Mechanical Systems Design Handbook

Macro- and Micromechanical and Tribological Properties 229

229

6

Macro- andMicromechanical andTribological PropertiesBharat Bhushan and Bal K. Gupta

1.0 INTRODUCTION

Mechanical properties of the solid surfaces and thin films areof interest as the mechanical properties affect friction and wearperformance of interfaces. Among the mechanical properties ofinterest, one or more of which can be obtained using commercial andspecialized hardness testers are: elastic-plastic deformation behav-ior, hardness, Youngs modulus of elasticity, scratch resistance,film-substrate adhesion, residual stresses, time-dependent creep andrelaxation properties, fracture toughness, and fatigue. For macrodevices, bulk properties are important. However, physical contacts atsliding interfaces in microelectromechanical systems (MEMS), suchas microsensors, microactuators, micromotors, microgear trains,microvalves, and magnetic recording heads typically occur at verylow loads, thus, friction and wear of sliding interfaces performance isprimarily controlled by the physical and chemical properties of a fewsurface atomic layers.[38][48][56][114][145][275] To protect these devicesagainst wear and corrosion and to achieve a low coefficient offriction, ultrathin coatings are sometimes deposited on the movingcomponents. For understanding and/or estimating the functionalbehaviors of mechanical devices of small sizes ranging from a

230 Handbook of Hard Coatings

couple of tens of microns to a few millimeters, and involving verylow loads on the orders of a few tens of nanonewtons, to a fewmillinewtons, measurements of mechanical and tribological proper-ties of thin coatings or the near-surface region of a bulk material onmicro- and nanoscales are of crucial importance. In the last decade,a variety of apparatuses have been developed to measure the me-chanical and tribological properties on micro- to nanoscales. Someof these common apparatuses are: depth-sensing mechanical proper-ties microprobe (Nanoindenter), atomic force microscope (AFM),and friction force microscope (FFM). These apparatuses operate atvery low loads and yield properties of the near surface region.

In this chapter, we will present an overview of techniques, andapparatuses used for measurement of mechanical and tribologicalproperties on the macro- to nanoscale. The diamond and amorphouscarbon coatings used extensively for controlling friction, wear, andcorrosion are chosen to exemplify the mechanical and tribologicalmeasurements made on the micro- and nanoscale.

2.0 MEASUREMENT OF MECHANICAL PROPERTIES

Hardness implies the resistance to local deformation. Mostcommonly used hardness measurements are: scratch hardness andstatic indentation hardness.[272] Scratch hardness depends on theability of one material to scratch another, or to be scratched byanother solid. The solid and thin film surfaces are scratched by asharp stylus made of hard material typically diamond, and either theloads required to scratch or fracture the surface, or delaminate thefilm or the normal/tangential load-scratch size relationships are usedas a measure of scratch hardness and/or interfacial adhe-sion.[2][30][37][56][76][131][133][139][147][199][223][224][261][272][273] [287][302]

The methods most widely used in determining the hardness ofmaterials are (quasi) static indentation methods. Indentation hard-ness is essentially a measure of their plastic deformation propertiesand only to a secondary extent with their elastic properties. In the


indentation methods, a spherical, conical, or pyramidal indenter isforced into the surface of the material which forms a permanent(plastic) indentation in the surface of the material to be exam-ined. The hardness number (GPa or kg/mm2) equivalent to theaverage pressure under the indenter, is calculated as the appliednormal load divided by either the curved (surface) area (Brinell,Rockwell, and Vickers hardness numbers), or the projectedarea (Knoop and Berkovich hardness numbers) of the contact be-tween the indenter and the material being tested, underload.[15][33][39][46][60][151][204][219][272][273][298]

In a conventional indentation hardness test, the contact area isdetermined by measuring the indentation size by a micro-scope after the sample is unloaded. At least, for metals, there is alittle change in the size of the indentation on unloading, so that theconventional hardness test is essentially a test of hardness underload, although it is subjected to some error due to varying elasticcontraction of the indentation.[262] More recently, in depth-sensing indentation hardness tests, the contact area is determinedby measuring the indentation depth during the loading/unloadingcycle.[38][39][60][65][101][207][211][218][228][230][282][304] Depth measure-ments have, however, a major weakness arising from piling-up,and sinking-in of material around the indentation. The measuredindentation depth needs to be corrected for the depression (or thehump) of the sample around the indentation, before it can be used forcalculation of the hardness.[99][100][111][210][218][230][304] Youngs modu-lus of elasticity is the slope of the stress-strain curve in the elasticregime. It can be obtained from the slope of the unloadingcurve.[210][218][230] Hardness data can be obtained from a depth sens-ing instrument without imaging the indentations with high reproduc-ibility. This is particularly useful for small indents required forhardness measurements of extremely thin films.

