Theory of unsaturated elastic contact of rough surfaces (original) (raw)
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A self-consistent model for the elastic contact of rough surfaces
The interaction of asperities plays an important role in the contact of rough surfaces. This paper develops a self-consistent contact model, in which the effect of asperity interaction is accounted for by applying the mean pressure around a representative asperity. Based on the Boussinesq's solution of a point force acting on an elastic half-plane, the problem is transformed into a singular integral equation. Using the Gauss-Legendre quadrature formula, we solve the integral equation numerically. The results demonstrate that when the ratio between the real contact area and the nominal one is small, the effect of asperity interaction is negligible and the present mode coincides with the Greenwood-Williamson model. However, when the area ratio gets larger, the interaction of asperities becomes prominent. For a given ratio between the real contact area to the nominal one, the self-consistent contact model predicts a higher load than the Greenwood-Williamson model, in agreement with relevant experimental results.
A Modified Approach in Modeling and Calculation of Contact Characteristics of Rough Surfaces
The Journal of Engineering Research [TJER]
A mathematical formulation for the contact of rough surfaces is presented. The derivation of the contact model is facilitated through the definition of plastic asperities that are assumed to be embedded at a critical depth within the actual surface asperities. The surface asperities are assumed to deform elastically whereas the plastic asperities experience only plastic deformation. The deformation of plastic asperities is made to obey the law of conservation of volume. It is believed that the proposed model is advantageous since (a) it provides a more accurate account of elasticplastic behavior of surfaces in contact and (b) it is applicable to model formulations that involve asperity shoulder-to shoulder contact. Comparison of numerical results for estimating true contact area and contact force using the proposed model and the earlier methods suggest that the proposed approach provides a more realistic prediction of elastic-plastic contact behavior.
On the Modeling of Elastic Contact between Rough Surfaces
Tribology Transactions, 2011
The contact force and the real contact area between rough surfaces are important in the prediction of friction, wear, adhesion, and electrical and thermal contact resistance. Over the last four decades various mathematical models have been developed. Built on very different assumptions and underlying mathematical frameworks, model agreement or effectiveness has never been thoroughly investigated. This work uses several measured profiles of real surfaces having vastly different roughness characteristics to predict contact areas and forces from various elastic contact models and contrast them to a deterministic fast Fourier transform (FFT)-based contact model. The latter is considered "exact" because surfaces are analyzed as they are measured, accounting for all peaks and valleys without compromise. Though measurement uncertainties and resolution issues prevail, the same surfaces are kept constant (i.e., are identical) for all models considered. Nonetheless, the effect of the data resolution of measured surface profiles will be investigated as well. A, vol. 295, pp. 300-319), along with an alternative definition of the plasticity index that is based on a multiscale approach. The results reveal that several of the theoretical models show good quantitative and qualitative agreement among themselves, but though most models produce a nominally linear relationship between the real contact area and load, the deterministic model suggests otherwise in some cases. Regardless, all of the said models reduce the complicated surface profiles to only a few key parameters and it is therefore unrealistic to expect them to make precise predictions for all cases.
The International Journal of Multiphysics, 2017
This paper studies the contact of general rough curved surfaces having nearly identical geometries, assuming the contact at each differential area obeys the model proposed by Greenwood and Williamson. In order to account for the most general gross geometry, principles of differential geometry of surface are applied. This method while requires more rigorous mathematical manipulations, the fact that it preserves the original surface geometries thus makes the modeling procedure much more intuitive. For subsequent use, differential geometry of axis-symmetric surface is considered instead of general surface (although this "general case" can be done as well) in Chapter 3.1. The final formulas for contact area, load, and frictional torque are derived in Chapter 3.2.
Rough surface contact analysis by means of the Finite Element Method and of a new reduced model
Comptes Rendus Mécanique, 2011
This article presents two approaches of a normal frictionless mechanical contact between an elastoplastic material and a rigid plane: a full scale finite element analysis (FEA) and a reduced model. Both of them use a representative surface element (RSE) of an experimentally measured surface roughness. The full scale FEA is performed with the Finite Element code Zset using its parallel solver. It provides the reference for the reduced model. The ingredients of the reduced model are a series of responses that are calibrated by means of FEA on a single asperity and phenomenological rules to account for asperity-asperity interaction. The reduced model is able to predict the load-displacement curve, the real contact area and the free volume between the contacting pair during the compression of a rough surface against a rigid plane. The CPU time is a few seconds for the reduced model, instead of a few days for the full FEA.
Finite-elements model for the contact of rough surfaces
Wear, 1994
In this paper the elastoplastic asperity-based model for the contact of rough surfaces is presented. The model adopts most of the basic asperity-based model's assumptions, introducing, however, a more realistic elastoplastic deformation law for the analysis of individual asperity deformation.
Some numerical experiments are conducted for studying the decrease of the elastic contact area in the elastic contact of fractal random surfaces when adding components of roughness of progressively smaller wavelengths. In particular, Fourier and Weierstrass random series are used, and a recent accurate and efficient method developed by the authors is used, involving superpositions of overlapping triangles. Some comparisons are made using two recent theories, that of Ciavarella et al. published in 2000 on the deterministic Weierstrass fractal profile, and that of Persson published in 2001 on random generic contact. We show that both theories tend to underpredict the contact area by a significant (and similar) factor in these representative cases in the region of light loads (partial contact), where the non-linearities of the contact mechanics are not included in neither of the formulations. In Persson's theory case, the discrepancy is particularly large at high fractal dimensions of the profile, where in theory the numerical experiments should be more closely reproducing a true Gaussian process. The Ciavarella et al. "Archard-like" theory, is only accurate when the parameter γ (the ratio of successive wavelengths) is unrealistically large. However, we only tested the Ciavarella et al. theory in the simplified "Hertzian approximation" form assuming partial contact at the peaks of contact, although we don't expect the full version to improve dramatically the results. (M. Ciavarella). 1 K.L. Johnson (personal communication) says that the real contact area is the single most important open problem in tribology. How can anything be said if we don't start with a reliable estimate of this quantity? 0043-1648/$ -see front matter
Contact Area and Static Friction of Rough Surfaces With High Plasticity Index
A model for the contact area and static friction of nominally flat rough surfaces and rough spherical surfaces is presented. The model extends previously published models, which are limited to plasticity index values below 8, to higher plasticity index values by accounting for fully plastically deformed asperities based on finite element results by Finite Element Study of Elasto-Plastic Hemispherical Contact Against a Rigid Flat," Trans. ASME, J. Tribol., 127, pp. 343-354]. The present model also corrects some deficiencies of the earlier models at very small plasticity index values below 0.5. Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 08/13/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Journal of Tribology JULY 2010, Vol. 132 / 031401-3 Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 08/13/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use