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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4. Results and discussion The crack orientations of the experimental tests described in Section 3 are here estimated by employing the methodology described in Section 2, for two different crack nucleation locations on the material surface: point A, located at the trailing edge of the contact, and point B, located in the center of the slip zone (that is, within the contact surface at a distance equal to ( ) 0.5 a c ⋅ − from the contact trailing edge). The results obtained are related to a length equal to twice the averaged grain size of the material, that is, 16 microns. The estimated values of crack path orientations related to point A and point B ( , th A θ and , th B θ , respectively) are listed in Table 3, along with the average experimental values, for each loading configuration. Moreover, the crack path orientations estimated by means of the analytical methodology previously described are compared to the experimental observations in Figure 1, for each loading configuration. Table 3. Crack path orientations for each loading configuration: mean value of the experimental observations, exp θ , and theoretical estimations related to both point A and point B ( , th A θ and , th B θ , respectively). Loading configuration No. exp θ [°] , th A θ [°] , th B θ [°] 1 24.4 5 24 2 31.2 5 25 3 34.8 4 27 4 35.9 5 25 5 44.2 5 25 It can be noted that all the estimations are inward the contact region, in accordance to the experimental observations. Moreover, as the crack nucleation location moves inward the contact region (that is, from point A to point B), the estimated values of crack orientation increase, with values between 4° and 5° at point A, and between 24° and 27° at point B. Furthermore, the accuracy of the estimations may be quantified by employing the root mean square error method (Vantadori et al., 2018). In particular, the value of the root mean square error, RMS T , can be computed for k experimental tests as follows: The values of RMS T obtained for the crack orientation estimations related to point A and point B are equal to 7.08 and 1.40, respectively. As a matter of fact, RMS T = 1 corresponds to a perfect estimation of the experimental results. Therefore, a crack nucleation location within the contact zone seems to better estimate the crack orientation. 5. Conclusions In the present paper, the crack path orientation of a 7050-T7451 aluminium alloy subjected to constant amplitude fretting fatigue loading has been investigated by means of an analytical methodology based on the joint application of the multiaxial fatigue criterion proposed by Carpinteri et al. and the critical direction method proposed by Araujo et al. An experimental campaign available in the literature has been analysed by means of the above methodology in order to determine the fretting fatigue crack path orientation. More precisely, the crack orientation has been determined by assuming two different locations of crack nucleation on the material surface, that is: the contact trailing edge and the center of the slip zone. The crack orientations estimated by considering the contact trailing edge as the crack nucleation point were inward the contact region, in accordance to the experimental observations, but in general with lower values measured from ( ) 2 1 10 k th exp θ θ i i Log k RMS T = = ∑ (1)