In addition to measurements of hardness and Youngs modulusof elasticity, static indentation tests have been used for measure-ments of a wide variety of material properties such as elastic-plasticdeformation behavior,[100][111][127][130][218][228][263] flow stress,[272]scratch resistance and film-substrate adhesion,[2][30][37][39][41][50]


[56][57][76][131][133][139][147][199][223][224][261][263][272][287][301][302][305][306] re-

sidual stresses,[168][183][270] creep,[19][84][144][178][206][290][297] stress re-laxation,[85][135][136][166][167][191][207][234][235][302] fracture toughness andbrittleness,[79][172][174][194][220][232] and fatigue.[177][307]

The extended load range of static indentation hardness testing isshown schematically in Fig. 1. We note that only the lower micro- andultra-microhardness, or nanohardness load range can be employedsuccessfully for measurements of extremely thin (submicron thick)films. The intrinsic hardness of surface layers or thin films becomesmeaningful only if the influence of the substrate material can beeliminated. It is therefore generally accepted that the depth of inden-tation should never exceed 30% of the film thickness.[15] The mini-mum load for most commercial microindentation testers available isabout 10 mN. Loads on the order of 50 N to 1 mN are desirable ifthe indentation depths are to remain few tens of a nanometer. In thiscase, the indentation size sometimes reaches the resolution limit of alight microscope and it is almost impossible to find such a smallimprint if the measurement is made with a microscope after theindentation load has been removed. Hence, either the indentationapparatuses are placed in situ a scanning electron microscope (SEM), orin situ indentation depth measurements are made. The latter mea-surements, in addition, would offer the advantages to observe thepenetration process itself. In viscoelastic/viscoplastic materials, sinceindentation size changes with time, in situ measurements of theindentation size is particularly useful, which can, in addition, providemore complete creep and relaxation data of the materials.

Figure 1. Extended load range of static indentation hardness testing.


In this section, we review various hardness test apparatuses formeasurements of mechanical properties of surface layers of bulkmaterials and extremely thin films (submicron in thickness) onmacro- to nanoscale.

2.1 Apparatuses for Hardness Measurement on Macroscale

Macrohardness measurements are generally used to determinebulk hardness. These include Brinell and Rockwell hardnesstesters.[46][272]

Brinell hardness is determined by forcing a hardened sphereunder a known load into the surface of a material, and measuring thediameter of the indentation left after the test. The load is maintainedfor about 30 seconds, and the diameter of indentation at the surface ismeasured with an optical microscope (10) after the ball has beenremoved. The Brinell hardness number (BHN) or simply the Brinellnumber, is defined in kilograms per square millimeter, as the ratio ofthe load used to the actual surface area of the indentation, which is, inturn, given in terms of the imposed load W, ball diameter D, and theindentation diameter d or depth of indentation h:

Eq. (1) DhW

dDDDWBHN

=

=

)(2

22

Hardened steel bearing balls may be used up to 450 BHN, butbeyond this hardness, especially treated steel or tungsten carbideballs should be used to avoid flattening of the indenter. The standardsize ball is 10 mm, and the standard loads are 3000, 1500, and 500kg, with 250, 125, and 100 kg sometimes used for softer materials,(for more details see Method of Brinell Hardness Testing, ASTME1061T). The load and the ball diameter should be adjusted to keepthe ratio d/D within the range of 0.3 to 0.5. The nearest edge of thespecimen should be no closer than 2.5 impression diameters, and thethickness should be more than one diameter. Since d/D is normallyless than 0.5, this means that for a 10-mm ball, the uninterrupted


width and depth of the specimen may have to be as great as 25 and 10mm, respectively, to avoid spurious side and bottom effects.

Use of the curved area in the Brinell test was originally intro-duced to try to compensate for the effects of work-hardening. It iscumbersome to use the surface area of indentation, though, so toovercome this disadvantage, Meyer hardness is defined in kilogramsper square millimeter, as the load used divided by the projected area ofindentation:

Eq. (2) 24

hardnessMeyer dW

=

In the Rockwell Hardness test, the indenter may be either asteel ball of some specified diameter or a spherical-tipped conicaldiamond of 120 angle with a 0.2-mm tip radius, called a Brale. Aminor load (or perload) of 10 kg is first applied, and this causes aninitial penetration that holds the indenter in place. At this point, thedial is set to zero, and the major load is applied. The standard loadsare 150, 100, and 60 kg. Upon removal of the major loads, thereading is taken while the minor load is still on. The hardness numbermay then be read directly from the scale that measures penetration.The Rockwell hardness number is defined by an arbitrary equation ofthe following form:

Eq. (3) tCCR = 21

where C1 and C2 are constants for a given indenter size, shape, andhardness scale, and t is the penetration depth in millimeters be-tween the major and minor loads. Although Rockwell hardnessincreases with Brinell hardness, the two are not proportional and thedimensions of the Rockwell hardness are not force per unit area. Infact, the Rockwell hardness number cannot be assigned any dimen-sions, since it is defined in an arbitrary Eq. (3).

