Nanoindentation of coatings

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2005 J. Phys. D: Appl. Phys. 38 R393

(http://iopscience.iop.org/0022-3727/38/24/R01)

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INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS

J. Phys. D: Appl. Phys. 38 (2005) R393–R413 doi:10.1088/0022-3727/38/24/R01

TOPICAL REVIEW

Nanoindentation of coatingsS J Bull

School of Chemical Engineering and Advanced Materials, University of Newcastle, Newcastle upon Tyne,NE1 7RU, UK

Received 1 July 2005, in final form 17 October 2005Published 2 December 2005Online at stacks.iop.org/JPhysD/38/R393

AbstractA range of mechanical properties of a coating/substrate system may be obtained using indentationtests, and with the emergence of continuously recording indentation testing with nanometrepenetration (often called nanoindentation) the mechanical properties of very thin coatings(<1 µm) and surface treated layers may be measured. This paper reviews the deformationmechanisms which occur and the methods for extracting mechanical properties of coatings fromnanoindentation load–displacement curves and introduces the differences observed whencompared with the testing of bulk materials. The importance of the relative hardness of coatingand substrate on the response of the system is highlighted, and the use of energy-based models forthe prediction of the performance of single and multilayered systems is discussed.

(Some figures in this article are in colour only in the electronic version)

Notation

α Ratio of elastic to plastic zone radiusA Deforming areas (subscripts s and i refer

to surface and interface, respectively)Ac Contact areaAcrack Crack areaβ Cone to pyramid indenter conversion factorβc Angular divergence of an indentation crackc Radial crack lengthc0 · · · cn Indenter shape function constantsd Indentation diagonal (Vickers indenter)δ Indenter displacementδc Contact depthδcrack Displacement at which ring crack is formedδcrit Critical displacement above which picture frame

cracks are formedδmax Maximum indenter displacementδres Residual indent depthδ0 Fitted residual indent depthε Indenter shape factorE Young’s modulus (subscripts c, s and i refer to

coating, substrate and indenter, respectively)Er Contact modulusγ Correction factor for Sneddon equationγi Interface energyγs Surface energyγ0 Strain amplitude�i Interfacial fracture energy

H Hardness (subscripts c, s and i refer to coating,substrate and indenter, respectively)

KIc Fracture toughnessL Length of cracked segmentmε Creep strain rate exponentmσ Creep stress exponentn Unloading curve fit exponentν Poisson’s ratio (subscripts c, s and i refer to

coating, substrate and indenter, respectively)P Indenter loadφ Phase difference between ac applied load and

measure displacementrc Radius of a radial or ring crack produced

during indentationR Radius of the plastic zoneReff Effective radius of elastically deformed region

around an indentationσr Residual strressσ0 Stress amplitudet Coating thicknessUfr Fracture dissipated energyV Deforming volume (subscripts c and s refer to

coating and substrate, respectively)We Elastic work of indentationWp Plastic work of indentationWt Total work of indentation (elastic plus plastic)ψ Indenter half angle%R Percentage elastic recovery

0022-3727/05/240393+21$30.00 © 2005 IOP Publishing Ltd Printed in the UK R393

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0

20

40

60

80

100

0 200 400 600 80 × 3

Fused Silica

Load

(m

N)

Displacement (nm)

Figure 1. Load displacement curves for fused silica at 5, 10 and100 mN peak loads. The excellent overlap of the loading curvesshows the uniformity of properties and smooth surface possible withthis material.

1. Introduction

The indentation test for assessment of the penetrationresistance of materials was developed over a hundred yearsago and is widely used by the industry for material assessmentand quality control. In such tests an indenter of knowngeometry is pressed into the surface under a fixed load andthe depth of penetration or the area of the resultant impressioncan be used as a measure of the resistance of the material todamage. This is often characterized in terms of the indentationhardness which is given by the load divided by the area ofthe impression. The initial quantified test using a hardenedsteel ball indenter was developed by Brinell as a means ofcharacterising the variability of the steel produced by thecompany who employed him [1], but a range of standardhardness tests have subsequently been developed which useindenters of different geometry (e.g. Vickers, Berkovich,Knoop and Rockwell tests [2–4]). One common feature of allthese tests is that measurement of the deformed areas or depthsbecomes difficult as the scale of the contact is reduced and thiscan be further affected by the roughness of the test surface. Forthis reason it is very difficult to assess the properties of thincoatings using traditional indentation tests unless the coatingthickness is greater than 10 µm.

In the last thirty years continuously recording indentationtechniques (CRIT) have been developed [5–7] and are widelyused in the assessment of coated materials because thedeformed volumes can be very small and the properties ofcoatings can be determined without major contributions fromsubstrate behaviour. In such tests a continuous record of loadand indenter displacement (and possibly other parameters suchas contact stiffness) is made as an indenter is pushed into andremoved from the test surface. These techniques have a uniqueability to probe mechanical properties at shallow contact depths(figure 1). These instruments allow precise control of eitherthe load or displacement during the test and can be performedwith applied forces as low as a few micronewtons making

indentations with depths in the nanometre range. It is for thisreason that the term nanoindentation was coined to describethe more sensitive measurements. Methods where load, depth,time and (sometimes) even contact stiffness are continuouslyrecorded have demonstrated considerable ability for studyingthe near-surface mechanical properties of materials (e.g.[8–10]). At very low loads (�100 mN) these techniques appearparticularly well suited to the characterization and study ofcoated and other surface-engineered systems (e.g. [8, 11–13]).Indeed, for thin film coated systems, they offer one of the fewpossible means of making mechanical property measurementsat scales sufficiently shallow to allow the mechanical responseof the films to be studied with minimal contribution from thesubstrate (see later). In addition, at increasing displacements,the effects of film and substrate can be measured together.Thus a wide range of behaviour of coated systems canbe investigated—that is, from coating-dominated behaviourto substrate-dominated responses—as the contact stressesand contact-affected volumes are systematically changed.Further, the technique offers the possibility of experimentallydetermining properties which may be very difficult to ascertainin other ways, e.g. the elastic moduli of coatings in themicrostructural and residual stress states in which they are usedin various coated systems [8, 14–16].

In nanoindentation testing the mechanical properties ofthe system can be extracted from the load–displacement curveand direct measurements of the impressions produced is notnecessary, though it can be an advantage in some cases as willbe discussed later in this review. Indeed it is development in theunderstanding of the nanoindentation process, the mechanismsof deformation and how these relate to the properties ofthe materials being tested, by workers such as Doerner andNix [17] and Oliver and Pharr [18] which has made thetechnique so useful for the assessment of the mechanicalproperties of coatings.

A discussion of all aspects of nanoindentation testingis very broad and beyond the scope of this review whichis restricted to a discussion of nanoindentation behaviour ofcoated systems and how this compares with the behaviourfor bulk materials. Further information can be found in otherreview papers [19–23] and the book by Fischer–Cripps [24].

A number of different coated systems have been studiedusing nanoindentation testing including hard coatings onsoft substrates for tribological applications, soft coatingson hard substrates (e.g. semiconductor metallization), hardcoatings on hard substrates (e.g. anti-reflection coatings onoptical elements) and soft coatings on soft substrates (e.g.protective polymer coatings on steel). The behaviour of thecoating/susbtrate system is critically dependent on the relativeproperties of coating and substrate as well as on the strengthof the interface between them, and this will be highlightedthroughout this review.

2. Nanoindentation load–displacement (P–δ) curves

A wealth of useful information can be derived straightfor-wardly from the load–displacement (P –δ) response of a coatedsystem when plotted for comparison with that of the substratealone at the same load. This mechanical fingerprint imme-diately reveals the differences in response conferred by the

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Figure 2. Processes occurring in the nanoindentation testing of acoated system: (a) hard coating on a soft substrate and (b) softcoating on a hard substrate.

coating as the load is increased to the maximum used for anygiven test (e.g. [8, 13]).

2.1. P –δ curves for coated systems

The behaviour observed critically depends on the properties ofboth the coating and the substrate and the size of the contactin relation to the thickness of the coating (figure 2). For ahard coating on a softer substrate plastic deformation of boththe coating and substrate may occur, and radial and pictureframe cracks are often observed at higher loads where thecoating is bent into the depression left by plastic deformation ofthe substrate. These through-thickness cracks are made muchworse if the substrate shows excessive pile-up due to its highlevel of work hardening (figure 2(a)). For a soft coating ona harder substrate there may be little or no fracture but thecoating is thinned beneath the indenter by plastic deformationand may be extruded from the edge of the contact due to thefact that it is trapped between a rigid indenter and a substrate(figure 2(b)).

Figure 3 shows load–displacement plots for TiN and CNx

coating systems at penetration depths where the contributionfrom the substrate is negligible. Figure 4 shows load–displacement curves from higher load tests on NbN coatingson two different steels where the contribution of the substrateis significant.

For the coating dominated cases in figure 3, the lowerindenter displacements at any given load are immediatelyapparent as are the reduced displacement (δmax) at themaximum applied load (Pmax), the decreased plastic work ofindentation (Wp—the area enclosed within the P –δ plot) andthe increased amount of elastic recovery (%R) in the indenterdisplacement during unloading. At low loads, many hardcoated systems can exhibit a perfectly elastic response, ofwhich the substrate alone was incapable, which is attractivefor tribological applications. However, it should be recognizedthat testing with a blunt tip (figure 5) can generate similarresults, particularly for very hard coatings.

As the substrate contribution becomes more significantthere is a change in the shape of the loading curves (figure 4(a)).

0

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P-δ curves for CNx on Si001, Si001 Substrate

& PVD TiN (Sharp Tip)

PVD TiN CNx on Si001Si001 Substrate

Loa

d, m

N

Displacement, nm

Figure 3. Nanoindentation load–displacement curves for 1 µm TiNand CNx coatings on silicon compared with the uncoated siliconsubstrate.

