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RESEARCH PAPERS

A Finite Element Study of the Residual Stress and Deformation in Hemispherical Contacts

[+] Author and Article Information
Robert Jackson, Itti Chusoipin, Itzhak Green

George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405

J. Tribol 127(3), 484-493 (Jun 13, 2005) (10 pages) doi:10.1115/1.1843166 History: Received February 20, 2004; Revised October 20, 2004; Online June 13, 2005
Copyright © 2005 by ASME
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References

Jackson,  R. L., and Green,  I., 2005, “A Finite Element Study of Elasto-Plastic Hemispherical Contact,” ASME J. Tribol., 127(2), pp. 343–354.
Kogut,  L., and Etsion,  I., 2002, “Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat,” ASME J. Appl. Mech., 69(5), 657–662.
Mesarovic,  S. D., and Fleck,  N. A., 2000, “Frictionless Indentation of Dissimilar Elastic-Plastic Spheres,” Int. J. Solids Struct., 37, 7071–7091.
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.
Tabor, D., 1951, The Hardness of Materials, Clarendon, Oxford, pp. 14–15.
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, 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, 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, 29–42.
Ye,  N., and Komvopoulos,  K., 2003, “Effect of Residual Stress in Surface Layer on Contact Deformation of Elastic-Plastic Layered Media,” ASME J. Tribol., 125, 692–699.
Quicksall,  J., Jackson,  R. L., and Green,  I., 2004, “Elasto-Plastic Hemispherical Contact for Varying Mechanical Properties,” IMechE J. of Eng. Trib.-Part J,218(4), pp. 313–322.
Shigley, J. E., and Mischke, C. R., 1989, Mechanical Engineering Design, 5th ed., McGraw-Hill, New York.
Fischer-Cripps,  A. C., 1999, “The Hertzian Contact Surface,” J. Mater. Sci., 34, 129–137.
Kogut,  L., and Etsion,  I., 2003, “Adhesion in Elastic-Plastic Spherical Microcontact,” J. Colloid Interface Sci., 261, 372–378.
Muller,  V. M., Derjaguin,  Y. P., and Toporov,  Yu. J., 1983, “On Two Methods of Calculation of the Force of Sticking of an Elastic Sphere to a Rigid Plane,” Colloids Surf., 7, 251–259.
Goodier, J. N., and Hodge, P. G., 1958, Elasticity and Plasticity, Wiley, New York.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge.
Dowling, N. E., 1993, Mechanical Behavior of Materials, Prentice-Hall, Englewood Cliffs, NJ.

Figures

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Diagram of loaded (b) and unloaded (c) contact of deforming elastoplastic hemispheres and a rigid flat
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Example of used FEM mesh
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Schematic of the coordinate system and boundary conditions used in the FEM
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The normalized radial surface displacement vs the normalized radial distance in the loaded condition for (a) small and (b) large normalized interference depths
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The normalized axial displacement vs the normalized radial distance in the loaded condition for (a) small and (b) large normalized interference depths
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The normalized radial residual displacement vs the normalized radial distance of the hemisphere unloaded from (a) small and (b) large normalized interference depths
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The normalized axial displacement vs the normalized radial distance of the hemisphere unloaded from (a) small and (b) large normalized interference depths
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Contour plots of the complete stress tensor for a hemispherical contact unloaded from ω* =3.92: (a) radial stress, σx/Sy, (b) axial stress, σy/Sy, (c) hoop stress, σz/Sy, and (d) shear stress, τxy/Sy
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Contour plots of the complete stress tensor for a hemispherical contact unloaded from ω* =35.0: (a) radial stress, σx/Sy, (b) axial stress, σy/Sy, (c) hoop stress, σz/Sy, and (d) shear stress, τxy/Sy
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Contour plot of the normalized elastic residual von Mises stress (σvm/Sy) at various unloaded normalized interferences: (a) ω* =2.14, (b) ω* =3.92, (c) ω* =5.71, and (d) ω* =15.00
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Contour plot of the normalized residual von Mises stress (σvm/Sy) at various unloaded normalized interferences at the onset and formation of plastic residual stresses: (a) ω* =25.0, (b) ω* =40.0, (c) ω* =68.6, and (d) ω* =100.0
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The normalized maximum von Mises residual stress of the unloaded hemisphere as a function of the unloaded ω*
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The normalized surface displacement of aluminum and steel hemispheres loaded to ω* =135 vs the normalized radial location
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The normalized residual surface displacement of aluminum and steel hemispheres unloaded from ω* =135 vs the normalized radial location
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Schematic for the approximation of the location of the critical contact radius before loading (solid line) and after loading (dashed line)

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