Issue 48

P. Dhaka et alii, Frattura ed Integrità Strutturale, 48 (2019) 630-638; DOI: 10.3221/IGF-ESIS.48.60 636 Further, for the same normal load of 750 N, a fully reversed tangential displacement of 15 µm (triangular waveform with 5 Hz frequency) was applied to the flat-with-rounded edge pad in the X-direction and one fretting cycle with elasto-plastic material behavior was simulated. The normal stress distribution was extracted from plate surface after quarter stroke in the forward direction. Fig. 6(a) shows the typical stress distribution for contact geometry with a=1.5 mm and R=1.35 mm. A tensile stress peak is observed on the trailing edge which is generally considered critical from the viewpoint of crack initiation [22]. Fig. 6(b) shows the variation of peak tensile stress with a/R ratio for both the cases, viz., variable ‘a’, constant ‘R’ and variable ‘R’, constant ‘a’. It can be observed that peak tensile stress decreases with an increase in a/R ratio. At a constant value of ‘R’, increase in a/R ratio means, increase in ‘a’ i.e. half-length of the flat region, which means that as the contact geometry becomes flatter/more conformal at the center, the tendency for crack initiation decreases. Similarly, at constant ‘a’ value, increase in a/R ratio means, decrease in ‘R’ i.e. radius of contact edge, which implies that as the corners become sharper, the resistance for crack initiation increases. This is surprising because in general, filleting at the corners is considered as a measure to relieve the stresses at the contact edges but that is not always true and it may even lead to an increase in stresses. Further, it agrees with the observations reported in the literature [13, 14] where researchers have found that fretting fatigue life decreases with the increase in the corner radius and it was attributed to increased stresses due to filleting at the corners. Effect of Material Yielding To check whether yielding of the material has any implications on the analysis presented in the previous section, finite element analyses were also carried out using elasto-plastic material behaviour. The elasto-plastic behaviour of material was modelled using Ramberg Osgood law. From Fig. 7(a), it can be observed that elasto-plastic analysis results deviate from elastic analysis results for lower values of a/R ratio for variable ‘a’ and constant value of ‘R’. This is because, with the decrease in ‘a’, contact geometry starts approaching cylinder-on-plate configuration and thus leading to increased non-conformality of the contact. This results in higher stresses which lead to sufficient yielding of material and hence, elasto-plastic analysis results deviate from the elastic analysis. Further, fitting a logarithmic trend line to the contact pressure variation obtained from elastic analysis shows that as ‘a’ tends to zero, contact pressure approaches to that of a cylinder-on-plate case with radius ‘R’ as 1.35 mm. From Fig. 7(b), it can be seen that when ‘R’ is varied keeping ‘a’ as constant, the elasto-plastic analysis results deviate from elastic analysis results at higher values of a/R ratio. This is because, with reduction in ‘R’, the contact geometry tends towards the flat-punch-on-half plane case, leading to highly localized stresses at the corners. Hence, the elasto-plastic analysis results deviate significantly from the elastic analysis results. Interestingly, the deviation between elastic and elasto- plastic analysis results becomes significant only about a/R value of approximately equal to one. Further, the elastic analysis predicts higher contact pressure and stresses as compared to elasto-plastic analysis and is likely to give the conservative estimate for the fretting wear volume and fretting fatigue life which are dependent on contact pressure and tensile stress in fretting direction respectively. (a) (b) Figure 7 : Effect of material yielding on the variation of maximum contact pressure with a/R ratio for (a) variable ‘a’ and constant ‘R’=1.35 mm, and (b) variable ‘R’ and constant ‘a’=1.5 mm.