This may be due to the plastic deformation of the substrateor the onset of through-thickness fracture or interfacialdetachment. A gradual change in the loading curve is generallyassociated with plastic deformation unless the difference incoating and substrate properties is very extreme, whereas asharper transition represents fracture in the coating as can beseen in the scanning electron micrographs of indentations inthe NbN coating in figures 4(b) and (c). Radial crackingis initially observed, following the edges of the Berkovichindenter. This is followed by picture frame cracking at the edgeof the impression when the substrate is hard (figure 4(c)) and acircular through-thickness crack at the edge of the plastic zonefor the softer substrate (figure 4(b)). Clearly microscopicalanalysis is essential if features in the load–displacement curveare to be fully understood.

For the soft coatings on a hard substrate the low loadbehaviour is different; the penetration depth at a givenload is greater than for the substrate in cases where thecoating dominates behaviour and the slope of the loadingcurve dramatically increases with indenter penetration asthe substrate contribution increases. In this case there isa relatively sharp transition between coating and substratedominated behaviour visible in the load–displacementcurve.

2.2. Detailed analysis of P –δ curves

The detailed appearance of the P –δ curve—especially whencoupled with the careful investigations of contact sites byhigh resolution microscopy—allows a number of deformationand fracture responses to be identified (see [8, 25, 26]). Forexample, sharp displacement discontinuities on loading (pop-ins) are usually associated with through-thickness fracture ofthe coating, delamination of the coating or even nucleation ofplasticity in the underlying substrate [8, 13, 26, 27]. Coupledwith consideration of the detailed shapes of the loading andunloading curves, this often allows conclusions to be drawnconcerning the detailed deformation mechanics of the coated

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(a)

0

100

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400

500

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0 500 1000 1500 2000 2500 3000

4µm NbN on Different Steels

ASP23304 Stainless

Load

(m

N)

Displacement (nm)

(b) (c)

Figure 4. (a) High load nanoindentation tests of 4 µm NbN coatings on soft (304 stainless steel) and hard (ASP23) steel substrates.Scanning electron micrographs of 500 mN indents in NbN coated (b) 304 stainless steel and (c) ASP23 high speed steel.

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 8 00

Loa

d, m

N

Displacement, nm

Blunt TipSharp Tip

Figure 5. Load–displacement response from a CNx coating onsilicon showing elastic behaviour with a blunt tip and elastic–plasticbehaviour with a sharp tip.

system [8, 25] while the size of any pop-in (at a given load)can allow the energy absorbed in each fracture process tobe measured—even at the nanojoule level [8]. For example,extreme fracture of the coating into separated islands on thesubstrate can lead to the slopes of both the loading andunloading curves moving towards those of the substrate, atransition which correctly identifies that the coating is failing

to provide either load support, enhanced contact stiffness orany significant increase in effective hardness [8, 25].

In nearly all indentation experiments the initial part ofthe loading curve is elastic and there is a transition to plasticbehaviour as the load applied increases. This transition isassociated with the contact induced stresses exceeding theyield stress of the material being tested. For a coating/substratesystem yield may occur in either the substrate or the coatingand where this occurs in a practical system depends on theproperties of coating and substrate, the thickness of the coatingand the geometry of the indenter. This is particularly importantif thin coatings (<1 µm) are to be tested. Although sharpBerkovich indenters are available, the typical tip end radiusof these is about 100 nm when new and about 250 nm whenused for a few months, increasing over the useful life of thetip. To test the properties of a thin coating and ensure that thecontact stresses are high enough to cause yield of the coatingbefore the substrate a sharp indenter is necessary. In the caseof a practical indenter the initial contact will thus be elastic,dominated by the spherical tip of the indenter. As the loadis increased the sloping sides of the indenter will come intocontact and the indenter behaves like a truncated cone. Itis often at this point that plastic deformation is initiated. Athigher loads the indenter can be treated as a sharp cone.

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-2

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0 50 100 150 200 25 00

Loa

d, m

N

Displacement, nm

PαδPαδ1.5

Pαδ2

Figure 6. Low displacement portion of the nanoindentationload–displacement (P –δ) curve showing the effects of the transitionfrom roughness dominated to elastic and then elastic–plasticdeformation on the variation of load with displacement.

This is visible in the early stages of the load–displacementcurve (figure 6). In general, the loading curve can be describedby a number of power law expressions depending on the loadand the indenter geometry and the roughness of the test sampleand the indenter. For a typical Berkovich indenter a numberof different regimes are typically observed (figure 6). At verylow penetration depths the load is approximately proportionalto the displacement. This is due to the interactions of theroughness of the indenter and the substrate and only persistsuntil the indenter penetration exceeds around five times thecombined surface roughness at the scale of the contact. Theremay be some localized plastic deformation at asperity tips inthis regime, but the contact is predominantly elastic. Thisis generally followed by a section where the load varies asdisplacement raised to the power of 1.5 which is typicalHertzian elastic behaviour. Although the indenter is notspherical, the blunted end of the tip promotes such behaviour.This is followed at higher loads by a regime where load isproportional to displacement squared and full elastic–plasticdeformation is observed beneath the indenter. There is usuallya transition between elastic and elastic–plastic behaviourwhich occurs over a range of loads and displacements and,for hard ceramic coatings and bulk materials, it may not bepossible to get full elastic–plastic behaviour in the practicalload ranges of the available nanoindenters. In such cases,pronounced indentation size effects are observed [28].

2.3. Potential for determining coating properties

Hainsworth et al [29] have shown that it is possible to calculatethe shape of the loading curve for sample materials of known E

and H values. Furthermore, careful P versus δ2 analysis of theloading curves from coated systems can be used to establisha regime of load and displacement over which the systemresponse is dominated by the coating and from which coatingonly data may be evaluated [30]. This suggests tractable waysforward not only for estimating the properties of coatings invirtual isolation of the substrate but also for identifying theexperimental conditions under which such observations canbe made.

Interestingly, for several systems involving fairly hardsubstrates, this P : δ2 analysis for many systems suggests

that ‘coating’ only properties may be measured with indenterdisplacements less than ∼1/10 of the coating thicknesst [30, 31]. This implies that up to this relative depth—whichis often taken as a rule of thumb estimate—both elastic andplastic deformation is concentrated within the coating with thesubstrate only providing elastic support of a small fraction ofthe load.

A brief further discussion of this may be valuable. Forcalculating the elastic contribution, models such as that ofYu et al [32] can be used to predict the proportion of theelastic deformation relatively occurring within the substrateand the coating. However, a relative plasticity criterion is moreimportant if the hardness of the coating is to be measured byindentation—that is, if we are to be sure that it is the coatingand not the substrate which is dominating the plastic response.If the sub-surface contact-induced shear stress distribution isbroadly likened to that from a Hertzian contact, then thisreaches a maximum of 0.3×p0 (p0 = mean contact pressure)at a depth of 0.47a (where a is the contact radius). The shearstress then decays with further depth (e.g. [33]). A necessarycriterion for measuring the plastic properties of the coating isthat it yields before the substrate. Thus, the maximum Hertzshear stress not only needs to lie in the coating but also needsto exceed the shear stress of the coating (as the contact loadis increased) before the shear stress experienced at depth ∼t

exceeds the shear yield stress of the substrate. For a typicalratio of coating : substrate hardness of ∼3 : 1, and with a typicalBerkovich or Vickers indenter geometry, this gives a necessaryindenter displacement of ∼t/10 [31, 34].

If the indenter is sharp, another way of looking at this isin terms of the size of the plastic zone formed beneath it asit is loaded on to the coated substrate. For a sharp indenter,plastic deformation starts in the coating at very low loads andthe size of the plastic zone increases as the load increases. Thiszone will grow until its radius is equal to the coating thicknessbefore the substrate beneath it starts to plastically deform. It isoften observed that the deforming volume beneath an indenteris approximately hemispherical [33,35], and for a bulk materialtested with a Vickers indenter it has been shown that the radiusof the plastic zone, R, is given by [36]

R = cd

2

(E

H

)1/2

cot1/3 ψ, (1)

where c is a constant (c ≈ 1), d is the indentation diagonal,E is the Young’s modulus of the material and ψ is theeffective indenter angle (it is usual to use the angle of a conewhich displaces an equivalent amount of material as a facettedindenter; this removes the problem of the effect of indenteredges when comparing between different blunt indenters [35]).Equation (1) may be re-written in terms of indentation depth,δ, such that

R = k2δ

(E

H

)1/2

cot1/3 ψ, (2)

where k2 is an indenter-specific constant. Values for k2 are3.5 and 3.64 for Vickers and Berkovich indenters and ψ =0.71 [37]. Since the two indenters are designed to displacethe same volume of material for a given contact area it is notsurprising that their constants are very similar. If we equate

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the indentation depth to the coating thickness and rearrangeequation (2) we have

δ

t= 0.4

(H

E

)1/2

. (3)

For a typical hard coating such as TiN, H/E = 0.1 and thusthe critical depth before substrate plastic deformation occursis 0.126t , close to the t/10 mentioned above. As we go tosofter coatings H/E is reduced and the critical δ/t drops toless than 10%. However, if the substrate is harder than thecoating it may not plastically deform in these circumstancesand this calculation approach is not valid. For instance, in thecase of an aluminium film on silicon coating properties may bemeasured in cases where the indenter penetration is less than0.6t [38]. Plastic deformation extends to the substrate interfacein this case and spreads laterally in the soft aluminium film.However, this has only a small effect on measured hardnessuntil the constraint of the material trapped between the indenterand the substrate becomes significant.

Obviously, the use of soft substrates (e.g. ductile metals,polymers, etc) will always create the situation where thesubstrate yields first with a harder coating then being elasticallybent and flexed into it followed by coating fracture. Under suchconditions, it will be impossible to measure the hardness of thecoating itself by indentation tests, at least without changing toa harder substrate.

