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Previous studies have shown that both threshold stress intensity factors and fatigue crack growth rates are dependent on crack size. The average growth rates for very short cracks considerably exceed those given by conventional stress intensity-crack growth laws fitted to long crack data. Elastic and elastic plastic fracture mechanics solutions are modified to predict this behavior of short cracks by introducing an effective crack length l0 into the solutions for intensity factors and the J integral method of analysis. The threshold stress at a very short crack length approaches the fatigue limit of the material, and therefore the value of l0 can be obtained once the threshold stress intensity factor and the fatigue limit are known. The accuracy of the term l0 in predicting crack growth rates for short cracks is found to be independent of the applied strain level. It varies linearly with the grain size of the material and can be considered at the surface as a measure of the reduced flow resistance of surface grains due to their lack of constraint.

Elastic and elastic-plastic fracture mechanics solutions are modified to predict the behaviour of short cracks. An effective crack length, ~e0 is introduced into the solutions for both the linear elastic stress intensity factor and the J integral. Crack growth results for short cracks, in both elastic and plastic strain fields of unnotched specimens, when interpreted in terms of the modified solutions, show excellent agreement with elastic long crack data. The modified J integral solutions are extended to plastically strained notches, and the solutions obtained are tested in the correlation of data for growth of sort cracks near notches of varying severity with data for long crack under elastic loading. Although constant stress amplitude tests of these notches gave crack growth rate versus crack length curves which varied from monotonically increasing for blunt notches, to an initial decrease followed by an increase of sharp notches, all the data fell within the long crack data when correlated by the J integral solutions. Conversely, these solutions can be used to predict elastic and inelastic short crack growth curves for notches of various severities.

An elastic plastic fracture mechanics solution for short fatigue cracks in smooth and notched specimens is presented which admits plasticity by replacing the conventional stress term with a strain term and accounts for the propagation of very short cracks by the introduction of an effective crack length which is equal to the actual length increased by length l0, the length constant l0 is characteristic of the material and material condition and is calculated from the smooth specimen endurance limit and the long crack threshold stress intensity. Crack growth results for cracks in both elastic and plastic strain fields of notched specimens when interpreted in terms of this strain based intensity factor showed excellent agreement with elastic long crack data. This intensity factor when combined with a propagation model that includes all stages of crack growth also successfully predicted the total fatigue life of the smooth and notched specimens studied here. The predicted propagation life of elliptical and circular notched specimens is in all cases within 50 percent of the actual fatigue lives.

During earthquake ground motion, diagonal braces in braced frames are subject to a series of cyclic loadings, alternately tension and compression. The brace can buckle and deform plastically, dissipating energy with damage accumulating in the steel. Eventually a crack may form and the brace fractures. To optimize energy dissipation, the effects of brace and gusset plate dimensions (thickness and length of the gusset plate, size of the brace, length of the brace), and material properties, on brace behaviour, need to be understood. Ten concentric bracing members, designed according to the weak brace – strong gusset concept, were tested. The objective was to investigate the effects of displacement history, brace effective slenderness ratio, and brace width/thickness ratio, on the hysteresis behaviour of bracing members. Displacement history was found to affect energy dissipation and fracture life. The effects of increasing the gusset plate thickness on the energy dissipation and the fracture life is not the same as reducing the effective slenderness ratio of the bracing member resulted from reducing the length of the HSS. New fracture life and energy life equations are proposed.