Hostname: page-component-7c8c6479df-xxrs7 Total loading time: 0 Render date: 2024-03-29T02:21:06.869Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  31 January 2011

D. Chicot*
Affiliation:
Laboratoire de Mécanique de Lille, LML-UMR 8107, U.S.T. Lille, IUT A GMP, 59653 Villeneuve d’Ascq, France
F. Roudet
Affiliation:
Laboratoire de Mécanique de Lille, LML-UMR 8107, U.S.T. Lille, IUT A GMP, 59653 Villeneuve d’Ascq, France
V. Lepingle
Affiliation:
Laboratoire de Mécanique de Lille, LML-UMR 8107, U.S.T. Lille, IUT A GMP, 59653 Villeneuve d’Ascq, France
G. Louis
Affiliation:
Ecole des Mines de Douai, 59508 Douai Cedex, France
*
a) Address all correspondence to this author. e-mail: didier.chicot@univ-lille1.fr
Get access

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.

Type
Articles
Copyright
Copyright © Materials Research Society 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Trunov, M.L., Dub, S.N., Nagy, P.M., and Kokenyesi, S.: Photo-plasticity of As2Se3 films investigated with combined nanoindentation and AFM methods. J. Phys. Chem. Solids 68, 1062 (2007).Google Scholar
2.Pane, I. and Blank, E.: Role of plasticity on indentation behavior: Relations between surface and subsurface responses. Int. J. Solids Struct. 43, 2014 (2006).CrossRefGoogle Scholar
3.Saraswati, T., Sritharan, T., Mhaisalkar, S., Breach, C.D., and Wulff, F.: Cyclic loading as an extended nanoindentation technique. Mater. Sci. Eng., A 423, 14 (2006).CrossRefGoogle Scholar
4.Richter, A., Daghlian, C.P., Ries, R., and Solozhenko, V.L.: Investigation of novel superhard materials by multi-cycling nanoindentation. Diamond Relat. Mater. 15, 2019 (2006).CrossRefGoogle Scholar
5.Gogotsi, Y.G., Domnich, V., Dub, S.N., Kailer, A., and Nickel, K.G.: Cyclic nanoindentation and Raman microspectroscopy study of phase transformations in semiconductors. J. Mater. Res. 15, 871 (2000).Google Scholar
6.Dub, S.N., Milman, Y.V., Lotsko, D.V., and Belous, A.N.: The anomalous behavior of Al-Cu-Fe quasicrystal during nanoindentation. J. Mater. Sci. Lett. 20, 1043 (2001).CrossRefGoogle Scholar
7.Kucharski, S. and Mróz, Z.: Identification of material parameters by means of compliance moduli in spherical indentation test. Mater. Sci. Eng., A 379, 448 (2004).Google Scholar
8.Kucharski, S. and Mróz, Z.: Identification of yield stress and plastic hardening parameters from a spherical indentation test. Int. J. Mech. Sci. 49, 1238 (2007).CrossRefGoogle Scholar
9.Komvopoulos, K. and Yang, J.: 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).CrossRefGoogle Scholar
10.Tymiak, N.I., Nelson, J.C., Bahr, D.F., and Gerberich, W.W.: Microindentation method for in situ stress measurements in precipitated iron sulphate films. Corros. Sci. 40, 1953 (1998).Google Scholar
11.Li, W.H., Shin, K., Lee, C.G., Wei, B.C., Zhang, T.H., and He, Y.Z.: The characterization of creep and time-dependent properties of bulk metallic glasses using nanoindentation. Mater. Sci. Eng., A 478, 371 (2008).CrossRefGoogle Scholar
12.Oliver, W-C. and Pharr, G.M.: Improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).Google Scholar
13.Szarko, M. and Bertram, J.E.A.: Loading rate sensivity of articular cartilage. J. Biomech. 39, S478 (2006).CrossRefGoogle Scholar
14.Nix, W.D. and Gao, H.: Indentation size effects in crystalline materials: A law for strain gradient plasticity. J. Mech. Phys. Solids 46, 411 (1998).Google Scholar
15.Chicot, D.: Hardness length-scale factor to model nano and micro-indentation size effects. Mater. Sci. Eng., A 499, 454 (2009).CrossRefGoogle Scholar
16.De Faria, D.L.A., Venancio Silva, S., and De Oliveira, M.T.: Raman microspectroscopy of some iron oxides and oxyhydroxides. J. Raman Spectrosc. 28, 873 (1997).Google Scholar
17.Bersani, D., Lottici, P.P., and Montenero, A.: Micro-Raman investigation of iron oxide films and powders produced by sol-gel syntheses. J. Raman Spectrosc. 30, 355 (1999).Google Scholar
