PSI - Issue 39

A.L. Pinto et al. / Procedia Structural Integrity 39 (2022) 409–418 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Strong optimum designing requirements by the modern industry in the recent decades led engineers and scientists to investigate fretting crack nucleation mechanisms closely, which resulted in the development of several methods aiming to predict early crack orientation (Cheng et al., 1994; Szolwinski and Farris, 1996; Lamacq et al., 1997; Neu et al., 2000; Ruiz and Chen, 1986). Recently, Cardoso et al. (2016) and Araújo et al. (2017) proposed The Critical Direction Method (CDM) in an attempt to predict crack initiation orientation in fretting problems. Since then, this method has become widespread because of its good accuracy and easy implementation. Firstly, the CDM was confronted with fretting tests conducted on steel alloys (Fouvry et al., 2008; Baietto et al., 2013). Vantadori et al. (2018) have considered the CDM for predicting the crack initiation angle of fretting tests conducted on an Al 7050 T7451 alloy. In this case, Carpinteri et al. (2011) multiaxial fatigue model was utilized in the analyses. Almeida et al. (2020) carried out fretting tests on an Al 7050-T7451 alloy aiming to investigate the influence of the following parameters on the crack initiation direction: tangential load amplitude, mean bulk stress and pad radius. This work investigates two methods for predicting crack initiation direction in fretting problems. In one of them, the CDM is combined with the standard strain-based version the SWT parameter. In the second, early crack propagation is simulated through a Linear Elastic Fracture Mechanics (LEFM) approach associated with the SWT parameter. Results from the CDM and the LEFM approach assessed in this work are confronted with experimental data available in the literature (Almeida et al., 2020). Details concerning the theories considered in this work are presented in Section 2. Section 3 describes the different methods investigated in this paper for predicting crack initiation direction. It also details the numerical FE model considered in the analyses. Section 4 presents the experimental data assessed, whereas, Section 5 and 6 provide, respectively, results of the analyses and conclusions. 2. Theoretical background 2.1. Multiaxial fatigue parameter In this work, the SWT parameter is considered to both estimate crack initiation lifetime and crack initiation direction, either considering the CDM or the LEFM crack propagation approach. This critical plane criterion was proposed by (Smith et al., 1970), and assumes that the crack propagates perpendicular to the direction of maximum principal stress and strain (Mode I of crack propagation). The SWT parameter can be defined as: = , , ., (1) where , max and , are, respectively, the maximum normal stress and the normal strain amplitude on the critical plane, which is defined as the one that maximizes the normal strain amplitude. 2.2. Theory of critical distance Generally, The Theory of Critical Distance (TCD) is used to deal with stress gradients present in geometrical discontinuities such as notches, holes and cracks (Taylor and Wang, 2000). However, due to the similarity between the stress gradients found in notches and in contact problems, many researches have been applying the TCD to tackle fretting fatigue problems (Araújo et al., 2007; Araújo et al., 2008; Fouvry et al., 2014). The TCD proposes the use of an effective stress, , that can appropriately characterize fatigue damage near the stress raiser. The evaluation of this effective stress can be carried out considering a volume, an area, a line or even a point. The latter was used in this work due to its simplicity. In this setting, stresses and strains have to be evaluated at a point /2 distant from the stress raiser for further application in multiaxial fatigue parameters. For high cycle fatigue (HCF), the critical distance, , assumes the following form: = 1 � ℎ −1 � 2 , (2)