Issue 33

J.A Araujo et al, Frattura ed Integrità Strutturale, 33 (2015) 427-433; DOI: 10.3221/IGF-ESIS.33.47 428 varying from 2 up to 10 compared to plain fatigue [3]. The most severe reduction of life is observed in partial slip conditions [4]. Indeed gross sliding can fastly remove small nucleated cracks before they can further propagate. Under fretting conditions, the loads involved generate a time varying non-proportional multiaxial stress field under the contact [5]. There is usually a high stress concentration on the contact interface but it is limited to a small region and hence decays fastly as one moves from the surface to the interior of the component [6]. In this setting, the use of non- local approaches, initially developed to estimate the fatigue endurance of notched specimens, have been extended to the fretting fatigue problem [7]–[9]. Araújo et al. [8] used the Theory of Critical Distances (TCD) in conjunction with the Modified Whöler Curve Method (MWCM) and showed that it was capable of estimating the results of fretting fatigue experiments showing a contact size effect with a good degree of accuracy (±20% error band). It is worthy noticing that notched components and mechanical assemblies under time varying loads present quite similar characteristics. In both configurations there are usually severe stress gradients and the state of stress becomes complex (multiaxial) as the analysis moves inside the material. The general aim of this work is to investigate whether it is possible to design fretting and notch fatigue configurations, which are nominally identical in terms of damage measured by a multiaxial fatigue index. Further, these designs must be such that the specimens can be machined within a good level of accuracy and with tight tolerances in both configurations (notch and fretting), turning the future experimental campaign reproducible and reliable. The advantage of proving that such experimental campaign can be generated is that it consists in a way to somehow isolate the role of the surface fretting wear in diminishing the material fatigue resistance of mechanical assemblies under partial slip. As both fatigue problems are equivalent in terms of fatigue loading over a material process zone, their resistance should be essentially similar, unless the influence of the small surface damage caused by the fretting wear, and which does not exist in the notch configuration, is greater than the authors expect it will have. Another quite important aspect that such experimental campaign could clear out is the fact that one can use the same fatigue modeling approach to design either industrial components containing geometrical discontinuities or mechanical couplings. This would avoid the need for lengthy and costly experimental programs considering complex geometries and specific test rigs to calibrate the fatigue material constants. M ATERIAL he material considered in this study was a 7050-T7451 aluminium alloy. Material properties were taken from Araújo et al. [10] and are presented in Tab. 1. Fatigue strength for fully reversed (stress ratio, R=-1) and repeated loading (R=0) are quoted for 10 7 cycles. Young’s Modulus Poisson’s ratio Yield strength 1   0  , 1 th R K   73.4 GPa 0.33 454 MPa 161 MPa 120 MPa 4.5 MPa  m Table 1 : Material properties of 7050-T7451 Al alloy. S TRESS TENSOR FOR ELASTIC CONTACT OF CYLINDERS UNDER PARTIAL SLIP AND IN THE PRESENCE OF A BULK FATIGUE LOAD he first step towards a solution for the subsurface stress field is to solve the contact problem itself, i.e., to find the magnitude and distribution of the surface tractions. In the present problem, the pad radius, R , the normal load per unit length, P , and the specimen thickness were defined so that each solid could be considered as an elastic half-space and the solution for the pressure distribution was Hertzian [11]. For pure fretting, the time varying tangential force Q (t) generates a shear traction described firstly by Cattaneo [12] and independently by Mindlin [13]. In partial slip condition, the contact is characterized by a central stick zone bordered by two sliding zones. In fretting fatigue, the effect of the bulk tension is to offset this stick zone. By superposing the normal and tangential contributions, it is possible to directly evaluate the resulting stress tensor using Muskhelishvili’s potential theory [14]. For synchronous and in phase load combinations, at the instants of maximum and minimum bulk/shear loads, the stress tensor turns out to be: T T