18.Sousa, M.H., Tourinho, F.A., and Rubim, J.C.: Use of Raman micro-spectroscopy in the characterization of MIIFe2O4 (M = Fe, Zn) electric double layer ferrofluids. J. Raman Spectrosc. 31, 185 (2000).Google Scholar
19.Quinn, G.D., Patel, P.L., and Lloyd, I.: Effect of loading rate upon conventional ceramic microindentation hardness. J. Res. Nat. Inst. Stand. Technol. 107, 299 (2002).CrossRefGoogle ScholarPubMed
20.Herrmann, K., Jennett, N.M., Wegener, W., Meneve, J., Hasche, K., and Seemann, R.: Progress in determination of the area function of indenters used for nanoindentation. Thin Solid Films 377–378, 394 (2000).Google Scholar
21.Fischer-Cripps, A.C.: Critical review of analysis and interpretation of nanoindentation test data. Surf. Coat. Technol. 200, 4153 (2006).CrossRefGoogle Scholar
22.Chicot, D. and Mercier, D.: Improvement in depth-sensing indentation to calculate the universal hardness on the entire loading curve. Mech. Mater. 40, 171 (2008).CrossRefGoogle Scholar
23.Hay, J.C., Bolshakov, A., and Pharr, G.M.: Critical examination of the fundamental relations used in the analysis of nanoindentation data. J. Mater. Res. 14, 2296 (1999).CrossRefGoogle Scholar
24.Shuman, D.J., Costa, A.L.M., and Andrade, M.S.: Calculating the elastic modulus from nanoindentation and microindentation reload curves. Mater. Charact. 58, 380 (2007).CrossRefGoogle Scholar
25.Antunes, J.M., Menezes, L.F., and Fernandes, J.V.: Influence of Vickers tip imperfection on depth-sensing indentation tests. Int. J. Solids Struct. 44, 2732 (2007).CrossRefGoogle Scholar
26.Doerner, M.F. and Nix, W.D.: A method of interpreting the data from the depth-sensing indentation instruments. J. Mater. Res. 1, 601 (1986).CrossRefGoogle Scholar
27.Sneddon, I.N.: The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965).Google Scholar
28.Gong, J., Miao, H., and Peng, Z.: Analysis of the nanoindentation data measured with a Berkovich indenter for brittle materials: Effect of the residual contact stress. Acta Mater. 52, 785 (2004).Google Scholar
29.Huang, Y., Zhang, F., Hwang, K.C., Nix, W.D., Pharr, G.M., and G Feng: A model of size effects in nano-indentation. J. Mech. Phys. Solids 54, 1668 (2006).CrossRefGoogle Scholar
30.Ma, Q. and Clarke, D.R.: Size-dependent hardness of silver single-crystals. J. Mater. Res. 10, 853 (1995).Google Scholar
31.Zong, Z., Lou, L., Adewoye, O.O., Elmustafa, A.A., Hammad, F., and Soboyejo, W.O.: Indentation size effects in the nano- and micro-hardness of fcc single crystal metals. Mater. Sci. Eng., A 434, 178 (2006).CrossRefGoogle Scholar
32.Lou, J., Shrotriya, P., Allameh, S., Buchheit, T., and Soboyejo, W.O.: Strain gradient plasticity length scale parameters for LIGA Ni MEMs thin films. Mater. Sci. Eng., A 441, 299 (2006).CrossRefGoogle Scholar
33.Qin, J., Huang, Y., Hwang, K.C., Song, J., and Pharr, G.M.: The effect of indenter angle on the microindentation hardness. Acta Mater. 55, 6127 (2007).Google Scholar
34.Zhao, M., Slaughter, W.S., Li, M., and Mao, S.X.: Material-length-scale-controlled nanoindentation size effects due to strain-gradient plasticity. Acta Mater. 51, 4461 (2003).Google Scholar
35.Zaiser, M. and Aifantis, E.C.: Geometrically necessary dislocations and strain gradient plasticity—A dislocation dynamics point of view. Scr. Mater. 48, 133 (2003).CrossRefGoogle Scholar
36.Bonifaz, E.A. and Richards, N.L.: The plastic deformation of non-homogeneous polycrystals. Int. J. Plast. 24, 289 (2008).Google Scholar
37.Reichmann, H.J. and Jacobsen, S.D.: High-pressure elasticity of a natural magnetite crystal. Am. Mineral. 89, 1061 (2004).CrossRefGoogle Scholar
38.Bradley, J.P., Harvey, R.P., and McSween, H.Y.: Magnetite whiskers and platelets in the ALH84001 Martian meteorite: Evidence of vapor phase growth. Geochim. Cosmochim. Acta 60, 5149 (1996).Google Scholar