PSI - Issue 39

Andrea Zanichelli et al. / Procedia Structural Integrity 39 (2022) 632–637 Author name / Structural Integrity Procedia 00 (2019) 000–000

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2. Analytical methodology employed An analytical methodology, recently proposed to perform the fretting fatigue assessment of metallic structural components (Vantadori and Zanichelli, 2021; Zanichelli and Vantadori, 2021), is here employed to estimate the crack nucleation orientation for an Al 7050-T7451 aluminium alloy subjected to fretting tests. In particular, such a methodology is based on the joint application of: (i) the multiaxial fatigue criterion by Carpinteri and co-workers (Carpinteri et al., 2015; Vantadori et al., 2020a), originally proposed for metallic structures under multiaxial constant amplitude fatigue loading; and (ii) the critical direction method by Araújo et al. (2017). The main steps of the proposed methodology are hereafter summarized: • the first step consists in the definition of the input data, that is, both specimen and pads geometric sizes, material properties, and loading conditions; • the second step deals with the analytical determination of the stress state within the specimen; • next, the hot-spot is located on the contact surface; • then, the orientation of the critical plane is determined, by means of a procedure based on both the Carpinteri criterion and the critical direction method; • finally, the fretting fatigue assessment of the component is performed at the verification point located at a distance equal to twice the average grain size of the material from the hot-spot, according to the Carpinteri criterion. It is important to highlight that the hot-spot is a point located on the contact surface, representing the crack nucleation point on the material surface. According to the original formulation of the analytical methodology employed here, such a point is assumed to be the point where the maximum value of the maximum principal stress is attained within a fretting loading cycle. Note that, in case of both cylindrical and spherical contacts, such a stress condition is attained at the trailing edge of the contact. This is usually in agreement with the fact that the main cracks are expected to nucleate in correspondence to the stress concentration region, that is, the edge of the contact. 3. Experimental campaign analysed Experimental tests in partial slip regime carried out at the University of Brasilia by Almeida et al. (2020) are hereafter analysed. Flat dog-bone specimens and cylindrical pads were used in order to carry out the fretting tests. The specimens were characterised by a square cross section 13x13 mm, whereas the cylindrical pad radius was equal to 70 mm. Both the specimens and the pads were made of 7050-T7451 aluminum alloy: the elastic modulus E , the Poisson coefficient v and the ultimate tensile strength u σ were equal to 71.7 GPa, 0.33 and 524 MPa, respectively (Almeida et al., 2020). The fatigue properties listed in Table 1 have been found in the literature (Chen et al., 2012). Note that the fatigue limits are related to 2 . 10 6 loading cycles.

Table 1. Fatigue properties of the Al 7050-T7451 (Chen et al., 2012). Fatigue property Fully reversed normal stress fatigue limit, , 1 af σ − 301 MPa Fully reversed shear stress fatigue limit, , 1 af τ − 127 MPa S-N curve slope under fully reversed normal stress, m -0.05 S-N curve slope under fully reversed shear stress, m* -0.08

The material examined is characterized by an average size of the small grains equal to 8 microns and a friction coefficient µ equal to 0.54 (Rossino et al., 2009). Five different fretting loading configurations were tested. In particular, the constant bulk load (when present) was applied firstly, in order to avoid the off-set of the slip zones. Secondly, the constant normal load P was applied and, finally, the cyclic tangential load Q(t) was added with a frequency equal to 10 Hz. Three different values of tangential