Issue 48

C. Santus, Frattura ed Integrità Strutturale, 48 (2019) 442-450; DOI: 10.3221/IGF-ESIS.48.42 443 There are several methodologies for fretting fatigue tests in the literature, as introduced by Hills and Nowell [2] and more recently discussed by De Pauw et al. [3]. Full-scale testing is a viable solution, for example as proposed by Azevedo et al. [4] for overhead conductor application, and by Santus [5] for oil drilling tubular connections. Alternatively, the floating fretting bridge configuration has been implemented, such as by Swalla and Neu [6], Mutoh and Xu [7] and Liu and Hill [8], where the specimen resembles a (plain) tensile coupon and a proving ring is applied to generate the lateral load and then control the contact pressure. However, with this solution, the two pad contacts of the bridge can experience different levels of slippage. This issue can be eliminated with the fixed solution, in which one side of the bridge is attached through an element of specific stiffness to the relatively rigid frame of the testing machine. This solution is quite common in laboratories, indeed there are several examples of this test rig setup, such as Szolwinski and Farris [9], Muñoz et al. [10], Araújo and Castro [11], Baietto et al. [12], De Pauw et al. [13], Hojjati-Talemi et al. [14], Vázquez et al. [15]. Other test setups have also been proposed, resembling the component under the actual load, still loaded with a laboratory testing machine, such as by Golden et al. [16,17] for blade dovetail connections. This approach was also followed for the shrink- fitted shaft-hub connection by Juuma [18,19], Alfredsson [20], Lanoue et al. [21], and finally by Bertini and Santus, and Bertini et al. [22,23]. There is experimental evidence of fretting crack paths in the literature, such as by Szolwinski and Farris [9], Swalla and Neu [6], Muñoz et al. [10], and Proudhon et al. [24]. The common evidence is that the crack orientation is almost always below the contact or, in other words, the crack direction is inward , however, with different angles. Around 20 years ago, Lamacq and Dubourg began investigating the early stages of fretting cracks [25,26]. In their papers, two types of crack initiations were defined: type I and type II, and this distinction was in relation to the crack initial orientation, which in turn suggested the kind of load causing the crack. Though both types of crack are inward, the type I crack is defined as initiating at a very shallow angle with respect to the surface, while type II cracks are observed as almost perpendicular to the contact profile. Therefore, the type II cracks are promoted by the cyclic tensile load, while the former can be assumed as being generated by the cyclic shear load. Proudhon et al. [24] provide a three-dimensional experimental visualization using X-ray micro-tomography, showing a clear example of a type II crack. In fact, despite some unavoidable material source of irregularity, the path was almost perpendicular to the surface with a small orientation inward below the contact. Type I cracks tend to initiate inside the contact slip regions, while type II cracks can be observed at the edge of the contact, or even slightly outside the contact where the tensile normal stress amplitude is still high. However, for both crack types, the orientation gradually turns perpendicular to the fretting surface after kinking or even some branching. In fact, the crack propagation is predominantly mode I when it is far from the stress concentration and the multiaxiality stress state induced by the contact. The initial propagation path of the fretting cracks has recently been modelled by several researchers, since it is key to a deeper understanding of fretting mechanics. Giner et al. [27] proposed the use of the Extended Finite Element Method (X-FEM) to introduce crack at the contact edge, without needing to re-mesh the model. The Erdogan and Sih criterion, or Maximum Tangential Stress (MTS), was followed by them and the modelled crack orientation resulted to grow outward the contact below the fretting surface, especially for low bulk stress values, thus not in agreement with the general trend of fretting fatigue cracks. Giner et al. [28] then assumed that the observed cracks were type II (i.e. tensile, in line with the Lamacq and Dubourg’s definition) as evident from their experiment, and they correctly predicted the initial orientation by selecting the angle for which the normal stress amplitude was maximum. After this initiation analysis, the X-FEM technique was again implemented, and the criterion of minimum shear stress range was applied to determine the angle for each step increment of the crack. The direction with the maximum normal stress amplitude was selected, from the two orthogonal directions for which the shear stress amplitude was minimum (close to zero). The predicted path was almost perpendicular to the surface, slightly inward with respect to the contact, and thus in good agreement with the experiments. Majzoobi and Abbasi [29,30] proposed setting the initial orientation in line with the experimental evidence, without proposing a criterion for the initial orientation, and then followed the Erdogan and Sih (MTS) criterion for the further propagation. The path obtained was inward with an angle of approx. 45°, though significantly dependent on the load phase, and a more inclined (inward) angle was found for the out-of-phase loading, thus obtaining a clear type I crack. Navarro et al. [31] tested the Fatemi-Socie (FS) and the Smith-Watson-Topper (SWT) critical plane approaches by averaging the stresses along an initial straight path. They found that the SWT parameter better correlated the angle in the very initial stage (20 μm), in agreement with the type II (tensile) crack, while FS predicted either an outward or inward crack, with a 90° angular distance. However, even the inward path was not in agreement with the experimental evidence as the predicted orientation was at a too largely inclined angle. Nevertheless, in the same series of tests, another specimen had an initial path inward which was reasonably classified as type I (shear). Araújo et al. [32] compared the SWT, FS and also the Modified Wöhler Curve Method (MWCM) criteria and considered different methods for averaging the rapidly changing stress distributions below the fretting surface, resembling the approach by Vantadori et al. [33], and Fouvry et al.