PSI - Issue 51

Michael Horvath et al. / Procedia Structural Integrity 51 (2023) 95–101 M. Horvath et al. / Structural Integrity Procedia 00 (2022) 000–000

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1. Introduction As modern production technologies focus on a near net-shape design of complexly formed components, cast steel alloys are widely utilized due to their high load bearing capabilities under demanding service conditions (Gao 2008, Bolouri et al. 2013, Jung et al. 2017). These complex geometries often provoke the formation of so-called hot spots, leading to increased occurrence of inherent shrinkage imperfections. Such porosity defects severely affect the fatigue strength of the designed component (Campbell 2011, Stefanescu 2017, Sigl et al. 2003, Schuscha et al. 2019a, Horvath et al. 2022). Due to the arbitrary spatial shape of local defect structures and its effect on the acting local multiaxial stress state, the application of local fatigue assessment concepts becomes evident in order to ensure a safe-life design. The Theory of Critical Distances (TCD) depicts a widely utilized concept to assess the fatigue strength of notched components (Taylor 1999, Taylor 2005, Chiandussi and Rossetto 2005). Therein, the linear-elastic stress at a certain distance from the stress concentrator (in terms of the Point Method), or the stress averaged over a specific length (Line Method), or area (Area Method), equals the fatigue strength of the base material, if the component is at threshold condition in terms of fatigue crack initiation. Regarding the Point Method, the critical distance equals half of the material intrinsic length a 0 , also known as the El-Haddad length, which is defined by Equation (1). � � � � ∙ � �� ����� �� � � � (1) As the material intrinsic length a 0 depends on the base material fatigue strength  0 and the long-crack growth threshold stress intensity factor range  K th,lc , fatigue strength predictions based on the TCD are strictly valid only for the high-cycle fatigue regime. However, Susmel and Taylor (Susmel and Taylor 2007) presented an extension of the TCD to assess the fatigue behaviour of notched components in the medium-cycle fatigue regime, by introducing the critical distance L M as a function of the number of cycles to failure N f . Herein L M ( N f ) follows a power law, which is given by Equation (2). � �� ∙� � � (2) The therein incorporated material parameters A and B depend on the applied load ratio R and are the result of a specimen-based calibration procedure, which utilizes S-N curves of plain and notched specimens (Susmel and Taylor 2007). The strain energy density concept depicts another local fatigue assessment concept which denotes that material strength is controlled by the strain energy density (SED) averaged over the so-called control volume, a finite volume in the vicinity of a stress concentrator. The methodology constitutes a unifying tool for fatigue assessment of arbitrary geometrical features, where analytical formulations for the evaluation of the elastic strain energy density for sharp and blunt notched specimens are reported in literature (Lazzarin and Berto 2005, Gómez et al. 2007). The size of the control volume is described by the material dependent control radius R c , which therefore affects the aggregated amount of strain energy considered for fatigue assessment. The value of R c correlates with the material intrinsic length as given by Equation (3) (Yosibash et al. 2004) for plain strain condition. � � ������������� ∙ � �� ����� �� � � � � ����������� � ∙ � (3)