Eigenstrain-Induced Stress in Elastic Cylinder

Abstract This article presents an analysis of the stress induced by a volumetric eigenstrain field in an elastic cylinder that is free to deform. This field is characterized by a transverse discontinuity at the midsection of the cylinder, which delimits an eigenstrain-free region from one where the eigenstrain increases linearly with distance from the midsection until it saturates. The study is motivated by recent observations on core damage caused by increased inelastic volume resulting from the progressive hydration of periclase (MgO) into brucite (MgOH) in core flooding experiments (Uno, M., Koyanagawa, K., Kasahara, H., Okamoto, A., and Tsuchiya, N., 2022. “Volatile-Consuming Reactions Fracture Rocks and Self-Accelerate Fluid Flow in the Lithosphere,” Proc. Natl. Acad. Sci., 119(3), p. e2110776118). These experiments have demonstrated that cracking of the core takes place only if the eigenstrain gradient behind the infiltration front is sufficiently large, a reflection of its dependence on the Damköhler number, defined as the ratio of hydraulic to hydration time scale. A finite element elastic analysis is conducted in terms of scaled parameters to identify the dependence of the location, magnitude, and orientation of the maximum tensile stress on the eigenstrain field, in particular its gradient at the discontinuity front. The analysis assumes a fixed front, in contrast to the dynamic infiltration front observed in the experiments. The asymptotic cases of small and large eigenstrain gradients are evaluated by examining the limiting cases of a ramp and a step variation of eigenstrain, respectively. The results reveal that a discontinuity in the eigenstrain or its gradient creates stress fields that could lead to tensile failure in the vicinity of the discontinuity front. These findings provide insights into the mechanisms of reaction-driven cracking in core flooding experiments on periclase samples.