Approximation of Rock Fracture Toughness using Scratch Test and Phase-Field Modeling Approach
Authors: Martogi Debora , Vaibhav Atul , Noshadravan Arash , Abedi Sara 
Published: October 2020

Abstract
Current experimental methods of assessing rock fracture toughness require a large sample size (i.e., Brazillian test, semi-circular bending, three-point bending), which cannot be extracted at greater depths and along horizontal well. Alternatively, fracture toughness can be evaluated at a finer scale using scratch testing. This study investigates the rock failure mechanism using micro-scratch testing and phase field modeling on rock fragments.
The phase field approach models the crack growth and initiation based on energy minimization principles and by portraying the crack surface as a diffused entity. The method has been known for its robustness in preventing numerical singularities due to sharp crack discontinuities in complex crack topologies. In the phase-field scheme, a regularization scalar order parameter is used to indicate the material’s state (from undamaged to damage) during fracture formation. The associated loss of stiffness in rock during fracture formations is captured by the coupling of selected energy degradation function with embedded scalar order parameter and partial differential equations defining the deformation, history, and phase-field evolutions. In doing so, information on stress strain development is needed to evaluate the change in free energy during cracks formation. In this study, scratch testing is used to obtain load-displacement data related to stress strain history. During the test, an indenter scratches the surface of the rock under increasing load. The critical loads where the crack initiates and the chipping spallation occurs are identified based on the microscopic observations, acoustic emission signals, recorded tangential force and recorded depth. The critical loads are used to determine the crack length associated with chipping formation, while the recorded force displacement data are used to obtain the dimensionless stress-strain curve. Both the crack lengths and the dimensionless stress strain curve are then used as the input to the phase field model developed to approximate the fracture toughness of the rock tested.
Scratch tests are performed on samples obtained from Eagle Ford formation. The experiments are conducted in short transverse and divider orientations. The crack formations are studied under the progressive load application. The critical loads where crack initiates and chips form are identified mainly based on the panoramic picture obtained after the test and the spikes seen on the Acoustic Emission signals. Preliminary results show that the fracture toughness is lower for samples tested in parallel to the bedding orientation (i.e., divider).
Fracture toughness of rocks has attracted wide attention in the last few years in the design and analysis of hydraulic fracturing for hydrocarbon and geothermal recovery. The currently proposed methodology allows for a quicker and more reliable way of approximating rock fracture toughness from small rock samples. The incorporation of the phase field model allows better prediction of rock fracture toughness as the method is capable of overcoming classical model limitations of quantifying crack initiation and crack propagation in the complex fracture networks.