Elastic-plastic Rough Surface Contact Research Articles

Evaluating Elastic-Plastic Wavy and Spherical Asperity-Based Statistical and Multi-Scale Rough Surface Contact Models with Deterministic Results.

The solution to an elastic-plastic rough surface contact problem can be applied to phenomena such as friction and contact resistance. Many different types of models have therefore been developed to solve rough surface contact. A deterministic approach may accurately describe the entire surface, but the computing time is too long for practical use. Thus, mathematically abbreviated models have been developed to describe rough surface contact. Many popular models employ a statistical methodology to solve the contact problem, and they borrow the solution for spherical or parabolic contact to represent individual asperities. However, it is believed that a sinusoidal geometry may be a more realistic asperity representation. This has been applied to a newer version of the stacked multiscale model and statistical models. While no single model can accurately describe every contact problem better than any other, this work aims to help establish guidelines that determine the best model to solve a rough surface contact problem by applying mathematical and deterministic models to two reference surfaces in contact with a rigid flat. The discrepancies and similarities form the basis of those guidelines.

EFFECT OF RATIO OF MATERIAL HARDNESSES, AVERAGE PRESSURE AND ROUGHNESS PARAMETERS ON ACTUAL CONTACT AREA OF ASSEMBLED SURFACES

The paper describes the influence of various factors, including the ratio of hardness, average pressure, radius of microasperities of the surface, affecting the value of the actual contact area of rough surfaces of flat parts mated in fixed joints. The study was carried out using the dependences obtained by the authors describing the elastic-plastic contact of rough surfaces.

A comparison of nanoscale measurements with the theoretical models of real and nominal contact areas

In this study, an experimental method is proposed to measure the real area of contact between an alumina sphere and an Al surface based on the adhesive transfer of the Au film and the scanning electron microscope in the back-scattered mode. A thin film of Au is sputtered on the alumina sphere before the indentation with the Al surface. After indentation, the interfaces of the alumina sphere and Al surface are observed by the scanning electron microscope. The contact area can be identified based on both the distributions of the alumina and Au on the alumina sphere and Al surface, respectively. The measured contact area at different nominal pressures are compared to predictions made by several popular theoretical elastic-plastic rough surface contact models.

The effect of resolution on the deterministic finite element elastic-plastic rough surface contact under combined normal and tangential loading

Three-dimensional deterministic models of rough surfaces can enrich the understanding of the influence of surface texture on contact and friction. However, most of the existing finite element contact models simply use the data measured from real rough surfaces directly and consider the shape between every two neighboring points to be a straight line. In this study, we proposed a possible harmonic description for the shape between the measured points. This is accomplished by using harmonic interpolation. The effect of resolution on the contact properties under normal loading and combined normal and tangential loading are investigated. This study provides a methodology to the finite element analysis of rough surface contact that may push the simulation results closer to reality.

Formulation and numerical analysis of elastic-plastic contact of rough surfaces subjected to normal load

In this report, a semi-analytical approach for three dimensional contact problem of two non-conformed, deformable bodies in contact under normal loading is presented. The contact surfaces could be rough or smooth. For plastic deformation, the perfect elasto-plasticity is assumed. Rough surfaces of different roughness profiles can be independently defined on each body surface. The numerical solution is based upon the analytical solution given by Boussinesq-Cerruti integral equations for an elastic half space [1]. Due to the geometry restriction, the bodies in contact are assumed as flat or nearly flat where the radii of curvature is very large as compared to the contact area size. The integral equations applied at each contact body are discretized on a rectangular grid defined at each contact surface and are evaluated by using multilevel and multi-summation technique (MLMS) [2]. In addition to the discretized integral equations, the contact condition and force balance equations in normal direction are imposed. Iterated conjugate gradient method (CGM) [2] is implement to find the displacement and tractions that satisfy the contact conditions. The surface displacement and tractions in normal direction, the real contact area, plastic contact area are obtained under the given conditions.

