Studies On Fatigue Crack Propagation In Cementitious Materials : A Dimensional Analysis Approach
Crack propagation in structures when subjected to fatigue loading, follows three different phases namely - short crack growth, stable crack growth and unstable crack growth. Accurate fatigue life prediction demands the consideration of every crack propagation phase rather than only the stable crack growth stage. Further, the use of existing crack growth laws in structures with small cracks under-predicts the growth rate compared to experimentally observed ones, thereby leading to an unsafe design and keeping the structure in a potentially dangerous state. In the present work, an attempt is made to establish fatigue crack propagation laws for plain concrete, reinforced concrete and concrete-concrete jointed interfaces from first principles using the concepts of dimensional analysis and self-similarity. Different crack growth laws are proposed to understand the behavior in each of the three regimes of the fatigue crack growth curve. Important crack growth characterizing material and geometrical parameters for each zone are included in the proposed analytical models. In real life applications to structures, the amplitude of cyclic loading rarely remains constant and is subjected to a wide spectrum of load amplitudes. Furthermore, the crack growth behavior changes in the presence of high amplitude load spikes within a constant amplitude history and this is incorporated in the model formulation. Using scaling laws, an improved understanding of the scaling behavior on different parameters is achieved. The models describing different regimes of crack propagation are finally unified to obtain the entire crack growth curve and compute the total fatigue life. In addition, crack growth analysis is performed for a reinforced concrete member by modifying the model derived for plain concrete in the Paris regime. Energy dissipation occurring due to shake-down phenomenon in steel reinforcement is addressed. The bond-slip mechanism which is of serious concern in reinforced concrete members is included in the study and a method is proposed for the prediction of residual moment carrying capacity as a function of relative crack depth. The application of the proposed analytical model in the computation of fatigue crack growth is demonstrated on three practical problems – beam in flexure, concrete arch bridge and a patch repaired beam. Through a sensitivity study, the influence of different parameters on the crack growth behavior is highlighted.
- Civil Engineering (CiE) 
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