Strategies for performing CRIT experiments on coatedand surface engineered systems have been proposed [11].Besides detailed examination of P –δ curves and theircomparison to substrate-only plots at the same loads,performing nanoindentation experiments over a range ofindenter displacements (δ) is necessary since experiencesuggests that many coatings flex elastically up to displacementsapproximately equal to the coating thickness (t). It is suggestedthat at least three series of tests are performed, namely withd < t (the regime where the coating is mainly flexing togenerate membrane stresses [39]), with d > t (where the onsetof coating fracture may occur and the substrate is playing asignificant role [40]) and with d � t (where the sectionsof broken coating may simply act as blunt extensions to theindenter profile). Simple evaluation of the P –δ plots (e.g.[8,25,27]) coupled with P –δ2 analyses [25,30,34] can then beused both to ideally different regimes of behaviour, to extractcoating-only properties when possible and to decide on the bestapproach for calculating E and H in each specific case [29].

For ion implanted surfaces, these approaches can beused successfully no matter whether the surface is radiationhardened or softened and amorphized. However, for thosecases where properties vary rapidly from the implanted surface,it will be necessary to develop techniques deconvolutingproperties as a ‘function of depth’. This is not trivial since,even for more isotropic specimens simply penetrated by theindenter, different portions of the indenter surface are samplingproperties of the specimen at various depths [8]. Thus, atbest, the load displacement data can only supply some complexintegration of all properties experienced over the range of depthsampled by the indenter profile. This problem is expected tobe complex for either inhomogeneous samples, functionally-graded materials or those with coatings which flex and bendto follow the contact profile. Indeed, extreme caution must

be advised before interpreting any CRIT data as providingproperties as a function of depth. This major issue has to beaddressed by careful analysis and modelling (see later).

2.4. Work of indentation from P –δ curves

CRIT experiments also allow measurement of the plasticwork of indentation (Wp) [8] which is given by the areaenclosed by the loading and unloading curves. In addition,techniques such as atomic force microscopy (AFM) may allowthe residual plastically deformed volumes of indentations tobe estimated (e.g. [41]). Thus, it may become possibleto meaningfully define hardnesses by a work of indentationper unit volume approach (e.g. [41–43]) which, although inprinciple numerically equal to the contact pressure definition ofhardness, provides new insights into understanding the energydissipation mechanisms involved in the deformation of coatedsystems and is a reasonable basis for modelling the indentationresponse of the coating/substrate system (see later).

2.5. Practical considerations

A further experimental consideration is the choice of indentershape and geometry. For example, it is already appreciatedthat spherical indenters are best used for investigating elasticproperties since the contact stress fields are tractable (e.g.[44]) and pointed indenters are best for looking at plasticproperties [8]. Flat-ended indenters may also be useful forsimulating behavioural responses to blunt asperity contacts(including investigating responses to contact fatigue) forcoatings to be used in applications such as gear and bearingsystems. For the assessment of coating fracture, sharperpyramidal indenters such as the cube corner indenter arepreferred.

Practically it is essential to ensure that the surfaces are bothflat enough for examination (e.g. only exhibit topography smallin scale compared with the indentation sizes) and to identifyfeatures (e.g. metal globules in some coated systems) whichcould lead to artefacts in the data. Post facto observations—usually employing high resolution light microscopy, scanningand transmission electron microscopy (SEM, TEM) andscanning probe microscopy (SPM) techniques—are criticalin determining the detailed deformation mechanisms of anysurface-engineered system. It is important to associate theoccurrence and extent of, for example, any coating fracture ordelamination with features in the load–displacement curve ifreliable data are to be obtained from the test. In particular, pile-up of material around the impression can have a considerableeffect on the accuracy of the hardness and Young’s modulusvalues which may be extracted from P –δ curves (see section 3).In some cases, it is also necessary to control the environmentduring CRIT tests to minimize the effects of chemo-mechanicaleffects (e.g. [45, 46]).

Since the indentation cycle and the position of the contactsites are both under software control, this allows manyindentations to be readily made on quite extensive sampleareas. Thus CRIT are also ideally suited to assessing the pointto point reproducibility of coated systems though as yet thisseems an under-exploited application.

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PVD TiN

Lo

ad

(m

N)

Displacement, δ (nm)

Loading

Unloading

Wp

Su

Sl

Figure 7. Load–displacement curve showing the unloading (Su) andloading (Sl) slopes used in the calculation of hardness and Young’smodulus. Also indicated is the plastic work of indentation Wp whichis the area bounded by the loading and unloading curves and thedisplacement axis.

3. Mechanical properties from nanoindentation

Since the nanoindentation test was developed from conven-tional hardness testing it is not surprising that one of the majormechanical properties obtained using the technique is hard-ness. However, since a continuous measure of load and dis-placement is obtained as a function of time and the load ordisplacement can be controlled during the test it is possible todetermine other properties such as creep or fracture resistancefrom a well designed nanoindentation test. This is discussedin the following sections.

3.1. Hardness and Young’s modulus

The most commonly used analysis method for obtaininghardness and modulus was developed by Oliver and Pharr [18].In this approach the total penetration depth is given by the sumof the plastic depth (contact depth), δc, and the elastic depth,δe, which represents the elastic flexure of the surface duringloading. Thus the total penetration depth, δ, is given by

δ = δc + δe (4)

and

δe = εP

Su, (5)

where Su is the slope of the unloading curve at maximumload (see figure 7) and ε is a constant which depends onindenter geometry (ε = 0.75 for Berkovich indenters). δc

can be calculated from equations (4) and (5) and the contactarea can be calculated from this if the relationship betweencontact depth and Ac is known. For an ideal Berkovich indenterAc = 24.5δ2

c , but most indenters are blunted at their end anda more complex tip area function is then required (see later).The hardness, H , is then given by equation (6):

H = P

Ac. (6)

Young’s modulus can be determined from the slope of theunloading curve using a modified form of Sneddon’s flat punchequation [47] where

Su = γβ2√π

Er

√Ac, (7)

where Er is the contact modulus which can be derived fromYoung’s modulus and Poisson’s ratio of the indenter and thetest material via

1

Er= 1 − ν2

m

Em+

1 − ν2i

Ei, (8)

where the subscripts m and i refer to the test material andindenter, respectively. The constant γ was introduced byJoslin and Oliver [48] to account for deviations from the idealSneddon behaviour predicted by finite element investigations.The constant β was introduced to correct for the fact that theBerkovich indenters generally used for this sort of experimentare not axially symmetric; in this study β = 1.034 [49]. Usingequations (4)–(8) it is possible to determine Young’s modulusof the test material if the properties of the indenter are known.For accurate determination a method for measuring Poisson’sratio of the test material is required but for most metals andceramics an estimated value of νm = 0.25 will give only asmall error as equation (8) shows that Er is not a sensitivefunction of νm.

A much more important concern is to accurately determinethe relationship between Ac and δc since this is rarely ideal.Oliver and Pharr [18] provide a method for achieving thiscalibration using indentation tests made in fused silica whichis elastically isotropic and can be assumed to have a constantYoung’s modulus with depth. This produces a tip function ofthe form

Ac = c0δ2c + c1δc + c2δ

0.5c + c3δ

0.25c + c4δ

0.125c + · · · . (9)

There are some problems with this approach because fusedsilica can have a thin water softened layer on its surface with alower Young’s modulus than the bulk but for most practicalindenters the area function is reasonably accurate above acontact depth of 20 nm. It is critical that regular calibrationsare performed as the detailed geometry of the indenter can bechanged by a single indentation cycle. For instance, work inthe author’s lab has shown that the tip radius of a Berkovichindenter (which was ≈50 nm when new) increased by about1 nm per sample tested over a period of six months. Carefultip calibration is essential for accurate work where residualindentation depths are less than 100 nm. The need for thissort of detailed and time-consuming calibration suggests thatan ideal analysis method would not be reliant on knowingthe precise Ac–δc relationship. If the area function is knownthe Oliver and Pharr method produces reasonable hardnessand Young’s modulus values for hard materials such as TiN(figures 8(a) and (b)).

Another potential problem with the Oliver and Pharranalysis method is that it cannot account for pile-up aroundthe indenter which effectively means that the true contact depthis measured from a position above the original surface of thematerial (figure 9). This is a particular problem for indentationtesting of very soft coatings such as nickel (figure 8(c))where the Oliver and Pharr method greatly overestimatesthe measured hardness compared with the traditional directmeasurement.

The final shortcoming of the Oliver and Pharr method isdriven by what happens in the very early stages of loading of theindenter. It is sometimes very difficult to decide at which point

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60

1 1 0 100 100

PVD TiN

Oliver and Pharr

Slopes

W ork of Indentation

Direct measurement of area by AFM

Ha

rds

s (

GP

a)

Load (mN)

480

520

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600

640

1 1 0 100 1000

PVD TiN

Oliver and Pharr

Slopes

Yo

un

g's

mo

du

lus

(G

Pa

)

Load (mN)

0.6

0.8

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1.2

1.4

1.6

1.8

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Electroplated Nickel

Oliver and PharrSlopes methodWork of indentation methodDirect area measurement by AFM

Load (mN)

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200

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300

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Electoplated Nickel

Oliver and Pharr

Slopes

Load (mN)

ne

Har

dn

ess

(GP

a)

Yo

un

g's

mo

du

lus

(GP

a)

(a) (b)

(c) (d)

Figure 8. Comparison of hardness (a), (c) and Young’s modulus (b), (d) of coatings determined by different techniques (a), (b) PVD TiNand (c), (d) electroplated nickel.

Ac Actual Ac Oliver and Pharr

Pile-up

Original surface

Figure 9. Cross-section through an indentation in a soft materialshowing the effect of pile-up. The Oliver and Pharr method [18]underestimates the contact area and thus overestimates hardness andYoung’s modulus.

the indenter is in contact with the surface, particularly in caseswhere there are soft surface layers involved. In addition, at thevery lowest loads there is likely to be a transition from elasticto plastic behaviour unless the indenter is exceptionally sharp.The net result of these factors is that there can be an appreciableoffset error in the load–displacement data, particularly for very

low load impressions. This manifests itself as an error in δmax

and hence in the measured hardness or modulus; at the verylowest loads in figure 8 the hardness and modulus tend todecrease due to the effects of the elastic–plastic transition.

