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Numerical analysis of longitudinal elastic-plastic waves with radial effects

  • P. Obernhuber
  • S. R. Bodner
  • M. Sayir
Original Papers

Summary

The two-dimensional problem of longitudinal elastic-plastic waves in circular rods taking radial-inertia effects into account is solved based on the finite-element method and an explicit integration algorithm. The elastic-plastic constitutive equations are the yield criterion of von Mises with isotropic work hardening and the Prandtl-Reuss flow rule. Numerical results are shown for the region near the impact end of a semi-infinite rod for two sets of boundary conditions, namely prescribed longitudinal velocity and prescribed longitudinal stress at the bar end. The lateral motion of the struck end is assumed to be unrestrained (zero shear stress).

The numerical results show response characteristics which deviate from the one-dimensional solution and which are in a good qualitative agreement with a number of experimental observations reported in the literature. These impact test results have been examined with respect to the predictions in order to separate radial- and strain-rate effects. Several specific calculations for the various test conditions have been performed to obtain quantitative agreement with experimental observations.

Keywords

Impact Test Result Radial Effect Explicit Integration Algorithm Isotropic Work 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Zusammenfassung

Das zweidimensionale Problem der elastisch-plastischen Längswellen in kreisförmigen Stäben unter Berücksichtigung der Querschwingungen wird mit Hilfe der finiten Elemente und eines expliziten Integrationsalgorithmus gelöst. Als Materialgleichungen wurden die von Misessche Flieβbedingung und das Flieβgesetz nach Prandtl-Reuss verwendet. Für den halbunendlichen Stab werden numerische Resultate fur den Bereich des belasteten Endes gezeigt, wobei entweder die Geschwindigkeit oder die Spannung am belasteten Ende vorgegeben ist. Zusätzlich wird angenommen, daβ sich das Stabende in der Querrichtung frei bewegen kann.

Die numerischen Resultate zeigen abweichend von der eindimensionalen Lösung Details, die gut mit einigen in der Literatur beschriebenen experimentellen Beobachtungen übereinstimmen. Diese Versuchsergebnisse wurden den numerischen Resultaten gegenübergestellt, um so den Einfluβ der Querschwingungen vom Einfluβ der Dehnungsgeschwindigkeit zu trennen. Um eine quantitative Übereinstimmung mit den experimentellen Beobachtungen zu erzielen, wurden einige Rechnungen mit den Versuchbedingungen als Eingabewerte durchgeführt.

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Copyright information

© Birkhäuser Verlag Basel 1986

Authors and Affiliations

  • P. Obernhuber
    • 1
    • 4
  • S. R. Bodner
    • 2
  • M. Sayir
    • 3
  1. 1.Electrowatt Engineering Services Ltd.ZürichSwitzerland
  2. 2.TechnionHaifaIsrael
  3. 3.Swiss Federal Institute of Technology (ETH)Zürich
  4. 4.Tauernkraftwerke AGSalzburgAustria

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