β P P R 2a Figure 1: A schematic for Brazilian disk under diametrical compression Failure Theories There are numerous failure criteria for crack initiation and propagation under mixed mode I-II loading condition. The most popular ones are: (1) the maximum tangential stress (σ) criterion, (2) the maximum energy release rate (G) criterion, and (3) the minimum strain energy density (S) criterion. The available experimental data shows that no distinct theoretical failure criterion is applicable to all cases. Also, these criteria imply that KIC is larger than KIIC, while experimental data show the opposite. Moreover, due to the fact that the existing failure criteria were developed based on the tensile loading rather than the compressive, they hold good only in the positive region (crack opening) and cannot predict the fracture behavior in the negative zone (crack opening) Many researchers have recommended using empirical relations for practical applications. Huang and Wang [4] and Sun [5] have used one of three empirical equations of straight line, ellipse, and homogenous quadratic to fit the experimental fracture toughness data in the (KI/ KIC)-(KII/ KIIC) plane. Also, an exponential relationship was used [6,7]. EXPERIMENTAL PROGRAM Sample Preparation Rock blocks were collected from a limestone rock formation outcropping in the Central Province of Saudi Arabia. Cores were obtained from these blocks using 98 mm and 84 mm coring tube pits. Cores were sliced into circular disks using a high-speed circular saw. The thickness (B) of the sliced disks was in the range of 20-24 mm. A notch was machined in the center of the disks. Straight notch was made using a 0.25 mm diamond-impregnated wire saw, while chevron notch was made using a slow-speed circular saw. The notch making process is explained in more details elsewhere [8]. Rock properties The investigated limestone rock was beige in color. Its physical properties included a dry density of 2.586 gm/cm3, a specific gravity of 2.737, and porosity of 5.4%. The mechanical characteristics included a uniaxial unconfined compressive strength of 105 MPa, a tensile strength of 2.31 MPa, a modulus of elasticity of 54 GPa, and a Poisson’s ratio of 0.276.
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