critical stress intensity (KIC)Gb and energy release rate (GIC)Gb for fracture along high angle grain boundaries are lower than KIC and GIC. The results are discussed with relevance to energy of comminution, and the influence of KIC on particle size during ultra fine grinding. Based on comparisons between the Bond work index and energy required to form new surface area via particle fracture, the energy efficiency of comminution is confirmed to be very low (∼1%).