PSI - Issue 2_B

Udaya B Sathuvalli et al. / Procedia Structural Integrity 2 (2016) 1771–1780 Sathuvalli, Rahman, Wooten and Suryanarayana / Structural Integrity Procedia 00 (2016) 000–000

1779

9

  1 fp fp A NRsF d  

(30)

The average area of the fully plasticized contacts is     1 co fp fp fp o fp A A N RsF d F d       

(31)

By substituting the expressions for A co and a c from Eqs. (31) and (29) into Eq. (26), we obtain the final expression for wear efficiency in terms of the surface characteristics and its material properties,       2 2 3 3 9 fp o K C s R G d F d              (32)

where

          2 5 1 1 2 3 . fp o fp fp fp F d F d F d F d      

  fp

   ,

(33)

G d





 is Greenwood and Williamson’s (1966) “plasticity index” defined in Eq. (23) and H is the hardness (equal to three times the uniaxial yield stress) of the wearing surface. 6. Results and discussion The wear efficiency for three common grades of OCTG steel are shown in Fig. 7. The y -axis represents the wear efficiency K according to Eq. (32). The value of K is a function of the separation d between the smooth slider and the mean summit plane (see Fig.2). For a given separation, the corresponding contact area and the load can be calculated by applying the Hertzian contact theory to the statistical ensemble of summits. The contact load for a given separation d has been calculated by Greenwood and Williamson (1966). The x -axis in Fig. 7 plots the contact load between the slider and the rough surface using the separation d as a parameter. To the best of our knowledge, there are no published profilometric data for OCTG steel surfaces. Therefore, we have used the data for summit radius and the summit height standard deviation given by McCool (1986) for 300.2 kpsi (2.07 GPa) steel. The wear efficiencies shown in Fig. 3 are in the range of 1.5 - 5 ×10 -3 . Rabinowicz (1965, pp 164) reports typical values of wear coefficients for clean unlubricated metal rubbing on similar metal to be 5.0 × 10 -3 . Hirst (1957) gives a value of 7.0 ×10 -3 for wear efficiency of mild steel on mild steel without lubricants. This suggests that the wear efficiencies calculated from Eq. (32) have the correct order of magnitude. The present development suggests that the wear efficiency decreases with hardness (decreasing plasticity index) at small contact loads ( ܲ < 0.2). The data provided by Bressan et al. (2008) and by Hirst (1957) suggest that wear efficiency decreases with hardness. Since their works do not contain information on surface morphology we cannot ascertain where their data lies with respect to our calculations. We believe that the relationship between wear efficiency and hardness, especially for OCTG steels needs further investigation. The current calculations suggest that at high plasticity index values, the wear efficiency reaches an asymptotic limit. This is in line with the hypothesis that the energy required to create wear particles comes from the residual energy in the contacts that were fully plasticized during loading. The available residual energy is limited by the yield strength of the wearing surface for a non-hardening material. White and Dawson (1987) provide results for K55, L80 and P110 casings worn by 6-3/8 in. (171.45 mm) API tooljoints in water and oil. Their results for wear in water based mud show wear efficiencies of 3.0 × 10 -5 to 1.9 × 10 -4 . The results for wear in oil based mud are 1.9 × 10 -4 to 5.1 × 10 -4 . Unfortunately, they do not provide data for wear between unlubricated surfaces. The development presented here can be used to estimate the volume V w of the typical wear particle. The strain energy density times the volume of the wear particle should approximately equal the recoverable elastic work done on a fully plastic contact, so that   2 ~ / 2 UL yp w W E V       (34) where W UL is calculated from Eq. (18) and E is elastic modulus of the wearing surface. If we assume that wear particle is hemispherical, we obtain particle diameters of the order of 0.4 mils (.01 mm) to 1 mil (0.025 mm) for K55 and Q125 steels. Rabinowicz (1965) estimates the size of wear particles for mild steel in the range 3 mils. The estimates from this work are somewhat lower than those reported by Rabinowicz (1965). Unfortunately, we did not find published measurements of wear particle sizes from oil field casings.