Fracture propagation in Indiana Limestone interpreted via linear softening cohesive fracture model

Abstract

We examine the use of a linear softening cohesive fracture model (LCFM) to predict single-trace fracture growth in short-rod (SR) and notched 3-point-bend (N3PB) test configurations in Indiana Limestone. The broad goal of this work is to (a) understand the underlying assumptions of LCFM and (b) use experimental similarities and deviations from the LCFM to understand the role of loading paths of tensile fracture propagation. Cohesive fracture models are being applied in prediction of structural and subsurface fracture propagation in geomaterials. They lump the inelastic processes occurring during fracture propagation into a thin zone between elastic subdomains. LCFM assumes that the cohesive zone initially deforms elastically to a maximum tensile stress (σ max ) and then softens linearly from the crack opening width at σ max to zero stress at a critical crack opening width w 1 . Using commercial finite element software, we developed LCFMs for the SR and N3PB configurations. After fixing σ max with results from cylinder splitting tests and finding an initial Young's modulus (E) with unconfined compressive strength tests, we manually calibrate E and w 1 in the SR model against an envelope of experimental data. We apply the calibrated LCFM parameters in the N3PB geometry and compare the model against an envelope of N3PB experiments. For accurate simulation of fracture propagation, simulated off-crack stresses are high enough to require inclusion of damage. Different elastic moduli are needed in tension and compression. We hypothesize that the timing and location of shear versus extensional micromechanical failures control the qualitative macroscopic force-versus-displacement response in different tests. For accurate prediction, the LCFM requires a constant style of failure, which the SR configuration maintains until very late in deformation. The N3PB configuration does not maintain this constancy. To be broadly applicable between geometries and failure styles, the LCFM would require additional physics, possibly including elastoplastic damage in the bulk material and more complicated cohesive softening models.

Brittle fracture phase-field modeling of a short-rod specimen

“…Rinehart et al [14] have performed a series of short-rod (SR) fracture experimentation on Indiana Limestone. Below is a summary of the experimental procedure, and its comparison to a linear softening cohesive fracture model for the short-rod test configuration (Rinehart et al [14]). Samples of Indiana Limestone that were weakly 1-2 cm planar-bedded calcarenite with medium-to coarse-grain size were machined to have a SR test configuration (see Figure 3.1).…”

“…Numerical formulations for the phase-field and gradient damage models are elaborated on to discuss di↵erences and similarities between the two. These fracture methods are demonstrated by simulation of the short-rod fracture test [14] and the Brazilian splitting test for Indiana Limestone. Previously published results by Rinehart et al [14] use a cohesive zone model for simulating the experiments.…”

“…These fracture methods are demonstrated by simulation of the short-rod fracture test [14] and the Brazilian splitting test for Indiana Limestone. Previously published results by Rinehart et al [14] use a cohesive zone model for simulating the experiments. The phase-field and gradient damage model solutions are compared and contrasted to these results.…”

“…A cohesive zone model uses a traction separation relationship to model fracture. The cohesive zone model used in the work Rinehart et al [14] was a bilinear relationship with linear elastic loading to a peak stress and linear softening once the crack width has reached a critical value (Bazant and Planas [1]). This linear softening model is the traction law of separation between cohesive surfaces (Figure 3.5).…”

“…This report uses the newly introduced phase-field and gradient damage model capabilities in the Sierra Solid Mechanics code, to model full scale three-dimensional cases of fracture growth for the short-rod (SR) experiments (Rinehart et al [14]). Both computational fracture models are investigated for convergence with mesh refinement.…”