Size effect in fatigue fracture of concrete

Crack growth caused by load repetitions in geometrically similar notched concrete specimens of various sizes is measured by means of the compliance method. It is found that the Paris law, which states that the crack length increment per cycle is a power function of the stress intensity factor amplitude, is valid only for one specimen size (the law parameters being adjusted for that size) or asymptotically, for very large specimens. To obtain a general law, the Paris law is combined with the size-effect law for fracture under monotonic loading, proposed previously by Bazant. This leads to a size-adjusted Paris law, which gives the crack length increment per cycle as a power function of the amplitude of a size-adjusted stress intensity factor. The size adjustment is based on the brittleness number of the structure, representing the ratio of the structure size d to the transistional size d₀, which separates the responses governed by nominal stress and stress intensity factor. Experiments show that d₀ for cyclic loading is much larger than d₀ for monotonic loading, which means that the brittleness number for cyclic loading is much less than that for monotonic loading. The crack growth is alternatively also characterized in terms of the nominal stress amplitude.