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Research Papers

Viscoplastic Effects Occurring in Impacts of Aluminum and Steel Bodies and Their Influence on the Coefficient of Restitution

[+] Author and Article Information
Robert Seifried1

Institute of Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germanyseifried@itm.uni-stuttgart.de

Hirofumi Minamoto

Department of Mechanical Engineering, Toyohashi University of Technology, 1-1 Tempaku-cho Toyohashi, Aichi 441-8580, Japanminamoto@mech.tut.ac.jp

Peter Eberhard

Institute of Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germanyeberhard@itm.uni-stuttgart.de

1

Corresponding author.

J. Appl. Mech 77(4), 041008 (Apr 09, 2010) (7 pages) doi:10.1115/1.4000912 History: Received February 20, 2009; Revised November 20, 2009; Published April 09, 2010

Generally speaking, impacts are events of very short duration and a common problem in machine dynamics. During impact, kinetic energy is lost due to plastic deformation near the contact area and excitation of waves. Macromechanically, these kinetic energy losses are often summarized and expressed by a coefficient of restitution, which is then used for impact treatment in the analysis of the overall motion of machines. Traditionally, the coefficient of restitution has to be roughly estimated or measured by experiments. However, more recently finite element (FE) simulations have been used for its evaluation. Thereby, the micromechanical plastic effects and wave propagation effects must be understood in detail and included in the simulations. The plastic flow, and thus the yield stress of a material, might be independent or dependent of the strain-rate. The first material type is called elastic-plastic and the second type is called elastic-viscoplastic. In this paper, the influence of viscoplasticity of aluminum and steel on the impact process and the consequences for the coefficient of restitution is analyzed. Therefore, longitudinal impacts of an elastic, hardened steel sphere on aluminum AL6060 rods and steel S235 rods are investigated numerically and experimentally. The dynamic material behavior of the specimens is evaluated by split Hopkinson pressure bar tests and a Perzyna-like material model is identified. Then, FE impact simulations and impact experiments with laser-doppler-vibrometers are performed. From these investigations it is shown that strain-rate effects of the yield stress are extremely small for impacts on aluminum but are significant in impacts on steel. In addition, it is demonstrated that it is possible to evaluate for both impact systems the coefficient of restitution numerically, whereas for the aluminum body a simple elastic-plastic material model is sufficient. However, for the steel body an elastic-viscoplastic material model must be included.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Approximation of static stress-strain curves

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Figure 2

Measured stress-strain curves for AL6060 and S235

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Figure 3

Strain-rate scaling factor β

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Figure 4

Finite element model of sphere to rod impact

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Figure 5

Experimental setup of sphere to rod impact

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Figure 6

Sphere velocity and impact force for impact with v0=3.05 m/s on the aluminum rod

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Figure 7

Effective plastic strain-rate along the axis of the aluminum rod for impact with v0=3.05 m/s

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Figure 8

Sphere velocity and impact force for impact with v0=3.05 m/s on the steel rod

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Figure 9

Effective plastic strain-rate along the axis of the steel rod for impact with v0=3.05 m/s

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Figure 10

Sphere velocity and impact force for impact with v0=0.32 m/s on the steel rod

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Figure 11

Effective plastic strain-rate along the axis of the steel rod for impact with v0=0.32 m/s

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Figure 12

Coefficient of restitution for impacts on aluminum and steel rod

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