An alternative method is based on determining anexpression for the slope of the loading curve, combiningthis with the unloading curve and the unloading equations,previously presented, to give equations for hardness or Young’smodulus [50]. Hainsworth et al [29] showed that when fullplasticity occurs the loading curve could be described by anequation of the form

P = Er

(φ

√Er

H+ ψ

√H

Er

)−2

δ2, (10)

where ψ and φ were constants determined by fittingequation (10) to experimental data. Equation (10) may bewritten as

P = Kδ2. (11)

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Malzbender et al [51] developed expressions for the constantsin equation (10) in terms of previously defined geometric andindenter-specific constants such that

K =(

1√C0

√Er

H+ ε

√π

4

√H

Er

)−2

. (12)

This approach is strictly only valid if both hardness andelastic modulus are invariant with depth. If equation (11) isdifferentiated to get the loading slope, Sl, and then combinedwith equations (7) and (12) it can be shown that

Su

Sl= Erγβ√

πC0H+

ε

2, (13)

and combining this with equations (6) and (7) to eliminatehardness we get an expression for Er:

Er = 1

2γβP

√π

C0

(S2

uSl

2Su − εSl

). (14)

Using equations (13) and (7) to solve for the contact area yields

Ac = C0P2

(2Su − εSl

SuSl

), (15)

which together with equation (3) enables the hardness to bedetermined:

H = 1

C0P

(SuSl

2Su − εSl

)2

. (16)

Equation (16) depends only on parameters that can beaccurately measured from load–displacement curves and aconstant representing the basic indenter geometry rather thanthe full tip shape function.

Figure 8(a) shows a comparison of the hardness andYoung’s modulus for PVD TiN determined by the conventionalOliver and Pharr method and this new slope technique. In orderto determine the slopes a power law fit of the form

P = k(δ − δ0)n, (17)

where k, δ0 and n are constants was undertaken. Only thetop 10% of the loading and unloading curves was fitted andthe result was numerically differentiated to give the requiredslopes. The results show a remarkably good agreement despitethe fact that the complicated tip end-shape calibration, whichis a feature of the Oliver and Pharr method, is not necessary forthe slopes method. Since tip shapes can change dramaticallyduring a set of measurements having a method which is notaffected by this is a major advantage. An even more significantadvantage comes from applying the same approach to thenickel data previously analysed (figure 8(b)). The results fromthe slopes method show an excellent agreement with directlymeasured and work of indentation derived data and does notoverestimate the hardness in the same way that the Oliver andPharr approach method does.

Young’s modulus determined by the Oliver and Pharrmethod and the slopes method for PVD TiN are the same withinexperimental errors and show the same trends with test load(figure 8(c)). The measured values are close to 600 GPa whichis often cited as the Young’s modulus of TiN [52]. However, in

the case of nickel (figure 8(d)), though the trends in data withload are identical the slopes method and Oliver and Pharr dataare offset. The higher values of Young’s modulus produced bythe Oliver and Pharr method are due to the incorrect value ofAc used in the calculation due to pile-up.

When nanoindentation testing a polycrystalline materialthe measured elastic modulus is often close to the Hillaverage [53], 211 GPa for nickel. However, the value derivedfrom the slopes method is lower than this since elasticanisotropy is important for single crystal samples or coatedsystems where the coating shows a high degree of preferredorientation.

When testing very soft materials the pile-up of materialsaround the indentation is critical in determining the accuracyof the data determined by either method. When the ratio ofyield stress to Young’s modulus (Y/E) is large (e.g. >0.05for materials with work hardening exponent, n, between 0 and0.5 [21]) the Oliver and Pharr procedure is valid. This is thecase for many hard materials such as ceramic coatings usedfor tribological protection. However, for metals the Oliver andPharr approach must be used with caution since the Oliverand Pharr method will overestimate the hardness and Young’smodulus for materials with a large work hardening exponent(∼0.5) where significant pile-up occurs. The pile-up problemis most severe when Y/E is small and n is close to zero whichis the condition for an almost perfectly plastic indentation.Consequently, in such cases the shape and size of the residualimpression can be accurately measured after indentation bytechniques such as SEM or AFM and the measured areascan be used to determine hardness or Young’s modulus withreasonable accuracy [54].

3.2. Yield stress and work hardening behaviour

For detailed mechanical calculations engineers would like thefull stress–strain curve behaviour for a coating. For a thincoating (<5 µm) this is impossible to obtain by conventionalmechanical testing techniques, so there has been a driving forceto extract the information from nanoindentation tests. Finiteelement techniques have been used in an attempt to directlyextract more primary mechanical properties such as yield stressand work hardening exponent as well as the elastic modulus.In these cases the finite element approach is generally used tomodel the nanoindentation load–displacement curve and matchthis to experimental data. Although this work has primarilybeen done for bulk materials [55–57] there are now somestudies on coated systems [58].

The results demonstrate that for given values of coatingand substrate Poisson’s ratio and indenter geometry the initialunloading slope is a function of the ratio of coating andsubstrate Young’s modulus only, and if the substrate propertiesare known it is relatively straightforward to determine thecoating properties. The yield strength for a perfectly plastic orlow hardening coating can easily be evaluated by matching themaximum load measured experimentally with modelled datafor the particular ratio of coating/substrate elastic properties.The yield strength of a strongly work hardening materialcannot be separately determined from the work hardeningbehaviour by modelling the load–displacement curves alone;for instance Cheng and Cheng [21] have shown that a steel load

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displacement curve may be accurately simulated with differentyield stress/work hardening exponent pairs.

This non-uniqueness has stimulated several authorsto develop more complex methods of extracting stress-strain information from nanoindentation load–displacementcurves. All of these methods require measuring andmodelling some extra information. For instance, O’Dowdand co-workers [58, 59] developed a procedure to obtainthe stress-strain relationships from indentation tests based ondimensional analysis and finite element calculations. Theirmethod consists of extracting information from the load–displacement curve and from surface profile measurementsof the contact area after unloading. Other workers haveused the pile-up geometry [60] or making tests with severalindenters of different geometry [61] to solve the problem.Despite the success of these methods the accuracy of the datathey generate must be questionable given the potential forgenerating considerable errors during measurement.

Although the non-uniqueness problem is a feature of testswith sharp indenters it does not apply to spherical indenters.There is a length scale inherent in the contact which breaksthe load proportional to displacement squared dependenceof the loading curve, thus offering the possibility of largenumbers of equations to solve for extracting the yield stressand work hardening exponent. There are several proposedmethods for extracting stress-strain behaviour using sphericalindentation (e.g. [62]); however they are generally not suitablefor assessing the properties of thin coatings due to the size ofthe spherical indenter needed to generate measurable data.

3.3. Dynamic mechanical properties

Oliver and Pharr [18] introduced a dynamic indentationtechnique called continuous stiffness measurement (CSM)where a small amplitude oscillation of relatively highfrequency is superimposed to the dc signal that controls theindenter load. In this way, it is possible to obtain the contactstiffness all along the load displacement curve and not onlyin the upper part of the curve as in the quasistatic indentationmethod discussed previously. Its applications are the studyof hardness, Young’s modulus, creep and fatigue of variousmaterials as a function of displacement [63].

Asif et al [64] developed a very similar technique,combining in the same machine the continuous stiffnessapproach and dynamic mechanical analysis (DMA) widelyused in the study of polymers to characterize viscoelasticproperties through the storage and the loss moduli of thesample. This is the so-called dynamic stiffness measurement(DSM) method, and the technique has been used to study thebehaviour of a range of amorphous materials and coatings. Inthese materials, when the indenter presses on the surface ofthe material, the total deformation of the material associatedwith that stress is not produced immediately. For example,if we hold the load constant at the end of the loading cycle,the material undergoes viscoelastic/viscoplastic deformationunder the indenter; hence the displacement of the indenter canincrease even when the load is being reduced (figure 10). Thisdynamic behaviour can be quantified through several variables:most significant are the storage modulus, E′, which is relatedto the elastic properties of the material or the energy recovered

0 100 200 300 400 500 600

Displacement(nm)

Load

(m

N)

0

100

200

300

400

500

Figure 10. Load–displacement curve for a polymeric coatingshowing time-dependent deformation.

after indentation, the loss modulus, E′′, related to the viscosityof the material or the energy lost during indentation in heat orfriction and tan δ which indicates the phase difference betweenthe applied stress and the resultant strain .

As a sinusoidal stress is applied by the ac signalsuperimposed upon the dc load signal the strain induced inthe material can be expressed as

γ = γ0 sin ω · t (18)

and the stress

σ = σ0 sin(ω · t +φ) = σ0 cos φ sin(ω · t)+σ0 sin φ cos(ω · t),(19)

where δ is the phase difference between them (0 < δ < 90).The first term represents the in-phase elastic response (relatedto E′) and the second the out of phase viscous response (relatedto E′′):

E′ = σ0 cos φ

γ0, (20)

E′′ = σ0 sin φ

γ0. (21)

Therefore

tan φ = E′′

E′ . (22)

Values of E′ and E′′ can be used to estimate Young’s modulus(E) through the equations:

E = E′ + iE′′, (23)

|E| =√

E′2 + E′′2. (24)

Amorphous fullerene-like CNx coatings have a lower densitythan the corresponding crystalline compound formed withatoms of carbon and nitrogen. Thus, while the sinusoidalloading is occurring the atoms or chains of atoms can moveinto free spaces in the structure and on their way back to theiroriginal positions the neighbouring atoms disturb the processmaking it slower and leading to the appearance of hystereticbehaviour (figure 11(a)). Since no residual impression remains

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0

100

200

300

400

500

600

0 10 20 30 40 5 0

Displacement

Load

(µN

)

(b)

(a)

µ

Figure 11. (a) Dynamic load–displacement curve for 1 µm CNx onSiC/Si showing the hysteretic behaviour. (b) AFM image of theindented region carried out by the tip which made it showing thelack of residual impression.

after the indentation cycle is complete (figure 11(b)) thisrepresents viscoelastic behaviour which can be characterizedin terms of the loss modulus (E′′) and the storage modulus (E′)by the method outlined previously.

