Stress Distribution in the Sample Neck during the Tensile Testing

  • Magdalena GromadaEmail author
  • Gennady Mishuris
  • Andreas Öchsner
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)


In this chapter, the considered issue is presented on the base of two different models of plasticity theory and the detailed derivation of formulae for the average normalised axial stress in the minimal section plane is shown based on different classical approaches. For the sake of fact that all classical derivations are presented in so-called Euler coordinates, the independent variables are coordinates in the current configuration of the point in the space, in which a material particle is located at the considered moment of time. Let us notice that in this coordinate system for the given deformation, an additional problem is the determination of the boundary positions along which the boundary conditions on the neck contour are estimated since they are continuous changing for each stage of deformation. However, this inconvenience can be recompensed by linear equilibrium equations [8].


Stress distribution in the sample with neck Classical and new approaches Deformation theory Flow theory 


  1. 1.
    P.W. Bridgman, Studies in large plastic flow and fracture with special emphasis on the effects of hydrostatic pressure (Harvard University press, Cambridge, 1964)Google Scholar
  2. 2.
    N.N. Davidenkov, N.I. Spiridonova, Mechanical methods of testing. Analysis of the state of stress in the neck of a tension test specimen. Proc Am Soc Test Mater 46, 1147–1158 (1947)Google Scholar
  3. 3.
    L. Dietrich, J. Miastkowski, W. Szczepiński, Limiting capacity of the construction elements (in Polish) (PWN, Warsaw, 1970)Google Scholar
  4. 4.
    Z. Gabryszewski, J. Gronostajski, Mechanics of process of plastic forming (in Polish) (PWN, Warsaw, 1991)Google Scholar
  5. 5.
    M. Gromada, G. Mishuris, A. Öchsner, An attempt to improve the evaluation of mechanical material properties from the axisymmetric tensile test. Israel J Chem 47, 329–335 (2007)CrossRefGoogle Scholar
  6. 6.
    M. Gromada, G. Mishuris, A. Öchsner, On the evaluation of mechanical properties from the axisymmetric tensile test. Arch Metall Mater 55, 295–300 (2010)Google Scholar
  7. 7.
    R. Hill, The mathematical theory of plasticity (Clarendon Press, Oxford, 1950)zbMATHGoogle Scholar
  8. 8.
    L.M. Kachanov, Foundations of the theory of plasticity (Mir Publishers, Moscow, 1974)Google Scholar
  9. 9.
    N.N. Malinin, J. Rżysko, Mechanics of materials (in Polish) (PWN, Warsaw, 1981)Google Scholar
  10. 10.
    M.E. Niezgodziński, T. Niezgodziński, Strength of materials (in Polish) (PWN, Warsaw, 2002)Google Scholar
  11. 11.
    W. Olszak, P. Perzyna, A. Sawczuk, Theory of plasticity (in Polish) (PWN, Warsaw, 1965)Google Scholar
  12. 12.
    W. Wrona, Ś. Romanowski, Mathematics for technical courses (in Polish) (PWN, Warsaw, 1967)Google Scholar
  13. 13.
    E. Siebel, S. Schwaigerer, On the mechanics of the tensile test (in German). Arch Eisenhuttenwes 19, 145–152 (1948)Google Scholar
  14. 14.
    Standard EN 10002 -1 Metallic materials—Tensile testing—Part 1: Method of test at ambient temperatureGoogle Scholar
  15. 15.
    W. Szczepiński, Introduction to analysis of plastic forming processes (in Polish) (PWN, Warsaw, 1967)Google Scholar
  16. 16.
    W. Szczepiński, Mechanics of plastic flow (in Polish) (PWN, Warsaw, 1978)Google Scholar
  17. 17.
    W. Szczepiński, Experimental methods of solid mechanics (in Polish) (PWN, Warsaw, 1984)Google Scholar

Copyright information

© Magdalena Gromada 2011

Authors and Affiliations

  • Magdalena Gromada
    • 1
    Email author
  • Gennady Mishuris
    • 2
  • Andreas Öchsner
    • 3
  1. 1.Ceramic Department CERELInstitute of Power EngineeringBoguchwalaPoland
  2. 2.Institute of Mathematics and PhysicsAberystwyth University, PenglaisCeredigionUK
  3. 3.Department of Applied Mechanics, Faculty of Mechanical EngineeringTechnical University of MalaysiaJohorMalaysia

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