A variety of combinations of indenters and major loads arepossible; the most commonly used are HRB or RB, which uses


1.59-mm diameter (1/16 inch) ball as the indenter and a major loadof 100 kg; HRC, or RC, which uses a cone as the indenter and a majorload of 150 kg; and HRA or RA, which uses a cone as the indenterand a major load of 60 kg. Rockwell B is used for soft metals andRockwell C and A are used for hard metals.

2.2 Apparatuses for Hardness Measurement on Microscale

Microhardness measurements allow the indenter to be shallowand of small volume so as to measure the hardness of brittle materialsor thin materials or coatings. The apparatuses include Vickers andKnoop hardness testers.[272] Both testers use highly polished dia-mond pyramidal indenters. The Vickers indenter is a diamond in theform of a square pyramid with face angles of 136 (corresponding toedge angles of 148.1) (Fig. 2a), and relatively low loads varyingbetween 1 and 120 kg are used. The Knoop indenter is a rhombic-based pyramidal diamond with longitudinal edge angles of 172.5and 130 (Fig. 2b). In general, the loads used in Knoop testers varyfrom about 0.2 to 4 kg. Smaller loads (as low as 1 to 25 g) also maybe used in Vickers and Knoop hardness measurements, the lengths ofthe diagonals of the indentation are measured using a mediumpowered microscope after the load is removed. If d is the mean valueof a diagonal in millimeters and W is the imposed load in kilogram,Vicker hardness number (V or HV), sometimes called diamond-pyramid hardness (DPH), is given by the load divided by the actualsurface area, that is,

Eq. (4) 28544.1

dWHV =

If l is the long diagonal in millimeters, Knoop hardness number(K or HK) is given by the load divided by the projected area of theindentation, that is,

Eq. (5) 2229.14

WHK =


The depth to the diagonal for the Vickers indenter is about 7and depth to the long diagonal (used for the Knoop indenter) is about30.5. The advantage of the Knoop indenter over the Vickers indenterin microhardness testing, lie in the fact that a longer diagonal isobtained for a given depth of indentation or a given volume ofmaterial deformed. The Knoop indenter is thus advantageous whenshallow specimen or thin, hard layers must be tested. The Knoopindenter is also desirable for brittle materials (such as glass or dia-mond), in which the tendency for fracture is related to the area ofstressed material.

Figure 2. Geometry and indentation with (a) a Vickers indenter and (b) a Knoopindenter.

(b)


2.3 Apparatuses for Hardness Measurement on Nanoscale

In this section, we review nanoindentation hardness appara-tuses in which the indent is imaged after the load has been removed,as well as the depth-sensing indentation apparatuses in which theload-indentation depth are continuously monitored during the load-ing and unloading processes. Earlier work by Alekhin, et al.,[6]Ternovskii, et al.,[279] and Bulychev, et al.,[72] led to the developmentof depth-sensing apparatuses. Prototype depth-sensing hardness ap-paratuses developed by several research groups are reviewed byBhushan.[38][39] A commercial depth-sensing nanoindentation hard-ness test apparatus manufactured by Nano Instruments Inc., is exten-sively used and is described in detail.

Nanoindentation Hardness Apparatuses With Imaging ofIndents After Unloading. For completeness, we first describe acommercially available microindentation hardness apparatus (ModelNo. Micro-Duromet 4000), that uses a built-in light optical micro-scope for imaging of indents after the sample is unloaded. It ismanufactured by C. Reichert Optische Werke AG, A-1171, Vienna,Box 95, Austria.[233] The indenters case is of the size of a micro-scope objective mounted on the objective revolver. The load range forthis design is from 0.5 mN to 2 N; therefore it is used for thicker films.

A commercial nanoindentation hardness apparatus for use in-side a scanning electron microscope (SEM), (Model No. UHMT-3)for imaging the indents after the sample is unloaded, is manufacturedby Anton Paar K.G., A-8054, Graz, Austria. The apparatus is mountedon the goniometer stage of the SEM. In this setup, the indenter ismounted on a double-leaf spring cantilever, and is moved against thesample by an electromagnetic system to attain the required indenta-tion load, which is measured by strain gages mounted on the leafsprings.[22][23] After the required load has been reached and the dwelltime has elapsed, the sample is unloaded, and the indentation diago-nal is measured by an SEM.

