Subsurface stress

The existence of asperity contacts in mixed lubrication causes great many local events and significant consequences. For example, the parameters describing lubrication and contact conditions, such as film thickness, pressure, subsurface stress, and surface temperature, fluctuate violently and frequently over time and space domain. It is expected that these local events would have significant effects on the service life of machine elements, but experimental measurements are difficult because of the highly random and time-dependent nature of the signals. Only a few successes were reported so far in experimental studies of mixed lubrication, mostly limited to the artificially manufactured... 

Zhu, D. and Hu, Y. Z., A Computer Program Package for the Prediction of EHL and Mixed Lubrication Characteristics, Friction, Subsurface Stresses and Flash Temperatures Based on Measured 3-D Surface Roughness," Tribol. Trans., Vol. 44, No. 3,2001, pp. 383-390. 

Fig. 3 shows the state of subsurface stress. The empty space in this figure shows a pore surrounded by solid rock. The vertical overburden pressure, S, is supported by two unequal forces the formation fluid (pore) pressure, p, and the vertical effective stress acting on the rock frame, o. By Newton s third law of motion... 

These results can be interpreted in terms of the subsurface stress distribution beneath the indenter [30]. For instance, the vertical extent of the stress field be-... 

Bossinesq equations based on elastic theory are the most commonly used methods for obtaining subsurface stresses produced by surface loads on semiinfinite, elastic, isotropic, homogeneous, weightless... 

This is a very important feature of XRDI. While some optical techniques can reveal surface stresses, the sensitivity of X-rays is much higher. X-rays can reveal subsurface stresses, and the technique can be made quantitative. 

Surface (adhesive) wear is the primary type of wear at the hip. Surface wear also occurs at the knee, but delamination wear, caused by a combination of subsurface stress and oxidation, is a major cause of damage at the knee. The resistance... 

The aim of this paper is to examine a number of dynamic contacts and to calculate the variation of film thickness, contact pressure and subsurface stress with time. It is hoped to offer some guidance as to when a quasi-steady treatment is likely to be acceptable and where more accurate analyses are required. 

Stresses at asperity or micro contacts within the overall Hertzian contact are key features, so that a thorough understanding of the stresses at asperity contacts is clearly needed. Useful insights into the behaviour of the contact of real surfaces can be obtained using dry elastic contact simulations [18,19] or elastic/plastic contact simulations [20]. However, it is necessary to consider the micro-EHL effects of the oil film since these influence the contact pressures and, through non-Newtonian and time-dependent behaviour, determine the traction forces at the micro contacts. The important subsurface stress field is therefore affected by the presence of a micro EHL film. In general when roughness is present the maximum sub-surface shear stress field occurs much closer to the surface as seen in the micro EHL simulations in section 4. 

Elsharkawy, A A and Hamrock, B J, 1991, "Subsurface stresses in micro-EHL line contacts", ASME Journal of Tribology, Vol 113, pp 645-655. 33.Sadeghi, F, 1991, "A comparison of the fluid model s effect on the internal stresses of rough surfaces", ASME Journal of Tribology Vol 113, pp 142-149. 

Results of detailed pressure and flash temperature distributions from two sample cases can be found in Figure 4, in comparison with those from the smooth surface solution. Subsurface stresses can also be calculated with the present computer program, and, as an example. Figure 5 illustrates the maximum shear stress distribution for the shaved surfaces, compared with that for the smooth surfaces. It has been observed from these cases that the pressure, film thickness and flash temperature... 

Analyzing the fatigue life of such lubricated rough contact requires the solutions of mixed lubrication, asperity contact, and subsurface stresses to be incorporated into a contact fatigue model. A full-scale micro EHL model [4]-[5] may be used for the mixed lubrication analysis. However, contacts arising in... 

Tangential contact stresses are calculated using the Amontons-Coulomb friction law, as was done for the dry contact. Subsurface stresses are calculated using a combination of FFT and MLMS [13-14]. 

Subsurface stresses are computed simultaneously for points lying at the same depth directly below the grid nodes. Therefore, the fatigue integral F is also computed layer by layer, as follows ... 

The patch contact problem is solved by iteration, as discussed in section 2.2. At the end of the iterative solution, the micro-contact area and micro-contact pressure distributions are determined for the current patch. The corresponding tangential contact stress distribution is obtained under the proportional traction approximation (Coulomb friction). The subsurface stresses corresponding to these surface stress distributions are computed using the fast Fourier transform (FFT) technique, and the fatigue life integral Fu for the current patch is obtained by integrating the subsurface stresses. 

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