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A Solution of Rigid–Perfectly Plastic Deep Spherical Indentation Based on Slip-Line Theory

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An Erratum to this article was published on 19 December 2015

Abstract

During indentation, it is often important to determine the relationship between the average pressure and the yield strength. This work uses slip-line theory to determine this relationship for the case of a rigid sphere indenting a frictionless perfectly plastic half-space (i.e., no hardening). The results show that the ratio between the average contact pressure and the yield strength decreases as the depth of indentation is increased. Note that the slip-line analysis does not include the effects of pileup or sink-in deformations. However, the slip-line theory has also been compared to data generated using the finite element method (FEM). The theory and the FEM results appear to agree well.

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References

  1. Jackson, R.L., Kogut, L.: A comparison of flattening and indentation approaches for contact mechanics modeling of single asperity contacts. ASME J. Tribol. 128(1), 209–212 (2006)

    Article  Google Scholar 

  2. Ishlinskii, A.J.: The problem of plasticity with axial symmetry and Brinell’s Test [An English Translation has been published by Ministry of Supply, A.R.D. (1947)]. J. Appl. Math. Mech. (U.S.S.R) 8, 233 (1944)

  3. Jackson, R.L., Green, I.: A finite element study of elasto-plastic hemispherical contact against a rigid flat. ASME J. Tribol. 127(2), 343–354 (2005)

    Article  Google Scholar 

  4. Tabor, D.: The hardness of materials. Clarendon Press, Oxford (1951)

    Google Scholar 

  5. Wadwalkar, S.S., Jackson, R.L., Kogut, L.: A study of the elastic-plastic deformation of heavily deformed spherical contacts. IMechE Part J: J. Eng. Tribol. 224(10), 1091–1102 (2010)

    Article  Google Scholar 

  6. Jackson, R., Green, I., Marghitu, D.: Predicting the coefficient of restitution of impacting elastic-perfectly plastic spheres. Nonlinear Dyn. 60(3), 217–229 (2010)

    Article  Google Scholar 

  7. Mesarovic, S.D., Fleck, N.A.: Spherical indentation of elastic–plastic solids. Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci. 455(1987), 2707–2728 (1999). doi:10.1098/rspa.1999.0423

  8. Kogut, L., Komvopoulos, K.: Analysis of spherical indentation cycle of elastic-perfectly plastic solids. J. Mater. Res. 19, 3641–3653 (2004)

    Article  Google Scholar 

  9. Ye, N., Komvopoulos, K.: Indentation analysis of elastic-plastic homogeneous and layered media: criteria for determining the real material hardness. J. Tribol. Trans. ASME 125(4), 685 (2003)

  10. Alcalá, J., Esqué-de los Ojos, D.: Reassessing spherical indentation: contact regimes and mechanical property extractions. Int. J. Solids Struct. 47(20), 2714–2732 (2010). doi:10.1016/j.ijsolstr.2010.05.025

    Article  Google Scholar 

  11. Yu, W.P., Blanchard, J.P.: An elastic-plastic indentation model and its solutions. J. Mater. Res. 11(9), 2358–2367 (1996). doi:10.1557/Jmr.1996.0299

    Article  Google Scholar 

  12. Chang, W.R., Etsion, I., Bogy, D.B.: An elastic-plastic model for the contact of rough surfaces. ASME J. Tribol. 109(2), 257–263 (1987)

    Article  Google Scholar 

  13. Zhao, Y., Maletta, D.M., Chang, L.: An asperity microcontact model incorporating the transition from elastic deformation to fully plastic flow. ASME J. Tribol. 122(1), 86–93 (2000)

    Article  Google Scholar 

  14. Kogut, L., Etsion, I.: Elastic-plastic contact analysis of a sphere and a rigid flat. ASME J. Appl. Mech. 69(5), 657–662 (2002)

    Article  Google Scholar 

  15. Field, J.S., Swain, M.V.: A simple predictive model for spherical indentation. J. Mater. Res. 8(02), 297–306 (1993). doi:10.1557/JMR.1993.0297

