Phase-Field Modeling of Chemically Assisted Crack Propagation

Abstract

We employ the phase-field technique to model the time-dependent crack propagation induced by combined mechanical loading and solid dissolution. Chemical dissolution causes the porosity of the solid to increase, thereby degrading its strength, stiffness, and fracture toughness. To accommodate the influence of porosity on the chemomechanical response of the solid, we employ a novel three-field solid displacement-phase-field variable-solid porosity finite element formulation with equal-order interpolation on all three independent variables. The model is validated against test results on a rock sample with a notch subjected to three-point bending, which shows degrading strength and stiffness of the sample with prior (Formula presented.) exposure. The model is also used to investigate the effect of degrading fracture toughness, evaluated from a degrading (Formula presented.) integral, on crack propagation in a rock with a blunted tip. The rate of chemical dissolution is determined from the transition state theory that gives rise to time-dependent processes such as creep and stress relaxation in fractured rocks, in addition to the viscous response inherent in the bulk material.