Contents lists available at ScienceDirect International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue Crack path and threshold condition for small fatigue crack growth in annealed carbon steels under fully-reversed torsional loading M. Endo ⁎ , K. Yanase Department of Mechanical Engineering, Fukuoka University, Fukuoka, Japan Institute of Materials Science and Technology, Fukuoka University, Fukuoka, Japan ARTICLE INFO Keywords: Small shear-mode cracks Three-dimensional crack path Torsional fatigue limit Threshold condition Annealed carbon steels ABSTRACT Torsional fatigue tests at an R of -1 were carried out near the fatigue limit, using smooth, round-bar specimens of annealed carbon steels with banded ferrite/pearlite and isotropic ferrite/pearlite structures. Precise polishing of the specimens made it possible to observe the interior geometry of fatigue cracks. While the crack-plane was macroscopically of shear-mode, it was irregular microscopically, bearing many kinked and branched cracks. Based on calculation of the stress intensity factor for propagating and non-propagating cracks, it was concluded that the torsional fatigue limit was determined by the threshold condition for continuous Mode I propagation into the ferrite/pearlite structure. 1. Introduction Under benign environmental conditions, the S-N curve of common low- and medium-carbon steels subjected to cyclic stress of a constant amplitude exhibits a well-defined knee point at the number of cycles before 10 7 cycles. A fatigue limit can thus be defined at the stress level of the knee point. The safe-life design of most machine and structural components scheduled to experience a vast number of cycles in their design lifetimes is usually based on the infinite-life criterion, for which the applied stress levels are kept below the fatigue limit stress level by a margin of safety [1]. It is known that the fatigue limit of steels is not the limiting stress for crack initiation, but for the non-propagation of a small crack [2]. Accordingly, it is essential to study the mechanisms of fatigue limit as they relate to a small fatigue crack problem. In order to determine the validity of multiaxial fatigue criteria, as well as to design materials against fatigue failure involving multiaxial stress, the behavior of small, shear-mode (Modes II and III) fatigue cracks must be thoroughly investigated. Owing to its practical im- portance (e.g., for the prevention of rolling contact fatigue failure), shear-mode crack behavior has been studied extensively. However, most of the available studies have focused on large shear-mode cracks (e.g., [3–10]), whereas research on small, shear-mode or mixed-mode fatigue cracks is quite limited, particularly in relation to near-threshold behavior. While studying the growth behavior of small shear-mode cracks, it should be noted that crack-size dependency will appear in the threshold condition [2], known as the Kitagawa effect in the case of Mode I cracks [11]. With regard to Mode III cracks, Toyama et al. [12] and Beretta et al. [13] first reported the crack-size dependency of fa- tigue crack growth in medium-carbon steel and in gear steel, respec- tively. Another factor to be considered is that Mode I branching and kinking can be characteristic of the growth behavior of small, shear- mode fatigue cracks. Murakami et al. [14] conducted torsional fatigue tests on bearing steel, observing the propagation of a 100–200-μm-long, shear-mode crack in the axial direction, followed by branching at an approximate angle of ± 70.5° normal to the local maximum normal stress (σ θmax ). In addition, Murakami and Takahashi [15] performed torsional fatigue tests on annealed, medium-carbon steel specimens with shear-mode pre-cracks of 200–1000 μm in length. The tests re- vealed that the fatigue limit could be successfully predicted by the application of the area parameter model in combination with the σ θmax criterion that was proposed by Erdogan and Sih [16]. Beretta et al. [13] and Tarantino et al. [17,18] presented an interesting ex- perimental method for examining the near-threshold behavior of a small, Mode III fatigue crack, involving the simulation of the rolling contact, fatigue loading condition. Pure torsion tests, as well as in-phase and out-of-phase, combined, axial-torsional fatigue tests, were carried out employing this method, using SAE 3153 gear steel and bearing steel specimens with small notches ranging from 125 to 630 μm in area . They investigated the growth and threshold mechanisms of small, Mode III fatigue cracks, or small, combined-mode (Modes I + III) fatigue cracks, by monitoring various aspects including, inter alia, the small crack effect, the interference of crack-faces and the interaction of https://doi.org/10.1016/j.ijfatigue.2019.03.027 Received 31 December 2018; Received in revised form 6 March 2019; Accepted 17 March 2019 ⁎ Corresponding author. E-mail address: endo@fukuoka-u.ac.jp (M. Endo). International Journal of Fatigue 125 (2019) 112–121 Available online 19 March 2019 0142-1123/ © 2019 Elsevier Ltd. All rights reserved. T