Storage and loss moduli have been obtained for fullerene-like CNx , amorphous carbon and fused quartz using a widerange of dynamic testing conditions. These materials havesimilar elastic properties. For comparison the as-receivedsurface of an injection moulded polypropylene bar has beentested in an amorphous region with the same indentationconditions. This is a semicrystalline polymer which has amuch lower Young’s modulus and therefore offers a usefulcomparison. Figure 12 shows the comparison data. Except atlow test loads and frequencies the storage, loss and Young’smoduli for fullerene-like CNx , amorphous carbon and fusedsilica are almost identical. All the moduli are lower forpolypropylene as expected. However, for all materials, the lossmodulus is about 40% of Young’s modulus (figure 13) whichimplies that the viscoelastic behaviour exhibited is controlledby the amorphous nature of the structure and that fullerene-like CNx is not behaving differently from the other materialsin this respect. The increase in the measured moduli at lowloads/frequencies is probably an artefact of the measurementtechnique.

0

100

200

300

400

500

orage Modulus

CNx (1 µm)

CNx (0.5 µm)

Quartz

a-C

Polypropylene

E' (

GP

a)

Load (µN) / Frequency (Hz) / D.Load (µN)

500/

1/0.

5

500/

1/1

500/

1/2

500/

2/2

500/

2/0.

5

500/

5/0.

5

500/

5/1

500/

5/2

500/

10/1

500/

10/2

1000

/1/0

.5

1000

/1/1

1000

/2/0

.5

1000

/2/1

1000

/2/2

1000

/5/0

.5

1000

/5/1

1000

/10/

0.5

1000

/10/

1

1000

/10/

2

1000

/5/2

1000

/1/2

500/

10/0

.5

500/

2/1

0

50

100

150

200

250

300

s

CNx (1 µm)CNx (0.5 µm)

Quartz

a-C

polypropylene

E ''

(G

Pa)

Load (µN) / Frequency (Hz) / D.Load (µN)

500/

1/0.

5

500/

1/1

500/

1/2

500/

2/2

500/

2/0.

5

500/

5/0.

5

500/

5/1

500/

5/2

500/

10/1

500/

10/2

1000

/1/0

.5

1000

/1/1

1000

/2/0

.5

1000

/2/1

1000

/2/2

1000

/5/0

.5

1000

/5/1

1000

/10/

0.5

1000

/10/

1

1000

/10/

2

1000

/5/2

1000

/1/2

500/

10/0

.5

500/

2/1

(b) Loss Modulu

(a) St

Figure 12. Dynamic indentation results for a range of testconditions with varying peak load, frequency and dynamic load: (a)storage modulus and (b) loss modulus.

0

20

40

60

80

1 0 0

R e la tive L o ss M o d u lu s

C N x (1 µ m )C N x (0 .5 µ m )Q ua rtz

a -CP o lyp ropylene

E''x

100/

E

L oad (µN ) / F r equency (Hz) / D . Load (µN )

500/

1/0.

5

500/

1/1

500/

1/2

500/

2/2

500/

2/0.

5

500/

5/0.

5

500/

5/1

500/

5/2

500/

10/1

500/

10/2

1000

/1/0

.5

1000

/1/1

1000

/2/0

.5

1000

/2/1

1000

/2/2

1000

/5/0

.5

1000

/5/1

1000

/10/

0.5

1000

/10/

1

1000

/10/

2

1000

/5/2

1000

/1/2

500/

10/0

.5

500/

2/1

Figure 13. Loss modulus as a percentage of Young’s modulus fordynamic indentation testing of amorphous materials.

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Table 1. Fracture events associated with ceramic coating/substratesystems.

Substrate Coating Fracture type

Ductile Brittle Through-thickness fracture, brittlefracture in coating parallel tointerface, ductile interfacial fracture,microfracture in coating

Brittle Brittle Bulk chipping, through-thicknessfracture, brittle interfacial fracture,microfracture in coating,microfracture in substrate

3.4. Fracture toughness and fracture energy

There are a number of different indentation fracture eventswhich might occur in a coating substrate system (table 1),the occurrence of which will depend on the relative toughnessof coating/substrate and any interfaces present. These failuremodes will be altered by plastic deformation in the substratewhich can lead to the superposition of bending stresses on tothose generated by the indentation.

Indentation methods have been developed for assessingthe fracture toughness of brittle materials over manyyears. Conventional indentation toughness methods wereinitially developed for monolithic bulk materials tested bymicroindentation when well-developed radial cracks form(e.g. Marshall and Lawn [65], Anstis et al [66]). The toughnessKIC is related to the applied load P and the crack dimension c:

KIC = χ

(E

H

)1/2P

c3/2, (25)

where E and H are Young’s modulus and hardness of thematerial. For Berkovich and Vickers indenters, χ = 0.016.This method has been extended to coated systems where radialcracks are well developed by some authors (e.g. [51, 67, 68]),generally for a coating much thicker than 1 µm. The values oftoughness obtained by this method will depend on the residualstress in the coating since equation (22) is strictly valid onlyin the absence of internal stresses. For hard coatings onharder and stiffer substrates, it may be reasonable to assumethe residual stress only modifies the crack shape. However,it is necessary to point out that this traditional method willbe invalid when the cracks are confined to the indentationimpression and coated systems consisting of a harder coatingon softer substrate are usually an example of this. Chen andBull [69] have shown that the radial cracks which run alongthe indenter edges in hard coatings on softer substrates aregenerally confined within the indentation impression providedthat the substrate is not sufficiently brittle that coating crackscan propagate into it. Therefore, the conventional indentationmethod is not valid as the cracks produced are not sufficientlywell developed.

An alternative approach to assess coating toughness wasproposed by Li et al [70, 71] and used the step in thenanoindentation load–displacement curve obtained under loadcontrol which is associated with chipping. In this modelthe load–displacement curve is extrapolated from step startpoint (assumed to be the onset of fracture) to its end point.This is illustrated in figure 14, where the curve OABD is themeasured loading curve and OAC is the extrapolated loading

0

50

100

150

200

Load

(m

N)

D isplacem ent (nm )

A B

C

D

O

300 600 900150 450 75 0500

Figure 14. Schematic of the extrapolation of a load versusdisplacement curve to determine the energy dissipated in fractureABC (the ld–dp method developed by Li and Bhushan [70, 71]).

curve from the initial loading part OA where no cracks occur.The difference between the extrapolated curve and the actualcurve (i.e. area ABC in figure 14) is assumed to be the fracturedissipated energy. Then, the coating toughness is given by

KIC =[

EcUfr

(1 − ν2c )Acrack

]1/2

, (26)

where Ufr, Acrack are the fracture dissipated energy and thefracture area; Ec and νc are Young’s modulus and Poisson’sratio of the coating. A measurement of fracture area may beobtained by the microscopical analysis of the fracture aroundthe indentation.

However, this method completely ignores the changein the elastic–plastic behaviour of the coated system whenfracture occurs. den Toonder et al [67] also argued that thearea ABC was not the actual energy dissipated by fracture.Furthermore, this method cannot be applied to tests carriedout under displacement control.

In order to eliminate the elastic–plastic deformationinfluence from substrate, it is preferred to perform smallindentations in thin coatings. For this reason, the cracks maybe not well developed compared with the indentation size.Since existing methods cannot work well in this aspect, anew method has been developed to assess this kind of ultra-small cracks in a very thin coating. Fracture behaviour maybe assessed from a plot of total work of indentation versusdisplacement (Wt–dp) curve. The total work of indentationis determined by the area under load–displacement curve upto a given displacement. The method to determine fractureevents is explained in figure 15. First, we extrapolate the initialWt–dp curve from the crack start point A to the crack endpoint C, we get the work difference CD after fracture; thenwe extrapolate the Wt–dp curve after cracking backwards tothe crack start point and thus we get the work difference ABat the onset of fracture. AB represents the difference betweenthe work of elastic–plastic deformation of the material beforeand after fracture whereas CD represents the work of elastic–plastic deformation plus the work of fracture (not including any

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0

1

2

3

4

5

0 0.5 1 1.5 2 2.5 .5

Tot

al w

ork

(arb

itrar

y un

its)

Displacement (arbitrary units)

A

B

C

DBeforecracking

Aftercracking

Figure 15. Schematic of extrapolating the total work versusdisplacement curve before and after cracking to determine thefracture dissipated energy CD–AB.

contribution from relaxation of residual stress in the coating)at the end of the crack event. The difference between the two(i.e. CD minus AB) is the total work dissipated in the fractureevent. It may be assumed that to calculate the strain energyrelease rate and fracture toughness, we may substitute the workdissipated in fracture for Ufr in equation (26). In order to dothis an accurate measurement of crack area is necessary.

The approach has been used to assess a range of oxidecoatings on glass with thicknesses in the range 200–400 nmusing a cube corner indenter which produces fracture inthe coatings at loads of around 1 mN [69]. Although theconventional indentation method [65, 66] cannot work wellfor these very thin layers, it is also used for comparison here.The coefficient χ for the cube corner indenter is 0.0319 [72].All these results are summarized in table 2. The data fromthe Wt–dp model is reasonable for the brittle coatings underinvestigation whereas the traditional indentation method justreturns the toughness of the glass substrate in most cases.

3.5. Interfacial fracture energy and adhesion

Coating detachment from the substrate during indentationtests can occur during loading or during unloading of theindenter when the adhesion is relatively poor, otherwise mainlythrough-thickness fracture is observed. When the indenter isloaded on to the coated sample, the coating around the indenteris under compressive stress. A thin coating may buckle torelieve the compressive stress (figure 16) and become detachedfrom the substrate. The buckles which form on loading occuradjacent to the impression where the coating is not pressed intothe surface by the applied load (figure 16(b)). A small pop-in may be observed associated with this (figure 16(c)). Onunloading these buckles propagate further and can detach theregion under the indenter—the buckled material may push backon the indenter giving the linear unloading observed in the P –d

curve (figure 16(c)). Alternatively, if the coating is relativelythick and has a high stiffness, a shear crack originates in it andpropagates down to the interface causing the coating to detach

from the substrate around the indenter (see SEM micrograph infigures 17(a) and (c). This is apparent in the load–displacementcurve, where a long pop-in can be observed in the loadingcurve as the indenter pushes the detached material out fromunderneath it.

