quantitative approach to determine the mechanical ...mazeran/publis/30.pdf · quantitative approach...

Quantitative approach to determine the mechanical propertiesby nanoindentation test: Application on sandblasted materials

Y. Xia a, M. Bigerelle b,n, S. Bouvier a, A. Iost c, P.-E. Mazeran a

a Laboratoire Roberval de Mécanique, Université de Technologie de Compiègne, 60205 Compiègne Cedex, Franceb Matériaux, surfaces et mise en forme, TEMPO, LAMIH, Université de Valenciennes, 59313 Valenciennes, Francec Laboratoire MSMP, Arts et Métiers ParisTech, ENSAM, CS 50008, 59046 Lille Cedex, France

a r t i c l e i n f o

Article history:Received 30 September 2013Received in revised form24 June 2014Accepted 23 July 2014

Keywords:NanoindentationRoughnessSandblastingMechanical properties

a b s t r a c t

A novel method is developed to improve the accuracy in determining the mechanical properties fromnanoindentation curves. The key point of this method is the simultaneous statistical treatment of severalloading curves to correct the zero point error and identify the material properties considering sizeeffects. The method is applied to four sandblasted aluminum-based specimens with different surfaceroughness. A linear relationship is obtained between the standard deviation of the initial contact errorand the roughness which highlights the effect of the surface roughness on the reproducibility of theindentation curves. Moreover, the smaller standard deviation of the hardness given by the methodconfirms the importance of considering the initial contact error for an accurate determination of thematerial properties.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Mechanical properties play a crucial role in contact mechanics andshould be determined accurately to predict the ability of a material toresist a plastic deformation, contact fatigue, and wear etc. Nanoinden-tation technique is largely used to determine mechanical propertiesnear the surface [1]. However, in the specific case of rough surfaces,the low reproducibility of the load–depth curves due to a baddetermination of the initial contact leads to an inaccurate estimationof the material properties (e.g. hardness) [2]. Experimentally, the initialcontact corresponds to the smallest reachable applied load; or whenthe contact stiffness becomes higher to a value given by a user [3].However, different problems may occur which affect the initial contacterror, e.g. the geometry of the indenter tip, the instrument systemerrors (false detection), the surface preparation and the roughness [4].In nanoindentation, the size of the imprint is too small to be measuredaccurately with optical microscopy. Therefore, the load–depth curveand the geometry of the indenter are used to determine the contactarea and consequently the material hardness. In case of rough surface,as indicated previously, the determination of the initial contact depthbecomes difficult, since the first contact points can be located on avalley or on a peak of the surface leading to an error in the value of theindentation depth and consequently in the true contact area [5]. Somemethods have been proposed to determine the initial contact point by

redefining the zero position [6] or using the slope of the indentationcurve [7]. However, these methods were mainly applied on sphericalindenters. Other authors propose to use a large set of nanoindentationtests, to quantify from each test the material properties. They averagethe computed data in order to characterize the material.

In the present work, a quantitative statistical method is used toanalyze a set of nanoindentation curves based on an innovativesimultaneous shifting of the loading curves [8–11]. The methodhighlights the influence of the roughness on nanoindentationcurve and leads to a more accurate determination of the mecha-nical properties. This method is applied to four sandblastedaluminum-based alloy 2017A specimens, which are abraded usingdifferent treatment parameters. The macro-hardness and theindentation size effect parameter are estimated. In addition, thesurface roughness effect on the initial contact point detection isevidenced and effectively considered to obtain a more accuratevalue of the macro-hardness.

2. Experimental details

2.1. Specimen preparation

The four specimens investigated in this study were extractedfrom a bar of aluminum-based alloy 2017A. The chemical compo-sition in wt%: Zn (0.25), Mg (0.4–1.0), Cu (3.5–4.5), Cr (0.1), Mn(0.4–1.0), Fe (0.7), Si (0.2–0.8), ZrþTi (0.25), Al (base). The disks

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/triboint

Tribology International

http://dx.doi.org/10.1016/j.triboint.2014.07.0220301-679X/& 2014 Elsevier Ltd. All rights reserved.

n Corresponding author. Tel.: þ33 6 16 29 76 04.E-mail address: [email protected] (M. Bigerelle).

