Contact mechanics of multilayered rough surfaces

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Abstract
The deposition of layers is an effective way to improve the tribological performance of rough surfaces. The contact mechanics of layered rough surfaces needs to be studied to optimize layer parameters. Since 1995 a lot of progress has been made in the development of numerical contact models, which analyze the contact behavior of layered rough surfaces with no assumption concerning the roughness distribution as well as the effect of interfacial liquid film on the contact statistics. These models predict the contact pressure profile on the interface and contact statistics, namely fractional contact area, the maximum value of contact pressure, von Mises and principal tensile stresses, and relative meniscus force. The results allow the specification of layer properties to reduce friction, stiction, and wear of layered rough surfaces. A comprehensive review of these numerical contact models is presented here. Based on the formulation of contact problems, these models are classified into three categories: direct formulation, weighted residual formulation, and minimum total potential energy formulation. The numerical methods applied in these models include Finite Difference Method (FDM), Finite Element Method (FEM), and Boundary Element Method (BEM). Typical examples of layered rough surfaces of contact simulated by those models are presented. The examples contain data for various surface topographies, elastic and elastic-plastic material properties, normal and tangential loading conditions, and dry and wet interfaces. A 3D BEM model based on a variational principle is described in detail for its capability to analyze the layered rough surfaces of contact involving a large number of contact points. Applications of the model to magnetic storage devices and MicroElectroMechanical Systems (MEMS) are presented. This review article contains 92 references.