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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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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