Analytical investigation on the unstable fracture toughness of fine-grained quartz-diorite rock considering the size effect

Abstract

In this paper, an analytical method was introduced to investigate the size effect on the unstable fracture toughness of fine-grained quartz-diorite. The analytical method can predict the axial load, crack mouth opening displacement, and crack resistance curve of the three-point bend specimen when the elastic modulus, tensile strength, fracture energy, and initial fracture toughness are given. Mode I fracture tests were conducted on the three-point bend specimen with five different depths to acquire these parameters. And, the effectiveness of the analytical method was validated by the experimental results. The analytical method is then utilized to compute the unstable fracture toughness of three-point bend specimens with different sizes and normalized initial crack lengths. The results reveal that unstable fracture toughness is a size-dependent parameter that first increases and then remains unchanged with the increase of the specimen size. The nominal stress follows Bažant’s size effect law and the unstable fracture toughness will converge to the size-independent mode I fracture toughness obtained by Bažant’s size effect model with the increase of specimen depth. Furthermore, for the specimen with a small depth, unstable fracture toughness decreases with the increase in normalized initial crack length, which further illustrates the boundary effect on the unstable fracture toughness of rock specimens.