Estimation of Dislocation Density in Metals from Hardness Measurements

  • A. A. H. AmeriEmail author
  • N. N. Elewa
  • M. Ashraf
  • J. P. Escobedo-Diaz
  • P. J. Hazell
Conference paper
Part of the The Minerals, Metals & Materials Series book series (MMMS)


A novel methodology to estimate the dislocation density in cubic metals by using microhardness measurements has been established. The proposed methodology is based on the Indention Size Effect (ISE) phenomena and strengthening mechanisms of materials at the micro-level. The methodology was validated by using experimental data of lean duplex stainless steel 2101 alloy. The results are confirmed via X-ray diffraction measurements and they substantiate that the proposed approach can be used as a general method to estimate dislocation density in metals.


Hardness Microstructure Dislocations Lean duplex 



The authors would like to thank Prof. Sean Cadogan in the School of Physical, Environmental and Mathematical Sciences at The University of New South Wales Canberra for his support in performing X-ray diffraction experiments. Dr. Md. Quadir at Faculty of Science and Engineering, Curtin University is also acknowledged for his help with EBSD measurements. Moreover, the authors are grateful for the support of A/Prof. Jodie Bradby and Mr. Christopher Tanner in the Department of Electronic Materials Engineering in the Research School of Physics and Engineering at the Australian National University in conducting nanoindentation experiments.


  1. 1.
    Miyajima Y, Okubo S, Abe H, Okumura H, Fujii T, Onaka S, Kato M (2015) Dislocation density of pure copper processed by accumulative roll bonding and equal-channel angular pressing. Mater Charact 104:101–106. doi: 10.1016/j.matchar.2015.04.009 CrossRefGoogle Scholar
  2. 2.
    Shintani T, Murata Y (2011) Evaluation of the dislocation density and dislocation character in cold rolled Type 304 steel determined by profile analysis of X-ray diffraction. Acta Mater 59:4314–4322. doi: 10.1016/j.actamat.2011.03.055 CrossRefGoogle Scholar
  3. 3.
    Kishor R, Sahu L, Dutta K, Mondal AK (2014) Assessment of dislocation density in asymmetrically cyclic loaded non-conventional stainless steel using X-ray diffraction profile analysis. Mater Sci Eng A 598:299–303. doi: 10.1016/j.msea.2014.01.043
  4. 4.
    Arsenlis A (1999) Crystallographic aspects of geometrically- necessary and statistically-stored dislocation density. Acta Metall 47:1597–1611. doi: 10.1016/S1359-6454(99)00020-8 Google Scholar
  5. 5.
    Rodríguez R, Gutierrez I (2003) Correlation between nanoindentation and tensile properties influence of the indentation size effect. Mater Sci Eng A 361:377–384. doi: 10.1016/S0921-5093(03)00563-X CrossRefGoogle Scholar
  6. 6.
    Nix WD, Gao H (1998) Indentation size effects in crystalline materials: a law for strain gradient plasticity. J Mech Phys Solid 46:411–425. doi: 10.1016/S0022-5096(97)00086-0 CrossRefGoogle Scholar
  7. 7.
    Durst K, Franke O, Böhner A, Göken M (2007) Indentation size effect in Ni-Fe solid solutions. Acta Mater 55:6825–6833. doi: 10.1016/j.actamat.2007.08.044
  8. 8.
    ISO, 14577 (2015) Metallic materials—instrumented indentation test for hardness and materials parametersGoogle Scholar
  9. 9.
    Totten GE, Xie L, Funatani K (2004) Handbook of mechanical alloy design. Marcel Dekker, 2004Google Scholar
  10. 10.
    Durst K, Backes B, Franke O, Göken M (2006) Indentation size effect in metallic materials: modeling strength from pop-into macroscopic hardness using geometrically necessary dislocations. Acta Mater 54:2547–2555. doi: 10.1016/j.actamat.2006.01.036 CrossRefGoogle Scholar
  11. 11.
    Yang B, Vehoff H (2007) Dependence of nanohardness upon indentation size and grain size—a local examination of the interaction between dislocations and grain boundaries. Acta Mater 55:849–856. doi: 10.1016/j.actamat.2006.09.004 CrossRefGoogle Scholar
  12. 12.
    Feng G, Nix WD (2004) Indentation size effect in MgO. Scr Mater 51:599–603. doi: 10.1016/j.scriptamat.2004.05.034 CrossRefGoogle Scholar
  13. 13.
    Qiu X, Huang Y, Nix WD, Hwang KC, Gao H (2001) Effect of intrinsic lattice resistance in strain gradient plasticity. Acta Mater 49:3949–3958. doi: 10.1016/S1359-6454(01)00299-3 CrossRefGoogle Scholar
  14. 14.
    Oliver WC, Pharr GM (1992) An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res 7:1564–1583. doi: 10.1557/JMR.1992.1564 CrossRefGoogle Scholar
  15. 15.
    Strubbia R, Hereñú S, Alvarez-Armas I, Krupp U (2014) Short fatigue cracks nucleation and growth in lean duplex stainless steel LDX 2101. Mater Sci Eng A 615:169–174. doi: 10.1016/j.msea.2014.07.076 CrossRefGoogle Scholar
  16. 16.
    Ribárik G (2001) MWP-fit: a program for multiple whole profile fitting of diffraction profiles by ab-initio theoretical functions. J Appl Crystallogr 34:669–676. doi: 10.1107/S0021889801011451 CrossRefGoogle Scholar
  17. 17.
    Ungár T, Borbély A (1996) The effect of dislocation contrast on x-ray line broadening: a new approach to line profile analysis. Appl Phys Lett 69:3173–3175. doi: 10.1063/1.117951 CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society 2017

Authors and Affiliations

  • A. A. H. Ameri
    • 1
    Email author
  • N. N. Elewa
    • 2
  • M. Ashraf
    • 1
  • J. P. Escobedo-Diaz
    • 1
  • P. J. Hazell
    • 1
  1. 1.School of Engineering and Information TechnologyThe University of New South WalesCanberraAustralia
  2. 2.School of Physical, Environmental and Mathematical SciencesThe University of New South WalesCanberraAustralia

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