PSI - Issue 66

Andrea Zanichelli et al. / Procedia Structural Integrity 66 (2024) 471–477 Author name / Structural Integrity Procedia 00 (2025) 000–000

473

3

2. Analytical methodology for fretting fatigue assessment An analytical methodology, recently proposed by the present authors (Vantadori and Zanichelli (2021); Zanichelli et al. (2022)), is here employed to perform the fretting fatigue assessment of metallic structural components. In particular, such a methodology allows us to evaluate both the crack initiation direction and the fatigue life of metallic structures under fretting fatigue elastic partial slip loading conditions in high-cycle fatigue. The main steps of the proposed methodology are hereafter summarized. The first step consists in the definition of the input data, that is, the geometric sizes, the material properties, and the loading conditions. Then, the stress state in the vicinity of the contact zone is computed within the specimen, either numerically or analytically for specific configurations, that is, the case of cylindrical or spherical pads. Note that, in the present research work, the analytical solution related to cylinder-to-flat contact situations (Hertz (1896)) is employed due to the configuration of the experimental fretting setup described in Section 3. Once the stress field is evaluated, the hot-spot, H , is located on the contact surface. In particular, H is assumed to be the point where the maximum value of the average maximum principal stress is attained. In the case of cylindrical or spherical hertzian contacts (that is the case of the configuration examined in the present paper), such a point is found to be at the contact trailing edge. Subsequently, the critical plane orientation is determined by exploiting the Critical Direction Method (Araújo et al., 2017) in conjunction with the Carpinteri criterion (Carpinteri et al., 2015), and by considering a length related to the average material grain size, d . More details related to the procedure to define the critical plane orientation can be found in Vantadori et al. (2022b). The orientation, crit  , maximizing a proper fatigue parameter (note that the fatigue parameter is the equivalent normal stress amplitude, N eq,a , defined according to the Carpinteri criterion), is assumed as the critical plane, and it represents the crack nucleation orientation. Finally, the number of loading cycles to failure, N f,cal , is obtained according to the Carpinteri criterion (Carpinteri et al. (2015); Carpinteri et al. (2018)), by means of an iterative procedure. It can be highlighted that the values of the stress components used for the fatigue life computation are obtained by considering the critical plane orientation being fixed and equal to crit  . Moreover, the point, P crit , where to perform the fretting fatigue assessment, is assumed to be located at the end of the segment, with length equal to 2 d , and direction defined by the angle crit  starting from the point H (Hot-spot) on the material surface assumed to be the crack nucleation location. 3. Experimental campaign analysed In this Section, the experimental campaign carried out by Araújo et al. (2004) is here described. In particular, experimental tests in partial slip regime were carried out on flat dog-bone specimens made of Al-4Cu. Both mechanical and fatigue properties of the material are listed in Table 1. Moreover, from a microstructural point of view, grains elongated in the longitudinal direction of the specimen were observed, with an average material grain size, d , equal to 50  m, measured in the direction perpendicular to the specimen surface.

Table 1. Mechanical and fatigue properties of the Al-4Cu alloy considered. Material property Elastic modulus, E

74 GPa

Poisson’s coefficient, v

0.33

Ultimate tensile strength, u  Coefficient of friction, 

465 MPa

0.75

, 1 af  

Fully reversed normal stress fatigue limit (at 2 . 10 6 cycles), Fully reversed shear stress fatigue limit (at 2 . 10 6 cycles), S-N curve slope under fully reversed normal stress, m S-N curve slope under fully reversed shear stress, m*

191 MPa 110 MPa

, 1 af  

-0.11 -0.11