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Accumulation of second order strain in cyclic loading of viscous bar

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Summary

The accumulation of second-order strain in dissipative isotropic media subject to cyclic loads is theoretically illustrated by the analysis of a viscous bar subject to various combinations of sustained and cyclic loading. In view of the nonlinearity of the governing differential equations which permit only approximate solutions, the second order interactions are illustrated by comparison of the computed “times to failure” under these combinations of loading.

Zusammenfassung

Die Anhäufungen von Verzerrung zweiter Ordnung in dissipativen isotropen Medien infolge zyklischer Belastungen wird durch Analyse eines viskosen Stabes unter verschiedenen Kombinationen konstanter und zyklischer Last theoretisch illustriert. Im Hinblick darauf, daß die Nichtlinearität der auftretenden Differentialgleichungen nur Näherungslösungen gestattet, werden die Wechselwirkungen zweiter Ordnung durch Vergleich der berechneten Lebensdauer bei verschiedenen Lastkombinationen veranschaulicht.

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References

  1. Ronay, M.: Second-Order Strain Accumulation in Cyclic Torsion. British J. Appl. Phys., Vol.16, 727–728 (1965).

    Google Scholar 

  2. Freudenthal, A. M. andM. Ronay: Second-Order Effects in Dissipative Media. Proc. Royal Soc. (London) A, Vol.292, 14–50 (1966).

    Google Scholar 

  3. Freudenthal, A. M. andM. Ronay: Accumulation of Second Order Effects in Dissipative Solids. Proc. IUTAM Symp. on Irreversible Aspects, of Continuum Mechanics, Vienna 1966, Springer, Wien (in print).

  4. Reiner, M. andA. Abir (Ed.): Proc. IUTAM Symp. on Second Order Effects, Haifa 1962, Pergamon Press, New York, 1964.

    Google Scholar 

  5. Wood, W. A.: Yield and Second Order Effects Induced by Cyclic Torsion in Copper Under Tension. Acta Metallurgica, Vol.15, 841–846 (1967).

    Google Scholar 

  6. Ronay, M.: On Second Order Strain Accumulation in Aluminium in Reversed Cyclic Torsion at Elevated Temperature. Internat. J. Solids and Structures, Vol.3, 167–176 (1967).

    Google Scholar 

  7. Reference 2, Second-Order Effects in Dissipative Media. Proc. Royal Soc. (London) A, Vol.292 (1966), p. 36.

    Google Scholar 

  8. Reiner, M.: A Mathematical Theory of Dilatancy. Am. J. Math. Vol.67, 350–362 (1945).

    Google Scholar 

  9. Reiner, M. andA. M. Freudenthal: Failure of a Material Showing Creep. Proc. Fifth Int. Congress Appl. Mech., Cambridge, Mass., 1938, 228–233.

  10. Orowan, E.: Mechanical Testing of Solids. Rep. British Rheol. Club Gen. Conf. on Principles of Rheol. Measurements, Bedford College 1946, Th. Nelson and Sons, London 1949, 161.

    Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, N.Y., USA

    A. M. Freudenthal &  P. F. Gou

Authors
  1. A. M. Freudenthal
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  2. P. F. Gou
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Freudenthal, A.M., Gou, P.F. Accumulation of second order strain in cyclic loading of viscous bar. Acta Mechanica 4, 137–148 (1967). https://doi.org/10.1007/BF01263426

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