Strain gradient plasticity to study hardness behavior of magnetite (Fe 3 O 4 ) under multicyclic indentation
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. Lepingle and G. Louis Ecole des Mines de Douai, 59508 Douai Cedex, France (Received 19 June 2008; accepted 29 September 2008)
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.
I. INTRODUCTION
To study the hardness behavior of a material, the depth-sensing indentation (DSI) technique is largely used since this method allows submitting the specimen to various indentation cycling modes. Indeed, if the specimen is loaded up to a specific value, unloaded and immediately reloaded, a cyclic indentation curve is produced. After the reloading, the cycle can reach the same ultimate load-depth values1,2 or higher values3,4 than the previous loading cycle. Such cyclic indentations were used by some researchers to study phase transformations under stress.5,6 Thus Kucharski and Mroz7,8 applied cyclic indentation to determine yield stress and plastic hardening by using a ball indenter. In this instance, differences between kinematic and isotropic hardening can be attributed to the fact that the yield stress during cyclic loading changes significantly in kinematic hardening but not in isotropic hardening.2 Besides, Komvopoulos and Yang9 explain the difference of cyclic indentation behavior by cumulative plasticity. In addition, Kucharski and Mroz8 found some abnormal additional divergences a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2009.0098 J. Mater. Res., Vol. 24, No. 3, Mar 2009
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in their results. They explained the apparent contradictions by errors in the determination of compliances (derivatives) of experimental penetration curves and in the measurement of the indentation depth. Moreover, numerous
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