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Strain gradient plasticity to study hardness behavior of magnetite (Fe3O4) under multicyclic indentation

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Abstract

The hardness of a material is generally affected by the indentation size effect. The strain gradient plasticity (SGP) theory is largely used to study this load dependence because it links the hardness to the intrinsic properties of the material. However, the characteristic scale-length is linked to the macrohardness, impeding any sound discussion. To find a relevant parameter, we suggest introducing a hardness length-scale factor that only depends on the shear modulus and the Burgers vector of the material and is easily calculable from the relation of the SGP theory. The variation of the hardness length-scale factor is thereafter used to discuss the hardness behavior of a magnetite crystal, the objective being to study the effect of the cumulative plasticity resulting from cyclic indentation. As a main result, the hardness length-scale factor is found to be constant by applying repeated cycles at a constant peak load whereas the macrohardness and the characteristic scale-length are both cycle dependent. When using incremental loads, the hardness length-scale factor monotonically decreases between two limits corresponding to those obtained at high and low loading rates, while the dwell-load duration increases. The physical meaning of such behavior is based on the modification of the dislocation network during the indentation process depending on the deformation rate.

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References

  1. M.L. Trunov, S.N. Dub, P.M. Nagy, and S. Kokenyesi: Photo-plasticity of As2Se3 films investigated with combined nanoindentation and AFM methods. J. Phys. Chem. Solids 68, 1062 (2007).

    Article  CAS  Google Scholar 

  2. I. Pane and E. Blank: Role of plasticity on indentation behavior: Relations between surface and subsurface responses. Int. J. Solids Struct. 43, 2014 (2006).

    Article  Google Scholar 

  3. T. Saraswati, T. Sritharan, S. Mhaisalkar, C.D. Breach, and F. Wulff: Cyclic loading as an extended nanoindentation technique. Mater. Sci. Eng., A 423, 14 (2006).

    Article  Google Scholar 

  4. A. Richter, C.P. Daghlian, R. Ries, and V.L. Solozhenko: Investigation of novel superhard materials by multi-cycling nanoindentation. Diamond Relat. Mater. 15, 2019 (2006).

    Article  CAS  Google Scholar 

  5. Y.G. Gogotsi, V. Domnich, S.N. Dub, A. Kailer, and K.G. Nickel: Cyclic nanoindentation and Raman microspectroscopy study of phase transformations in semiconductors. J. Mater. Res. 15, 871 (2000).

    Article  CAS  Google Scholar 

  6. S.N. Dub, Y.V. Milman, D.V. Lotsko, and A.N. Belous: The anomalous behavior of Al-Cu-Fe quasicrystal during nanoindentation. J. Mater. Sci. Lett. 20, 1043 (2001).

    Article  CAS  Google Scholar 

  7. S. Kucharski and Z. Mróz: Identification of material parameters by means of compliance moduli in spherical indentation test. Mater. Sci. Eng., A 379, 448 (2004).

    Article  Google Scholar 

  8. S. Kucharski and Z. Mróz: Identification of yield stress and plastic hardening parameters from a spherical indentation test. Int. J. Mech. Sci. 49, 1238 (2007).

    Article  Google Scholar 

  9. K. Komvopoulos and J. Yang: Dynamic analysis of single and cyclic indentation of an elastic–plastic multi-layered medium by a rigid fractal surface. J. Mech. Phys. Solids 54, 927 (2006).

    Article  Google Scholar 

  10. N.I. Tymiak, J.C. Nelson, D.F. Bahr, and W.W. Gerberich: Microindentation method for in situ stress measurements in precipitated iron sulphate films. Corros. Sci. 40, 1953 (1998).

    Article  CAS  Google Scholar 

  11. W.H. Li, K. Shin, C.G. Lee, B.C. Wei, T.H. Zhang, and Y.Z. He: The characterization of creep and time-dependent properties of bulk metallic glasses using nanoindentation. Mater. Sci. Eng., A 478, 371 (2008).

    Article  Google Scholar 

  12. W-C. Oliver and G.M. Pharr: Improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).

    Article  CAS  Google Scholar 

  13. M. Szarko and J.E.A. Bertram: Loading rate sensivity of articular cartilage. J. Biomech. 39, S478 (2006).

    Article  Google Scholar 

  14. W.D. Nix and H. Gao: Indentation size effects in crystalline materials: A law for strain gradient plasticity. J. Mech. Phys. Solids 46, 411 (1998).

    Article  CAS  Google Scholar 

  15. D. Chicot: Hardness length-scale factor to model nano and micro-indentation size effects. Mater. Sci. Eng., A 499, 454 (2009).

    Article  Google Scholar 

  16. D.L.A. De Faria, S. Venancio Silva, and M.T. De Oliveira: Raman microspectroscopy of some iron oxides and oxyhydroxides. J. Raman Spectrosc. 28, 873 (1997).

    Article  Google Scholar 

  17. D. Bersani, P.P. Lottici, and A. Montenero: Micro-Raman investigation of iron oxide films and powders produced by sol-gel syntheses. J. Raman Spectrosc. 30, 355 (1999).

    Article  CAS  Google Scholar 

  18. M.H. Sousa, F.A. Tourinho, and J.C. Rubim: Use of Raman micro-spectroscopy in the characterization of MIIFe2O4 (M = Fe, Zn) electric double layer ferrofluids. J. Raman Spectrosc. 31, 185 (2000).

