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Energy Loss in the Impact of Elastic Spheres on a Rigid Half-Space in Presence of Adhesion

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Abstract

Adhesion can cause energy losses in asperities or particles coming into dynamic contact resulting in frictional dissipation, even if the deformation occurring is purely elastic. Such losses are of special significance in impact of nanoparticles and friction between surfaces under low contact pressure to hardness ratio. The objective of this work is to study the effect of adhesion during the normal impact of elastic spheres on a rigid half-space, with an emphasis on understanding the mechanism of energy loss. We use finite element method for modeling the impact phenomenon, with the adhesion due to van der Waals force and the short-range repulsion included as body forces distributed over the volume of the sphere. This approach, in contrast with commonly used surface force approximation, helps to model the interactions in a more precise way. We find that the energy loss in impact of elastic spheres is negligible unless there are adhesion-induced instabilities. Significant energy loss through elastic stress waves occurs due to jump-to-contact and jump-out-of-contact instabilities and can even result in capture of the elastic sphere on the half-space.

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References

  1. Nosonovsky, M.: Model for solid-liquid and solid-solid friction of rough surfaces with adhesion hysteresis. J. Chem. Phys. 126, 224701 (2007)

    Article  Google Scholar 

  2. Israelachvili, J.N.: Intermolecular and Surface Forces, 3 Edition. Academic Press, SanDiego, CA (2011)

    Google Scholar 

  3. Szoszkiewicz, R., Bhushan, B., Huey, B.D., Kulik, A.J., Gremaud, G.: Correlations between adhesion hysteresis and friction at molecular scales. J. Chem. Phys. 122, 144708 (2005)

    Article  Google Scholar 

  4. Sundararajan, G.: A comprehensive model for the solid particle erosion of ductile materials. Wear 149, 111–127 (1991)

    Article  Google Scholar 

  5. Tsai, C.-J., Pui, D.Y.H., Liu, B.Y.H.: Capture and rebound of small particles upon impact with solid surfaces. Aerosol Sci. Tech. 12(3), 497–507 (1990)

    Article  Google Scholar 

  6. Wall, S., John, W., Wang, H.-C., Goren, S.L.: Measurements of kinetic energy loss for particles impacting surfaces. Aerosol Sci. Tech. 12(4), 926–946 (1990)

    Article  Google Scholar 

  7. Brach, R.M., Dunn, P.F., Li, X.: Experiments and engineering models of microparticle impact and deposition. J. Adhes. 74(1–4), 227–282 (2000)

    Article  Google Scholar 

  8. Chokshi, A., Tielens, A.G.G.M., Hollenbach, D.: Dust coagulation. Astron. J. 407, 806–819 (1993)

    Article  Google Scholar 

  9. Dominik, C., Blum, J., Cuzzi, J.N., Wurm, G.: Growth of dust as the initial step toward planet formation. In: Reipurth, B., Jewitt, D., Keil, K. (eds.) Protostars and Planets V., pp. 783–800. The University of Aizona Press, Arizona (2007)

    Google Scholar 

  10. Dahneke, B.: Particle bounce or capture search for an adequate theory: I. conservation-of-energy model for a simple collision process. Aerosol Sci. Tech. 23(1), 25–39 (1995)

    Article  Google Scholar 

  11. Johnson, K.L., Pollock, H.M.: The role of adhesion in the impact of elastic spheres. J. Adhes. Sci. Technol. 8(11), 1323–1332 (1994)

    Article  Google Scholar 

  12. Thornton, C., Yin, K.K.: Impact of elastic spheres with and without adhesion. Powder Technol. 65(1–3), 153–166 (1991)

    Article  Google Scholar 

  13. Reed, J.: Energy losses due to elastic wave propagation during an elastic impact. J. Phys. D Appl. Phys. 18(12), 2329–2337 (1985)

    Article  Google Scholar 

  14. Uchic, M.D., Dimiduk, D.M., Florando, J.N., Nix, W.D.: Sample dimensions influence strength and crystal plasticity. Science 305, 986–989 (2004)

    Article  Google Scholar 

  15. Stronge, W.J.: Impact Mechanics. Cambridge University Press, Cambridge (2000)

    Book  Google Scholar 

  16. Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1987)

    Google Scholar 

  17. Love, A.E.H.: A Treatise on the Mathematical Theory of Elasticity. 4th edn. Dover Publications, New York (1944)

    Google Scholar 

  18. Raman, C.V.: On some applications of Hertz’s theory of impact. Phys. Rev. 15, 277–284 (1920)

    Article  Google Scholar 

  19. Tillet, J.P.A.: A study of the impact of spheres on plates. Proc. Phys. Soc. B 67, 677–688 (1954)

    Article  Google Scholar 

  20. Hunter, S.C.: Energy absorbed by elastic waves during impact. J. Mech. Phys. Solids 5, 162–171 (1957)

    Article  Google Scholar 

  21. Johnson, K.L., Kendall, K., Roberts, A.D.: Surface energy and the contact of elastic solids. Proc. R. Soc. Lond. A 324, 301–313 (1971)

    Article  Google Scholar 

  22. Derjaguin, B.V., Muller, V.M., Toporov, Y.P.: Effect of contact deformations on the adhesion of particles. J. Colloid Interface Sci. 53(2), 314–326 (1975)

    Article  Google Scholar 

  23. Muller, V.M., Derjaguin, B.V., Toporov, Y.P.: On two methods of calculation of the force of sticking of an elastic sphere to a rigid plane. Colloid. Surf. 7, 251–259 (1983)

