List of Symbols a Contact area aec Elastic critical contact area aepc Elastoplastic critical contact area al The largest contact area of asperity A Sample cross-sectional area Ar The total real contact area K Permeability C Water compressibility Cf Fracture compressibility E Young’s moduli F Contact load Fec Elastic critical contact load Fmax Maximum contact load before unloading Fne Contact load for elastic deformation Fnep Contact load for elastoplastic deformation H Hardness of the asperity K Hardness coefficient L Sample length R Radius of asperity Sd Maximum depth of valleys Sh Maximum absolute height Sm Arithmetical mean height Sp Maximum peak height Vu Volume of the upstream chamber Vd Volume of the downstream chamber Y The yield strength of material α The fitting parameter of the pressure decay curve δ Normal displacement μ Fluid viscosity ν Poisson’s ratio ω Deformation of the asperity ωc Critical deformation at the inception of plastic deformation ωmax Maximum contact interference before unloading ωres Residual contact interference after complete unloading

Analysis of Fractured Rock Permeability Evolution Under Unloading Conditions by the Model of Elastoplastic Contact Between Rough Surfaces

A revised contact stiffness model of rough curved surfaces based on the length scale

Contact mechanics in tribological and contact damage–related problems: A review

This paper investigates the fluidic leak rate through metal sealing surfaces by developing fractal models for the contact process and leakage process. An improved model is established to describe the seal-contact interface of two metal rough surface. The contact model divides the deformed regions by classifying the asperities of different characteristic lengths into the elastic, elastic-plastic and plastic regimes. Using the improved contact model, the leakage channel under the contact surface is mathematically modeled based on the fractal theory. The leakage model obtains the leak rate using the fluid transport theory in porous media, considering that the pores-forming percolation channels can be treated as a combination of filled tortuous capillaries. The effects of fractal structure, surface material and gasket size on the contact process and leakage process are analyzed through numerical simulations for sealed ring gaskets.

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Fractal modeling of fluidic leakage through metal sealing surfaces

It has been shown experimentally that boundary friction is proportional to load (commonly known as Amontons’ law) for more than 500 years, and the fact that it holds true over many scales (from microns to kilometres, and from nano-Newtons to Mega-Newtons) and for materials which deform both elastically and plastically has been the subject of much research, in order to more fully understand its wide applicability (and also to find any deviations from the law). Attempts to explain and understand Amontons’ law recognise that real surfaces are rough; as such, many researchers have studied the contact of rough surfaces under both elastic and plastic deformation conditions. As the focus on energy efficiency is ever increasing, machines are now being used with lower-viscosity lubricants, operating at higher loads and temperatures, such that the oil films separating the moving surfaces are becoming thinner, and there is a greater chance of mixed/boundary lubrication occurring. Because mixed/boundary lubrication occurs when the two moving rough surfaces come into contact, it is thought timely to review this topic and the current state of the theoretical and experimental understanding of rough-surface contact for the prediction of friction in the mixed/boundary lubrication regime.

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Rough Surface Contact Modelling—A Review

A revised Majumdar and Bushan model of elastoplastic contact between rough surfaces

Because the result of the MB fractal model contradicts with the classical contact mechanics, a revised elastoplastic contact model of a single asperity is developed based on fractal theory. The critical areas of a single asperity are scale dependent, with an increase in the contact load and contact area, a transition from elastic, elastoplastic to full plastic deformation takes place in this order. In considering the size distribution function, analytic expression between the total contact load and the real contact area on the contact surface is obtained. The elastic, elastoplastic and full plastic contact load are obtained by the critical elastic contact area of the biggest asperity and maximun contact area of a single asperity. The results show that a rough surface is firstly in elastic deformation. As the load increases, elastoplastic or full plastic deformation takes place. For constant characteristic length scale G, the slope of load-area relation is proportional to fractal dimension D. For constant fractal dimension D, the slope of load-area relation is inversely proportional to G. For constant D and G, the slope of load-area relation is inversely proportional to property of the material ϕ, namely with the same load, the material of rough surface is softer, and the total contact area is larger. The contact mechanics model provides a foundation for study of the friction, wear and seal performance of rough surfaces.

Li Gan

Papers

A revised Majumdar and Bushan model of elastoplastic contact between rough surfaces

Elastoplastic contact mechanics model of rough surface based on fractal theory