Issue 48

P. Dhaka et alii, Frattura ed Integrità Strutturale, 48 (2019) 630-638; DOI: 10.3221/IGF-ESIS.48.60 631 behaviour of a mating pair is affected by many parameters which include material properties, contact geometry, and loading conditions, with contact geometry being one of the crucial parameters. Contact geometry directly affects the completeness and conformality of a contact. In case of a complete contact, the nominal area of contact is fixed geometrically and is independent of normal load whereas, for an incomplete contact, the contact area increases with an increase in normal load. Further, if the largest characteristic dimension of the contact zone (contact radius) is considerably smaller than the smallest radius of the curvature of a mating pair, then the contact becomes non-conformal contact while vice-versa forms a conformal contact [7]. Most of the studies reported in the literature have generally focused on non-conformal and incomplete contacts viz. cylinder on plate configurations, with very few studies on conformal and complete contact. A flat with rounded edge-on- plate contact is a type of conformal and partially complete contact. The relevance of analyzing flat with rounded edge contact lies in the fact that it is impractical to machine a flat surface with perfectly sharp corners owing to machining constraints which inevitably leads to corner radii. Another interesting application is in the case of an aero-engine compressor where the contact pressure distribution at the blade-disc dovetail interface can be represented by a flat-with- rounded-edge geometry [8]. While in the case of a flat punch with sharp corners, singularity is present at contact edge and asymptotic contact pressure distribution is obtained, the rounding of the corners in a flat with rounded-edge leads to contact pressure falling to zero at the edge of the contact. This results in a non-uniform pressure distribution with constant pressure at the center and pressure peaks at the corners [9]. Ciavarella et al. [9-11] in one of their seminal works, proposed the analytical solution for the contact tractions in the case of partially flat contacts subjected to oscillating tangential and bulk load. Further, Warmuth et al. [12] observed that fretting in less conforming contacts leads to considerably higher wear rates compared to conformal contacts. They proposed that the difference in contact pressure because of different contact geometry was not the contributory factor for different wear rates rather it was attributed to the effect of contact geometry on debris flow in the contact zone. Many researchers [13, 14] studied the effect of radii of corners in the partially flat pad on fretting fatigue life and found that, in general, fretting fatigue life drops with an increase in corner radii which was attributed to increased stresses with rounding. In the present work, effect of both half-length of central flat region (‘a’) and corner radii (‘R’) has been studied to understand its influence on the contact tractions and explore the possibility of quantifying the effect of contact geometry using a single parameter like a/R ratio or contact zone size. Finite element analysis was carried out for the both elastic and elasto-plastic case to understand the interrelation between yielding and contact geometry. M ETHODOLOGY inite element methods tend to be quite advantageous in analyzing the contact problems which, otherwise are either infeasible to deal using experimental methods or prove to be cumbersome when subtle information regarding contact tractions is required. In the present work, a two-dimensional finite element analysis was carried out for a flat-with-rounded-edge pad on plate configuration. The geometric dimensions for flat-with-rounded-edge pad were taken from Fouvry et al. [9] which is a scaled-down model and represents the contact pressure distribution for a real blade-disc dovetail interface. The central flat region ‘2a’ was taken as 3 mm while the radius at the corners(‘R’) was 1.35 mm. The plate was modelled with width ‘l’ and depth ‘b’ of 20 mm and 10 mm respectively. The model was meshed using 2-D plane strain, first order quadrilateral elements with reduced integration (CPE4R) and triangular elements (CPE3). These elements are generally preferred over second-order elements which give fluctuating pressure distribution for contact problems with friction [15]. The mesh was sufficiently refined in the contact zone and mesh size of 2 µm was used while regions away from the contact zone were meshed using coarser mesh. The geometry and meshed model are shown in Fig. 1 (a) and 1 (b) respectively. The material behaviour for the flat with rounded edge pad and plate was modelled using Ti- 6Al-4V which is one of the widely used titanium alloys in aero-engines for fretting prone assemblies. The elasto-plastic behaviour of Ti-6Al-4V was modelled using Ramberg-Osgood law with material properties as given in Tab. 1 [16]. The Ramberg-Osgood deformation plasticity model available in ABAQUS ® is generally used to describe elastic-plastic behaviour in applications pertaining to fracture mechanics and doesn’t require separate definition for elastic and plastic segment of the stress-strain curve [17]. The Ramberg-Osgood coefficient and exponent were obtained by fitting a power law relationship in plastic strain vs. true stress response normalized with respect to corresponding yield point values using the following equation [18]: 0 0 n p             F