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Numerical determination of the parameters of Krupkowski's function for a torsion test taking into consideration the strain hardening ranges

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Abstract

A method has been proposed for determining the parameters of a function describing the strain hardening curve for a torsion test taking into consideration the strain hardening ranges. Certain measures for the approximation quantity have been defined by means of which it is possible to formulate the criterion of the occurrence of these ranges. Experimental verification of the method was carried out using nickel of 99.95% purity. Test pieces of a circular cross-section were subjected to a torsion test at ambient temperature without taking into consideration the strain hardening rate.

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Abbreviations

τ (γR):

shear stress of the metal deformed up toγ R

γR :

shear strain at a distanceR from the centre of the test-piece

d :

diameter of the test-piece undergoing torsion,d=2R

l :

length of the test-piece

α :

angle of torsion

M :

torsion moment

γ 1;k; m; c :

material parameters

σ :

effective stress

z :

measure of deformation in form of actual cold work

z 1 :

initial deformation equivalent of latent cold work

dL 0 :

the elementary work of deformation per unit of volume

γ I/II :

boundary between the strain hardening ranges I and II

γ II/III :

boundary between the strain hardening ranges II and III

A; H; S; SS; B:

approximation quantity measures described in the Section 3

References

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Authors and Affiliations

  1. Institute for Metal Research, Polish Academy of Sciences, Kraków, Poland

    A. Grabianowski

  2. Institute of Mathematics, Polish Academy of Sciences, Kraków, Poland

    J. Kloch

Authors
  1. A. Grabianowski
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  2. J. Kloch
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Grabianowski, A., Kloch, J. Numerical determination of the parameters of Krupkowski's function for a torsion test taking into consideration the strain hardening ranges. J Mater Sci 18, 1323–1330 (1983). https://doi.org/10.1007/BF01111949

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  • DOI: https://doi.org/10.1007/BF01111949

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