Dynamic Contact of a Rigid Sphere With an Elastic Half-Space: A Numerical Simulation

[+] Author and Article Information
Jeffrey L. Streator

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

J. Tribol 125(1), 25-32 (Dec 31, 2002) (8 pages) doi:10.1115/1.1509772 History: Received February 21, 2002; Revised July 01, 2002; Online December 31, 2002
Copyright © 2003 by ASME
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Timoshenko, S., and Goodier, S. N., 1951, Theory of Elasticity, 3rd edition, McGraw-Hill, New York.
Thornton,  C., and Zemin,  N., 1998, “A Theoretical Model for the Stick/Bounce Behavior of Adhesive Elastic-Plastic Spheres,” Powder Technol., 99, pp. 154–162.
Komvopoulos,  K., 1996, “Surface Engineering and Microtribology for Micromechanical Systems,” Wear, 200, pp. 305–327.
Bowden, F. P., and Tabor, D., 1950, Friction and Lubrication of Solids, Oxford, London.
Archard,  J. F., 1953, “Contact and Rubbing of Flat Surfaces,” J. Appl. Phys., 24, pp. 981–988.
Dahneke,  B., 1971, “The Capture of Aerosol Particles by Surfaces,” J. Colloid Interface Sci., 37(2), pp. 342–353.
Dahneke,  B., 1973, “Measurements of Bouncing of Small Latex Spheres,” J. Colloid Interface Sci., 45(3), pp. 584–589.
Tsai,  C.-J., Pui,  D. Y. H., and Liu,  B. Y. H., 1990, “Capture and Rebound of Small Particles Upon Impact with Solid Surfaces,” Aerosol. Sci. Technol., 12, pp. 497–507.
Johnson,  K. L., Kendall,  K., and Roberts,  A. D., 1971, “Surface Energy and the Contact of Elastic Solids,” Proc. R. Soc. London, Ser. A, A324, pp. 301–313.
Xu,  M., and Willeke,  K., 1993, “Right-Angle Impaction and Rebound of Particles,” J. Aerosol Sci., 24(1), pp. 19–30.
Brach,  R. M., and Dunn,  P. F., 1992, “A Mathematical Model of the Impact and Adhesion of Microspheres,” Aerosol. Sci. Technol., 16, pp. 51–64.
Li,  X., Dunn,  P. F., and Brach,  R. M., 1998, “Experimental and Numerical Studies on the Normal Impact of Microspheres with Surfaces,” J. Aerosol Sci., 30(4), pp. 439–449.
Brach,  R. M., Dunn,  P. F., and Cheng,  W., 1999, “Rotational Dissipation During Microsphere Impact,” J. Aerosol Sci., 30(10), pp. 1321–1329.
Johnson,  K. L., and Pollock,  H. M., 1994, “The Role of Adhesion in the Impact of Elastic Spheres,” J. Adhes. Sci. Technol., 8(11), pp. 1323–1332.
Derjaguin,  B. V., Muller,  V. M., and Toporov,  Y. P., 1975, “Effect of Contact Deformations on the Adhesion of Particles,” J. Colloid Interface Sci., 53(2), pp. 314–326.
Chang,  W. R., and Ling,  F. F., 1992, “Normal Impact Model of Rough Surfaces,” ASME J. Tribol., 114(3), pp. 439–447.
Muller,  V. M., Yushchenko,  V. S., and Derjaguin,  B. V., 1980, “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), pp. 91–101.
Tabor,  D., 1977, “Surface Forces and Surface Interactions,” J. Colloid Interface Sci., 58, pp. 2–13.
Greenwood,  D., 1997, “Adhesion of Elastic Spheres,” Proc. R. Soc. London, Ser. A, A453, pp. 1277–1297.
Feng,  J. Q., 2001, “Adhesive Contact of Elastically Deformable Spheres: A Computational Study of Pull-Off Force and Contact Radius,” J. Colloid Interface Sci., 238, pp. 318–323.
Rogers,  L. N., and Reed,  J., 1984, “The Adhesion of Particles Undergoing and Elastic-Plastic Impact with a Surface,” J. Phys. D, 17(4), pp. 677–689.
Wall,  S., John,  W., Wang,  H.-C., and Goren,  S., 1990, “Measurements of Kinetic Energy Loss for Particles Impacting Surfaces,” Aerosol. Sci. Technol., 12, pp. 926–946.
Thornton,  C., and Ning,  Z., 1998, “A Theoretical Model for the Stick/Bounce Behavior of Adhesive Elastic-Plastic Spheres,” Powder Technol., 99, pp. 154–162.
Quesnel,  D. J., Rimai,  D. S., and Demejo,  L. P., 1995, “Molecular Dynamic Modeling of Interfacial Energy,” J. Adhes. Sci. Technol., 9(8), pp. 1015–1030.
Quesnel,  D. J., Rimai,  D. S., and Demejo,  L. P., 1995, “Molecular Dynamic Modeling of Particle Adhesion,” J. Adhes., 51(1–4), pp. 49.
Rimai,  D. S., Quesnel,  D. J., and Busnaina,  A. A., 2000, “The Adhesion of Dry Particles in the Nanometer to Micrometer-size Range,” Colloids and Surfaces, A: Physicochemical and Engineering Aspects, 165, pp. 3–10.
Atkins, P. W., 1990, Physical Chemistry, W. H. Freeman & Co., New York.
Muller,  V. M., Derjaguin,  B. V., and Toporov,  Y. P., 1983, “On Two Methods of Calculation of the Force of Sticking of an Elastic Sphere to A Rigid Plane,” Colloids and Surfaces, 7, pp. 251–259.
Isrealachvili, J., 1992, Intermolecular and Surface Forces, Academic Press, London.
Graff, K. F., 1975, Wave Motion in Elastic Solids, Ohio State University Press, Columbus, OH.
Gear, C. W., 1971, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, NJ.
Johnson, K., 1985, Contact Mechanics, Cambridge University Press, New York.
Maugis,  D., 1991, “Adhesion of Spheres: The JKR-DMT Transition Using a Dugdale Model,” J. Colloid Interface Sci., 50(1), pp. 243–269.
Pashley,  M. D., 1984, “Further Consideration of the DMT Model for Elastic Contact,” Colloids and Surfaces, 12, pp. 69–77.


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Schematic of the interface under investigation, a rigid sphere and an elastic half-space, along with coordinate systems
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Illustration of grid system used for numerical computations (see text)
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Trajectories of the sphere and half-space origin during an approach-separation event, along with the force history
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(a) Radial profile of the sphere and surface along with the radial pressure distribution at t*=400 for the approach conditions of Fig. 3; and (b) pressure profile at t*=1600 compared with the corresponding Hertzian pressure profile. Sphere motion was arrested at maximum interference point (t*=400).
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The ratio of maximum compressive forces to the Hertzian force versus Tabor’s parameter for two approach-separation speeds
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Maximum attractive forces during approach and separation versus Tabor’s parameter at two approach-separation speeds, compared to the DMT and JKR model predictions
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Pull-off force versus approach-separation speeds for three values of interference for μ=0.1
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Net energy transfer to the half-space during the approach-separation event versus Tabor’s parameter
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Force histories for an approach-rest-separation process for two values of Tabor’s parameter
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Time history of a snap on process with the sphere position fixed. Profiles of the elastic half-space are shown for various times.



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