Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Archives of Civil Engineering

The Journal of Polish Academy of Sciences

4 Issues per year

SCImago Journal Rank (SJR): 0.251
Source Normalized Impact per Paper (SNIP): 0.521

Open Access
See all formats and pricing
More options …
Volume 58, Issue 4

Effect of Initial Porosity on Material Response Under Multi-Axial Stress State for S235JR Steel

P.G. Kossakowski
  • Chair of Strength of Materials and Concrete Structures, Faculty of Civil Engineering and Architecture, Kielce University of Technology, Kielce, Poland
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2012-12-28 | DOI: https://doi.org/10.2478/v.10169-012-0024-x


The effect of the initial porosity on the material response under multi-axial stress state for S235JR steel using the Gurson-Tvergaard-Needleman (GTN) material model was examined. Three levels of initial porosity, defined by the void volume fraction f0, were considered: zero porosity for fully dense material without pores, average and maximum porosity according to the metallurgical requirements for S235JR steel. The effect of the initial porosity on the material response was noticed for tensile elements under multi-axial stress state defined by high stress triaxiality σme = 1.345. This effect was especially noticeable at the range of the material failure. In terms of the load-bearing capacity of the elements, the conservative results were obtained when maximum value of f0 = 0.0024 was used for S235JR steel under multi-axial stress state, and this value is recommended to use in the calculations in order to preserve the highest safety level of the structure. In usual engineering calculations, the average porosity defined by f0 = 0.001 may be applied for S235JR.

Keywords : Initial porosity; initial void volume fraction f0; Gurson-Tvergaard-Needleman material model; multi-axial stress states; high stress triaxiality; voids; numerical calculations; S235JR steel.


  • 1. A. Biegus, D. Czepiżak, Experimental and numerical studies upon load-bearing capacity of locallystrengthened corrugated sheets, Archives of Civil Engineering, 55, 1, 11-28, 2009.Google Scholar

  • 2. A. Biegus, D. Czepiżak, Evaluation of resistance of corrugated sheets under bending by a concentratedloads from the local suspensions, Archives of Civil Engineering, 56, 4, 283-297, 2010.Google Scholar

  • 3. P. Iwicki, Sensitivity analysis of buckling loads of bisymmetric i-section columns with bracing elements, Archives of Civil Engineering, 56, 1, 69-88, 2010.Google Scholar

  • 4. U. Radoń, Analysis of reliability and stability of bar structures, Archives of Civil Engineering, 56, 2, 155-172, 2010.Google Scholar

  • 5. M. Kamiński, P. Swita, Reliability modeling in some elastic stability problems via the generalizedstochastic finite element method, Archives of Civil Engineering, 57, 3, 275-295, 2011.Google Scholar

  • 6. J. Chróścielewski, M. Rucka, K. Wilde, W. Witkowski, Formulation of spectral truss element forguided waves damage detection in spatial steel trusses, Archives of Civil Engineering, 55, 1, 43-63, 2009.Google Scholar

  • 7. W. Witkowski, M. Rucka, K. Wilde, J. Chróścielewski, Wave propagation analysis in spatial framesusing spectral timoshenko beam elements in the context of damage detection, Archives of Civil Engineering, 55, 3, 367-402, 2009.Google Scholar

  • 8. W. Gilewski, M. Sitek, The inf-sup condition tests for shell/plate finite elements, Archives of Civil Engineering, 57, 4, 425-447, 2011.Google Scholar

  • 9. P.W. Bridgman, Studies in large plastic flow and fracture, McGraw-Hill, New York 1952.Google Scholar

  • 10. A.L. Gurson, Continuum theory of ductile rupture by void nucleation and growth: Part I - Yieldcriteria and flow rules for porous ductile media, Journal of Engineering Materials and Technology, Transactions of the ASME, 99, 1, 2-15, 1977.Google Scholar

  • 11. V. Tvergaard, Influence of voids on shear band instabilities under plane strain conditions, International Journal of Fracture, 17, 4, 389-407, 1981.CrossrefGoogle Scholar

  • 12. V. Tvergaard, A. Needleman, Analysis of the cup-cone fracture in a round tensile bar, Acta Metallurgica, 32, 1, 157-169, 1984.CrossrefGoogle Scholar

  • 13. A. Needleman, V. Tvergaard, An analysis of the ductile rupture in notched bars, Journal of the Mechanics and Physics of Solids, 32, 6, 461-490, 1984.CrossrefGoogle Scholar