    Article  Google Scholar 

  16. Follansbee, P.S., Sinclair, G.B.: Quasi-static normal indentation of an elasto-plastic half-space by a rigid sphere—I: analysis. Int. J. Solids Struct. 20(1), 81–91 (1984). doi:10.1016/0020-7683(84)90078-7

    Article  Google Scholar 

  17. Biwa, S., Storåkers, B.: An analysis of fully plastic Brinell indentation. J. Mech. Phys. Solids 43(8), 1303–1333 (1995). doi:10.1016/0022-5096(95)00031-D

    Article  Google Scholar 

  18. Richmond, O., Morrison, H.L., Devenpeck, M.L.: Sphere indentation with application to the Brinell hardness test. Int. J. Mech. Sci. 16(1), 75–82 (1974). doi:10.1016/0020-7403(74)90034-4

    Article  Google Scholar 

  19. Taljat, B., Pharr, G.M.: Development of pile-up during spherical indentation of elastic–plastic solids. Int. J. Solids Struct. 41(14), 3891–3904 (2004). doi:10.1016/j.ijsolstr.2004.02.033

    Article  Google Scholar 

  20. Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1985)

    Book  Google Scholar 

  21. Jackson, R.L., Green, I.: A statistical model of elasto-plastic asperity contact between rough surfaces. Trib. Int. 39(9), 906–914 (2006)

    Article  Google Scholar 

  22. Kogut, L., Jackson, R.L.: A comparison of contact modeling utilizing statistical and fractal approaches. ASME J. Tribol. 128(1), 213–217 (2005)

    Article  Google Scholar 

  23. Kogut, L., Etsion, I.: A finite element based elastic-plastic model for the contact of rough surfaces. Tribol. Trans. 46(3), 383–390 (2003)

    Article  Google Scholar 

  24. Ciavarella, M., Delfine, G., Demelio, G.: A ‘re-vitalized’ Greenwood and Williamson model of elastic contact between fractal surfaces. J. Mech. Phys. Solids 54(12), 2569–2591 (2006)

    Article  Google Scholar 

  25. Sepehri, A., Farhang, K.: Closed-form equations for three dimensional elastic-plastic contact of nominally flat rough surfaces. J. Tribol. Trans Asme 131(4) (2009). doi:10.1115/1.3204775

  26. Beheshti, A., Khonsari, M.M.: Asperity micro-contact models as applied to the deformation of rough line contact. Tribol. Int. 52, 61–74 (2012). doi:10.1016/j.triboint.2012.02.026

    Article  Google Scholar 

  27. Lee, C.-H., Eriten, M., Polycarpou, A.A.: Application of elastic-plastic static friction models to rough surfaces with asymmetric asperity distribution. ASME J. Tribol. 132(3), 031602-031601-031611 (2010)

  28. Li, L., Etsion, I., Talke, F.E.: Contact area and static friction of rough surfaces with high plasticity index. ASME J. Tribol. 132(3), 031401-031401-031410 (2010)

  29. Gao, Y.F., Bower, A.F.: Elastic-plastic contact of a rough surface with Weierstrass profile. Proc. R. Soc. A 462, 319–348 (2006)

    Article  Google Scholar 

  30. Jackson, R.L., Streator, J.L.: A multiscale model for contact between rough surfaces. Wear 261(11–12), 1337–1347 (2006)

    Article  Google Scholar 

  31. Goedecke, A., Jackson, R., Mock, R.: A fractal expansion of a three dimensional elastic–plastic multi-scale rough surface contact model. Tribol. Int. 59, 230–239 (2013)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Auburn University, Auburn, AL, USA

    Robert L. Jackson, Hamid Ghaednia & Sara Pope

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  1. Robert L. Jackson
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  2. Hamid Ghaednia
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  3. Sara Pope
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Correspondence to Robert L. Jackson.

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Jackson, R.L., Ghaednia, H. & Pope, S. A Solution of Rigid–Perfectly Plastic Deep Spherical Indentation Based on Slip-Line Theory. Tribol Lett 58, 47 (2015). https://doi.org/10.1007/s11249-015-0524-3

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