Depth-Sensing Nanoindentation Hardness Apparatus andIts Modifications. General Description and Principle of Operation.The most commonly used commercial depth-sensing nanoindentation


hardness apparatus is manufactured by Nano Instruments Inc., 1001Larson Drive, Oak Ridge, Tennessee 37830. Ongoing developmentof this apparatus have been described by Pethica, et al.,[228] Oliver, etal.,[216] Oliver and Pethica,[217] Oliver and Pharr,[218] and Pharr andOliver.[230] This instrument is called Nanoindenter. The most recentmodel is Nanoindenter II.[16] The apparatus continuously monitorsthe load, and the position of the indenter relative to the surface of thespecimen (depth of an indent), during the indentation process. Thearea of the indent is then calculated from a knowledge of the geom-etry of the tip of the diamond indenter. The load resolution is about75 nN, and position of the indenter can be determined to 0.1 nm.Mechanical properties measurements can be made at a minimumpenetration depth of about 20 nm (or a plastic depth of about 15nm).[216] Description of the instrument which follows, is based onRef. 16.

The Nanoindenter consists of three major components: (1) theindenter head, (2) an optical microscope, and (3) a X-Y-Z motorizedprecision table for positioning and translating the sample betweenthe optical microscope and indenter, Fig. 3a. The loading systemused to apply the load to the indenter consists of a magnet and coil inthe indenter head, and a high precision current source, Fig. 3b. Thedisplacement sensing system consists of a special three-plate capaci-tive displacement sensor, used to measure the position of the in-denter, Fig. 3b. The indenter column is attached to the moving plate.This plate-and-indenter assembly is supported by two leaf springscut in such a fashion as to have very low stiffness. At the bottom ofthe indenter rod, a three-sided pyramidal diamond tip (Berkovichindenter, discussed next) is generally attached. The indenter headassembly is rigidly attached to the U beam, and sample rides on theX-Y-Z table, Fig. 3a. The optical microscope is also attached to the Ubeam. The position of an indent on a specimen is selected using themicroscope (max. magnification of 1500). The spatial resolution ofthe position of the table in the X-Y plane is 400 nm.


(a)

(b)Figure 3. Schematics of the Nanoindenter II (a) showing the major components-the indenter head, an optical microscope and a X-Y-Z motorized precision tableand (b) showing the details of indenter head and controls (microscope which isdirectly behind indenter and massive U bar are not shown for clarity).[16]


The Nanoindenter also comes with a continuous stiffness mea-surement device.[217][229] This device makes possible the continuousmeasurement of the stiffness of a sample, which allows the elasticmodulus to be calculated, as a continuous function of time (orindentation depth). Useful data can be obtained from indents withdepths as small as 20 nm. Because of the relatively small timeconstant of the measurements, the device is particularly useful instudies of time-dependent properties of materials.

Weihs, et al.,[295] used acoustic emission (AE) sensors to detectcracking during indentation tests using Nanoindenter. Acoustic emis-sion (AE), measurement is a very sensitive technique to monitorcracking of the surfaces and subsurfaces. The nucleation and growthof cracks result in a sudden release of energy within a solid, thensome of the energy is dissipated in the form of elastic waves. Thesewaves are generated by sudden changes in stress, and in displace-ment that accompany the deformation. If the release of energy issufficiently large and rapid, then elastic waves in the ultrasonicfrequency regime (acoustic emission) will be generated, and thesecan be detected using piezoelectric transducers (PZTs), via expan-sion and compression of the PZT crystals.[38][249][312] The energydissipated during crack growth can be estimated by the rise time ofthe AE signal. Weihs, et al.,[295] mounted commercial transducerwith W impregnated epoxy backing for damping underneath thesample. The transducer converts the AE signal into voltage, that isamplified by an oscilloscope, and used for continuous display of AEsignal. Any correlation between the AE signal, and the load-dis-placement curves can be observed (also see Refs. 302 and 306).

The Berkovich Indenter. The main requirements for the in-denter are high elastic modulus, no plastic deformation, low friction,smooth surface, and a well defined geometry that is capable ofmaking a well defined indentation impression. The first four require-ments are satisfied by choosing the diamond material for the tip. Awell defined perfect tip shape is difficult to achieve. Berkovich is athree-sided pyramid, and provides a sharply pointed tip compared tothe Vickers or Knoop indenters, which are four-sided pyramids and


have a slight offset (0.51 m).[38][39][273] Because any three nonpar-allel planes intersect at a single point, it is relatively easy to grind asharp tip on an indenter if Berkovich geometry is used. However, anindenter with a sharp tip suffers from a finite, but an exceptionallydifficult to measure tip bluntness. Experimental procedures havebeen developed to correct for the tip shape, to be described later.

