A relationship between tensile strength and mode I fracture toughness of rocks using the critical distance

Abstract

Correlations between material parameters are useful because they provide a first estimation of unknown parameters. Here, the correlation between the tensile strength and the mode I fracture toughness of rocks is studied. Some researchers have proposed empirical correlations based on a certain amount of empirical data and a fitting process. On the other hand, a few researchers have considered that the proportionality coefficient could be related to a rock property with units of length. Here, a linear relationship without an intercept at the origin between the tensile strength and the mode I fracture toughness of rocks is theoretically confirmed using the theory of critical distances (TCD). A comprehensive experimental database is presented and comparisons with this data from the literature (including tests at different temperatures) confirm the linear relationship and values of the critical distance of several millimeters (e.g., 3–15 mm). However, the scatter is large because there are different sources of uncertainty in the correlation, such as the testing method. Finally, the physical meaning of the critical distance is explored and its linear correlation with the grain size using the experimental database.

Experimental Study on the Effect of Cyclic Heating and Water Cooling on Mixed-Mode I-II Fracture Characteristics of Sandstone

“…The higher the tensile strength of the specimen, the greater its resistance to fracture in pure mode I. Hua et al [46,54] also pointed out that the tensile strength and mode I fracture toughness of sandstones after wet and dry cycling conforms to a linear relationship. Given that the crack tip experiences tensile stress under pure mode I loading, it is widely acknowledged among scholars that a correlation exists between pure mode I fracture toughness and tensile strength [58,59,62]. Likewise, shear strength is commonly associated with the fracture toughness in pure mode II conditions [63].…”