Frontiers in Earth Science (Sep 2024)
Numerical calibration for fracture parameters of three-point bending semi-circular specimens
Abstract
This study aims to refine the fracture characterization of three-point bending semi-circular specimens used in rock fracture toughness assessments. The primary objective is to improve the accuracy of such evaluations by developing numerical simulations of specimens with pre-engineered cracks of varying geometries. Numerical simulations were conducted using the finite element method. The interaction integral method was employed to quantify the stress intensity factors (SIFs) and T-stress at crack tips. Initially, the model’s accuracy was validated by replicating stress singularities at crack tips in a benchmark circular disk with a central straight crack. Following validation, dimensionless fracture parameters specific to the three-point bending semi-circular specimens were calibrated. The numerical results demonstrate that the dimensionless stress intensity factor (YI) increases with both the relative crack length (a/R) and the spacing between support points. Notably, for relative crack lengths a/R ≤ 0.5, the dimensionless T-stress assumes negative values, initially decreasing and then increasing as the relative crack length increases. The findings of this study provide valuable insights into the fracture behavior of three-point bending semi-circular specimens with pre-engineered cracks. Based on the observed trends in the dimensionless fracture parameters, it is recommended that relative crack lengths within the range of 0.2–0.6 be used to maintain the accuracy of rock fracture toughness tests. The finite element method used in this study serves as a robust tool for calibrating fracture parameters, thereby laying a strong foundation for the application of these specimens in rock fracture toughness evaluations.
Keywords
