Studies on the Modeling of Fatigue Crack Growth and Damage in Concrete : A Thermodynamic Approach

Abstract

Fatigue in concrete is a complex phenomenon involving formation of microcracks, their coalescence into major crack and simultaneous formation of the fracture process zone ahead of the crack tip. Complex phenomena are best dealt through an energy approach and hence it is reasonable to use the theory of thermodynamics. Fracture mechanics and damage mechanics are two theories that are based on physically sound principles and are used to describe failure processes in materials. The former deals with the study of macroscopic cracks, whereas the latter defines the state of microcracking. In this study, the concepts from these theories are utilized to improve our understanding and modeling of fatigue process in concrete. In this thesis, a closed form expression for the thermodynamic function entropy is proposed and examined for its size independency and its use as a material property to characterize failure of concrete under fatigue. In the thermodynamic formalism, dissipative phenomena are described by a dissipation potential or its dual, from which evolution laws for internal variables could be defined. In this work, closed form expressions for dual of dissipation potential are derived using concepts of dimensional analysis and self-similarity within the framework of fracture mechanics and damage mechanics. Consequently, a fatigue crack propagation law and a fatigue damage evolution law are proposed respectively. A method is proposed in this study to correlate fracture mechanics and damage mechanics theories by equating the potentials obtained in each theory. Through this equivalence, a crack could be transformed into an equivalent damage zone and vice versa. Also, damage state corresponding to a given crack in a member can be quantified in terms of a damage index. An analytical way of computing size independent S-N curves is proposed, using a nonlocal damage theory by including aggregate size and specimen size in the formulation. It is realized from this study that fracture mechanics and damage mechanics theories should be used in a unified manner in order to accurately model the process of fatigue in concrete. Furthermore, based on the models developed in this study, several damage indicators for fatigue of concrete are proposed. The advantages and limitations of each of these indices are presented such that, the relevant damage index could be used, based on available parameters. Additionally, deterministic sensitivity studies are carried out to determine the most important parameters influencing fatigue life of a concrete member.