A Self-Consistent Scheme for Elastic-Plastic Asperity Contact

Authors: Xu Jianguo

Abstract:

In this paper, a generalized self-consistent scheme, or “three phase model", is used to set up a micro-mechanics model for rough surface contact with randomly distributed asperities. The dimensionless average real pressure p is obtained as function of the ratio of the real contact area to the apparent contact area, 0 A / A r . Both elastic and plastic materials are considered, and the influence of the plasticity of material on p is discussed. Both two-dimensional and three-dimensional rough surface contact problems are considered.

Keywords: Contact mechanics, plastic deformation, self-consistent scheme.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1077809

References:

[1] J. R. Barber, and M. Ciavarella, "Contact mechanics," International Journal of Solids and Structures, Vol. 37, pp. 29-43, 2000.
[2] K. L. Johnson, Contact Mechanics. Cambridge, UK: Cambridge University publisher, 1985.
[3] H. H. Yu, and Z. Suo, "A model for wafer bonding by elastic accommodation," Journal of the Mechanics and Physics of Solids, Vol. 46, No. 5, pp. 829-844, 1998.
[4] A. Majumdar, and B. Bhushan, "Characterization and modeling of surface roughness and contact mechanics," in Micro/Nano tribology, 2nd ed., B. Bhushan Ed. New York, USA: CRC Press, 1999.
[5] B. Bhushan, Principles and applications of tribology. New York, USA: John Eiley & Sons, 1999.
[6] R. M. Christensen, "A critical evaluation for a class of micro-mechanics models," Journal of the Mechanics and Physics of Solids, Vol. 38, Issue 3, pp. 379-404, 1990.
[7] R. M. Christensen, Mechanics of composite materials. New York, USA: John Wiley, 1979.
[8] H. Fan, Introduction to tensor analysis and applications (Part C). Nanyang Technological University, SG: lecture note, 2000.
[9] R. Hill, "A self-consistent mechanics of composite materials," Journal of the Mechanics and Physics of Solids, Vol. 13, Issue 4, pp. 213-222, 1965.
[10] B. Budiansky, "On the elastic moduli of some heterogeneous materials," Journal of the Mechanics and Physics of Solids, Vol. 13, Issue 4, pp. 223-227, 1965.
[11] H. Fan, and K.Y. Sze, "A micro-mechanics model for imperfect interface in dielectric materials," Mechanics of Materials, vol. 33, pp. 363-370, 2001.
[12] F. Erdogan, "Mixed boundary value problems in mechanics," in Mechanics Today, Vol. 4. New York, USA: Pergamon Press, 1975.
[13] ANSYS User-s Manual, Release 5.6.2. 2000.
[14] W H. M. estergaard, "Bearing pressures and cracks," Journal of Applied Mechanics, Vol. 6(A), pp. 49-53, 1939.
[15] J. Dunders, K. C. Tsai, and L. M. Keer, "Contact between elastic bodies with wavy surfaces," Journal of Elasticity, Vol. 3, No. 2, pp. 109-115, 1973.
[16] H. Fan, and K. Y. Sze, "A self-consistent scheme for asperity contact," Key Engineering Materials, Vol. 227, pp. 17-22, 2002.
[17] B. Bhushan, Tribology and Mechanics of Magnetic Storage Device, 2nd Ed. New York, USA: Springer, 1996.