Energy-based approach for fracture assessment of several rocks containing U-shaped notches through the application of the SED criterion

This work presents an energetic continuum approach for the fracture assessment of rocks containing U-shaped notches and subjected to Mode I loading conditions. Three different methodologies are proposed, all based on the premise that brittle failure will occur when the average strain energy density over a certain control area reaches a critical value that only depends on the material, as stated by the Strain Energy Density (SED) criterion. The first method proposed (A) deals with the application of the SED criterion through an expression with a series of already tabulated parameters, which are particularised for the analysed rocks by rational extrapolation. By contrast, the second method (B) aims to obtain numerically the previously extrapolated parameters, and the third method (C) directly relates the strain energy density with the applied load, without the use of those parameters. The research is based on the results obtained from an exhaustive experimental programme comprising 300 fracture specimens tested in four-point bending conditions. These tests combine parallelepiped samples made of six different types of rocks (two marbles, two limestones, a sandstone and a granite) and containing eight different notch radii (varying from 0.15 mm up to 15 mm). Thus, this work aims to show the potential, capacity and limitations of the SED criterion in rock fracture analyses, by comparing the experimentally obtained fracture loads to those predicted by the three proposed methodologies.