Journal of Materials Science

, Volume 43, Issue 9, pp 3351–3363 | Cite as

Analysis of fracture limit curves and void coalescence in high strength interstitial free steel sheets formed under different stress conditions

  • R. NarayanasamyEmail author
  • N. L. Parthasarathi
  • R. Ravindran
  • C. Sathiya Narayanan


Void formation, which is a statistical event, depends on inhomogeneities present in the microstructure. The analysis on void nucleation, their growth and coalescence during the fracture of high strength interstitial free steel sheets of different thicknesses is presented in this article. The analysis shows that the criterion of void coalescence depends on the d-factor, which is the ratio of relative spacing of the ligaments (δd) present between the two consecutive voids to the radius of the voids. The computation of hydrostatic stress (σm), the dominant factor in depicting the evolution of void nucleation, growth and coalescence and the dimensional analysis of three different types of voids namely oblate, prolate and spherical type, have been carried out. The ratio of the length to the width (L/W) of the oblate or prolate voids at fracture is correlated with the mechanical properties, microstructure, strains at fracture, Mohr’s circle shear strains and Triaxiality factors. The Lode angle (θ) is determined and correlated with the stress triaxiality factor (T), ratio of mean stress (σm) to effective stress (σe). In addition, the Void area fraction (Va), which is the ratio of void area to the representative area, is determined and correlated with the strain triaxiality factor (To).


Steel Sheet Hydrostatic Stress Minor Strain Lode Angle Triaxial Stress State 



Major strain


Minor strain


Thickness strain


Effective strain of macroscopic equivalent strain


Hydrostatic or mean strain

γ12, γ23, γ13

Mohr’s circle shear strains (the subscripts 1, 2 & 3 represent major, minor and thickness strains)


Ligament thickness

d-factor/ ratio

Ratio of δd to radius of void


Lode factor or lode angle


Stress triaxiality factor or ratio


Stress triaxiality factor or ratio


Effective stress


Mean or hydrostatic stress


Void area fraction


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • R. Narayanasamy
    • 1
    Email author
  • N. L. Parthasarathi
    • 1
  • R. Ravindran
    • 1
  • C. Sathiya Narayanan
    • 1
  1. 1.Department of Production EngineeringNational Institute of TechnologyTiruchirappalliIndia

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