failure modes called mixed mode [1,2]. In the case of rocks, the combination of Mode-I and ModeII (mixed Mode I-II) failure is more common. Therefore, consideration of mixed Mode I-II loading in addition to pure Mode-I becomes important in fracture toughness investigation. Due to this mixed mode failure pattern, in addition to mode-I, fracture toughness under mode-II becomes important to be considered. When Brazilian disks with an inclined central notch are tested under diametral compression (Figure 1), a variety of mixed mode I-II fracture cases are obtained. For a particular material, a fracture locus or envelope can be obtained by plotting normalized modeII versus mode-I fracture toughness. The envelope obtained could be used as a failure criterion in fracture toughness study for a particular material and testing condition in a way similar to the use of Mohr-Coulomb failure envelope for strength. Usually, the fracture toughness of rock is determined at ambient conditions. However, under varying temperatures and confining pressures, the measured fracture toughness has been shown to vary. The fracture toughness behavior of a deep-seated rock formation requires the testing to be conducted in a manner that simulates the in-situ conditions such as temperature and confining pressure. THEORETICAL BACKGROUND Facture Toughness When a notched rock specimen is subjected to an externally applied load, stress concentrates in the vicinity of the crack tip. When this concentrated stress reaches a critical value, failure occurs due to propagation of the preexisting crack. The fracture toughness is then calculated in terms of the stress intensity factor (SIF). In this paper, a circular Brazilian disk with a central notch under diametrical compression (Figure 1) was used to investigate fracture toughness. The following mathematical expressions, proposed by Atkinson et al. [3], were used for the fracture toughness calculation: K P a RB N I I = π (1) K P a RB N II II = π (2) where, KI is Mode-I stress intensity factor; KII is Mode-II stress intensity factor; R is radius of the Brazilian disk; B is thickness of the disk; P is compressive load at failure; a is half crack length; and NI and NII are non-dimensional coefficients which depend on a/R and the orientation angle ( β) of the notch with the direction of loading. For linear elastic fracture mechanics (LEFM), the small crack approximation proposed by Atkinson et al. [3] can be used to determine the values of NI and NII for half crack to radius ratio (a/R ≤ 0.3), as follows: ( )2 2 2 2 ) (1 4 cos 4 sin 1 4 sin a R N I β β β ∗ − + = − (3) ( )( ) [ ]2 2 5 2 8cos a R N II − = + β (4) Fracture toughness for pure Mode-I ( β = 0) is taken as KIC; and that for pure Mode-II ( β ≈ 29 o) is taken as KIIC.
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