Berkovich indenter is a three-sided (triangular-based), pyrami-dal diamond, with a nominal angle of 65.3 between the (side) face,and the normal to the base at apex, an angle of 76.9 between edgeand normal, and with a radius of the tip less than 0.1 m (Fig. 4a).[33]Typical indenter is shaped to be used for indentation (penetration)depths of 1020 m. The indents appear as equilateral triangles (Fig.4b), and the height of triangular indent l is related to the depth h as

Eq. (6a) 44.619.76cot

32

=

=

lh

(a)

(b)

Figure 4. (a) Schematic of a Berkovich tip and (b) impression of a indentationmade by Berkovich tip.


The relationship h(l) is dependent on the shape of the indenter. Theheight of the triangular indent l is related to the length of one side ofthe triangle a as

Eq. (6b) l = 0.866aand

Eq. (6c) 44.71

=

a

h

The projected contact area (A) for the assumed geometry is given asEq. (7) A = 0.433a2 = 23.97h2

The exact shape of the indenter tip needs to be measured fordetermination of hardness, and Youngs modulus of elasticity. Sincethe indenter is quite blunt, direct imaging of indentations of smallsize in the scanning electron microscope is difficult. Determinationof tip area function will be discussed later.

Analysis of Indentation Data. An indentation curve is therelationship between load W and displacement (or indentation depth orpenetration depth) h, which is continuously monitored and recordedduring indentation. Stress-strain curves, typical indentation curves,the deformed surfaces after tip removal, and residual impressions ofindentation for ideal elastic, rigid-perfectly plastic, and elastic-per-fectly plastic, and real elastic-plastic solids are shown in Fig. 5. Foran elastic solid, the sample deforms elastically according to Youngsmodulus, and the deformation is recovered during unloading. As aresult, there is no impression of the indentation after unloading. Fora rigid-perfectly plastic solid, no deformation occurs until yieldstress is reached, when plastic flow takes place. There is no recoveryduring unloading, and the impression remains unchanged. In the caseof elastic-plastic solid, it deforms elastically according to Youngsmodulus, and then it deforms plastically. The elastic deformation isrecovered during unloading. In the case of elastic-perfectly plasticsolid, there is no work hardening.


All engineering surfaces follow real elastic-plastic deforma-tion behavior with work hardening.[151] The deformation pattern of areal elastic-plastic sample during and after indentation is shownschematically in Fig. 6. In this figure, we have defined the contactdepth (hc) as the depth of indenter in contact with the sample underload. The depth measured during the indentation (h) includes thedepression of the sample around the indentation in addition to thecontact depth. The depression of the sample around the indentation(hs = h-hc) is caused by elastic displacements and must be subtractedfrom the data to obtain the actual depth of indentation or actualhardness. At peak load, the load and displacement are Wmax and hmax,respectively, and the radius of the contact circle is a. Upon unload-ing, the elastic displacements in the contact region are recovered andwhen the indenter is fully withdrawn, the final depth of the residualhardness impression is hf.

Figure 5. Schematics of stress-strain curves, typical indentation curves, de-formed surfaces after tip removal, and residual impressions of indentation, forideal elastic, rigid-perfectly plastic, elastic-perfectly plastic (ideal) and realelastic-plastic solids.


Schematic of a load displacement curve is shown in Fig. 7.Based on the work of Sneddon[255] to predict the deflection of thesurface at the contact perimeter for a conical indenter and a paraboloidof revolution, Oliver and Pharr[218] developed an expression for hc atthe maximum load (required for hardness calculation) from hmax,

Eq. (8a) maxmaxmax / SWhhc =

where =0.72 for the conical indenter, =0.75 for the paraboloid ofrevolution, and =1 for the flat punch, and Smax is the stiffness (=1/compliance), equal to the slope of unloading curve (dW/dh) at themaximum load. Oliver and Pharr[218] assumed that behavior ofBerkovich indenter is similar to that of conical indenter, since cross-sectional areas of both types of indenters varies as the square of thecontact depth, and their geometries are singular at the tip. Therefore,for Berkovich indenter, ~ 0.72. Thus hc is slightly larger thanplastic indentation depth (hp) which is given by

Eq. (8b) maxmaxmax / SWhhp =

Figure 6. Schematic representation of the indenting process illustrating thedepression of the sample around the indentation and the decrease in indentationdepth upon unloading.[218]


We note that Doerner and Nix[100] had underestimated hc by assum-ing that hc = hp. Based on the finite element analysis of the indenta-tion process, Laursen and Simo[171] showed that hc cannot be as-sumed equal to hp for indenters which do not have flat punchgeometry.

Figure 7. Schematic of load-displacement curve.

