PSI - Issue 60

348 Nagaraja Bhat Y V et al. / Procedia Structural Integrity 60 (2024) 345–354 Y V N Bhat, M A Davinci, A Kumar, N L Parthasarathi, S I S Raj, D Samataray, B.K. Sreedhar / StructuralIntegrity Procedia 00 (2019) 000– 000

3. Theoretical studies

The wear depth of the pin is estimated theoretically using phenomenological equations like Archard wear equation (euqation-1, Arhcard, 1956) and modified Archard wear equation i.e. Sarkar’s model (equation-3, Sarkar 1980) which includes the effect of friction. The Archard wear equation relates wear depth of the pin with the contact stresses and sliding distance using a coefficient which is known as specific wear coefficient. h=K  PS (1)    =   (2) ℎ=  1+3   (3)   =     (4) Hegadekatte et.al, 2006 & 2008 proposed a Global Incremental Wear Model (GIWM) for prediction of wear depth of pin having spherical end with respect to the sliding distance. The results of this model were compared with the experimental results obtained for silicon nitride & WC-Co materials at room temperature. In the present study, differential form of Archard/Sarkar wear equation is solved in GIWM using iterative numerical integration method i.e. Euler’s forward integration. The differential form of Archard wear equation (euqation-4) and Sarkar model (equation-5) are written as     =   (5)     =  1+3   (6) For Archard/Sarkar equation, specific wear coefficient and coefficient of friction values obtained from the experiments are used. In the first iteration of GIWM, when the sliding distance is zero, Hertzian contact theory is used to establish the contact radius (a 0 ) between the pin and the disc as explained using equations 7 to 9. a  =       (7)    =    +    (8)    =      +      (9) The Young’s modulus and Poison’s ratio for 440C material is taken as 200 GPa and 0.3 respectively. The average contact stress P 0 (equation-10) and the elastic deformation h 0 e (equation-11, W. C. Oliver, et.al, 1992) are estimated using Hertzian contact area. Use of average contact stress instead actual Hertzian contact stress, which varies locally across the contact area, is the main approximation of GIWM. P  =     (10) h   =      (11) Equations 12 and 13 represent the integral form of Archard wear equation and Sarkar wear model respectively. Once average contact stress P 0 is known, wear depth of the pin is estimated for small sliding distance using numerical integration equations derived either for Archard wear equation (equation-14) or Sarkar wear model