Energy-based equivalence between damage and fracture in concrete under fatigue

Damage in concrete members, occur in a distributed manner due to the formation and coalescence of micro-cracks, and this can easily be described through a local damage approach. During subsequent loading cycles, this distributed zone of micro-cracks get transformed into a major crack, introducing a discrete discontinuity in the member. At this stage, concepts of fracture mechanics could be used to describe the behavior of the structural member. In this work, an approach is developed to correlate fracture and damage mechanics through energy equivalence concepts and to predict the damage scenario in concrete under fatigue loading. The objective is to smoothly move from fracture mechanics theory to damage mechanics theory or vice versa in order to characterize damage. The analytical methods developed here have been exemplified with some already available data in the literature. The strength and stiffness reduction due to progressive cracking or increase in damage distribution, has been characterized using the available indices such as the strength reduction and stiffness reduction factors. It is seen through numerical examples, that the strength and stiffness drop indices using fracture and damage mechanics theory agree well with each other. Hence, it is concluded, that through the energy approach a discrete crack may be modeled as an equivalent damage zone, wherein both correspond to the same energy loss. Finally, it is shown that by knowing the critical damage zone dimension, the critical fracture property such as the fracture energy can be obtained.