Please cite this article as: Xia Y, et al. Quantitative approach to determine the mechanical properties by nanoindentation test:Application on sandblasted materials. Tribology International (2014), http://dx.doi.org/10.1016/j.triboint.2014.07.022i

Tribology International ∎ (∎∎∎∎) ∎∎∎–∎∎∎

www.sciencedirect.com/science/journal/0301679X

www.elsevier.com/locate/triboint

http://dx.doi.org/10.1016/j.triboint.2014.07.022



mailto:[email protected]





were 30 mm in diameter and 20 mm thickness. To ensure all thesamples have the same mechanical and topographical initial state,a pre-polishing with 120, 320 and 1000 silicon carbide grit papersand a fine polishing with a 3 mm grain size diamond DP-Spraylubricant were performed successively. The specimens were thensandblasted using a jet of Al2O3 particles with a diameter ofapproximately 500 μm in a CSF 70V (ARENA, France) machine.The parameters of the sandblasting process for different speci-mens named S1–S4 are listed in Table 1.

2.2. Roughness measurement

The topography of the treated specimens was measured using athree-dimensional (3D) roughness tactile profilometer TENCORTM

P10. The vertical sensitivity of the profilometer is 10 nm and thehorizontal sensitivity is 50 nm. A stylus with a tip radius of 2 μmhas been used to probe the surface under a 5�10�5 N load. Two-dimensional (2D) high-resolution profiles have been recordedwith a measurement length of 5 mm at a speed of 200 μm/s. Eachprofile is described by 25,000 points (0.2 μm between each point).For each specimen, 30 profiles are recorded.

2.3. Nanoindentation

Nanoindentation experiments were conducted on four sand-blasted surfaces using a Nano Indenter XP (MTS System) equippedwith a Berkovich tip indenter. The Continuous Stiffness Measure-ment (CSM) method was used; the harmonic oscillation depth andfrequency were 2 nm and 45 Hz, respectively. For each specimen,100 nanoindentations were made with a constant strain rate equal0.05 s�1 until an indentation depth of 3000 nm is achieved. Fig. 1displays the loading section of the nanoindentation curvesobtained for the specimen S4. To avoid any statistical artifacts,only the parts of the curves whose load value are less than0.8 times the maximum load are kept.

3. Model and method

3.1. Multi-scale surface profile treatment

The evaluation length of surface profile has a critical effect onthe roughness study [12]. Indeed, it was observed that differentevaluation lengths will give different roughness parameters. Theinitial roughness profiles were experimentally measured for agiven length. However, this length is so long comparing with thenanoindentation scale that is not suitable for nanoindentationstudy. A relevant evaluation length for the roughness calculationshould be selected. Hence, the aim of the multi-scale surfaceprofile treatment is to find the most suitable evaluation length ofthe surface roughness in nanoindentation study. In this treatment,the topographic profile was divided into equal parts whose lengthis the evaluation length. Then, a multi-scale composition of eachoriginal profile was carried out [13]. For one original topographicprofile, the new profiles reset using different evaluation lengthsare very different as shown in Fig. 2. Compared with the profilerectified using the shorter evaluation length (15 μm), the profilecalculated using the longer evaluation length (521 μm) appearsmore wavy. The value of the quadratic roughness called Rq alsodepends on the evaluation length (Fig. 3). For each specimen, thequadratic roughness increases with an increasing evaluationlength and approaches an asymptotic value. Comparing the fourspecimens, it can be observed that the surface roughness producedby different sandblasted parameters decreases from S1 to S4whatever the evaluation lengths. It means that a higher jetpressure, shorter distance and bigger angle in sandblasting testproduce rougher surface (higher Rq).

