A Finite Element Study of Elasto-Plastic Hemispherical Contact Against a Rigid Flat

[+] Author and Article Information
Robert L. Jackson, Itzhak Green

George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405e-mail: gt2433a@prism.gatech.edu

J. Tribol 127(2), 343-354 (Apr 07, 2005) (12 pages) doi:10.1115/1.1866166 History: Received April 29, 2004; Revised September 08, 2004; Online April 07, 2005
Copyright © 2005 by ASME
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Greenwood,  J. A., and Williamson,  J. B. P., 1966, “Contact of Nominally Flat Surfaces,” Proc. R. Soc. London, Ser. A, 295, pp. 300–319.
Timoshenko, S., and Goodier, J. N., 1951, Theory of Elasticity, McGraw-Hill, New York.
Green,  I., 2002, “A Transient Dynamic Analysis of Mechanical Seals Including Asperity Contact and Face Deformation,” Tribol. Trans., 45(3), pp. 284–293.
Kogut,  L., and Etsion,  I., 2002, “Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat,” Trans. ASME, J. Appl. Mech., 69(5), pp. 657–662.
Chang,  W. R., Etsion,  I., and Bogy,  D. B., 1987, “An Elastic-Plastic Model for the Contact of Rough Surfaces,” ASME J. Tribol., 109, pp. 257–263.
Zhao,  Y., Maletta,  D. M., and Chang,  L., 2000, “An Asperity Microcontact Model Incorporating the Transition From Elastic Deformation to Fully Plastic Flow,” ASME J. Tribol., 122, pp. 86–93.
Jacq,  C., Nelias,  D., Lormand,  G., and Girodin,  D., 2003, “Development of a Three-Dimensional Semi-Analytical Elastic-Plastic Contact Code,” ASME J. Tribol., 125, pp. 653–667.
Vu-Quo,  L., Zhang,  X., and Leesburg,  L., 2000, “A Normal Force-Displacement Model for Contacting Spheres Accounting for Plastic Deformation: Force Driven Formulation,” ASME J. Appl. Mech., 67, pp. 363–371.
Abbott,  E. J., and Firestone,  F. A., 1933, “Specifying Surface Quality-A Method Based on Accurate Measurement and Comparison,” Mech. Eng. (Am. Soc. Mech. Eng.), 55, pp. 569–572.
Greenwood,  J. A., and Tripp,  J. H., 1971, “The Contact of Two Nominally Flat Rough Surfaces,” Proc. Inst. Mech. Eng., 185, pp. 625–633.
Tabor, D., 1951, The Hardness of Materials, Clarendon Press, Oxford.
Davis, J. R., 1999, Metals Handbook, 2nd ed., ASM International, Metals Park, OH.
Francis,  H. A., 1976, “Phenomenological Analysis of Plastic Spherical Indentation,” ASME J. Eng. Mater. Technol., 98, pp. 272–281.
Oliver,  W. C., and Pharr,  G. M., 1992, “An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation,” J. Mater. Res., 7(6), pp. 1564–1583.
Mesarovic,  S. D., and Fleck,  N. A., 2000, “Frictionless Indentation of Dissimilar Elastic-plastic Spheres,” Int. J. Solids Struct., 37, pp. 7071–7091.
Kral,  E. R., Komvopoulos,  K., and Bogy,  D. B., 1993, “Elastic-Plastic Finite Element Analysis of Repeated Indentation of a Half-Space by a Rigid Sphere,” ASME J. Appl. Mech., 60, pp. 829–841.
Kral,  E. R., Komvopoulos,  K., and Bogy,  D. B., 1995, “Finite Element Analysis of Repeated Indentation of an Elastic-Plastic Layered Medium by a Rigid Sphere, Part I: Surface Results,” ASME J. Appl. Mech., 62, pp. 20–28.
Kral,  E. R., Komvopoulos,  K., and Bogy,  D. B., 1995, “Finite Element Analysis of Repeated Indentation of an Elastic-Plastic Layered Medium by a Rigid Sphere, Part II: Subsurface Results,” ASME J. Appl. Mech., 62, pp. 29–42.
Streator,  J. L., 2003, “Dynamic Contact of a Rigid Sphere With an Elastic Half-Space: A Numerical Simulation,” ASME J. Tribol., 125, pp. 25–32.
Tian,  H., and Saka,  N., 1991, “Finite element analysis of an elastic-plastic two-layer half-space: normal contact,” Wear, 148, pp. 47–68.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge.
Giannakopoulos,  A. E., Larsson,  P. L., and Vestergaard,  R., 1994, “Analysis of Vickers Indentation,” Int. J. Solids Struct., 31, pp. 2679–2708.
Barber,  J. R., and Ciavarella,  M., 2000, “Contact Mechanics,” Int. J. Solids Struct., 37, pp. 29–43.
Liu,  G., Wang,  G. J., and Lin,  C., 1999, “A Survey of Current Models for Simulating the Contact between Rough Surfaces,” Tribol. Trans., 42, pp. 581–591.
Johnson, K. L., 1968, “An Experimental Determination of the Contact Stresses Between Plastically Deformed Cylinders and Spheres,” Engineering Plasticity, Cambridge University Press, Cambridge, pp. 341–361.
Reddy, J. N., 1993, An Introduction to the Finite Element Method, 2nd ed., McGraw-Hill, New York.
Shigley, J. E., and Mischke, C. R., 1989, Mechanical Engineering Design, 5th ed., McGraw-Hill, New York.
Quicksall, J., Jackson, R. L., and Green, I., 2004, “Elasto-plastic Hemispherical Contact for Varying Mechanical Properties,” accepted for publication in J. Eng. Tribol.-Part J.
Williams, J. A., 1994, Engineering Tribology, Oxford University Press, Oxford.
Goodier, J. N., and Hodge, P. G., 1958, Elasticity and Plasticity, Wiley, New York.
Chang, W. R., 1986, “Contact, Adhesion, and Static Friction of Metallic Rough Surfaces,” Ph.D. thesis, University of California, Berkeley, pp. 18–23.


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Spherical contact model before contact (a), during mostly elastic deformation (b), and during mostly plastic deformation (c)
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Finite element mesh of a sphere generated by ANSYS™
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FEM predicted contact area
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FEM predicted contact force
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Average contact pressure to yield strength ratio
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Average contact pressure to yield strength ratio
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Progression of change in hardness with deformed geometry
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Predicted average pressure to yield strength ratio for various models
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Displacement at edge of contact area plotted as a function of penetration depth
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Stress plots from ANSYS™, showing the evolution of the stress distribution from (a) elasto-plastic (not yet plastic on surface) to (d) just before fully plastic




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