Fracture-mechanics-based analytical and finite element evaluation of the virtual crack closure integral for filled-crack

This paper presents a fracture-mechanics-based analytical framework for evaluating the virtual crack closure integral (VCCI) of structures containing filled cracks. Building on the formulation of Fowkes et al., closed-form expressions for the stress and displacement fields in the vicinity of a filled crack are derived by explicitly accounting for the presence of a wedge-shaped filling material. Using these fields, the virtual crack closure integral is analytically evaluated for the filled-crack problem. Finite element simulations are also conducted using ANSYS to evaluate the J-integral at the crack tip, which is equivalent to the VCCI. Comparisons between the analytical and numerical results for different filling material properties and crack depths show excellent agreement, validating the proposed formulation. The influence of the wedge angle on VCCI is examined. The applicability of the stress intensity factor to filled cracks is also discussed, and its limitations and relationship to energy-based fracture parameters are clarified. In addition, the effects of Poisson’s ratio of both the filling material and the surrounding matrix are investigated. The proposed model provides an efficient tool for evaluating fracture parameters in filled-crack systems and can be readily incorporated into simplified static and dynamic structural analyses, thereby supporting the development of more reliable and resilient structures and contributing to infrastructure sustainability.