Analytical and experimental investigation on the effect of loading rate on the fracture toughness and fracture envelope in brittle rocks

Abstract

Fracture toughness of brittle rocks is an essential factor for analyzing and designing many problems in rock mechanics such as crack initiation and propagation in rock masses, hydraulic fracturing, geothermal energy, etc. This parameter is closely related to the strain rate to which the rock mass is subjected. Therefore, the effect of strain rate on the fracture toughness under three loading modes (pure mode I, mixed mode loading I/II and pure mode II) by taking into account crack propagation speed was investigated in this work. Experiments were conducted on rectangular specimens of hornfels rock and two fracture criteria that include maximum tangential stress criterion (ϭ-criterion) and minimum strain energy density criterion (S-criterion) were adopted to verify their ability to predict the fracture envelope as a function of the strain rate. Results indicated that by increasing the strain rate from 6 × 10−4 to 6 × 10−2 S−1, fracture toughness under pure mode I, mixed mode loading I/II and pure mode II increased by 1.6, 1.8 and 1.9 orders of magnitudes, respectively. The fracture toughness under pure mode I and mixed mode loading I/II almost has the same increment rate versus strain rate (∼21). While the increment rate of the fracture toughness under pure mode II (∼37) is larger than that under pure mode I and mixed mode loading I/II. S-criterion indicated that by increasing the crack propagation speed, fracture envelope moves up and the fracture resistance for growth under mixed mode loading I/II increases. While for ϭ-criterion, two cases can be distinguished, for crack propagation speed less than 80% the Rayleigh wave speed, fracture envelope moves down by increasing the crack propagation speed, and the vice is versa for crack propagation speed greater than 80% of the Ryleigh wave speed. S-criterion is better than ϭ-criterion to characterize the fracture envelope under low strain rate, and for high strain rates, S-criterion should be developed to better characterize the fracture envelope.