  • 14. PN-EN 1993-1-10:2007 Eurocode 3: Design of Steel Structures - Part 1-10: Material Toughness and Through-thickness Properties.Google Scholar

  • 15. G. Sedlacek, M. Feldmann, B. Kühn, D. Tschickardt, S. Höhler, C. Müller, W. Hensen, N. Stranghöner, W. Dahl, P. Langenberg, S. Münstermann, J. Brozetti, J. Raoul, R. Pope, F. Bijlaard, Commentary and Worked Examples to EN 1993-1-10 “Material toughness and through thicknessproperties“ and other toughness oriented rules in EN 1993, JRC Scientific and Technical Reports, European Commission Joint Research Centre, 2008.Google Scholar

  • 16. P.G. Kossakowski, An analysis of the load-carrying capacity of elements subjected to complex stressstates with a focus on the microstructural failure, Archives of Civil and Mechanical Engineering, 10, 2, 15-39, 2010.Google Scholar

  • 17. P.G. Kossakowski, W. Trąmpczyński, Numerical simulation of S235JR steel failure with considerationof the influence of microstructural damages [in Polish], Przeglad Mechaniczny, 4, 15-22, 2011.Google Scholar

  • 18. P.G. Kossakowski, Simulation of ductile fracture of S235JR steel using computational cells with microstructurally-based length scales, Journal of Theoretical and Applied Mechanics, 50, 2, 589-607, 2012.Google Scholar

  • 19. P. Kossakowski, Simulation of the plastic range of structural steel performance under the complex stress based on the Gurson-Tvergaard-Needleman model, [in Polish], Przeglad Budowlany, 3, 43-49, 2012.Google Scholar

  • 20. P.G. Kossakowski, Influence of initial porosity on strength properties of S235JR steel at low stress triaxiality, Archives of Civil Engineering, 58, 3, 293-308, 2012.Google Scholar

  • 21. A.G. Franklin, Comparison between a quantitative microscope and chemical method for assessment on non-metallic inclusions, Journal of the Iron and Steel Institute, 207, 181-186, 1969.Google Scholar

  • 22. PN-EN 10025-1:2005 Hot Rolled Products of Structural Steels - Part 1: General Technical Delivery Conditions.Google Scholar

  • 23. PN-EN 10002-1:2004 Metallic Materials - Tensile Testing - Part 1: Method of Test at Ambient Temperature.Google Scholar

  • 24. J. Faleskog, X. Gao, C.F. Shih, Cell model for nonlinear fracture analysis - I. Micromechanics calibration, International Journal of Fracture, 89, 4, 355-373, 1998.CrossrefGoogle Scholar

  • 25. Abaqus 6.10 Analysis User’s Manual, Dassault Systèmes, Providence 2010.Google Scholar

  • 26. L. Xia, C.F. Shih, Ductile crack growth - I. A numerical study using computational cells with microstructurally-based length scales, Journal of the Mechanics and Physics of Solids, 43, 2, 233-259, 1995.CrossrefGoogle Scholar

  • 27. L. Xia, C.F. Shih, Ductile crack growth - II. Void nucleation and geometry effects on macroscopic fracture behavior, Journal of the Mechanics and Physics of Solids, 43, 12, 1953-1981, 1995.Google Scholar

  • 28. X. Gao, J. Faleskog, C.F. Shih, Cell model for nonlinear fracture analysis - II. Fracture-process calibration and verification, International Journal of Fracture, 89, 4, 375-398, 1998.CrossrefGoogle Scholar

  • 29. A.M. Kanvinde, G.G. Deierlein, The Void Growth Model and the Stress Modified Critical Strain Model to predict ductile fracture in structural steels, Journal of Structural Engineering, 132, 12, 1907-1918, 2006.Google Scholar

  • 30. J.W. Hancock, A.C. Mackenzie, On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states, Journal of Mechanics and Physics of Solids, 24, 2-3, 147-160, 1976. Google Scholar

About the article

Published Online: 2012-12-28

Published in Print: 2012-12-01

Citation Information: Archives of Civil Engineering, Volume 58, Issue 4, Pages 445–462, ISSN (Online) 1230-2945, DOI: https://doi.org/10.2478/v.10169-012-0024-x.

Export Citation

© Polish Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

P.G. Kossakowski
Archives of Civil and Mechanical Engineering, 2015, Volume 15, Number 1, Page 195

Comments (0)

Please log in or register to comment.
Log in