An Isotropic Self-Consistent Homogenization Scheme For Chemo-Mechanical Healing Driven By Pressure Solution In Halite

Abstract

Mechanical healing is the process by which a damaged material recovers mechanical stiffness and strength. Pressure solution is a very effective healing mechanism, common in crystalline media. Chemical reactions initiate at the location of microstructure defects, which would be very difficult to account for in a homogenization scheme that separates the solid and the pore phases, as is classically the case. Here, we propose a novel chemo-mechanical homogenization model in which the inclusion is not a grain, but rather, a space that contains a pore and discontinuities, where chemical processes take place. Mass and energy balance equations are rigorously established to predict the chemical eigenstrain of each inclusion, which, added to the elastic deformation, provides the microstrain of each inclusion. From there, Hill's inclusion-matrix interaction law is used to upscale strains and stresses at the scale of a Representative Elementary Volume (REV). The model was calibrated against experimental results published in the literature for salt rock. Subsequent sensitivity analyses show that in samples with same porosity but with inclusions that have different initial void sizes, inclusions with larger voids have a negligible healing rate and they are slowing down the overall healing rate of the REV. The highest healing rate is reached in samples with uniformly distributed void sizes. In addition, the healing rate increases with the initial porosity, but the final porosity change does not depend on the initial porosity of the sample. Principal stresses of higher magnitude are noted in the inclusions that are part of REVs of high initial porosity. In specimens with smaller inclusions (i.e., smaller grains), principal stresses are more widely distributed in magnitude and the healing rate is higher. The proposed homogenization method paves the way to many future developments for upscaling chemo-mechanical processes in heterogeneous media, and can be used to design self-healing materials.