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TECHNICAL PAPERS

# A Mathematical Model for Frictional Elastic-Plastic Sphere-on-Flat Contacts at Sliding Incipient

[+] Author and Article Information
L. Chang, H. Zhang

Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA 16802

J. Appl. Mech 74(1), 100-106 (Dec 09, 2005) (7 pages) doi:10.1115/1.2178838 History: Received June 27, 2005; Revised December 09, 2005

## Abstract

This paper presents a mathematical model for frictional elastic-plastic sphere-on-flat contacts at sliding incipient. The model is developed based on theoretical work on contact mechanics in conjunction with finite-element results. It incorporates the effects of friction loading on the contact pressure, the mode of deformation, and the area of contact. The shear strength of the contact interface is, in this paper, assumed to be proportional to the contact pressure with a limiting value that is below the bulk shear strength of the sphere. Other plausible interfacial-shear-strength characteristics may also be implemented into the contact model in a similar manner. The model is used to analyze the frictional behavior of a sphere-on-flat contact where the experimental data suggest that the interfacial shear strength is similar in nature to the one implemented in the model. The theoretical results are consistent with the experimental data in all key aspects. This sphere-on-flat contact model may be used as a building block to develop an asperity-based contact model of rough surfaces with friction loading. It may also serve in the modeling of boundary-lubricated sliding contacts where the interfacial shear strength in each micro-contact is coupled with its flash temperature and related to the lubricant/surface physical-chemical behavior.

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## Figures

Figure 1

Experimental results shown in Fig. 7 of Ref. 1

Figure 2

Experimental and theoretical results shown in Fig. 8 of Ref. 1 (the theoretical curve is generated by the model of Ref. 4)

Figure 3

Effects of friction on the critical normal approaches and modes of deformation in an elastic-perfectly-plastic cylinder-on-flat contact

Figure 4

Schematic of the slip-line field solution of a rigid-perfectly-plastic wedge under combined action of normal and tangential loading

Figure 5

Theoretical results corresponding to the experimental data of Fig. 1 (c=0.3 and τ¯m=0.35)

Figure 6

Theoretical results corresponding to the experimental data of Fig. 2 (c=0.3 and τ¯m=0.35)

Figure 7

Contact area and friction-induced junction growth with c=0.3 (A—frictionless, B—τ¯m=0.35, C—τ¯m=0.7, and D—τ¯m=1.0)

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