PSI - Issue 39

Lucia Morales-Rivas et al. / Procedia Structural Integrity 39 (2022) 515–527 Author name / Structural Integrity Procedia 00 (2019) 000–000

516

2

bainitic steels [Caballero, et al.(2007)]. The strength originates from a matrix formed by nanoscale bainitic ferrite plates with a mean thickness of 20-40 nm, while a morphologically heterogeneous second phase, carbon-enriched retained austenite features, is in part responsible for the toughness, when it possesses a proper stability. Such properties make this microstructure a reliable candidate for manufacture of engineering components including in rail-wheel system, gears, bearings, and automotive industry [Rementeria, et al.(2015, Kumar and Singh(2021)]. Thus, prior to the large-scale implementation of the microstructure for industrial purposes, the in-service behaviour should be precisely studied in order to exploit the full potential of the material. Taking into account that the engineering materials usually are imperfect and contain impurities such as non-metallic inclusions and holes, acting as stress raisers [Kaynak, et al.(1996)], the profound investigation of the fatigue crack initiation and propagation phenomena is essential for the real estimation of the stress levels during the in-service life of the components. However, most of the studies to date centred around the behaviour of the fatigue long cracks [Bu and Stephens(1986, Kitagawa and Takahashi(1976, Williams(2001, Suresh and Ritchie(1984, El Haddad, et al.(1979)]. Therefore, much work should be devoted to the characteristics associated with the fatigue crack initiation and first stages of crack propagation, as they involve the longest part of the fatigue life time. Moreover, it is before crack initiation and within the short-crack regime when the local microstructure mainly dominates the damage mechanisms. There exist various criteria by which the short cracks can be defined. One is based on the definition provided by Zerbst, et al.(2018), suggesting that cracks of a length comparable to the microstructural features are called microstructurally short cracks; and cracks of a length comparable to the plastic zone ahead of the crack tip are classified as physically short cracks. A range of mechanisms have been suggested to describe the fatigue short crack behaviours, among all, the crack closure, chemical and electrochemical effects, and crack tip interaction with the microstructural features [Bu and Stephens(1986)]. The Kitagawa-Takahashi diagram [Kitagawa and Takahashi(1976)] is a widely-used tool for fracture mechanics based design and the fracture control concept [Williams(2001)]. It combines the fatigue endurance limit of the smooth materials, namely 0 (dashed straight black line 1 in Fig. 1) and the propagating/non-propagating fatigue threshold for long cracks (dashed straight red dashed line 2 in Fig. 1) into a single plot. Such a plot describes the nominal fatigue strength, ℎ , as a function of crack length, . The threshold defined by line 2 is function of Δ K th , the fatigue long crack growth threshold, as described by the linear elastic fracture mechanics (LEFM) theory, where Δ K stands for the stress intensity factor range. It was stated by Suresh and Ritchie(1984) that the Δ K approach for the long-crack propagation overestimates the defect tolerant lifetime calculations for the short-crack regime. In that sense, the Kitagawa-Takahashi diagram was modified by El Haddad, et al.(1979), proposing a smooth curve as a gradual transition from the endurance limit to the threshold for the long cracks. Thereby ℎ of both long and short cracks is calculated by the following equation (red curve in Fig. 1): ℎ = ΔK th � ( + 0 ) (1) where 0 (see diagram in Fig. 1) is the El Haddad-Smith-Topper’s parameter, characteristic of each material, defined as: 0 = π 1 ( ΔK th Δσ 0 ) 2 (2) It thus draws an area for non-propagating cracks of all lengths (grey region in Fig. 1). More recently, Atzori, et al.(2003, Atzori, et al.(2005) extended the Kitagawa-Takahashi diagram to a generalised diagram valid for the fatigue limit estimation of the components having cracks, defects, and notches under mode I stress distribution, and accordingly, provided the basis for the analysis of the real components by adding the shape factor, α , into the Eq. 1 to get the following expression: