L. Chang

An Asperity Microcontact Model Incorporating the Transition From Elastic Deformation to Fully Plastic Flow

This paper presents an elastic-plastic asperity microcontact model for contact between two nominally flat surfaces. The transition from elastic deformation to fully plastic flow of the contacting asperity is modeled based on contact-mechanics theories in conjunction with the continuity and smoothness of variables across different modes of deformation. The relations of the mean contact pressure and contact area of the asperity to its contact interference in the elastoplastic regime of deformation are respectively modeled by logarithmic and fourth-order polynomial functions. These asperity-scale equations are then used to develop the elastic-plastic contact model between two rough surfaces, allowing the mean surface separation and the real area of contact to be calculated as functions of the contact load and surface plasticity index. Results are presented for a wide range of contact load and plasticity index, showing the importance of accurately modeling the deformation in the elastoplastic transitional regime of the asperity contacts. The results are also compared with those calculated by the GW and CEB models, showing that the present model is more complete in describing the contact of rough surfaces.

A micro-contact and wear model for chemical–mechanical polishing of silicon wafers

Abstract A micro-contact and wear model for chemical–mechanical polishing (CMP) of silicon wafers is presented in this paper. The model is developed on the basis of elastic–plastic micro-contact mechanics and abrasive wear theory. The synergetic effects of mechanical and chemical actions are formulated into the model. A close-form equation of material removal rate from the wafer surface is derived relating to the material, geometric, chemical and operating parameters in a CMP process. The model is evaluated by comparing the theoretical removal rates with those experimentally determined. Good agreement is obtained for both chemically active and inactive polishing processes. The model reveals some insights into the micro-contact and wear mechanisms of the CMP process. It suggests that the removal rate is sensitive to the particle concentration in the slurry, more sensitive to the applied load and operating speed and most sensitive to the surface hardness and slurry particle size. The model may be used to study the effects of different materials, geometry, slurry chemistry and operating conditions on CMP processes.

A Model of Asperity Interactions in Elastic-Plastic Contact of Rough Surfaces

This paper present a micro-contact model incorporating asperity interactions in elastic-plastic contact of rough surfaces. The effect of the asperity interactions on the local deformation behavior of a given micro-contact is first modeled based on the Saint-Venants Principle and Loves Formula. The local contact interference is related in closed form to the local contact load, the global mean pressure and material parameters. This micro-contact model equation is then integrated into the elastic-plastic contact model developed in Zhao et al. (2000) to allow the asperity interactions and plastic deformation to be considered simultaneously. The effects of the asperity interactions on the mean surface separation, the real area of contact and the redistribution of the contact load among contacting asperities of different heights are studied. The results show that the asperity interactions can significantly affect the mean surface separation and microcontact load redistribution. The results also reveal that the effect of asperity interactions can be largely cancelled out by the effect of asperity plastic deformation.

A mathematical model for chemical–mechanical polishing based on formation and removal of weakly bonded molecular species

Abstract This paper presents a mathematical model that describes the chemical–mechanical synergy and mechanism of material removal in chemical–mechanical polishing (CMP). The physical basis of the model is that chemical reactions convert strongly bonded surface atoms/molecules to weakly bonded molecular species while the mechanical action delivers the energy that is needed to break the weak molecular bonds, thereby removing the surface materials at the molecular scale. Three key variables are defined to describe the chemical–mechanical synergetic effects. Close-form equations are derived relating these variables to the process parameters, making use of the concepts of chemical–mechanical equilibrium, chemical kinetics, contact mechanics, molecular binding energy and random-process probability. The model is applied to the process of silicon-wafer CMP. The governing equation of the material removal reveals some insights into the process. It also offers some sensible explanations to the effects of the operating and material parameters on the rate of material removal and process quality.

A deterministic model for line-contact partial elastohydrodynamic lubrication

A deterministic model for partial elastohydrodynamic lubrication (EHL) is presented in this paper. The modelling methodology adopts some of the concepts used in the stochastic modelling of partial EHL and some of the procedures for deterministic calculation of asperity pressures. The model is shown to be capable of simulating the basic process of asperity interaction and solid-to-solid contact within an EHL conjunction of rough surfaces. Deterministic results of transient partial EHL in line contacts are obtained when one pair or multiple pairs of asperities collide. The model may help to gain a fundamental understanding of the transient behaviour of asperity interactions in lubricated concentrated contacts of rough surfaces. Asperity pressures may be calculated more accurately than the conventional analyses under dry and static contact conditions. The work represents a first attempt in deterministic modelling of tribo-contacts operating in the mixed regime of micro-EHL and boundary lubrication. Future work will aim at developing more realistic models incorporating factors such as three-dimensional asperity contacts, asperity plastic deformation, thermal effects and the effect of tribo-chemistry.

On the Pressure Rippling and Roughness Deformation in Elastohydrodynamic Lubrication of Rough Surfaces

The Objective of this paper is to conduct a qualitative analysis on the effects of lubricant shear thinning, lubricant shear heating and the roughness-induced transients on the pressure rippling and roughness deformation that occurs under elastohydrodynamic lubrication (EHL) conditions. To facilitate the analysis, the numerical solutions to an example problem (EHL) line contact between a perfectly smooth surface and a sinusoidal rough surface are presented. This micro-EHL problem is first solved using the conventional model of a Newtonian lubricant and a stationary rough surface under isothermal conditions

A Mathematical Model for Frictional Elastic-Plastic Sphere-on-Flat Contacts at Sliding Incipient

This paper presents a mathematical model for frictional elastic-plastic sphere-on-flat contacts at sliding incipient. The model is developed based on theoretical work on contact mechanics in conjunction with finite-element results. It incorporates the effects of friction loading on the contact pressure, the mode of deformation, and the area of contact. The shear strength of the contact interface is, in this paper, assumed to be proportional to the contact pressure with a limiting value that is below the bulk shear strength of the sphere. Other plausible interfacial-shear-strength characteristics may also be implemented into the contact model in a similar manner. The model is used to analyze the frictional behavior of a sphere-on-flat contact where the experimental data suggest that the interfacial shear strength is similar in nature to the one implemented in the model. The theoretical results are consistent with the experimental data in all key aspects. This sphere-on-flat contact model may be used as a building block to develop an asperity-based contact model of rough surfaces with friction loading. It may also serve in the modeling of boundary-lubricated sliding contacts where the interfacial shear strength in each micro-contact is coupled with its flash temperature and related to the lubricant/ surface physical-chemical behavior.

On Mechanisms of Fatigue Life Enhancement by Surface Dents in Heavily Loaded Rolling Line Contacts

This paper studies mechanisms of surface dents in enhancing the fatigue life of rolling bearings previously reported in Akamatsu et al. (1). First, transient micro-EHL analyses of heavily loaded contacts between rough surfaces with multiple dents are conducted under near rolling conditions. Contacts with various dent dimensions, dent arrangements under different loading and kinematic conditions are investigated. Results show that surface dents generate no favorable micro-EHL effects to enhance the contact fatigue life. Subsequent analyses, in conjunction with other published studies, suggest that the fatigue life enhancement likely comes from the reduced local traction at asperity contacts through the oil pots effects of the dents. The effects of the surface dents on contact fatigue life may depend on the lubrication regime in which the contact is operating, being favorable in poor lubrication conditions but adverse in well-lubricated contacts. Since rolling bearings are usually designed to operate in a healthy regime of lubrication, fatigue life enhancement by artificially introducing dents on bearing surfaces may not extend to field applications.

A Line-Contact Micro-EHL Model With Three-Dimensional Surface Topography

A mathematical model is presented fn this paper that can be used to analyze the effect of 3-D surface topography on the thermal, transient micro-elastohydrodynamic lubricatioin (EHL). The model efficiently incorporates the surface deformation due to the 3D pressure rippling and the lubricant side flow around the asperities. The resulting computer implementation requires little additional storage space and does not reduce computational efficiency from its 2-D counterpart. The model is shown to sensibly describe the physical problems. The results presented in this paper and in a separate paper (Chang et al., 1993c) show that the lubricant local side flow significantly affects the contact conditions of the EHL of rough surfaces, especially under high sliding

Deterministic modeling and numerical simulation of lubrication between rough surfaces—a review of recent developments

Abstract Significant progress has been made in the past ten years on deterministic modeling and analysis of lubricated rough contacts operating in the regime of micro-elastohydrodynamic lubrication (EHL). This progress has opened new avenues for analytical-computational studies of tribo-contacts that operate in the mixed regime of micro-EHL and boundary lubrication. Work to this date suggests that deterministic modeling of mixed-film lubrication problems is feasible and may reveal insights into the dynamic behavior of asperity interactions, mechanisms of friction and wear, and modes of contact failure.