3.2. Load–depth curves treatment

Hardness is usually defined as

H¼ P=Ac; ð1Þwhere Ac is the contact area. With a Berkovich indenter, thecontact area Ac can be expressed using the contact depth hc:

Ac ¼ αh2c ; ð2Þ

where α is depending on the geometry of the indenter, hc is thereal contact depth defined by Oliver and Pharr's method:

hc ¼ h�εindenterPS; ð3Þ

where h is the measured displacement into the sample, S is thestiffness of contact and εindenter is a geometrical constant equalto 0.75 for a Berkovich indenter. Thus, the previous equationbecomes:

P ¼ αHh2c ð4Þ

Then, we take into account the possibility of an IndentationSize effect (ISE, i.e. an increase in hardness with decreasing depthof penetration at small depths) through the use of Vingsbo'slaw [14] defined as

H¼H0þβ=hc; ð5Þwhere H0 is the macroscopic hardness and β is the ISE factor. It isworth noting that the linear relationship between the load and thepenetration depth at the early stage of the indentation test gathersdifferent phenomena known as the ISE. Such linear relationshipyields to a proportionality between H and 1=hc , through a constantterm, β, named ISE factor.

Thus, Eq. (4) is modified as follows:

P ¼ αðH0þβ=hcÞh2c ¼ αðH0h

2c þβhcÞ ð6Þ

Table 1Sandblasting parameters for four 2017A specimens. The angle is the included anglebetween the spray gun and specimen surface.

Specimen Pressure (bar) Distance (cm) Angle (deg)

S1 1 15 90S2 1 30 90S3 0.5 30 90S4 0.5 30 60

Fig. 1. Loading part of the load versus indentation depth curves for the sand blasted2017A specimen S4.

Y. Xia et al. / Tribology International ∎ (∎∎∎∎) ∎∎∎–∎∎∎2





Eq. (6) is having a similar formula with the Bernhardt model[15], but different indentation depth is used in the equations asexpressed by Eq. (7). The Bernhardt model uses the measureddisplacement into the sample, while the proposed model uses thereal contact depth.

P ¼ α1h2þα2h; ð7Þ

where h is the measured displacement into the sample, α1 and α2

are parameters related to the geometry of the indenter tip and thematerial properties.

In our method, all the experimental loading curves are firstlyfitted by Eq. (6). A reference curve is arbitrarily selected from allthe loading curves. Considering the original point of the referencecurve is the reference initial contact point, the other loadingcurves could be written as follows:

P ¼ α½H0ðhcþΔhcÞ2þβðhcþΔhcÞ�; ð8Þwhere Δhc is the initial contact error, i.e. the distance between theexperimental curves and the reference one in the indentationdepth axis. Here, we suppose the macro-hardness and the ISEfactor are constant for a specimen. A least-squares regressionanalysis is used to obtain the mechanical properties. It is a processof minimization to make the experimental curves best match the

reference curve:

minH0 ;Δh1 :::Δhn ;β

∑n

i ¼ 1∑pj

j ¼ 1fPi;j�α½H0h

2cjþð2H0ΔhciþβÞhcjþH0Δh2ciþβΔhci�g2;

ð9Þwhere i is the ith loading curve and j refers to the jth couple point(P, h) of one loading curve.

The bootstrap is a statistical method of simple random sam-pling with replacement [16]. For getting the value of H0 and β withtheir confidence intervals, a double bootstrap on the 100 originalexperimental loading curves of each specimen is performed. Thefirst bootstrap is used to reduce the heterogeneity of material ingradient direction. It ensures that all the points in one curve areindependent and identically distributed. The second bootstrapaims at reducing the variable of nanoindentation tests in differentsurface zone. It is also a good means to delete the error induced bythe random choosing of the reference curve. For each bootstrap,the reference curve is chosen again. This process is repeated morethan 1000 times in order to reduce the artificial factors.

3.3. Loading curves simulation

To investigate the effect of the initial contact point errors on themacro-hardness and ISE factor determination, a numerical simula-tion of load–depth curves has been performed for each specimen.The numerical curves are created according to Eq. (6), where themacro-hardness H0 and ISE factor β are equal to the mean valueidentified by the proposed model based on the experimental data.The placement of numerical curves is only defined by the standarddeviation of the initial contact error ðσΔÞ. In the first part, thesystemic origin of all the numerical curves is supposed at the zeroof x-axis. Each numerical curve is placed along the x-axis accord-ing to the Gaussian distribution with different standard deviations.In the second part, we suppose that there is a gap between thesystemic origin of all the numerical curves and the zero of thex-axis, note as Δ. Then each numerical curve is placed along thex-axis conforming to the Gaussian distribution with differentstandard deviation. The number of numerical curves is equal tothe number of experimental curves for each specimen.

