PSI - Issue 19

L.C. Araujo et al. / Procedia Structural Integrity 19 (2019) 19–26 L.C. Araújo et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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of several researchers over the last decades (Murakami (2002), Endo and Ishimoto (2006)). The importance of this type of study is due to the detrimental nature of these defects and inclusions, that can be observed in the recent failures in crankshafts of Brazilian thermal electric power-plants. The steel of the crankshafts contains non-metallic inclusions that can be observed in the region of initiation of cracks, as can be seen in the Fig. 1.

Fig. 1. Non-metallic inclusion in the region of initiation of the crack, (a) fracture surface and (b) inclusion detail. A parameter that has been widespread and that relates the fatigue strength of internally defective metallic materials or with small defects and inclusions is the √ , proposed by Murakami (2002). This method has been used to estimate the uniaxial fatigue limit, , successfully in many cases without the need of fatigue tests. And it was expanded by Yanase and Endo (2014) in order to also estimate the torsional fatigue limit, . Recently, researchers have been working on developing new models to predict the effect of these small defects on fatigue resistance of materials subjected to complex multiaxial loading conditions (Endo and Ishimoto (2006)). However, in this work, the effect of small defects in the fatigue strength of materials will be modeled without the use of any new criteria. The feasibility of combining classic models of multiaxial fatigue with the fatigue limit estimated from the √ parameter will be tested. For this, the models of Crossland (1956), Findley (1959) and Susmel and Lazzarin (2002) are used. 2. Multiaxial fatigue models The Crossland (1956) model which is a multiaxial fatigue strength model based on stress invariants evaluates the fatigue resistance from the history of the deviatoric stress tensor. This is expressed as follows: √2 + = (1) where is the amplitude of the history of the deviatoric stress tensor, is the maximum hydrostatic stress, and are parameters of the material and can be obtained from Eq. 1, with the fatigue limit obtained from simple uniaxial tests ( 0 ) and simple torsional tests ( 0 ), both with loading ratio R of -1, and are obtained as follows: = 0 0 − √3 (2) and = 0 (3) The critical plane models of Findley and Susmel and Lazzarin consider that for metallic materials the driving force