Influence of a Hard Surface Layer on the Limit of Elastic Contact—Part I: Analysis Using a Real Surface Model

Abstract

A numerical simulation technique for calculating the pressure distribution and the deformed geometry of an elastic half-space which has a hard surface layer in contact with a rigid indenter with a rough surface is presented. In order to reduce the computing time, the Conjugate Gradient Method (CGM) is applied to solve a set of linear equations for unknown pressures. In each iteration of the CGM, the Fast Fourier Transform (FFT) is used for the task of multiplying a direction vector by an influence coefficient matrix. An FFT-based scheme for evaluating subsurface stresses in the layer and the substrate is also presented. As an example, the pressure distribution and the deformed geometry of a steel surface coated with a TiN layer in contact with a rigid rough indenter are calculated. The subsurface stresses are also compared with von Mises yield criterion to investigate the deformation mode at the asperity contacts. The results show that the limit of elastic contact is highly dependent on the layer thickness and the surface roughness.

Elastic deformation of soft coatings due to lubrication forces

“…The four boundary conditions in our configuration are an axisymmetric normal stress and a negligible shear stress on top of soft coating, together with sticky boundary conditions on bottom surface. For this case, a closed form for the surface deformation, which is needed to calculate ℎ( , ) in Equation 1 was derived previously in the context of indentation, 30,31 and used by others in the context of elastohydrodynamics. 20,32 The surface deformation can be calculated from: (1 ) 4 ( ) Leroy and Charlaix used the approach outlined in Equations 2-4 to characterize the force response of an oscillatory motion on a thin or a thick coating mediated by a liquid.…”

An extension of the Hertz theory for three-dimensional coated bodies

“…The FRF of the surface normal displacement due to pressure on the surface of a 3-D body is expressed as follows [17],…”

Simulation and Mitigation of Pattern and Process Dependencies in Nanoimprint Lithography

“…Sub-surface stresses can similarly be estimated by convolving contact pressures with the appropriate kernel functions [37]. The convolution itself can be effected using fast Fourier transforms [38], [39] or other summation methods. The solution for the contact-pressure distribution has successfully been performed with iterative conjugate-gradient methods combined with kinematic constraints on the surface deformation, or with methods that seek a minimum of elastic potential energy in the layer.…”

“…Efficient numerical simulations of the deformations of elastic and elastic-plastic bodies [37], [38] have been widely used by researchers in tribology. These simulations rely on a description of the deformation of the material's surface in response to a point-load, together with, in the elastic-plastic cases, a criterion for yielding of the material.…”