Cohesive model applied to fracture propagation in Indiana Limestone

Abstract:

We apply a cohesive fracture (CF) model to results of short-rod (SR), notched 3-point-bend (N3PB) tests, and Brazil tests in Indiana Limestone. Calibration and validation of the model are performed within a commercial finite element modeling platform. By using a linear traction-displacement softening response for a defined fracture-opening displacement (w₁) following peak tensile stress (σ_crit), the CF model numerically lumps different spatially distributed inelastic processes occurring at and around fracture tips into a thin zone within an elastic domain. Both the SR and the N3PB test specimen geometries use a notch partway through the sample to control the location of fracture propagation. We develop a mesh for both the SR and N3PB geometries with a narrow cohesive zone in the center of notches. From the Brazil tests, we find a tensile splitting stress (σ_split) of 5.9 MPa. We use a σ_split as the peak tensile stress (σ_crit) for all simulations. The Young’s modulus (E) and the critical crack opening distance (w₁) of the CF model are calibrated against the SR data. The model successfully captures the elastic, yield, peak, and initial and late failure behavior and compares favorably against the N3PB tests. Differences in force-displacement and crack propagation are primarily caused by: more mixed-mode (shear and opening) crack propagation in N3PB than in SR tests, causing a higher peak; and transition from compression (high E) to tension (low E) in a larger volume of the N3PB sample than in the SR geometry. This material is based upon work supported as part of the Center for Frontiers of Subsurface Energy Security, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0001114. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.