Fig. 3. Evolution of the Root Mean Square roughness (Rq) versus the evaluationlengths.

Fig. 2. Multi-scale profile reconstructions corresponding to different evaluation length.

Y. Xia et al. / Tribology International ∎ (∎∎∎∎) ∎∎∎–∎∎∎ 3





4. Results and discussion

4.1. Surface roughness and initial contact error correction

The experimental nanoindentation curves of the four sand-blasted 2017A specimens with different roughness have beentreated using the proposed method. Fig. 4 plots the loading curvesof S4 after the shifting with the initial contact errors. Obviously,the shifted curves are closer than the original experimental curvesshown in Fig. 1. It suggests that the error on the initial contactpoint detection could be reduced by the model.

The distribution of the initial contact error for each sandblasted2017A specimen calculated based on the statistical method using adouble Bootstrap has been shown in Fig. 5. It could be observedthat the standard deviation of the initial contact error, which couldbe described as the width of red fitting line, decreases with thesurface roughness from S1 to S4. For this reason, the investigationof relationship between the roughness and the standard deviationof initial contact error is valuable for quantifying the effect ofsurface roughness on nanoindentation data. As described inprevious Section 3.1, the evaluation length is an important factoron the studying of surface roughness. Hence, the primary issue isto find the most appropriate evaluation length of roughness

analysis in the nanoindentation study. Firstly, a multiplicity ofcalculations on surface roughness Rq has been done using differentevaluation lengths for each specimen. Then the linear regressionsbetween the calculated surface roughness Rq and the standarddeviation of initial contact error σðΔhcÞ have been studied to findthe strongest correlation. Fig. 6 shows the plot of linear coefficientof determination (R2) versus the different evaluation lengths. It isclear to see that there is a high correlation between the roughnessRq and the standard deviation of the initial contact error when theevaluation length is around 15 μm. It means the best evaluationlength of roughness identification in this nanoindentation test is15 μm, which is also in the size of the indentation print. In thisscale, the indenter can be considered as a surface “probe”. In otherwords, the initial contact error correction is just like shifting theindentation curves according to the amplitude of surface topo-graphy. Fig. 7 depicts the best linear relation between the standarddeviation of initial contact error and the surface roughness Rq(standard deviation of the amplitude of surface topography)calculated with the evaluation length of 15 μm. It shows theeffectiveness of the initial contact error correction. The proposedmodel allows predicting the mechanical properties based onnanoindentation test on sandblasted surface without link to theroughness itself.

Fig. 4. Shifted load versus indentation depth curves for the sand blasted 2017Aspecimen S4.

Fig. 5. Distribution of initial contact error for each sandblasted 2017A specimen calculated using a double bootstrap.

Fig. 6. Evolution of the linear correlation coefficient (R2) versus different evaluationlengths.






4.2. Hardness and ISE factor

In order to observe the effect of initial contact errors on thevalue of the mechanical properties, the experimental data aretreated in two different conditions: ignoring or considering theinitial contact errors. These two conditions respectively corre-spond to the Δhc ¼ 0 (not shifting curves) or Δhca0 (shiftingcurves) in Eq. (9). Fig. 8 shows the value of the macro-hardness H0

for each sandblasted 2017A specimen calculated with (a) ignoringor (b) considering the initial contact error. First of all, the macro-hardness for the four specimens calculated in condition (a) is inthe range of 1.01–1.54 GPa with the standard deviation around0.1 GPa. For condition (b), the macro-hardness is in the range of

1.63–1.93 GPa with a smaller standard deviation around 0.02 GPa,which is less than the first condition. It is also more accurate thanthe average value given by the nanoindentation system (around270.3 GPa). Secondly, the mean value of macro-hardness forcondition (b) decreases with a decreasing surface roughness fromS1 to S4. A possible explanation for this trend is the existence ofthe strain hardening layer induced by the sandblasting process.In the sandblasting process, a shorter distance for S1 or a strongerjet pressure for S2 means a higher impact stress. This higherimpact stress produces a rougher surface and creates a thicker strainhardening layer in the subsurface region, which could change thesurface mechanical properties. Thus, the macro-hardness decreasesfrom specimen S1 to S3. The difference of the sandblasting para-meters for S3 and S4 is the angle between the jet and the surface.For the smaller angle of S4, the sand particles shoot from a non-vertical direction. This procedure can be divided into two steps:abrading on the initial surface and rebounding from the sandblastedsurface [17]. The latter process must dissipate a part of energy doneby the sand particles impact. Thus, the work to abrading the initialsurface for S4 that the sand particles shooting to the surface with aangle must be weaker than the situation for S1 that sand particlesshooting in a vertical direction.