For a Vickers indenter with ideal pyramidal geometry (ideallysharp tip), projected contact area to depth relationship is givenas[38][100]

Eq. (9a) 25.24 chA =

Since the area to depth relationship is equivalent for both typicalBerkovich and Vickers pyramids, Eq. (9) holds for Berkovich in-denter as well. Though we have derived a slightly different expres-sion for A(h) presented in Eq. (7) for the assumed Berkovich indentergeometry, we use Eq. (9) for A(h) in this chapter, as this relationship

Displacement, h


is most commonly used in the analysis of the indentation hardnessdata.

As shown in Fig. 6, the actual indentation depth, hc, producesa larger contact area than would be expected for an indenter with anideal shape. For the real indenter used in the measurements, thenominal shape is characterized by an area function F(hc) whichrelates projected contact area of the indenter to the contact depth(Eq. 9a),

Eq. (9b) )(2/1 chFA =

The functional form must be established experimentally prior to theanalysis.

Determination of Load Frame Compliance and IndenterArea Function. As stated earlier, measured displacements are thesum of the indentation depths in the specimen, and the displacementsof suspending springs, and the displacements associated with themeasuring instruments, referred to as load frame compliance. There-fore, to accurately determine the specimen depth, load frame compli-ance must be known. The exact shape of the diamond indenter tipneeds to be measured because hardness and Youngs modulus ofelasticity depend on the contact areas derived from measured depths.The tip gets blunt and its shape significantly affects the prediction ofmechanical properties (Figs. 810).

The method used in the past for determination of area functionhas been to make a series of indentations at various depths inmaterials in which the indenter displacement is predominantly plas-tic, and measure the size of the indentations by direct imaging.[100][228]Optical imaging cannot be used to accurately measure submicronsize impressions. Because of the shallowness of the indent impres-sions, SEM images result in poor contrast.


(a)

(b)

Figure 8. (a) Predicted projected contact area as a function of indentation depthcurves for various tip radii and measured data, (b) predicted load as a function ofindentation depth curves for various tip radii and measured data.[254]


Oliver and Pharr [218] proposed an easier method for determin-ing area functions that requires no imaging. Their method is basedonly on one assumption, that Youngs modulus is independent ofindentation depth. They also proposed a method to determine load-frame compliance. We first describe the methods for determining ofload frame compliance followed by the method for area function.They modeled the load frame and the specimen as two springs inseries, thus

Eq. (10) C = Cs + Cfwhere C, Cs, and Cf are the total measured compliance, specimencompliance and load frame compliance, respectively. The measuredcompliance C is given by

Eq. (11a) C = dh/dWThe relationship for the sample compliance Cs (inverse of

stiffness S) for an (Vickers, Knoop, and Berkovich) indenter is given as

Eq. (11b)2/1

21

=

AEC

r

s

where

i

i

s

s

r Ev

Ev

E

22 111 +

=

and dW/dh is the slope of the unloading curve at the maximum load(Fig. 7), Er, Es, and Ei are the reduced modulus and elastic moduli ofthe specimen and the indenter, and s and i are the Poissons ratiosof the specimen and indenter. C (or S) is the experimentally mea-sured compliance (or stiffness) at the maximum load during unload-ing and A is the projected contact area at the maximum load.

From Eqs. (10) and (11), we get

Eq. (12)21

21 /

r

f A

ECC

+=


From Eq. (12), we note that if the modulus of elasticity is constant, aplot of C as a function of A1/2 is linear and the vertical intercept givesCf. It is obvious that most accurate values of Cf are obtained whenthe specimen compliance is small, i.e., for large indentations.

Using the measured Cf value, they calculated contact areas forindentations made at shallow depths on the aluminum with measuredEr, and/or on a harder fused silica surface with published values ofEr, by rewriting Eq. (12) as

Eq. (13) 22 )(11

4 fr CCEA

=

from which an initial guess at the area function was made by fitting Aas a function hc data to an eighth order polynomial

Eq. (14) 128/184/132/12125.24 ccccc hChChChChA +++++=

where C1 through C8 are constants. The first term describes theperfect shape of the indenter; the others describe deviations from theBerkovich geometry due to blunting of the tip.

2.4 Mechanical Properties by Nanoindentation

Hardness And Modulus Of Elasticity. Berkovich hardnessHB (or HB) is defined as the load divided by the projected area of theindentation. It is the mean pressure which a material will supportunder load. From the indentation curve, we can obtain hardness at themaximum load as,

Eq. (15) HB W A= max /where Wmax is the maximum indentation load and A is the projectedcontact area at the peak load. The contact area at the peak load isdetermined by the geometry of the indenter and the correspondingcontact depth hc using Eq. (3a) and (4b). Plot of hardness as afunction of indentation depth for polished single-crystal silicon (111),


with and without tip shape calibration, is shown in Fig. 9. We notethat, for this example, tip shape calibration is necessary and thehardness is independent of corrected depth.