Friction analysis at elastic-plastic contact of rough surfaces using n-point asperity model

The paper describes a theoretical study of friction at elastic-plastic contact of rough surfaces in n-point asperity model framework and based on accurate finite element analysis of elastic-plastic deformation of single asperity contact. Plasticity index, a well-defined nondimensional parameter is used to study the prospective situations arising out of variation in material properties and surface roughness. Using practical values of material properties and surface roughness parameters, results are obtained for the behavior of applied load, friction force, and coefficient of friction as a function plasticity index and mean separation of surfaces. It is observed that with increase in amount of plastic deformation, the load required to be applied for maintaining a particular level of separation between contacting surfaces increases while the frictional force decreases. Coefficient of friction is independent of applied load in predominantly plastic domain of deformation but varies nonlinearly in other domains of deformation. Also, for the same applied load the coefficient of friction increases with increase in elastic deformation.

A Study of Elastic-plastic Contact of Rough Surfaces Using N-point Asperity Model

A theoretical study of elastic-plastic contact of rough surfaces is considered based on n-point asperity model and accurate finite element analysis (FEA) of elastic-plastic deformation of single asperity contact. Kogut and Etsion (2003) formulations for intermediate elastic-plastic regimes of deformation are integrated with pure elastic model of Greenwood and Williamson (1966) and pure plastic model of Abbott and Firestone (1933) to obtain contact load and area in rough surface contact. Using practical values of material properties and surface roughness parameters, the load–separation and area-separation behaviour of surfaces are studied.

A Static Friction Model for Elastic-Plastic Contacting Rough Surfaces

A model that predicts the static friction for elastic-plastic contact of rough surfaces is presented. The model incorporates the results of accurate finite element analyses for the elastic-plastic contact, adhesion and sliding inception of a single asperity in a statistical representation of surface roughness. The model shows strong effect of the external force and nominal contact area on the static friction coefficient in contrast to the classical laws of friction. It also shows that the main dimensionless parameters affecting the static friction coefficient are the plasticity index and adhesion parameter. The effect of adhesion on the static friction is discussed and found to be negligible at plasticity index values larger than 2. It is shown that the classical laws of friction are a limiting case of the present more general solution and are adequate only for high plasticity index and negligible adhesion. Some potential limitations of the present model are also discussed pointing to possible improvements. A comparison of the present results with those obtained from an approximate CEB friction model shows substantial differences, with the latter severely underestimating the static friction coefficient.

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

This paper presents 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-Venant’s Principle and Love’s 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 micro-contact load redistribution. The results also reveal that the effect of asperity interactions can be largely cancelled out by the effect of asperity plastic deformation.

Linear elastic contact of the Weierstrass profile

A contact problem is considered in which an elastic half–plane is pressed against a rigid fractally rough surface, whose profile is defined by a Weierstrass series. It is shown that no applied mean pressure is sufficiently large to ensure full contact and indeed there are not even any contact areas of finite dimension — the contact area consists of a set of fractal character for all values of the geometric and loading parameters. A solution for the partial contact of a sinusoidal surface is used to develop a relation between the contact pressure distribution at scale n − 1 and that at scale n . Recursive numerical integration of this relation yields the contact area as a function of scale. An analytical solution to the same problem appropriate at large n is constructed following a technique due to Archard. This is found to give a very good approximation to the numerical results even at small n , except for cases where the dimensionless applied load is large. The contact area is found to decrease continuously with n , tending to a power–law behaviour at large n which corresponds to a limiting fractal dimension of (2 − D ), where D is the fractal dimension of the surface profile. However, it is not a ‘simple’ fractal, in the sense that it deviates from the power–law form at low n , at which there is also a dependence on the applied load. Contact segment lengths become smaller at small scales, but an appropriately normalized size distribution tends to a limiting function at large n . † The authors dedicate this paper to the memory of Dr J. F. Archard, 1918–1989.