Therefore, the strain hardening layer in S4 is thinner than S3,which denotes a smaller elastic recovery in nanoindentation tests,hence a lower macro-hardness. Moreover, the mean value ofmacro-hardness given by condition (b) is around 1.5 times thevalue given by condition (a) for the specimens S1–S3. But thisdifference is not distinct for specimen S4. Moreover, Fig. 9 showsthe ISE factor of each sandblasted 2017A specimen calculatedwith (a) ignoring or (b) considering the initial contact error.

Fig. 7. Linear relation between the standard deviation of initial contact error andthe Root Mean Square roughness for the evaluation length equal to 15 μm.

Fig. 8. Macro-hardness for each sandblasted 2017A specimen calculated using novel method (a) ignoring or (b) considering the initial contact error.

Fig. 9. Indentation size effect factor β for each sandblasted 2017A specimen calculated using novel method (a) ignoring or (b) considering the initial contact error, where the insetfigures show an indentation print of specimen S1 (left) and of specimen S4 (right) measured using scanning electron microscopy. The pile-up is the critical origin of ISE for S4.






After considering the initial contact error, the ISE factor becomeszero for the specimens S1–S3. But this factor is almost same for thespecimen S4 (around 400 mN/nm). It means except the systemicerrors, the initial contact error is directly related with the surfaceroughness for the specimens having rough surface (S1–S3). This“artificial” ISE can be reduced by considering the initial contacterror. For the fine surface S4, the surface roughness is no longerthe most important effect on initial contact error. The pile-uparound the indentation print is probably the best explanation forthe ISE occurrence (inset figures in Fig. 9) [18–20]. This effect willnot be diminished by considering the initial contact error. Theobservation of Fig. 6 permits to note that the difference of themechanical properties between two conditions decreases with thedecreasing of the standard deviation of the initial contact error,which directly relies on the surface roughness (decreases from S1to S4). It is worth to highlight that the averages of all the initialcontact errors are statistically zero even they are a little differentwith real zero. If infinite indentation curves are studied, theaverages of the initial contact errors could equal to zero.

To explain this difference of the value of mechanical propertiescomputed with these two conditions, the loading curves havebeen simulated by the method described in Section 3.3. For eachspecimen, one hundred curves are simulated with each standarddeviation σΔ (variable between 0 and 500 nm) of the distancebetween the simulated curves and the origin point. The average ofthe distances between the simulated curves and the origin point issupposed to equal zero, i.e. the systemic origin of all the numericalcurves is supposed at the zero of the x-axis. This distance justcorresponds to the initial contact error of the experimental curves.Comparing with the experimental results controlled by all theparameters, the simulated results are just controlled by theimposed standard deviation. Fig. 10 shows the variation of simu-lated macro-hardness for the four specimens, as a function ofthe standard deviation of the distance between the origin andthe actual position of simulated curves. For each specimen, theaverage of simulated macro-hardness decreases with the increas-ing of the imposed standard deviation and it arrives to the highestvalue when σΔ¼0. It means the macro-hardness will increaseby considering the initial contact error in condition (b). If thestandard deviation of initial contact error is lower, the differenceof macro-hardness is smaller. It proves the rationality that thedifference of macro-hardness between two conditions is bigger forrough surface S1–S3, but smaller for S4. The simulated curves

shown in inset figure with different standard deviations (0 nm and125 nm) can explain this phenomenon. Higher standard deviationcorresponds to a bigger dispersion of the simulated curves aroundzero point. The simulated curves with bigger dispersion just like toflatten the loading curve obtained by applying the proposedmodel. This flattening process, due to the minimization of thesum of squared residuals of the standard deviation, decreases themacro-hardness of the identified curves.