    Article  Google Scholar 

  24. Maugis, D.: Adhesion of spheres: the JKR-DMT transition using a dugdale model. J. Colloid Interface Sci. 150(1), 243–269 (1992)

    Article  Google Scholar 

  25. Johnson, K.L., Greenwood, J.A.: An adhesion map for the contact of elastic spheres. J. Colloid Interface Sci. 192, 326–333 (1997)

    Article  Google Scholar 

  26. Bhaskaran, H., Gotsmann, B., Sebastian, A., Drechsler, U., Lantz, M.A., Despont, M., Jaroenapibal, P., Carpick, R.W., Chen, Y., Sridharan, K.: Ultralow nanoscale wear through atom-by-atom attrition in silicon-containing diamond-like carbon. Nat. Nanotechnol. 5, 181–185 (2010)

    Article  Google Scholar 

  27. Anantheshwara, K., Bobji, M.S.: In situ transmission electron microscope study of single asperity sliding contacts. Tribol. Int. 43, 1099–1103 (2010)

    Article  Google Scholar 

  28. Greenwood, J.A., Williamson, J.B.P.: Contact of nominally flat surfaces. Proc. R. Soc. Lond. A 295, 300–319 (1966)

    Article  Google Scholar 

  29. Tolstoi, D.M.: Significance of the normal degree of freedom and natural normal vibrations in contact friction. Wear 10, 199–213 (1967)

    Article  Google Scholar 

  30. Butt, H.-J., Kappl, M.: Surface and Interfacial Forces. 4th edn. Wiley-VCH, Weinheim (2010)

    Book  Google Scholar 

  31. Cho, S.-S., Park, S.: Finite element modeling of adhesive contact using molecular potential. Tribol. Int. 37(9), 763–769 (2004)

    Article  Google Scholar 

  32. Sauer, R.A., Li, S.: A contact mechanics model for quasi-continua. Int. J. Numer. Methods Eng. 71, 931–962 (2007)

    Article  Google Scholar 

  33. Bobji, M.S., Xavier, S., Jayadeep, U.B., Jog, C.S.: Adhesion-induced instability in asperities. Tribol. Lett. 39(2), 201–209 (2010)

    Article  Google Scholar 

  34. Simo, J.C., Tarnow, N.: The discrete energy-momentum method: conserving algorithms for nonlinear elastodynamics. Z. Angew. Math. Phys. 43(5), 757–792 (1992)

    Article  Google Scholar 

  35. Jog, C.S., Motamarri, P.: An energy-momentum conserving algorithm for nonlinear transient analysis within the framework of hybrid elements. J. Mech. Mater. Struct. 4(1), 157–186 (2009)

    Article  Google Scholar 

  36. Tsai, C.-J., Pui, D.Y.H., Liu, B.Y.H.: Elastic flattening and particle adhesion. Aerosol Sci. Tech. 15(4), 239–255 (1991)

    Article  Google Scholar 

  37. Muller, V.M., Yushchenko, V.S., Derjaguin, B.V.: On the influence of molecular forces on the deformation of an elastic sphere and its sticking to a rigid plane. J. Colloid Interface Sci. 77(1), 91–101 (1980)

    Article  Google Scholar 

  38. Attard, P., Parker, J.L.: Deformation and adhesion of elastic bodies in contact. Phys. Rev. A 46(12), 7959–7971 (1992)

    Article  Google Scholar 

  39. Jog, C.S.: Improved hybrid elements for structural analysis. J. Mech. Mater. Struct. 5(3), 507–528 (2010)

    Article  Google Scholar 

  40. Jog, C.S.: Continuum Mechanics, Volume I of Foundations and Applications of Mechanics. 2nd edn. Alpha Science Intl. Ltd., Oxford (2007)

    Google Scholar 

  41. Burnham, N.A., Colton, R.J., Pollock, H.M.: Interpretation of force curves in force microscopy. Nanotechnology 4, 64–80 (1993)

    Article  Google Scholar 

  42. Maugis, D.: Contact, Adhesion and Rupture of Elastic Solids. 2nd edn. Springer-Verlag, Berlin (2000)

    Book  Google Scholar 

  43. Smith, J.R., Bozzolo, G., Banerjea, A., Ferrante, J.: Avalanche in adhesion. Phys. Rev. Lett. 63(12), 1269–1272 (1989)

    Article  Google Scholar 

  44. Pethica, J.B., Sutton, A.P.: On the stability of a tip and flat at very small separations. J. Vac. Sci. Technol. A 6(4), 2490–2494 (1988)

    Article  Google Scholar 

  45. Greenwood, J.A.: Adhesion of elastic spheres. Proc. R. Soc. Lond. A 453, 1277–1297 (1997)

    Article  Google Scholar 

  46. Tabor, D.: Surface forces and surface interactions. J. Colloid Interface Sci. 58(1), 2–13 (1977)

    Article  Google Scholar 

  47. Greenwood, J.A.: On the DMT theory. Tribol. Lett. 26(3), 203–211 (2007)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Institute of Technology Calicut, Kozhikode, India

    U. B. Jayadeep

  2. Department of Mechanical Engineering, Indian Institute of Science, Bangalore, India

    M. S. Bobji & C. S. Jog

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  1. U. B. Jayadeep
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  2. M. S. Bobji
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  3. C. S. Jog
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Correspondence to M. S. Bobji.

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Jayadeep, U.B., Bobji, M.S. & Jog, C.S. Energy Loss in the Impact of Elastic Spheres on a Rigid Half-Space in Presence of Adhesion. Tribol Lett 53, 79–89 (2014). https://doi.org/10.1007/s11249-013-0245-4

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  • DOI: https://doi.org/10.1007/s11249-013-0245-4

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