Research Articles

An Experimental Study of the Dynamic Elasto-Plastic Contact Behavior of Metallic Granules

[+] Author and Article Information
John Lambros

e-mail: lambros@illinois.edu
Department of Aerospace Engineering,
University of Illinois at Urbana-Champaign,
104S Wright Street,
306 Talbot Laboratory,
Urbana, IL, 61801

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received February 6, 2012; final manuscript received July 5, 2012; accepted manuscript posted July 27, 2012; published online January 22, 2013. Editor: Yonggang Huang.

J. Appl. Mech 80(2), 021009 (Jan 22, 2013) (10 pages) Paper No: JAM-12-1052; doi: 10.1115/1.4007254 History: Received February 06, 2012; Revised July 05, 2012; Accepted July 27, 2012

A controllable experimental method using a two-hemispherical-bead setup and a split Hopkinson pressure bar (SHPB) apparatus is implemented to study the dynamic elasto-plastic contact laws between ductile beads in contact. Beads made of four different metals, either rate sensitive (stainless steel 302 and 440C) or rate insensitive (Al alloy 2017 and brass alloy 260), are used. The experimental elasto-plastic contact force-displacement curves are obtained under different loading rates. The effects of material rate sensitivity and bead pair size on the contact laws are studied, and the way that the rate sensitivity of the materials translates to rate sensitivity contact force-displacement relations is explored. The transmitted energy ratio, which is related to the macroscale concept of a coefficient of restitution, is also calculated and, for all materials, shows a decrease with increasing impact speed. In addition, the experimental contact force–displacement data, residual compressive displacement, and diameter of yield area are compared with predictions from several widely-used theoretical models to generalize these experimental results to arbitrary contact situations.

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Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge, UK, Chap. 4.
Daraio, C., Nesterenko, V. F., Herbold, E. B., and Jin, S., 2006, “Energy Trapping and Shock Disintegration in a Composite Granular Medium,” Phys. Rev. Lett., 96(5), p. 058002. [CrossRef] [PubMed]
Porter, M. A., Daraio, C., Szelengowicz, I., Herbold, E. B., and Kevrekidis, P. G., 2009, “Highly Nonlinear Solitary Waves in Heterogeneous Periodic Granular Media,” J. Phys. D, 238(6), pp. 666–676. [CrossRef]
Vu-Quoc, L., Zhang, X., and Lesburg, 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. [CrossRef]
Li, F., Pan, J., and Sinka, C., 2009, “Contact Laws Between Solid Particles,” J. Mech. Phys. Solids, 57, pp. 1194–1208. [CrossRef]
Kumar, P. R., and Geubelle, P., 2012, “Wave Propagation in Elasto-Plastic Granular Systems,” Phys. Rev. E (to be submitted).
Cundall, P., and Strack, O., 1979, “A Discrete Numerical Model for Granular Assemblies,” Geotechnique, 29, pp. 47–65. [CrossRef]
Sadd, M. H., Tai, Q. M., and Shukla, A.1993, “Contact Law Effects on Wave-Propagation in Particulate Materials Using Distinct Element Modeling,” Int. J. Non-Linear Mech., 28(2), pp. 251–265. [CrossRef]
Luding, S., 2004, “Molecular Dynamics Simulations of Granular Materials,” The Physics of Granular Media, H.Hinrichsen, and D.Wolf, eds., Wiley-VCH, Weinheim, Germany.
Awasthia, A. P., Smith, K. J., Geubellea, P. H., and Lambros, J., 2012, “Propagation of Solitary Waves in 2D Granular Media: A Numerical Study,” Mech. Mater. (submitted).
Kuwaara, G., and Kono, K., 1987, “Restitution Coefficient in a Collision Between Two Spheres,” Jpn. J. Appl. Phys., 26, pp. 1230–1233. [CrossRef]
Stronge, W. J., 1995, “Theoretical Coefficient of Restitution for Planar Impact of Rough Elasto-Plastic Bodies,” Proceedings of the ASME/AMD Symposium, Impact Waves, and Fracture, Vol. 205, Los Angeles, CA, June 28–30, pp. 351–362.
Thornton, C., 1997, “Coefficient of Restitution for Collinear Collisions of Elastic-Perfectly Plastic Spheres,” ASME J. Appl. Mech., 64, pp. 383–386. [CrossRef]
Mesarovic, S. D., and Fleck, N. A., 2000, “Frictionless Indentation of Dissimilar Elastic-Plastic Spheres,” Int. J. Solids. Struct.,37, pp. 7071–7091. [CrossRef]
Wu, C., Li, L., and Thornton, C., 2005, “Energy Dissipation During Normal Impact of Elastic and Elastic–Plastic Spheres,” Int. J. Impact Eng., 32, pp. 593–604. [CrossRef]
Jackson, R. L., Green, I., and Marghitu, D. B., 2010, “Predicting the Coefficient of Restitution of Impacting Elastic-Perfectly Plastic Spheres,” Nonlinear Dyn., 60, pp. 217–229. [CrossRef]
Labous, L. R., Rosato, A. D., and Dave, R. N., 1997, “Measurements of Collisional Properties of Spheres Using High-Speed Video Analysis,” Phys. Rev. E., 56, pp. 5717–5725. [CrossRef]
Weir, G., and Tallon, S., 2005, “The Coefficient of Restitution for Normal Incident, Low Velocity Particle Impacts,” Chem. Eng. Sci., 60, pp. 3637–3647. [CrossRef]
Stevens, A. B., and Hrenya, C. M., 2005, “Comparison of Soft-Sphere Models to Measurements of Collision Properties During Normal Impacts,” Powder Technol., 154, pp. 99–109. [CrossRef]
Minamoto, H., and Kawamura, S., 2011, “Moderately High Speed Impact of Two Identical Spheres,” Int. J. Impact Eng., 38, pp. 123–129. [CrossRef]
King, H., White, R., Maxwell, I., and Menon, N., 2011, “Inelastic Impact of a Sphere on a Massive Plane: Nonmonotonic Velocity-Dependence of the Restitution Coefficient,” Europhys. Lett., 93, p. 14002. [CrossRef]
Black, J. T., and Kohser, R. A., 2003, DeGarmo's Materials and Processes in Manufacturing, 9th ed., Wiley, Hoboken, NJ.
Nordberg, H., 2004, “Note on the Sensitivity of Stainless Steels to Strain Rate,” Research Report No. 04.0-1, AvestaPolarit Research Foundation, Sheffield Hallam University, Sheffield, UK.
Euro Inox, 2002, “Design Manual For Structural Stainless Steel—Commentary,” The Steel Construction Institute, Ascot, UK, Chap. C3.
Chen, W., and Song, B., 2011, Split Hopkinson (Kolsky) Bar: Design, Testing and Applications, Springer, New York.
On, T., and Lambros, J., 2012, “Development of Solitary Waves in 1-D Ductile Granular Chain,” Mech. Mater., (to be submitted).