Table 2 summarizes the mean value and associated standarddeviations of macro-hardness for experimental and simulatedcurves (a) with or (b) without the consideration of initial contacterror. The results calculated for experimental and simulated curvesin condition (a) are similar. The slight difference is broughtprincipally by the hypotheses in the curve simulation. In thecurves simulation, the systemic origin is supposed to be zero.

Fig. 10. Variation of the macro-hardness of the simulated curves for the fourspecimens, as a function of the standard deviation of the distance between the zeroand the actual position of the simulated curves. In the inset figures, the thin curvesare the simulated loading curves obtained before the optimization while the boldones obtained after optimization with the proposed model.

Table 2Mean values and associated standard deviation of the macro-hardness of four2017A specimens.

Specimen Experimental curves Simulated curvescondition (a):Δhc¼0Condition (a):

Δhc¼0Condition (b): Δhca0

H0

(GPa)σ (H0)(GPa)

H0

(GPa)σ (H0)(GPa)

σ (Δhc)(nm)

H0

(GPa)σ (H0)(GPa)

S1 1.01 0.11 1.93 0.0200 402 0.84 0.13S2 1.06 0.11 1.88 0.0170 325 1.18 0.10S3 1.17 0.10 1.82 0.0067 204 1.48 0.06S4 1.54 0.02 1.63 0.0069 126 1.53 0.02

Fig. 11. Variation of the (a) macro-hardness H0 and (b) ISE factor β for specimen S4.These values were identified using the simulated curves and are represented as afunction of the systemic shift from the origin point Δ, for three standard deviationsof shifts σ and three ISE factors β.






But this hypothesis strongly relates with the sensibility for thedetection of the contact between indenter and surface. It ispossible that the systemic origin is not in zero. Therefore, a newsimulation with a variable systemic origin of all the numericalcurves has been performed. The variable interval of systemic originis from �500 nm to 500 nm, note as Δ. It is the gap between thesystemic origin and the zero of x-axis. Then the simulated curvesare placed with three imposed standard deviations of the distancebetween the systemic origin and the actual position of the curvesσ (0, 100 and 200 nm) and three indentation size effect factors β(positive, negative and zero). Fig. 11 shows the results of these newsimulations. It could be observed that the error on the position ofsystemic origin brings the error on the macro-hardness determi-nation. At the same time, the macro-hardness error also dependson the ISE factor and the imposed standard deviation. Fig. 12represents the simulated curves after the optimization using theproposed model Eq. (9) with considering or neglecting the initialcontact error for specimen S4. In the treatment, the systemicorigin shift is equal to 0 nm or 500 nm and the ISE factor is equalto �1000, 0 or 1000 mN/nm. The curve obtained considering theinitial contact error is shown in bold while the thin curve isobtained assuming this error is equal to zero. But the estimatedmacro-hardness by later optimization (Δhc¼0) are variable whenthe imposed systemic origin shift and the ISE factor are changed. Itclearly means that the negligence of the initial contact error intreatment can induce a bad estimation of the macro-hardnessvalue, even if the curves are similar enough. Some detailedarguments have been given in previous work [21].

5. Conclusions

The proposed initial contact error correction method is able toaccurately evaluate the mechanical properties of differentaluminum-based alloy 2017A sandblasted samples using nanoin-dentation test. The estimated macro-hardness is in the range of1.63–1.93 GPa with a small deviation around 0.02 GPa, which ismore accurate than the one calculated by the nanoindentationsystem using average curves (around 270.3 GPa). Furthermore, amulti-scale surface analysis is performed to determine the bestevaluation length, which leads to an appropriate description of thesurface topography. A linear relation between the standard devia-tion of the initial contact error and the standard deviation of theamplitude of surface topography is found which clearly highlightsthe effect of surface roughness on the indentation results. Finally,

the best evaluation length for roughness analysis is found to beequal to 15 μm, which is almost of the same order of magnitude asthe indentation imprint.

Acknowledgment

Contract grant sponsor: China Scholarship Council (CSC),No. 2010008045.

References

[1] Oliver WC, Pharr GM. Measurement of hardness and elastic modulus byinstrumented indentation: advances in understanding and refinements tomethodology. J Mater Res 2004;19:3–20.