To quantify the adhesion in such cases the expressionproposed by den Toonder et al [67] may be used, in whichthe curved geometry of the chipped segment of the coatingand the residual stress in the coating are used to calculatethe adhesion energy or interfacial fracture energy, �i. Theinterfacial fracture energy is calculated using

�i = 1.42Et5

L4

((a/L) + (βcπ/2)

(a/L) + βcπ

)2

+t (1 − ν)σ 2

r

E

+3.36(1 − ν)t3σr

L2

((a/L) + (βcπ/2)

(a/L) + βcπ

), (27)

where E is the Young’s modulus of the coating; t is thethickness of the coating; ν is the Poisson’s ratio of the coating;σr is the residual stress in the coating and a, L and βc definethe geometry of the chipped piece (figure 18). The higherthe value of �i, the better the adhesion between coating andsubstrate. This equation is very sensitive to the precise valuesof thickness and crack length measured and care must be takento determine these to a high level of accuracy.

This expression is based on a model suggested byThouless [73] which assumes that (i) the in-plane load on thedelaminated sector due to indentation causes the growth ofthe delamination area and (ii) the coating chips at the momentof buckling of the sector are due to the same plane in-load.The results for the interfacial fracture energy are presentedin table 3. In the case of the coatings on SiC on siliconthe detachment occurs at or near the CNx /SiC interface asdetermined by XPS analysis of the fracture surfaces.

The values obtained are somewhat higher than thoseobtained for pure metals on the same substrates (typically1–10 J m−2) but are typical of harder metal and ceramiccoatings where considerable plastic deformation occurs at thecrack tip during delamination.

3.6. Time dependent deformation

Several workers have reported on creep behaviour duringindentation experiments on different materials [74–76].During these experiments an increase in the penetration depthis registered when the load is held constant at the maximumapplied load, and if creep is not accounted for this can leadto variability in the hardness and modulus values [76]. Theamount of creep registered in a material depends on the loadingand unloading rates and on the duration of the hold segment atpeak load, as well as on the material itself. Different holdperiods are required for each material to correct for creepbehaviour [76] during indentation.

For hard coatings such as TiN the effect of creep isgenerally negligible, but amorphous materials and in particularsoft metals are very significantly affected by creep processesand this must be taken into consideration if high quality datais to be obtained from them in the nanoindentation test.

The creep behaviour of amorphous CNx has been studiedin order to prove the accuracy of the hardness and moduliresults presented, and a loading rate and hold period were

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Table 2. The energy release rates and toughness calculated for the solar control fracture coating components are investigated in this studybased on the radial through-thickness fracture.

Energy release rateof coating GIC

(J m−2) calculated Toughness of coating KIC (MPa√

m)by the Wt–dpmodel presented Calculated by the Wt–dp model Estimated by Lawn method

400 nm TiOxNy /glass 24.4 ± 1.4 1.8 ± 0.2 0.9 ± 0.1240 nm ITO/glass 36.3 ± 8.2 2.2 ± 0.3 0.9 ± 0.1400 nm ITO/glass 32.7 ± 4.4 2.1 ± 0.2 0.7 ± 0.1400 nm SnO2/glass 29.3 ± 9.8 1.9 ± 0.3 1.3 ± 0.1

Figure 16. (a) Schematic diagram of the detachment of a thincoating due to buckling in response to compressive stress around theindenter. (b) SEM micrograph for a 1 µm thick CNx coating onSi(001) showing coating fracture during loading and unloading ofthe indenter at 500 mN applied load. (c) Corresponding P –δ curveshowing linear unloading at the bottom of the unloading curveassociated with buckling of the coating.

proposed to correct for creep behaviour in CNx coatings [77].Indentation creep experiments were carried out on 1 µm thickCNx coatings on 3C SiC(001) at applied loads of 1 mN,for which coating only response to nanoindentation can beobtained.

Since creep does not only occur during the hold segmentat maximum applied load but also during the whole loading

Figure 17. (a) Schematic diagram showing coating detachmentduring loading of the indenter. (b) Step in the loading curve due tothrough-thickness cracking of the coating and spalling. (c) SEMmicrograph showing coating detachment during loading of theindenter for a 1 µm thick CNx coating on 3C SiC (001)substrate.

L

β

2a

Radial crack

Chipped coatingsegment

Figure 18. Schematic of the geometry of a chipped segmentshowing the dimensions used in calculating interfacial toughness.

period, a detailed analysis of the creep behaviour of the CNx

as a function of the loading rate was carried out. Proportionalloading (dP/P ) indentation experiments have been carriedout and compared with constant loading rate experiments of1 and 100 µN s−1. In these experiments, the indentations areperformed at a prescribed loading rate until a fixed maximumload is reached. Then the indenter is quickly unloaded to70% of the maximum applied load and a 60 s hold segment

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Table 3. Interfacial fracture energy of CNx coatings (1 µm thick)deposited on different substrates.

Substrate �i (J m−2)

Si (001) 27 ± 5Al2O3 21 ± 41 µm 3C SiC on (001) silicon 5.1 ± 0.91 µm 3C SiC on (111) silicon 5.3 ± 0.9

0

0.2

0.4

0.6

0.8

1

0 20 40 60 8 00

dP/P: H=6.8GPa, E=67.5GPa

1µN/s: H=4.9GPa, E=61.3GPa

100µN/s: H=6.4GPa, E=70.4GPa

Loa

d, m

N

Displacement, nm

Figure 19. Comparison between the loading curves correspondingto (dP/P ), 1 µN s−1 (dP ) and 100 µN s−1 (dP ) loading rates for1 µm thick CNx coating on 3C SiC(001) showing similar behaviour.

is included to allow for thermal drift correction. Finally, theindenter is unloaded to 100% of the maximum applied load.

Constant and proportional loading rate indentationexperiments follow similar unloading trends but differ inthe way the loading process is carried out. Whereas creep,independently of the loading rate, does not affect proportionalloading (dP/P ) experiments, it has an important effect onconstant loading rate experiments [78]. One way of correctingfor creep in this type of experiments is choosing a high enoughloading rate for the material not to creep during loading of theindenter. Therefore, if creep significantly affects the materialduring the indentation experiment under the test conditionsused, it should be registered in the loading curve. Cheng andCheng [78] have proposed a relationship between load anddisplacement that accounts for creep behaviour during loadingin constant loading rate experiments,

P ∝ δ2/(mε+1), (28)

where mε is the creep strain rate exponent. In their paper, theyhave also proved that for proportional loading experiments P isproportional to δ2. This suggests that if there are no differencesin the loading curves presented by both loading experimentsthe creep exponent should be zero and therefore creep is notaffecting the measurements. This is what is observed whencomparing the load–displacement curves corresponding to a100 µN s−1 constant loading rate and the proportional loadingapproach (see figure 19). However, for a constant loadingrate of 1 µm s−1 creep effects are important (see figure 19)leading to erroneous values of hardness and Young’s modulus.

Thus, a constant loading rate of 100 µN s−1 for indentationexperiments is necessary to avoid creep during indentationof CNx .

Chudoba and Richter [76] have suggested that, except formaterials presenting steady state or viscous creep, choosing anadequate hold period at peak load will avoid any influenceof the loading rate on the modulus and hardness valuesobtained from the unloading slope using the Oliver and Pharranalysis [18]. The displacement of the indenter during a holdat peak load, �δ, may then be given by

�δ = A ln(Bt + 1), (29)

where t is the time and A and B are constants. The holdperiod necessary to avoid creep effects can be defined as thehold time necessary to ensure that the increase in depth is lessthan 1% of the indentation depth. This has been assessed fora range of indentations at 1 mN peak load on a 1 µm CNx filmon 3C SiC on (001) silicon using a peak hold of 60 s duringwhich displacement data are continuously monitored. There isconsiderable scatter in the measured data so that the necessaryhold period varies from 20 to 57 s, and it is therefore suggestedthat a 60 s hold at peak load is used when testing CNx coatingsto avoid the effects of creep. This is similar to the hold periodnecessary for fused silica tested under the same conditions. Asthe peak load in the test increases the hold period is reduced—for fused silica a hold period of 15 s is suitable for a 250 mNpeak load indent, but the substrate begins to play an increasingrole for the CNx coating.

It is clear that the indentation creep behaviour of fullerene-like CNx is very similar to fused silica and given this it mightbe expected that their dynamic indentation behaviour is alsosimilar as discussed previously.

Creep of aluminium metallization on silicon can beassessed by analysing the change in indenter displacementduring a high load hold period (figure 20). The creep strainis defined as the change in indenter displacement during thehold period divided by the indenter displacement at the startof the hold period and is plotted in figure 17(b). This istypical of the behaviour of a high creep material. At roomtemperature the material beneath the indenter is expected toundergo exhaustion creep processes so that the creep rate dropsto zero after an initial transient response. Such behaviour isobserved for higher melting point materials such as nickel butwas not observed for the aluminium metallization tested here.Thus a steady state viscous creep component is added to thetransient behaviour. Metallization viscous creep rates are afactor of three or so higher than for bulk material (figure 21).Both transient creep strain and viscous creep rate drop asthe coating thickness increases (figure 22). This result issomewhat surprising as the creep-resistant substrate will haveless influence on the result as the coating thickness increases.It is also observed that the creep strain decreases with load. Atlow loads creep is fast because the few dislocations availabledo not encounter many other dislocations or obstacles to creepmotion. Indeed it is observed that dislocation-free singlecrystal samples show no creep at loads low enough that noplastic deformation occurs but that rapid creep is observedonce plastic deformation starts (or if there are pre-existingdislocations in the material). At higher loads more plastic

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0

50

100

150

200

0 20 40 60 80 100 120

Load

(µ

N)

Displacement (nm)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 10 20 30 40 50 6 0

59 m Al on silicon

Creep strain

Cre

ep s

trai

n

Creep time (s)

(a)

0n(b)

Figure 20. (a) Load–displacement curve with a peak load holdsuitable for the assessment of creep behaviour. (b) Variation ofcreep strain with time during the hold period showing typicalbehaviour.

deformation occurs, and work hardening reduces dislocationmobility and hence the creep rate.

