Issue 35

L. C. H. Ricardo et alii, Frattura ed Integrità Strutturale, 35 (2016) 456-471; DOI: 10.3221/IGF-ESIS.35.52 461 fictitious crack surfaces in the plastic zone ( a  x < a afict ), as in the original Dugdale model, and also over some distance in the crack wake (a open  x < a), where the plastic elongations of the strip L(x) exceed the fictitious crack opening displacements V(x) . The compressive stress applied in the crack wake to insure L(x)=V(x) are referred to as the contact stresses. The fatigue crack growth is simulated using the strip material as shown schematically in Fig. 2. Figure 2 : Schematic Small Scale Yield Model. Ricardo et al. [46] discuss the importance in the determination of materials properties like crack opening and closing stress intensity factor. The development of crack closure mechanisms, such plasticity, roughness, oxide, corrosion, and fretting product debris, and the use of the effective stress intensity factor range, has provided an engineering tool to predict small and large crack growth rate behavior under service loading conditions. The major links between fatigue and fracture mechanics were done by Christensen [47] and Elber [48]. The crack closure concept put crack propagation theories on a firm foundation and allowed the development of practical life prediction for variable and constant amplitude loading, by such as experienced by modern day commercial aircrafts. Numerical analysis using finite elements has played a major role in the stress analysis crack problems. Swedlow [49] 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 [16], or strip yield, using the plasticity induced approach in the models considering normally plane stress or strain effects. Schijve [50], 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. 3 shows the different K values.