Fracture loads of ISRM-suggested notched semi-circular bend rock specimens using finite fracture mechanics

Abstract

The International Society for Rock Mechanics (ISRM) recommends notched Brazilian semi-circular bend specimen (NSCB) to measure fracture parameters of rocks. However, the testing accuracy is limited by the mechanical processing precision of the specimen, especially the notch tip, thus the testing results of fracture parameter is often strongly affected by the curvature radius of the notch tip. Moreover, traditional fracture mechanics methods find it challenging to quantify the effect of notch geometry on fracture properties. This paper proposes a semi-analytical method based on finite fracture mechanics (FFM) to predict the effects of geometric parameters of the notch and specimen on the critical load of U-notched semi-circular bend specimen (U-NSCB). First, the stress fields at the notch tip of U-NSCB specimen and the stress intensity factor (SIF) at the virtual crack tip ahead of the U-notch were determined using finite element simulations combined with the contour integral method, and a relationship between the mechanical properties of U-NSCB specimen and the geometry of the U-notch was established to characterize the effects caused by changes in notch geometry. Second, a semi-analytical solution was developed using the coupled FFM criterion to predict the critical load at crack initiation for U-NSCB specimens. Finally, three-point bending tests were conducted on U-NSCB specimens made of Fangshan marble (FM) with different notch lengths and curvature radii to validate the effectiveness and accuracy of the semi-analytical method. The inherent fracture toughness of the marble was also inversely obtained based on the FFM prediction results. The research findings showed that the predictions from the FFM with point stress criterion were more accurate than those from the FFM with line stress criterion, with a maximum deviation of 6.81% from the experimental results. The proposed FFM semi-analytical method helps to improve testing accuracy of the NSCB method and offers a new approach for predicting the critical load of other specimens with finite size.