The characterization of a plain concrete equivalent elastic fatigue crack resistance curve under various loading regimes

Concrete is a quasi-brittle material that exhibits a large residual bridging stress zone in the wake of a dominant crack tip. These stresses often influence the `size effect' observed in standard strength tests. In fatigue, they often cause a `load history' effect that alters the propagation rate by mitigating the stress intensities located at the crack tip. This mitigation often leads to the formation of two distinct crack rate regions known as the deceleration and acceleration region, respectively.;The cyclically induced residual bridging stresses also influence the `size effect' that is manifested through the logC in the Paris Law. In this study, it is shown that with the use of size dependent equivalent cyclic crack resistance curve, one may obtain a unique and size-independent set of Paris parameters.;A total of 48 three point bending single-edge notch specimens were tested. Two different sizes were studied under both quasi-static and fatigue loading. The fatigue tests were conducted using three different loading regimes: constant, variable, and random amplitude loading.;Under quasi-static loading, a new method to determine an equivalent cyclic crack resistance curve is proposed. It is a hybrid experimental technique driven by two governing beam equilibrium conditions and a `corrected' crack length criterion. The proposed technique back-calculates 4 bridging parameters that govern an assumed exponential stress distribution. A weight function was then used to determine the equivalent resistance curve as a function of crack extension and applied load. The behavior of the cyclic equivalent resistance curve was then parameterized. It is then concluded that the back-calculated bridging stress distribution could be used to determine the capacity of the structure with a moment equilibrium condition and a resistance that could be used for fatigue loading scenarios.;Under constant amplitude fatigue loading, it is shown that the equivalent cyclic crack resistance curve is directly related to the crack propagation rate and can be obtained if the following two conditions are satisfied: i) the crack resistance starts at zero, and ii) the post-peak slope is defined. It is then shown that if these conditions are satisfied, a unique 3 parameter equivalent resistance curve is obtainable using only experimental crack rate and stress intensity data.;Fatigue tests were then carried out under constant, variable, and random amplitude loading. The results suggest that the proposed functional form of the equivalent crack resistance curve under quasi-static loading is adequate in describing the equivalent fatigue resistance under the three fatigue loading regimes. In addition, it is also shown that if a size dependent fatigue resistance curve is inserted into the Paris law, logC and n become unique.;Finally, the fatigue damage under variable and random amplitude loading is simulated using the average values for the larger size specimens. The simulated fatigue fracture prediction is compared to the prediction using a linear damage rule (LDR). The error is shown in terms of number of cycles to failure, N, and depends on the loading sequence. The adequacy of the LDR is assessed under a random concrete pavement stress distribution and is shown to over-predict damage by nearly 30 % if the LDR is calibrated with constant amplitude loading tests.