Introduction of a Scaling Factor for Fracture Toughness Measurement of Rocks Using the Semi-circular Bend Test

Abstract

This article discusses the scale dependence of the mode $$\mathrm {I}$$ I fracture toughness of rocks measured via the semi-circular bend (SCB) test. An extensive set of experiments is conducted to scrutinise the fracture toughness variations with size for three distinct rock types with radii ranging from 25 to 300 mm. The lengths of the fracture process zone (FPZ) for different sample sizes are measured using the digital image correlation (DIC) technique. A theoretical model is also established that relates the value of fracture toughness to the sample size. This theorem is based on the strip-yield model to estimate the length of FPZ, and the energy release rate concept to relate the FPZ length to the fracture toughness. This theoretical model does not rely on any experimental-based curve-fitting parameter, but only on the tensile strength of the rock type as well as the fracture toughness at a specific sample size. The size effects predicted by the theoretical model is in a good agreement with the experimental data on both fracture toughness and the FPZ length. Finally, theoretical correction factors are introduced for various geometrical configurations of the SCB specimen, using which a scale-independent mode $$\mathrm {I}$$ I fracture toughness of the rock material can be estimated from the results of experiments performed on small samples.

True Mode $$\mathrm {III}$$ Fracturing of Rocks: An Axially Double-Edge Notched Brazilian Disk Test

“…7a and Table 3 indicate a sign of convergence at higher ligament length. Similar observation has been reported for mode I and true mode II fracture toughness tests, where fracture toughness values increase with the ligament length and tend to converge at higher ligament lengths (Wei et al 2016a(Wei et al , 2021Ghouli et al 2021;Bahrami et al 2021). This phenomenon, which is also referred to as size or scale effect, introduces a minimum size requirement for obtaining the size independent fracture toughness (Kuruppu et al 2014;Backers and Stephansson 2012).…”

A stress-based approach for considering the size effect on the mixed mode fracture behavior of rock

“…In a specific size related to the specimen material, the crack tip is enough far from the back boundary and the critical distance is relatively constant after this size. This point has been demonstrated both theoretically 38,41,44 and experimentally 32,58,59 in the literature. Also, various formulae have been suggested for describing the size dependency of r c .…”

“…Moreover, some fracture criteria can be found in the literature to describe the size-dependent fracture behavior of rock specimens subjected to mode I, mode II, and mixed mode I/II loading. 30,32,41,[44][45][46] Almost all of the aforementioned criteria is written according to the coefficients of stress or strain terms proposed by Williams 14 such as stress intensity factors K I and K II , T-stress and coefficients A 3 and B 3 . Hence, these coefficients should be first determined.…”

“…Revealed from experimental results is that the size of specimen has a great influence on the fracture behavior of rock. [29][30][31][32][33] Therefore, size effect on the fracture resistance of rock should be known to correlate the results obtained from the laboratory-size specimens to the real rock structures.…”

“…Moreover, some fracture criteria can be found in the literature to describe the size‐dependent fracture behavior of rock specimens subjected to mode I, mode II, and mixed mode I/II loading. 30,32,41,44–46…”