An alternative method to determine the exponentdescribing creep behaviour is to consider the creep rate, ε,measured in the holding period as a function of load. It isgenerally observed that

ε = kσmσ , (30)

where mσ is the creep stress exponent (mσ = 1/mε), k is aconstant and σ is the applied stress. It may be assumed that

ε ∝ δ

δand σ ∝ P

δ2, (31)

and therefore mσ is the slope of the ln (δ/δ) versus ln (P/δ2)

plot.Using this approach reasonable values of the creep stress

exponent have been determined for aluminium films on silicon(mσ ∼ 5 (figure 23) compared with 4.4 for bulk aluminium)provided that the indenter penetration at the start of the creephold is sufficient. In the loading curve load is proportional

0

0.1

0.2

0.3

0.4

0.5

0 20 40 60 8 00

Single Crystal Al

Polycrystalline Al

Evaporated Al

Cre

ep s

trai

n

Time (s)

Figure 21. Comparison of indentation creep behaviour of bulk andthin film aluminium.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 10 20 30 40 50 6 0

Evaporated Aluminium on Silicon

45nm110nm195nm590nm

Cre

ep s

trai

n

Creep hold time (s)

Figure 22. Effect of coating thickness on the indentation creep ofevaporated aluminium on silicon.

to displacement to the power of 1.65, despite the fact thatconsiderable plastic deformation has occurred and creep hastherefore occurred during loading. Using equation (28) thisgives a value of mε = 0.21 which converts to mσ = 4.75showing the good agreement between the two approaches. Atlower penetrations a much higher creep exponent is observed(mσ ∼ 9) which is comparable to that observed when testingsingle crystal materials or materials with a large grain size.Clearly the scale of the stressed volume when compared withthe size of the microstructural units is critical in determiningbehaviour. Very low load nanoindentation offers the possibilityof assessing the performance of individual grains and theproperties measured are often considerably different fromthose measured at high load which average over many grainsand include the effects of grain boundaries.

Creep equations for modelling aluminium metallizationstructures by finite element modelling have been determined

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3

4

5

6

7

8

9

10

0 20 40 60 80 100 120 140 160

Evaporated

Sputtered

Cre

ep e

xpon

ent

Displacement at start of creep (nm)

Single crystal or large grainsize polycrystal values

Figure 23. Creep exponent for sputtered and evaporated aluminiumfilms on silicon as a function of the indenter displacement at the startof the creep hold.

0

100

200

300

400

500

600

0 500 1000 1500 2000 2500

Sputtered (with creep)Evaporated (with creep)Evaporated (no creep)Sputtered (no creep)

Yie

ld s

tre

ss (

MP

a)

Coating thickness (nm)

Figure 24. Yield stress values required to fit nanoindentationload–displacement curves with and without the inclusion of creepparameters derived from a high load hold period.

by fitting the creep during the hold period using finiteelement modelling of the nanoindentation load–displacementdata [79, 80]. This requires good yield stress and workhardening data with all the inherent difficulties in extractionmentioned previously. Including creep into the fitting approachchanges the yield stress (the tangent modulus remains fixed)required to give a good fit to the experimental data (figure 24).The behaviour of sputtered and evaporated aluminium isidentical if creep is included whereas considerable differencesare observed if this is not the case.

4. Modelling the indentation response ofcoating/substrate systems

While depth-sensing indentation methods uniquely have theability to measure E and H , there are several problems and

challenges associated with analysing the data from CRIT toproduce E and H values for coated systems. For example, E

and H values can be calculated from the contact stiffness andplastic contact areas determined from the unloading curve bystandard procedures [17, 18]. At one extreme, fracture of thecoating leads to the measured values of E being equal to that ofthe substrate alone (e.g. [8, 25]). However, under less severecontact conditions, great care has to be taken in apportioningthe contributions to H and E from the coating, the substrate andthe interface. Further, the interpretation of H poses questionsas to the exact plastic deformation mechanisms involved—particularly with regard to whether the coating is plasticallydeforming under the indenter or is simply being bent and flexedto conform to the sample shape as the substrate beneath thecoating deforms plastically (e.g. [8, 39]). In the latter case—which is arguably how coatings should behave to providedamage protection—any hardness enhancement measured asbeing conferred by the coating has more to do with the elasticproperties of the coating (controlling flexure) than anythingto do with its intrinsic hardness [8, 40]. Thus, great care hasto be taken before any models such as the laws of mixturesare applied (e.g. [81, 82]). Clearly, the guiding principle is tounderstand the deformation mechanisms of the system beforeapplying any model to the interpretation of its responses.

However, the range of behaviour shown in the CRITresponse of coated systems has led to a number of new modelsappearing to explain various system responses to surfacecontact (e.g. [25, 39, 40, 83]). Thus, models now exist toexplain the load support by the coating through its elasticflexure before fracture (the drum-skin effect [39]) and alsoto explain the hardness enhancement which persists after thecoating has fractured but where elastic flexure of the coatingstill resists the pile-up of the plastically deformed substratefrom underneath [25, 40].

Though much progress has been made with FE modellingof the indentation behaviour of coated systems the complexityof the models and the lack of good constitutive data formany coating materials means that its use for assessingmodern multilayer or graded coatings is questionable exceptin cases where elastic contact is maintained [84]. There hastherefore been a need to develop a method of modelling thehardness behaviour of a complex coating system in the absenceof good data which can also be used to make predictionsabout the performance of different coating architectures.One such model has been developed based on the energydissipation mechanisms during deformation which contributeto the irreversible work of indentation. This approachhas been successfully used to model single layer [37, 85],multilayer [37, 86], superlattice [37] and graded coatings [87]and is discussed in more detail in the following.

When modelling coating/substrate system hardness it hasbeen customary to start with the basic definition of hardness,H , as a pressure, but an alternative but equivalent definition ofhardness is [88]

H = W

V, (32)

where W is the plastic work of indentation and V is thedeforming volume. Any mechanism that contributes to energydissipation in the indentation cycle is automatically includedin the work of indentation, which is just the sum of these

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contributions. In instrumented indentation testers where loadand indenter displacement are continuously monitored, W canbe measured directly. However, a direct measurement of V isnot possible and if the deforming volume is to be used as abasis for modelling it needs to be related to something that ismeasurable, such as the indenter displacement. Equation (2)gives us a direct relationship between the plastic depth of theimpression and the radius of the plastic zone; this plastic depth(contact depth) can be measured experimentally or calculatedfrom load–displacement data obtained by nanoindentation forthe validation of any model.

The system hardness modelling approach consists of thefollowing [37, 83–86]. All layers present in the sample arecharacterized by a bulk hardness, H0, and a bulk elasticmodulus, E0. H0 will vary depending on the grain size of thematerial. All major interfaces are characterized by a surfaceenergy term; the main interfaces are the surface (energy γs),the coating/substrate interface (energy γi) and the energy ofany internal interfaces in the coating (energy γ (n) where n isthe number of the interface in question). For any plastic zoneof radius R the total deforming volume can be calculated asa hemisphere (V = 2πR3/3) and this can be apportioned tocoating layers and the substrate by simple geometric analysis(slices through a hemisphere). Similarly the area of all theinterfaces contained within the deforming volume can becalculated. From equation (32) the work of indentation is justthe deforming volume of each layer multiplied by H0 for thatlayer so the total plastic work is the sum of these for all layers inthe deforming volume. To this plastic work needs to be addedthe work of deforming the interfaces which is just the areaof the interface multiplied by the appropriate surface energy.Dividing the total work by the total deforming volume givesthe effective hardness of the composite. This can be expressedin terms of plastic depth using equation (2) where E and H arethe effective Young’s modulus and hardness of the deformedmaterial [85].

It should be recognized that the γ values used do notrepresent true surface energies as might be obtained from brittlefracture experiments. Rather they represent the extra energynecessary to deform the interface (or interphase) which willinclude plastic deformation, fracture and frictional effects.

The modelling of a coating substrate system is relativelystraightforward. Two interfaces must be considered. Thus

H = (VsH0(s) + VcH0(c) + Asγs + Aiγi)

V, (33)

where Vc and Vs are the deforming volumes of coating andsubstrate, H0(c) and H0(s) are the bulk hardnesses of coatingand substrate, As is the surface area and Ai is the interfacialarea within the plastic deforming region. When the radius ofthe plastic zone is less than the coating thickness this interfacemay be ignored, and the modelling proceeds exactly as in theprevious section. Thus

H = H c0 +

Kc

δ, (34)

where H c0 is the bulk hardness of the coating and Kc describes

the coating indentation size effect behaviour [28]. However,when the radius of the plastic zone exceeds the coating

thickness both coating and substrate properties contribute tothe measured hardness. In this case

H =(

3t

2R− 1

2

t3

R3

)H c

0 +

(1 − 3t

2R+

1

2

t3

R3

)H s

0 +3γs

2R

+

(3

2R− 3t2

2R3

)γi. (35)

Here R is the radius of the plastic zone which is assumed tobe the same in the coating and substrate. Previous hardnessmodels based on the volume-law-of-mixtures [89, 90] havebeen based on plastic zone radii calculated from bulk substrateand coating properties. For a hard coating on a soft substrate,such as TiN on steel, the radius of the plastic zone in thesubstrate can be more than three times that in the substrateat the same test load. As plastic deformation expands from thecoating into the substrate there must be a rapid expansion ofthe plastic zone since at large loads the substrate will dominateindentation behaviour. At intermediate loads the deformationin the coating constrains substrate deformation, and the extentof deformation in the substrate near the coating substrateinterface is reduced. In previous work the radius of the plasticzone some distance away from the interface was assumed to bethe same as that for the bulk substrate. However, experimentalmeasurements of plastic zone sizes in this study have shownthat this greatly overestimates the substrate plastic zone size.In fact, as the indenter penetration increases there is a smoothgrowth of the plastic zone radius from the coating dictated sizeto that of the substrate. Deviations from the hemisphericalshape can be accounted for by the interfacial energy, γi.