Figure 9. Hardness as a function of indentation depth for polished single-crystalsilicon (111) calculated from the area function with and without tip shapecalibration.[100]

Figure 10. Compliance as a function of inverse of indentation depth for tungstenwith and without tip shape calibration. A constant modulus with 1/depth wouldbe indicated by the straight line. The slope of the corrected curve is 480 GPa,which compares reasonably well to the known modulus of tungsten (420 GPa).The small y-intercept of about 0.3 nm/mN is attributed to load frame compliance,not removed.[100]

uncorrected shape

corrected shape


It should be pointed out that hardness measured using thisdefinition may be different from that obtained from the more con-ventional definition, in which the area is determined by direct mea-surement of the size of the residual hardness impression. The reasonfor the difference is that, in some materials, a small portion of thecontact area under load is not plastically deformed, and as a result,the contact area measured by observation of the residual hardnessimpression may be less than that at peak load. However, for mostmaterials, measurements using two techniques give similar results.

Even though during loading, a sample undergoes elastic-plas-tic deformation, the initial unloading is an elastic event. Therefore,the Youngs modulus of elasticity or simply called elastic modulusof the specimen can be inferred from the initial slope of the unload-ing curve (dW/dh) called stiffness (1/compliance) (at the maximumload) (Fig. 7). The modulus of elasticity is calculated from Eq. (12).It should be noted that the contact stiffness is measured only at themaximum load and no restrictions are placed on the unloading databeing linear during any portion of the unloading.

Hardness And Modulus of Elasticity of Thin Films FromThe Composite Response of Film and Substrate. As mentionedpreviously, for a thin film on a substrate, if the indentation exceedsabout 30% of the film thickness, then measured hardness is affectedby the substrate properties. A number of researchers have attemptedto derive expressions that relate thin-film hardness to substratehardness, composite hardness (measured on the coated substrate),and film thickness, and so allow the calculations of these quantitiesgive the remaining three.[34][35][69][70][74][152][244] Here we discusstwo models based on volume law of mixtures, (volume fractionmodel) and finite element simulation.

Sargent[244] suggested that the hardness of a film/substratecomposite is determined by a weighted average of the volume ofplastically deformed material in the film (Vf), and that in the sub-strate (Vs),

Eq. (16)VV

HVV

HH ssf

f +=


where V = Vf + Vs. The deformed volumes of film and substrate canbe calculated using expanding spherical cavity model.[151] Burnettand Rickerby[73][74] found it necessary to incorporate a further weigh-ing factor to deforming volume, to obtain a reasonable fit to experi-mental data. This factor accounts for the differences in relative sizesof the plastic zones in the film and substrate. Equation (16) ismodified as for a soft film on the hard substrate,

Eq. (17a)VV

HVV

XHH ssf

f +=3

and for the hard film on the soft substrate,

Eq. (17b)VV

XHVV

HH ssf

s

3+=

where X is the ratio of plastic zone volumes given as,

Eq. (17c)n

sf

sf

EHHE

X

=

They found that n, determined empirically, ranged from 1/2 to 1/3.Bhattacharya and Nix[34] modeled the indentation process us-

ing finite element method to study the elastic-plastic response ofmaterials. Bhattacharya and Nix[35] calculated elastic and plasticdeformation associated with submicron indentation by a conicalindenter of thin films on substrates, using the finite-element method.The effects of the elastic and plastic properties of both the film andsubstrate on the hardness of the film/substrate composite were stud-ied by determining the average pressure under the indenter as afunction of the indentation depth. They developed empirical equa-tions for film/substrate combinations for which the substrate is either


harder or softer than the film. For the case of a soft film on a hardersubstrate, the effect of substrate on film hardness can be described as

Eq. (18a)

+=2

exp11f

c

s

f

s

f

s

f

st

h

EEH

HHH

where Ef and Es are the Youngs moduli, f and s are the yieldstrengths and Hf and Hs are the hardnesses of the film and substrate,respectively. H is the hardness of the composite, hc is the contactindentation depth, and tf is the film thickness. Similarly for the caseof a hard film on a softer substrate, the hardness can be expressed as

Eq. (18b)

+=f

c

s

fs

f

s

f

s

f

st

h

EE

HH

HH

HH

21exp11

Composite hardness results were found to depend only veryweakly on Poissons ratio (v), and for this reason, this factor was notconsidered in the analysis. In Fig. 11, they show the compositehardness results as a function of (hc/tf), for cases in which the filmand substrate have different yield strengths. We note that hardness isindependent of the substrate for indentation depths less than about0.3 of the film thickness, after which the hardness slowly increases/decreases because of the presence of the substrate. In Fig. 12, theyshow the composite hardness results for cases in which the film andsubstrate have different Youngs moduli. It is observed that thevariation of hardness with depth of indentation in these cases isqualitatively similar to cases in which the film and substrate havedifferent yield strengths, although the hardness changes more gradu-ally than in the previous cases. Burnett and Rickerby[75] and Fabes etal.[111] have applied Eqs. (19)(21) to calculate the film hardnessfrom the measured data for various films and substrates.


