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Research Papers: Contact Mechanics

Plastic Yield Conditions for Adhesive Contacts Between a Rigid Sphere and an Elastic Half-Space

[+] Author and Article Information
Yu-Chiao Wu

Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA 02115

George G. Adams

Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA 02115adams@coe.neu.edu

J. Tribol 131(1), 011403 (Dec 04, 2008) (7 pages) doi:10.1115/1.3002329 History: Received May 19, 2008; Revised September 04, 2008; Published December 04, 2008

Hertz contact theory allows the onset of yielding to be predicted for those contacts in which the effect of adhesion can be neglected. However, in microscale contacts, such as those that occur in microelectromechanical systems (MEMS), yielding will occur for lower loads than those predicted by Hertz. For such cases, the Johnson–Kendall–Roberts (JKR), Derjaguin–Muller–Toporov (DMT), and Greenwood–Johnson (GJ) theories extend the Hertz theory to include the effect of adhesion. The present study gives yield conditions for the JKR, DMT, and Greenwood–Johnson theories of adhesion. Attention is first focused on the initiation of yield along the axis of symmetry of an elastic half-space contacted by a rigid sphere. The results show that the critical loads for the three adhesion theories are close together, but differ significantly from that predicted by Hertz. In fact, it is possible for yielding to occur due to adhesion alone, without an external load. A curve-fit formula is given for the yield load as a function of an adhesion parameter for different Poisson’s ratios. Results are then obtained for the onset of plastic deformation away from the axis of symmetry using the Greenwood–Johnson theory of adhesion.

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Figures

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Figure 1

A rigid sphere contacting an elastic half-space

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Figure 2

Subsurface von Mises stress contours for the JKR theory with ν=0.3, φ=0.600, and PJKR=4.90, which corresponds to the onset of yield at z/a=0.409

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Figure 3

Subsurface von Mises stress contours for the DMT theory with ν=0.3, φ=0.600, and PDMT=5.09, which corresponds to the onset of yield at z/a=0.481

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Figure 4

Subsurface von Mises stress contour for the GJ theory with ν=0.3, μ=1, φ=0.600, and PGJ=4.91, which corresponds to the onset of yield at z/a=0.434

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Figure 5

Subsurface von Mises stress contour for the GJ theory with ν=0.3, μ=2, φ=0.600, and PGJ=4.90, which corresponds to the onset of yield at z/a=0.423

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Figure 6

Dimensionless load for the initiation of yield versus the adhesion parameter for different values of Poisson’s ratio. Results are for the JKR theory (PJKR∗ in solid lines), DMT theory (PDMT∗ in dot-dashed lines), and GJ theory (PGJ∗ with μ=1 in dotted lines and with μ=2 in dashed lines).

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Figure 7

Dimensionless load for the initiation of yield versus the adhesion parameter for the GJ theory (μ=1, 1.4, 2.0, 3.0, and 4.0) and for Poisson’s ratio of 0.3. Results include yield away from the axis of symmetry which are shown in the nearly vertical lines.

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