Issue 36

L. C. H. Ricardo et alii, Frattura ed Integrità Strutturale, 36 (2016) 201-215; DOI: 10.3221/IGF-ESIS.36.20 206 allowed the development of practical life prediction for variable and constant amplitude loading, by such as experienced by modern day commercial aircrafts. Figure 4 : Schematic Small Scale Yield Model. Numerical analysis using finite elements has played a major role in the stress analysis crack problems. Swedlow [40] was one of the first to use finite element method to study the elastic-plastic stress field around a crack. The application of linear elastic fracture mechanics, i.e. the stress intensity factor range,  K , to the “small or short” crack growth have been studied for long time to explain the effects of nonlinear crack tip parameters. The key issue for these nonlinear crack tip parameters is crack closure. Analytical models were developed to predict crack growth and crack closure processes like Dugdale [12], or strip yield, using the plasticity induced approach in the models considering normally plane stress or strain effects. Schijve [41], discussing the relation between short and long cracks presented also the significance of crack closure and growth on fatigue cracks under services load histories. The ultimate goal of prediction models is to arrive at quantitative results of fatigue crack growth in terms of millimeters per year or some other service period. Such predictions are required for safety and economy reasons, for example, for aircraft and automotive parts. Sometimes the service load time history (variable amplitude loading) is much similar to constant amplitude loading, including mean load effects. In both cases quantitative knowledge of crack opening stress level S op is essential for crack growth predictions, because  K eff is supposed to be the appropriate field parameter for correlating crack growth rates under different cyclic loading conditions. The correlation of crack growth data starts from the similitude approach, based on the  K eff , which predicts that same  K eff cycles will produce the same crack growth increments. The application of  K eff to variable amplitude loading require prediction of the variation of S op , during variable amplitude load history, which for the more advanced prediction models implies a cycle by cycle prediction. The Fig. 5 shows the different K values. The application of  K eff is considerably complicated by two problems: (1) small cracks and (2) threshold  K values (  K th ). Small cracks can be significant because in many cases a relatively large part of the fatigue life is spent in the small crack length regime. The threshold problem is particularly relevant for fatigue under variable amplitude spectrum, if the spectrum includes many “small” cycles, those ones with small stress/load amplitude. It is important to know whether the small cycles do exceed a threshold  K value, and to which extension it will occur. The application of similitude concept in structures can help so much, but the results correlation is not satisfactory and the arguments normally are:  The similarity can be violated because the crack growth mechanism is no longer similar.  The crack can be too small for adopting K as a unique field parameter.