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Article

Impact of a Rigid Sphere on an Elastic Homogeneous Half-Space

[+] Author and Article Information
J. Yang, K. Komvopoulos

Department of Mechanical Engineering, University of California, Berkeley, CA 94720

J. Tribol 127(2), 325-330 (Apr 07, 2005) (6 pages) doi:10.1115/1.1828078 History: Received February 12, 2004; Revised June 04, 2004; Online April 07, 2005
Copyright © 2005 by ASME
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Figures

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Schematic representation of propagation of dilatational waves in a semi-infinite half-space due to impact of a rigid sphere for (a) small and (b) large surface interference. The solid curves are envelopes of the spherical wave fronts.
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Finite element meshes of elastic homogeneous half-space impacted by a rigid sphere used in the (a) small and (b) large surface interference simulations
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Contours of dimensionless uz displacement in an elastic homogeneous half-space impacted by a rigid sphere: (a) β=0.5 (Ṽi=1×10−2 and δ̃=1.25×10−5) and (b) β=4.47 (Ṽi=1×10−2 and δ̃=1×10−3). The dashed curves are envelopes of the spherical wave fronts.
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Contours of dimensionless ur displacement in an elastic homogeneous half-space impacted by a rigid sphere: (a) β=0.5 (Ṽi=1×10−2 and δ̃=1.25×10−5) and (b) β=4.47 (Ṽi=1×10−2 and δ̃=1×10−3). The dashed curves are envelopes of the spherical wave fronts.
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Ratio of real-to-truncated contact radius a/a versus β for dimensionless indentation velocity Ṽi=2.24×10−3 and 4.48×10−3
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Dimensionless contact pressure distribution for (a) β=0.632 (Ṽi=1×10−2 and δ̃=2×10−5), (b) β=4 (Ṽi=1×10−2 and δ̃=8×10−4), and (c) β=40 (Ṽi=1×10−3 and δ̃=8×10−4). For each pressure distribution, the Hertzian pressure profile obtained for the same surface interference is also shown for comparison.
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Dimensionless mean contact pressure pm versus β for dimensionless indentation velocity Ṽi=2.24×10−3 and 4.48×10−3
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Dimensionless mean contact pressure at the instant of initial contact pm0 versus dimensionless indentation velocity Ṽi for different values of Poisson ratio, ν
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Contours of dimensionless (a) σzz stress and (b) εzz strain in an elastic half-space impacted by a rigid sphere for β=0.447 (Ṽi=1×10−2 and δ̃=1×10−5)
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Contours of dimensionless u̇z velocity in an elastic half-space impacted by a rigid sphere for β=0.447 (Ṽi=1×10−2 and δ̃=1×10−5)
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A comparison of finite element method (FEM) results and approximate theory solutions of (a) dimensionless strain energy ES and (b) dimensionless kinetic energy EK of an elastic half-space impacted by a rigid sphere versus β for dimensionless indentation velocity Ṽi=1×10−2

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