PHASE FIELD MODELLING OF FRACTURE PROPERTIES FROM SCRATCH TEST

Abstract

Scratch test is one of the oldest concepts for characterizing mechanical properties of a material. The inference of the relationship between scratch force and material property is still a contemporary topic in applied mechanics. It has applications ranging from assessment of wear of metals and strength of rocks to skin biomechanics and the recent nanoscale evaluation of scratch damage in polymers. Despite the seeming simplicity of the procedure, a fundamental understanding of the underlying mechanism remains indistinct. The complexity lies with the prediction of mechanism that drives the scratch resistance, i.e. the chipping of material. The objective of this research is to revisit the characterization of fracture properties of shale materials from scratch test measurements. This problem of considering scratching as a fracture process has been approached through experiments and theories but there is a big gap when it comes to associate the experimental results with a computational approach which is analogous to the actual mechanism. We propose that this phenomenon can be described in a diffuse sense with a phase field approach utilizing a prescribed length scale parameter which takes the chipping off length into account. The surface energy linked to the crack propagation arising from the movement of the scratch-blade against brittle sample is evaluated using a functional expressed in terms of a scalar order parameter (phase field variable) and its gradients. This parameter is linked to the displacement problem through an energy degradation function which reflects the stiffness loss in the material volume as it suffers damage. Thus, the coupled system of partial differential equations for displacement as well as the scalar parameter obtained from total energy minimization regulate phase field evolution and impose the stress equilibrium. These equations are solved numerically using finite element models for both the displacement and the crack phase field. The model uses experimental data of scratch test conducted on few samples of shale. Through the analysis of several numerical examples reinforced with the experimental data we validate a computational model which can be used to predict fracture property of a material and the essential failure mechanism.