PSI - Issue 57

Lucas Carneiro Araujo et al. / Procedia Structural Integrity 57 (2024) 144–151 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction The investigation of the impact of small defects on the fatigue strength of metallic materials has garnered attention from numerous researchers in recent decades (Murakami, 2019; Murakami & Endo, 1986, 1994; Murakami & Nemat-Nasser, 1983). Notably, the √ parameter proposed by Murakami and Endo (Murakami & Endo, 1986), along with its adaptations and variations (Beretta & Murakami, 1998; Murakami, 2012, 2019; Murakami & Endo, 1994), has emerged as a prominent model addressing this issue. Nevertheless, the models based on the √ parameter have predominantly been applied in the context of uniaxial fatigue. In recent years, there has been a surge in studies aimed at exploring the fatigue behavior of materials with small defects under more complex loading conditions (Araújo et al., 2019; Castro et al., 2019; Endo & Ishimoto, 2006; ENDO & ISHIMOTO, 2007; Endo & Yanase, 2014; Groza et al., 2018; Karolczuk et al., 2008; Machado et al., 2020; Nadot & Billaudeau, 2006; Vantadori et al., 2022; Yanase & Endo, 2014a). This research is crucial due to the prevalence of multiaxial stress states in practical engineering components, arising from either geometric considerations or combined loading scenarios. This study introduces a novel multiaxial fatigue model proposed by the authors, which can be considered as a modification of Smith, Watson, and Topper (SWT) Criterion (Dowling, 2013; Smith et al., 1970). This new model establishes a connection between the fatigue limit of the material, determined by the √ parameter, and values associated with the principal stresses induced by the applied loads. These values include their amplitude and the maximum value observed during the loading cycle. Computing these parameters is a non-trivial task, particularly under non-proportional multiaxial loading conditions, where both the magnitude and direction of the principal stresses vary dynamically. Consequently, calculating the amplitude of the principal stresses presented a significant challenge that, to the best of the authors' knowledge, has not yet been addressed by previous researchers. To evaluate the validity of the proposed model, the authors considered a combination of previously generated and new experimental data of the high strength steel AISI 4140 (DIN 42CrMo4), which is used in the manufacture of various mechanical components. The test data covered a range of loading conditions, such as traction-compression, torsion, and combined loadings with different ratio between shear and normal stresses amplitudes, in-phase and 90° out of phase. In addition, specimens were tested in two conditions: (i) smooth specimens, considering the effect of non-metallic inclusions, and (ii) specimens where a superficial micro hole with a straight bottom was machined with 550 μ m in diameter and depth. 2. New model proposal In previous studies on combined loads, it has been observed that small defects can exhibit short, non-propagating cracks in the fatigue limit condition (Endo, 1999; Endo & Ishimoto, 2006; Endo & McEvily, 2011). These cracks have been found to generally propagate in a direction perpendicular to the maximum principal stress. As a result, several models have been proposed to establish a relationship between the fatigue limit and the values associated with the principal stresses (Endo, 1999; Endo & Ishimoto, 2006; Yanase & Endo, 2014b). In contrast to existing models, which utilize instantaneous values of the principal stresses to calculate fatigue damage, the newly proposed model considers the amplitude value associated with the principal stresses as one of its governing variables. Essentially, this model can be regarded as a modification of the well-known Smith, Watson, and Topper (SWT) Parameter (Dowling, 2013; Smith et al., 1970), and it can be expressed as follows in Eq. 1. SWT mod =√ , , (1) Where SWT mod represents the Modified Smith, Watson, and Topper parameter, , denotes the maximum value of the greatest principal stress observed at any given time during the loading cycle, and , represents the amplitude of the principal stresses. It is important to note that the calculation of the principal stress amplitude is a complex process, which will be explained in greater detail later on. This relationship offers the advantage of not relying on any material constants. Finally, a mechanical component containing a small defect and subjected to a specific loading history will be deemed safe if the inequality of Eq. 2 is satisfied.