Propagation, arrest, and reactivation of thermally driven fractures in an unconfined half-space using stability analysis

Abstract

Thermal fracturing is a common phenomenon occurring during significant cooling or heating in diverse engineering problems and natural processes. Multiple thermal fractures caused by cooling may initiate, propagate, arrest, and reactivate under thermal stresses and inter-fracture stress interactions, leading to typical hierarchical fracture patterns. The reactivation, further propagation, and permanent arrest of initially arrested fractures have not been accounted for in existing analytical modeling. In this study, all the processes of thermal fracturing in an unconfined half-space plane are investigated using a plane strain model. A dimensionless solution is developed by solving the coupled elasticity equation and fracture-propagation criterion and performing stability analysis, with fractures discretized by the displacement discontinuity method, all in terms of dimensionless variables. A new stability criterion stricter than the classic one (without reactivation) is introduced to account for fracture reactivation and permanent arrest. The dimensionless solution, applied to ceramic quenching as an example, is validated using a two-dimensional, finite element method-based fracture model that automatically considers all processes of thermal fracturing. The solution includes two generic profiles of dimensionless fracture spacing and length scaled by the material’s properties (i.e., toughness, Young’s modulus, Poisson ratio, and linear thermal expansion coefficient) and the surface-cooling condition. At late time, the profile of fracture length (l) can be simplified by a scaling law of l∝t with cooling time t. An algorithm is developed to produce the evolution of fracture pattern of interest, which is also validated by the numerical fracture model. Comparison of these solutions (with fracture reactivation) to those without reactivation indicates that fracture reactivation starts to affect fracture spacing and thus pattern after reaching a small fracture length and such an effect increases with fracture length and cooling time. These developed solutions are applicable to rapid and accurate prediction of evolution of fracture length, spacing, and pattern in thermal shock problems.