Elasto-plastic statistical model of strongly anisotropic rough surfaces for finite element 3D-contac

Elasto-plastic statistical model of strongly anisotropic rough surfaces

for finite element 3D-contact analysis

Ryszard Buczkowski a ,Michal Kleiber

b,c,*a

Technical University of Szczecin,Division of Applied Mechanics,Piastow 41,71-065Szczecin,Poland b Institute of Fundamental Technological Research,Polish Academy of Sciences,Swietokrzyska 21,00-049Warsaw,Poland

c Department of Mathematics an

d Information Sciences,Warsaw University of Technology,Poland

Received 23February 2005;received in revised form 15November 2005;accepted 15November 2005

Abstract

The complete elasto-plastic microcontact model of anisotropic rough surfaces is proposed.The description of anisotropic random surfaces is restricted here to strongly rough surfaces;for such surfaces the summits are represented by highly eccentric elliptic paraboloids having their semi-major axes oriented in the direction of the grain.The present model is based on the volume conservation of asperities in which the plasticity index is modified to suit more general geometric contact shapes during plastic deformation process.This model is utilized to determine the total contact area,contact load and contact stiffness which are a mixture of both the elastic and plastic com-ponents.For low nominal pressures both the elastic and elasto-plastic contact stiffness is found to be almost linear in relation to the normal load.The elastic and elasto-plastic stiffness coefficients decrease with increasing variance of the surface height about the mean plane.The standard deviation of slopes and standard deviation of curvatures have no observable effects on the normal contact stiffness.Ó2006Elsevier B.V.All rights reserved.

Keywords:Rough surfaces;Statistical modelling;Contact stiffness;Finite element method

1.Introduction

For machined metal surfaces the height,slope and curvature of asperities are random and have the Gaussian or nearly Gaussian probability distribution.This fact suggests that the geometry of such surfaces can be described statistically assuming they are described by a limited number of variables.On the basis of probability theory Greenwood and William-son [1](GW model),Whitehouse and Archard [2],Nayak [3,4],Bush et al.[5–7],Sayles and Thomas [8],Whitehouse and Phillips [9–11]and Greenwood [12]have made an important advancement in developing the asperity based-model.

The observation of Pullen and Williamson [13]that the volume of deformed asperities is conserved stimulated Chang,Etsion and Bogy [14](CEB model)to adopt it in their elasto-plastic model of deformed spheres.They introduced an improved model where the asperity deformations are primarily elastic but there is also a significant number of asperities beyond their elastic limit.Recently,Horng [15]extended the CEB model to describe a more general case of an elliptical contact of asperities.On the other hand,surfaces machined by turning,honing or grinding,have orientation corresponding to the direction of motion of the cutting tools relative to the workpieces,and a model of anisotropic rough surfaces must be then employed.In such cases,it is necessary to include both the principal curvatures taking into account the directional 0045-7825/$-see front matter Ó2006Elsevier B.V.All rights reserved.doi:10.1016/j.cma.2005.11.014*

Corresponding author.Address:Institute of Fundamental Technological Research,Polish Academy of Sciences,Swietokrzyska 21,00-049Warsaw,Poland.

E-mail address:michal.kleiber@.pl (M.Kleiber).

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