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Fig. 1

Sketch of the normal point contact problem: (a) illustration of “point” contact, and (b) theoretical force-displacement curves

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Fig. 2

Quasi-static and dynamic constitutive behaviors of Al alloy 2017, brass alloy 260, and stainless steel 302

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Fig. 3

Sketch of the modified SHPB used to determine plastic force-displacement contact laws and a photograph of the specimen region. The incident bar is made of steel and the transmitter bar is made of aluminum. A momentum trap and pulse shaping are used to control the incident signal.

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Fig. 4

Comparisons between the single-whole-bead (SWB) and two-hemispherical-bead setups (THB): (a) single-whole-bead setup (SWB), (b) two-hemispherical-bead setup (THB), (c) face forces in the SWB setup, (d) face forces in the THB setup, (e) transmitted pulse of the SWB setup, and (f) transmitted pulse of the THB setup

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Fig. 5

Contact force displacement curves for strain rate insensitive materials at varied loading rates: (a) Al alloy 2017, and (b) brass alloy 260

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Fig. 6

Contact force displacement curves for strain rate sensitive materials at varied loading rates: (a) stainless steel 302, and (b) stainless steel 440C

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Fig. 7

Transmitted energy ratio of different loading rates

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Fig. 8

Comparison between the experimental and theoretical contact force displacement curves

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Fig. 9

Comparison between the experimental and theoretical residual contact displacements under different maximum contact forces: (a) Al alloy 2017, and (b) brass alloy 260

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Fig. 10

Top view images of the yield areas for different beads and the diameter measured method: (a) Al alloy 2017, (b) brass alloy 260, and (c) stainless steel 302

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Fig. 11

Comparison between the experimental and theoretical diameters of the yield areas under different maximum contact forces: (a) Al alloy 2017, and (b) brass alloy 260

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Fig. 12

Relationship between the maximum contact displacement the and square of the diameter of the yield area

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Fig. 13

Scan location and direction for obtaining the cross section profiles

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Fig. 14

Cross section profiles of the yield area at different loading rates: (a) Al alloy 2017, and (b) brass alloy 260

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Fig. 15

Original and normalized contact force-displacement curves for brass alloy 260 bead pairs with different sizes: (a) original, and (b) Hertzian normalized



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