Improved Elastic Contact Model Accounting for Asperity and Bulk Substrate Deformation

Abstract

An improved elastic contact model for a single asperity system is proposed accounting for both the effects of bulk substrate and asperity deformations. The asperity contact stiffness is based on the Hertzian solution for spherical contact, and the bulk substrate stiffness on the solution of Hertzian pressure on a circular region of the elastic halfspace. Depending on the magnitude of the applied load, as well as the geometrical and physical properties of the asperity and bulk materials, the bulk substrate could have considerable contribution to the overall contact stiffness. The proposed single asperity model is generalized using two parameters based on physical and geometrical properties, and is also verified using finite element analysis. A parametric study for a practical range of geometric and physical parameters is performed using finite element analysis to determine the range of validity of the proposed model and also to compare it with the Hertz contact model. The single asperity model is extended to rough surfaces in contact and the contact stiffness from the proposed model and the simpler Greenwood-Williamson asperity model are compared to experimental measurements.

Elastic–Plastic Spherical Contact Modeling Including Roughness Effects

“…The results are presented for a typical plasticity index w = 2 and three different values of x c * = 1, 2, and 5. The combination of the displacement of the bulk of the sphere and asperities can be described as a system of two nonlinear springs in series (see, e.g., [14]). Initially, at small loads, the stiffness of the asperities is much smaller than that of the bulk and hence, the contribution of the asperities to the total displacement is dominant.…”

A universal model for the load–displacement relation in an elastic coated spherical contact

“…The authors presented an effective modulus of elasticity of the coated sphere and showed that this effective modulus is mainly influenced by the interference. Yeo et al [28] investigated a single spherical asperity of a coated rough surface. The study is focused on a hard coating and soft substrate and assumes that the entire asperity is made of the harder coating material.…”

Nanoindentation modeling of a nanodot-patterned surface on a deformable substrate

“…In this model, a uniform pressure or uniform displacement is added to the substrate to account for the effect of asperity interaction. Yeo et al (2009) studied the elastic deformation of the substrate for a hard coating on a soft substrate and developed a 'two springs in series' concept to model the deformation of the substrate. Based on this concept, Yeo et al (2010) modeled the asperity interactions in the contact between a flat punch and a flat rough surface.…”

“…Therefore, a model that treats each asperity individually is desirable to model the nanoindentation of the Ni NDPS. Yeo et al (2009Yeo et al ( , 2010) developed a model that treats each asperity individually and considers the asperity interactions. However, this model is an elastic model and is not suitable for modeling the nanoindentation of a Ni NDPS, in which plastic deformation occurs readily.…”

“…Because the thickness and the lateral dimension of the substrate are orders of magnitude larger than the dimension of the bottom of the nanodots, the substrate can be viewed as an elastic half-space. Yeo et al (2009Yeo et al ( , 2010 assumed elastic deformation of the substrate in a study of a hard coating on a soft substrate. They used Hertzian contact pressure at the asperity-substrate interface.…”