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Yield criterion and second-order effects in plane-stress

Fließbedingung und Effekte zweiter Ordnung für den ebenen Spannungszustand

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Summary

A yield criterion in planestress state is derived here based on isotropic representation of a scalar valued function depending upon symmetric 2×2 stress and strain matrices. The material has been assumed to be incompressible. In particular, for tension-torsion loading the yield surface is nonsymmetric with respect to the torsional stress axis. Due to the non-symmetry, the yield condition describes the second-order effect relating to axial-strain accumulation in cyclic torsion, and at the same time it has got a very simple form compared to other yield conditions describing this effect.

Zusammenfassung

Hergeleitet wird eine Fließbedingung für den ebenen Spannungszustand, die auf der isotropen Darstellung einer skalarwertigen Funktion von symmetrischen 2×2 Spannungs- und Verzerrungsmatrizen basiert. Der Werkstoff wird dabei inkompressible vorausgesetzt. Für Belastung Zug-Torsion ist die Fließfläche nicht symmetrisch bezüglich der Torsionsspannungsachse. Zufolge dieser Unsymmetrie beschreibt die Fließbedingung Effekte zweiter Ordnung durch Anhäufung von achsialer Verzerrung bei zyklischer Torsion und besitzt eine im Bergleich zu anderen, denselben Effekt beschreibenden Fließbedingungen einfache Gestalt.

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Abbreviations

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\sigma }\) :

stress matrix

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\varepsilon } ^p\) :

plastic strain matrix

f :

yield function

λ,d μ:

scalar parameter

tr:

trace of a matrix

L 1,L 2 :

invariants of stresses

M 1,M 2 :

invariants of plastic strain matrix

N 1 :

joint invariant of stress and plastic strain matrices

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, Canada

    H. P. Shrivastava,  Z. Mroz &  R. N. Dubey

Authors
  1. H. P. Shrivastava
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  2. Z. Mroz
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  3. R. N. Dubey
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Additional information

With 2 Figures

Visiting Professor at the University of Waterloo on leave of absence from the Institute of Fundamental Technical Research, Wasaw, Poland.

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Shrivastava, H.P., Mroz, Z. & Dubey, R.N. Yield criterion and second-order effects in plane-stress. Acta Mechanica 17, 137–143 (1973). https://doi.org/10.1007/BF01260885

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  • DOI: https://doi.org/10.1007/BF01260885

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