    Article  CAS  Google Scholar 

  19. G.D. Quinn, P.L. Patel, and I. Lloyd: Effect of loading rate upon conventional ceramic microindentation hardness. J. Res. Nat. Inst. Stand. Technol. 107, 299 (2002).

    Article  CAS  Google Scholar 

  20. K. Herrmann, N.M. Jennett, W. Wegener, J. Meneve, K. Hasche, and R. Seemann: Progress in determination of the area function of indenters used for nanoindentation. Thin Solid Films 377–378, 394 (2000).

    Article  Google Scholar 

  21. A.C. Fischer-Cripps: Critical review of analysis and interpretation of nanoindentation test data. Surf. Coat. Technol. 200, 4153 (2006).

    Article  CAS  Google Scholar 

  22. D. Chicot and D. Mercier: Improvement in depth-sensing indentation to calculate the universal hardness on the entire loading curve. Mech. Mater. 40, 171 (2008).

    Article  Google Scholar 

  23. J.C. Hay, A. Bolshakov, and G.M. Pharr: Critical examination of the fundamental relations used in the analysis of nanoindentation data. J. Mater. Res. 14, 2296 (1999).

    Article  CAS  Google Scholar 

  24. D.J. Shuman, A.L.M. Costa, and M.S. Andrade: Calculating the elastic modulus from nanoindentation and microindentation reload curves. Mater. Charact. 58, 380 (2007).

    Article  CAS  Google Scholar 

  25. J.M. Antunes, L.F. Menezes, and J.V. Fernandes: Influence of Vickers tip imperfection on depth-sensing indentation tests. Int. J. Solids Struct. 44, 2732 (2007).

    Article  Google Scholar 

  26. M.F. Doerner and W.D. Nix: A method of interpreting the data from the depth-sensing indentation instruments. J. Mater. Res. 1, 601 (1986).

    Article  Google Scholar 

  27. I.N. Sneddon: The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965).

    Article  Google Scholar 

  28. J. Gong, H. Miao, and Z. Peng: Analysis of the nanoindentation data measured with a Berkovich indenter for brittle materials: Effect of the residual contact stress. Acta Mater. 52, 785 (2004).

    Article  CAS  Google Scholar 

  29. Y. Huang, F. Zhang, K.C. Hwang, W.D. Nix, G.M. Pharr, and G Feng: A model of size effects in nano-indentation. J. Mech. Phys. Solids 54, 1668 (2006).

    Article  Google Scholar 

  30. Q. Ma and D.R. Clarke: Size-dependent hardness of silver single-crystals. J. Mater. Res. 10, 853 (1995).

    Article  CAS  Google Scholar 

  31. Z. Zong, L. Lou, O.O. Adewoye, A.A. Elmustafa, F. Hammad, and W.O. Soboyejo: Indentation size effects in the nano- and micro-hardness of fcc single crystal metals. Mater. Sci. Eng., A 434, 178 (2006).

    Article  Google Scholar 

  32. J. Lou, P. Shrotriya, S. Allameh, T. Buchheit, and W.O. Soboyejo: Strain gradient plasticity length scale parameters for LIGA Ni MEMs thin films. Mater. Sci. Eng., A 441, 299 (2006).

    Article  Google Scholar 

  33. J. Qin, Y. Huang, K.C. Hwang, J. Song, and G.M. Pharr: The effect of indenter angle on the microindentation hardness. Acta Mater. 55, 6127 (2007).

    Article  CAS  Google Scholar 

  34. M. Zhao, W.S. Slaughter, M. Li, and S.X. Mao: Material-length-scale-controlled nanoindentation size effects due to strain-gradient plasticity. Acta Mater. 51, 4461 (2003).

    Article  CAS  Google Scholar 

  35. M. Zaiser and E.C. Aifantis: Geometrically necessary dislocations and strain gradient plasticity—A dislocation dynamics point of view. Scr. Mater. 48, 133 (2003).

    Article  CAS  Google Scholar 

  36. E.A. Bonifaz and N.L. Richards: The plastic deformation of non-homogeneous polycrystals. Int. J. Plast. 24, 289 (2008).

    Article  CAS  Google Scholar 

  37. H.J. Reichmann and S.D. Jacobsen: High-pressure elasticity of a natural magnetite crystal. Am. Mineral. 89, 1061 (2004).

    Article  CAS  Google Scholar 

  38. J.P. Bradley, R.P. Harvey, and H.Y. McSween: Magnetite whiskers and platelets in the ALH84001 Martian meteorite: Evidence of vapor phase growth. Geochim. Cosmochim. Acta 60, 5149 (1996).

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Laboratoire de Mécanique de Lille, LML-UMR 8107, U.S.T. Lille, IUT A GMP, 59653, Villeneuve d’Ascq, France

    D. Chicot & F. Roudet

  2. Ecole des Mines de Douai, 59508, Douai Cedex, France

    V. Lepingle & G. Louis

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  1. D. Chicot
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  2. F. Roudet
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  3. V. Lepingle
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  4. G. Louis
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Correspondence to D. Chicot.

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Chicot, D., Roudet, F., Lepingle, V. et al. Strain gradient plasticity to study hardness behavior of magnetite (Fe3O4) under multicyclic indentation. Journal of Materials Research 24, 749–759 (2009). https://doi.org/10.1557/jmr.2009.0098

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  • DOI: https://doi.org/10.1557/jmr.2009.0098

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