[2] Fischer-Cripps AC. Critical review of analysis and interpretation of nanoin-dentation test data. Surf Coat Technol 2006;200:4153–65.

[3] Fischer-Cripps AC. A review of analysis methods for sub-micron indentationtesting. Vacuum 2000;58:569–85.

[4] Ullner C. Requirement of a robust method for the precise determination of thecontact point in the depth sensing hardness test. Measurement 2000;27:43–51.

[5] Pharr G. Measurement of mechanical properties by ultra-low load indentation.Mater Sci Eng A 1998;253:151–9.

[6] Kalidindi SR, Pathak S. Determination of the effective zero-point and theextraction of spherical nanoindentation stress–strain curves. Acta Mater2008;56:3523–32.

[7] Brammer P, Bartier O, Hernot X, Mauvoisin G, Sablin SS. An alternative to thedetermination of the effective zero point in instrumented indentation: use ofthe slope of the indentation curve at indentation load values. Mater Des2012;40:356–63.

[8] Bigerelle M, Mazeran PE, Rachik M. The first indenter-sample contact and theindentation size effect in nano-hardness measurement. Mater Sci Eng C2007;27:1448–51.

[9] Marteau J, Mazeran PE, Bouvier S, Bigerelle M. Zero-point correction methodfor nanoindentation tests to accurately quantify hardness and indentation sizeeffect. Strain 2012;48:491–7.

[10] Marteau J, Bigerelle M, Xia Y, Mazeran PE, Bouvier S. Quantification of firstcontact detection errors on hardness and indentation size effect measure-ments. Tribol Int 2013;59:154–62.

[11] Xia Y, Bigerelle M, Marteau J, Mazeran PE, Bouvier S, Iost A. Effect of surfaceroughness in the determination of the mechanical properties of material usingnanoindentation test. Scanning 2014;36:134–49.

[12] Bigerelle M, Mathia T, Bouvier S. The multi-scale roughness analyses andmodeling of abrasion with the grit size effect on ground surfaces. Wear2012;286:124–35.

[13] Bigerelle M, Van Gorp A, Iost A. Multiscale roughness analysis in injection-molding process. Polym Eng Sci 2008;48:1725–36.

[14] Vingsbo O, Hogmark S, Jçönsson B, Ingemarsson A. Indentation hardness ofsurface-coated materials. Philadelphia, USA: ASTM STP; 1986.

[15] Bernhardt E. On microhardness of solids at the limit of Kick's similarity law. ZMet 1941;33:135–44.

[16] Bigerelle M, Anselme K. Bootstrap analysis of the relation between initialadhesive events and long-term cellular functions of human osteoblastscultured on biocompatible metallic substrates. Acta Biomater 2005;1:499–510.

Fig. 12. Simulated curves after the optimization using the proposed model equation (5) with considering or neglecting the initial contact error for specimen S4. In thetreatment, the systemic origin shift is equal to 0 nm or 500 nm and the ISE factor is equal to �1000, 0 or 1000 mN/nm. The curve obtained considering the initial contacterror is shown in bold while the thin curve is obtained assuming this error is equal to zero.



http://refhub.elsevier.com/S0301-679X(14)00282-5/sbref1














































[17] Carter G, Bevan IJ, Katardjiev IV, Nobes MJ. The erosion of copper by reflectedsandblasting grains. Mater Sci Eng A 1991;132:231–6.

[18] Iost A, Bigot R. Indentation size effect: reality or artefact? J Mater Sci1996;31:3573–7.

[19] Lee Y, Hahn J, Nahm S, Jang J, Kwon D. Investigations on indentation sizeeffects using a pile-up corrected hardness. J Phys D Appl Phys 2008;41:074027.

[20] Kim J, Kang S, Lee J, Jang J, Lee Y, Kwon D. Influence of surface-roughness onindentation size effect. Acta Mater 2007;55:3555–62.

[21] Ho HS, Xia Y, Marteau J, Bigerelle M. Influence de l'amplitude de la rugosité desurfaces sablées sur la mesure de dureté par nanoindentation. Matér Technol2013;101:305–14.

















quantitative approach to determine the mechanical ...mazeran/publis/30.pdf · quantitative approach...

Documents