For this reason an optimization approach is adopted.Starting with a small value of R equation (34) is used todetermine the measured hardness. R is then incremented andthe process repeated until it exceeds the coating thickness andthen equation (35) is used. R is converted to depth usingequation (2), the calculated hardness and an effective valueof E. Since E and H are varying as the plastic volumechanges from coating dominated to substrate dominated theplastic depth changes from coating to substrate controlled. Theeffective Young’s modulus values are given by

E = Ec0 for Reff � t,

E =(

3

2

t

Reff− 1

2

t3

R3eff

)Ec

0 +

(1 − 3

2

t

Reff+

1

2

t3

R3eff

)×Es

0 for Reff > t, (36)

where Reff is the effective radius of the elastically deformedregion which is likely to be larger than the plastic zone radius.Nanoindentation hardness and Young’s modulus results for a2.8 µm NbN coating on stainless steel (figure 25) show that anyeffect of the increased range of elastic deformation on effectiveYoung’s modulus is small but significant and thus we can write

Reff = αR. (37)

α can be determined by fitting to measured Young’s modulusdata as in figure 21 and is typically of the order of three.

The hardness prediction for the NbN coating isshown in figure 26 compared with experimental data fromnanoindentation and conventional microhardness testing.Agreement is good at low depths and is also reasonable athigh depths but the agreement is less good in the intermediate

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Topical Review

Figure 25. Variation of nanoindentation hardness and Young’smodulus with contact depth for 2.81 µm cathodic arc NbN onstainless steel.

0

10

20

30

40

50

0 500 1000 1500 200 500

2.81µ m Cathodic Arc NbN on Stainless Steel

Experimental

Basic Model

Picture frame cracking

Circular cracking

Har

dne

ss (

GP

a)

Depth (nm)

Figure 26. Predicted and experimental variation of hardness withdepth for 2.81 µm cathodic arc NbN on stainless steel. Modellingparameters: Hf = 24 GPa, Ef = 475 GPa, γs = 15000 J m−2,Hs = 1.7 GPa, Es = 210 GPa, γi = 5000 J m−2 and α = 2.0.

range. Agreement can be improved by modifying the fittingparameters but in doing this the quality of the fit for Young’smodulus is much worse.

For the NbN coating tested at 250 mN peak load thereis a change in the shape of the nanoindentation loadingcurve at about 600 nm depth which corresponds to the depthat which the deviation between the modelled hardness andYoung’s modulus and the experimental data is first observed(figure 4(a)). SEM shows that a circular through-thicknesscrack is produced at this load (figure 4(b)) outside theindentation. Thus fracture explains the deviation between themodelled and measured hardness and Young’s modulus.

To include the effects of fracture in the model we assumethat the coating within the cracked region does not contribute tothe plastic work of indentation after fracture occurs. Fractureusually occurs when the plastic zone in the substrate is verywell established so we can consider the volume of coating to bea cylindrical disc with the thickness of the coating. The areaof the crack produced is small compared with the volume itencloses, so we also assume that the surface energy of the crackplays only a minor part in the work of indentation. We can then

consider two separate cases:

(1) a single circular crack, radius rc, which occurs atindentation depth, δcrack. The area of the region bounded by thecrack does not change as the load is increased as is observedfor the cathodic arc NbN coating (figure 4(b)). In this casethe correction for modelled hardness and Young’s modulus isgiven by

�H = 3(tH c0 + γs + γi)r

2c

2R3,

�E = 3tEcr2c

2R3eff

,

(38)

and is constant for any depth greater than δcrack. In this studyrc = 6.6 µm and δcrack = 600 nm.

(2) picture frame cracks, radius kcδ, where kc is a constantand δ is the plastic indentation depth. These form above acritical depth, δcrit . In this case the area of material bounded bypicture frame cracks increases linearly with indentation size.In this case the correction for modelled hardness and Young’smodulus is given by

�H = 3(tH c0 + γs + γi)k

2c δ

2

2R3,

�E = 3tEck2c δ

2

2R3eff

,

(39)

and increase linearly with indentation depth above δcrit .A simple estimate for kc is that it relates the depth to the radiusof an equivalent cone with the same volume as the impression.Thus, for a Berkovich indentation

kc =√

24.5

π. (40)

In practice kc is bigger than this since picture frame crackingoccurs outside the impression as coating material is bent toconform to the pile-up around it. Typically this occurs over aregion twice the radius of the impression, a factor which hasbeen used here.

Corrected hardness predictions for the two approaches areshown in figure 26. The hardness modelled by the pictureframe cracking method shows the closest fit to experimentaldata over the complete depth range tested despite the obviouscircular crack in the micrograph in figure 4(b). Detailedinvestigation of the impression in this case shows that nestedpicture-frame cracks are produced which are the majorcontributor to the loss of hardness. This is a particular featureof the indentation of vapour deposited coatings where thecolumnar grain boundaries which run perpendicular to theinterface provide easy paths for crack nucleation. Indeedseveral workers have reported that shear failure of theseboundaries is the dominant mechanism for the formation ofthe impression in these materials (e.g. [91]). In this casethe coating does not plastically deform but nested regions ofcoating are pushed down into the substrate as it plasticallydeforms beneath them giving a stepped interface betweencoating and substrate in the impression.

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5. Discussion

The previous sections have shown that it is possible to measurea range of properties of the coating substrate systems by usingan appropriate nanoindentation technique. However, it shouldbe emphasized that extreme care is necessary if coating onlyproperties are required. The widely quoted 10% rule of thumb,i.e. that the indentation depth must be less than 10% of thecoating thickness if coating-only properties are to be extracted,is not applicable in all cases for hardness assessment and shouldnot be used at all for Young’s modulus assessment. The elasticstress fields associated with an indentation penetrate verymuch deeper than the stresses which cause plastic deformation,and therefore there will be a substrate contribution when theindenter penetration is much less than 10% of the coatingthickness. Typically indenter penetrations of less than 1% ofcoating thickness are needed to measure elastic properties withany reliability.

For hard coatings of reasonable thickness (>200 nm) it isusually possible to get an accurate measure of coating hardnessif the substrate hardness is sufficient (>10 GPa). A well-calibrated indenter with low tip-end radius is an essentialrequirement. As there is no pile-up the Oliver and Pharrmethod [18] for data analysis works well. However, whenhard coatings are deposited on metallic substrates it should berealized that there may be some creep in the substrate materialduring the indentation cycle and the loading rates need to bemaximized to generate reliable data. To generate indentationfracture for a hard coating generally requires indenter loadshigh enough to cause plastic deformation of the substrate. Theradial–median fracture patterns associated with indentations inbulk brittle materials are rarely observed, except in the case ofvery thick coatings (>10 µm) whereas radial and picture framecracks inside the impression (due to the bending of the coatingto conform to the indenter shape) are very common. Thisis driving the development of new ways of assessing coatingtoughness.

For soft coatings both creep and pile-up effects need tobe considered, and the analysis of the indentation impressionby post facto AFM is extremely useful. In many cases themeasured Young’s modulus of the coating/substrate systemis much higher than the bulk material values might predictdue to pile-up but is reduced due to the effects of creep. Anindependent measure of the area of the impression can resolvewhich of these dominate.

It is possible to plot properties such as hardness or Young’smodulus as a function of indent depth (or more usually indenterdisplacement), and this has sometimes been suggested to givethe profile of properties through the coating and into thesubstrate. The modelling approach outlined here demonstratesthat this is not a valid interpretation. The properties measuredat a given depth are a summation of the indentation response atall depths up to this, weighted towards the surface layers. Moreadvanced modelling will be required to extract the variation ofproperties with depth from indentation analysis.

6. Conclusions

In summary, given the appropriate experimental approaches,continuously recording load–displacement instruments can

provide a wealth of unique information regarding surface-engineered systems. A number of conclusions may be drawn.

(1) Informed use of nanoindentation techniques and care ininterpreting data are required if we are to learn moreabout the detailed behaviour of such systems rather thansimply trying to assess their hardnesses. When dealingwith coated systems the ratio of indenter displacement tocoating thickness is critical in dictating whether coatingor substrate dominates the indentation response.

(2) Detailed analysis of the nanoindentation load–displacementcurve allows the transition between elastic and plasticindentation behaviour to be assessed, and other deforma-tion mechanisms can be related to features in the loaddisplacement curve if careful high resolution microscopyis coupled with the indentation technique.

(3) For assessing very thin films (<1 µm) it is essential touse a high quality tip with as small a tip end radius aspossible. Practically tip radii are rarely smaller than 50 nmand this makes it difficult to generate plastic deformationin coatings less than 200 nm thick. Extraction of themechanical properties of such thin coatings thereforerequires a modelling approach.

(4) In the absence of pile-up or creep the hardness and Young’smodulus of many coating materials can be successfullymeasured by nanoindentation using the Oliver and Pharrapproach. Care must still be taken to account forindentation size effects. Creep and fracture behaviour canalso be assessed if appropriate test methods are used.

(5) The development of better models allowing furtherinsights into deformation mechanisms to be deduced fromCRIT data, together with deconvolution of ‘the depthproblem’ by appropriate modelling, can only enhancethe power of CRIT to characterize the properties andperformance of surface engineered systems.

Finally, it has to be remembered that nanoindentationtechniques are only one of the ways of investigating theproperties of surface-engineered systems, albeit providingunique data at high spatial resolutions. Thus, insights providedby CRIT may help to interpret, or even reveal inconsistenciesin/with, the results provided by other tests which may beyielding data in different ways and at different scales.

Acknowledgments

The author would like to acknowledge the significantcontributions to this work from colleagues at Newcastle,particularly Professor T F Page who instigated much of whathas been presented.

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