Structural concrete is the most widely used material in the construction of bridges, pave-ments, runways, dams and other infrastructures which are subjected to uctuating loads during its service period. Concrete contains internal aws in the form of micro-cracks as an inherent property. When subjected to fatigue loading, distributed micro-cracks are formed at the sites of pre-existing aws, which subsequently, localize to form a major crack and propagates. The crack growth curve of a structural component when subjected to fatigue loading depicts a sigmoidal pattern. This curve is divided into three distinct regions namely sub-threshold crack propagation (short crack), stable crack propagation (long crack) and unstable crack propagation depending on the crack propagation rate. Most of the fatigue life is spent in the sub-critical stage (small crack) before the for-mation of long cracks. Hence, from the view of estimating the fatigue life, the crack initiation and early crack propagation (short crack stage) phase are the most important and correct concepts need to be developed. Hence, in this work, the behavior of propa-gation and non-propagationof short cracks in concrete when subjected to fatigue loading is addressed. Small non-propagating cracks are usually found at notch roots when the nominal stress range is below certain limits that depend on the notch sensitivity. Analysis is performed on geometrically similar three-point bend beams of three di erent sizes and subjected to fatigue loading in order to determine the important factors that a ect the notch sensitivity and to determine the minimum stress range required for the initiation and propagation of short cracks. A criterion for crack initiation and propagation is proposed based on linear elastic fracture mechanics. Using this criterion, the maximum length of non-propagating crack that can be formed from fatigue loading alone and the minimum stress range required to propagate a crack without arrest are computed. It is observed that the notch sensitivity increases with increase in beam size, decrease in notch-tip aspect ratio and increase in the fatigue limit of the material. Since the probability of formation of a non-propagating crack at a notch tip decreases with increase in notch sensitivity, and since it is desirable not to have a non-propagating crack in experimental investigations, it is essential to design a specimen with higher notch sensitivity. A crack spends a considerable amount of time in the short crack regime. The short cracks are found to propagate at higher rates than the long cracks at the same nominal stress intensity factor which is known as the short crack anomaly. It is important to consider this anomaly in the prediction of the residual life of damaged concrete structures. Hence, in the present work, an analytical model is developed using the principles of dimensional analysis and self-similarity in order to estimate the rate of short crack growth in concrete. The important parameters such as load range, threshold value of stress intensity factor range, modulus of elasticity, tensile strength, fracture energy, stress ratio, crack size and the maximum aggregate size are considered in the development of the short crack growth model. The model is calibrated and validated using the experimental results that are available in the literature. A probabilistic analysis is carried out to determine the sensitivity of each of the di erent parameters that has been considered on the crack growth rate using the coe cient of variation method. It is found that the crack length is the most sensitive parameter to short crack growth rate followed by the load range. A term called `characteristic fatigue life of short crack' is de ned as the number of fatigue cycles that can be applied such that not more than ve percent of the short cracks is expected to proceed to the long crack regime. Furthermore, the fatigue life of a crack spent in the short crack regime is determined through a reliability based study using the Monte Carlo technique. It is found that the smaller sized specimens have larger fatigue life in the short crack regime than the larger specimens.

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.

The aim of this diploma thesis is to estimate the residual fatigue lifetime of the model train axle. Primarily, the thesis is focused on determination of the stress intesity factor, the main variable for estimation of the residual fatigue lifetime. At first, the theoretical approaches of estimation of the residual fatigue lifetime are listed and then the residual fatigue lifetime of the model train axle is estimated.