Wear model

Zhao, Y., and Change, L., A Micro-Contact and Wear Model for Chemical-Mechanical Polishing, Wear, Vol. 252, 2002,... 

Figure 8.8 shows the resulting saturation indices for halite and anhydrite, calculated for the first four samples in Table 8.8. The Debye-Hiickel (B-dot) method, which of course is not intended to be used to model saline fluids, predicts that the minerals are significantly undersaturated in the brine samples. The Harvie-Mpller-Weare model, on the other hand, predicts that halite and anhydrite are near equilibrium with the brine, as we would expect. As usual, we cannot determine whether the remaining discrepancies result from the analytical error, error in the activity model, or error from other sources. 

Fig. 8.8. Saturation indices of Sebkhat El Melah brine samples with respect to halite (left) and anhydrite (right), calculated using the B-dot (modified Debye-Huckel) and Harvie-Mpller-Weare models.

In a first calculation, we specify that the fluid maintains equilibrium with whatever minerals precipitate. Minerals that form, therefore, can redissolve into the brine as evaporation proceeds. In react, we set the Harvie-Moilcr-Weare model and specify that our initial system contains seawater... 

An example application of the contact wear model to simulation of the polish of an embedded array (assuming no material in the trenches within the array) is shown in Fig. 29. One can also observe the evolution of the pressure distribution, where clear sharp pressure concentrations at the edges of the features can be seen. Such localized pressures work to rapidly round the corners of features undergoing polish. 

Zhao Y, Chang L. A micro-contact and wear model for chemical-mechanical polishing of silicon wafers. Wear 2002 252 220-226. 

Runnels assumes the existence of a continuous fluid layer between the pad and the wafer and models planarization using a feature scale fluid-based-wear model. Runnels uses fluid mechanics to model the normal and shear stresses that are developed at the feature scale. Material removal rate is assumed to depend only upon the shear stress, Ot, according to ... 

Marion G. M. andFarrenR. E. (1999) Mineral solubilities in the Na-K-Mg-Ca-Cl-S04-H20 system a re-evaluation of the sulfate chemistry in the Spencer-Mpller-Weare model. Geochim. Cosmochim. Acta6 i, 1305-1318. 

Pickles MJ, Joiner A, Weader E, Cooper Y, Cox TF Abrasion of human enamel and dentine caused by toothpastes of differing abrasivity determined using an in situ wear model. Int Dent J 2005 55 188-193. 

H.C. Meng and K.C. Ludema, Wear models and predictive equations Their form and content, Wear, 181-183, 443-457,1995. 

The three models have been compared to calculations of the solubility of gypsum in 0.5 molal NaCl with varying concentrations of Na2S04 ( ) (Figure 3). Results of the WATEQ and amended WATEQ models were not similar to those of the Harvie and Weare model. However, results of the fit model were similar to those of the Harvie and Weare model. The fit model and the Harvie and Weare model used gypsum-solubility measurements to fit model parameters. 

Figure 3. Comparision of gypsum solubilities calculated by the Harvie and Weare model (23) and ion-association aqueous models in 0.5-molal NaCl solutions with varying concentrations of Na2S04.

Load is one of the basic physical quantities governing wear in engineering practice and thus, explicitly or implicitly, it is a parameter in any wear model. For instance, Eqns 13-30 and 13-37 are explicitly linear with respect to load and therefore plots of volumetric wear rate against load in log-log coordinates should have a slope of unity. Ar-... 

The effect of reiterative feedback, therefore, is a major consideration in the construction of wear models that realistically take into account the influence of changing physical parameters on the course of wear. In some cases these changes are the result of the course of wear itself, such as the decrease of contact pressure as the conjunction area enlarges under constant load. In other cases, the externally imposed magnitude of a parameter such as load or rubbing speed will determine the influence that reiteration of contact will have on the course of wear. 

The problem of wear when the fluid film lubricant is no longer intact is associated with the asperity contact of structured surfaces. The contact behavior of such surfaces was discussed in Chapter 12 wear models governed by asperity contact were described in Chapter 13. Theoretically the laws controlling fluid film thickness can be coupled with asperity contact models to yield quantitative descriptions of the course of wear. In this section we shall deal with those cases in which the function of the lubricant is only to provide a fluid film separating the two rubbing bodies, and the events at the contact, once it is established, are determined by the interaction of mechanical parameters such as load and rubbing speed with the properties of the contacting interface. 

On the other hand, there are the data for the influence of compounded antiwear additives in ester-type fluids, as shown in Table 14-1, These data show good conformity with the partial elastohydrodynamic wear model and the effect of compounded antiwear additives is what is anticipated in an adhesive wear process. 

The most comprehensive fatigue wear model (2) proposed In the literature was used to predict wear rates to within 30 percent or less of the experimentally measured values (J). The exponent t was determined from notched cylindrical specimens In reverse bending. The number of contacts and the areas were determined from surface profiles of the polymer and the counterface after steady-state wear was attained. The wear data was obtained from a polymer pin sliding on a rotating cylinder. 

For the polylmides, at the 5 N load, the wear rates were negatively correlated with the cycles to initiate wear. This result is consistent with the fatigue wear model which states that the wear rate is Inversely proportional to the number of cycles to fatigue failure. Comparing the cycles to initiate at the 5 and 10 N load, it is noted that cycles to initiate significantly Increase for the... 

L. Mattel, F. Di Pucdo, B. Picdgallo, E. Ciulli, Lubrication and wear modelling of artificial hip joints a review, Tribol. Int. 44... 

S. Montgomery, D. Kennedy, N. O Dowd, Analysis of wear models for advanced coated materials. Proceedings of the International Conference on Materials, Tribology, Recycling (2009), Lipanj (Croatia). 

Bragdon C.R., H. Malchau, S.L. Larson, et al. 2002. Validation of digital radiography, for use with radiostereometric analysis (RSA) using a dynamic phantom wear model. Transactions of the 48th Orthopedic Research Society 27 1020. 

Montoro-Cazoria, D., Perez-Ocon, R, Segovia, M. C. 2007. Survival probabilities for shock and wear models governed by phase-type distributions. Quality Technology Quatitative Management, 4(1), 85-94. 

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