(a)

(b)

Figure 11. Effect of relative yield strengths of the film and the substrate on thecomposite hardness for (a) a soft film on a hard substrate and (b) a hard film on asoft substrate.[35]


(a)

(b)Figure 12. Effect of relative Youngs moduli of the film and the substrate on thecomposite hardness for (a) a soft film on a hard substrate and (b) a hard film on asoft substrate.[35]


Doerner and Nix[100] empirically modeled the influence of thesubstrate on the elastic measurement of very thin film in an indenta-tion test using the following expression for the compliance

Eq. (19)

b

Ev

At

Ev

A

t

Ev

AdWdhC

i

if

s

f

f

f

f

+

+

+

==

22

2

1exp

1

exp11

21 2

1

where the subscripts f, s, and i refer to the film, substrate, andindenter, respectively. The term A is equal to (24.5)1/2hc for theVickers or Berkovich indenter. The film thickness is tf, and b is the yintercept for the compliance versus 1/depth plot, obtained for thebulk substrate, which can be neglected in most cases. The weighingfactors [1-exp(-tf / A )] and exp (-tf / A )] have been added toaccount for the changing contributions of the substrate and film tothe compliance. The factor can be determined empirically.

Kings analysis[157] verified that Eq. (19) is an excellent func-tional form for describing the influence of the substrate, and theoreti-cally determined the values of for various indenter shapes. Thevalue of was found to depend on the indenter shape and size andfilm thickness and was found to be independent of Ei/Es. The valuesof as a function of A /tf for Berkovich (triangular) indenters areshown in Fig. 13. The values of are found to be similar for squareand triangular indenters. Bhattacharya and Nix[35] analyzed the de-formations of a layered medium in contact with a conical indenterusing the finite-element method. Their analysis also verified therelationship given in Eq. (19).


Viscoelastic/Plastic Properties. Most materials including ce-ramics, and even diamond are found to creep at temperatures wellbelow half their melting points, even at room temperature. Indenta-tion creep and indentation load relaxation (ILR) tests are used formeasurement of the time-dependent flow of materials. These offer anadvantage of being able to probe the deformation properties of a thinfilm as a function of indentation depth and location.

In the indentation creep test, the hardness indenter maintains itsload over a period of time under well controlled conditions, andchanges in indentation size are monitored.[19][144][178][206][290][297]Nanoindenters are also used for indentation creep stud-ies.[178][182][234][235] Indentation creep is influenced by a large num-ber of variables, such as the materials plastic deformation proper-ties, diffusion constants, normal load of indenter, duration of theindentation, and the test temperature.

In a typical ILR test, the indenter is first pushed into the sampleat a fixed displacement rate until a predetermined load or displace-ment is achieved, and the position of the indenter is then fixed. Thematerial below the indenter is elastically supported, and will con-tinue to deform in an nonelastic manner, thereby tending to push theindenter farther into the sample. Load relaxation is achieved byconversion of elastic strain in the sample into inelastic strain in thesample. During the test, the load and position of the indenter, and thespecimen are continuously monitored. Normally the indenter motion

Figure 13. Parameter as a function of normalized indenter size for Berkovichindenter indenting a layered solid surface.[157]


is held constant, and the changes in the load are monitored as afunction of time. It is possible to obtain the plastic indentation ratefrom the indentation load and total depth information during therelaxation run.[85][136][207] The resulting load relaxation data arereported in the form of log (indentation pressure) as a function of log(plastic indentation strain rate).[135][166][167][302]

The indentation pressure is calculated by dividing the load bythe projected area of the indenter. Once the plastic indentation depthis known as a function of time, the projected area is determinedexperimentally as described earlier. The plastic indentation strainrate [(1/h)(dh/dt), where h is the current indentation depth] is calcu-lated in the manner similar to that for bulk relaxation data.

The strain rate sensitivity of materials is measured in terms ofstress exponent, n which is defined by the equation,

Eq. (20) nA pressure)on (indentati = raten indentatio Plastic

where A and n are the constants. The stress exponent is found as aslope of a log-log plot of plastic indentation rate (or strain rate) andindentation pressure. In the ILR test, the continuous change in thecontact area results in continuous changes in both plastic indentationrate and pressure. Thus, data from a single indentation test, which mayspan several orders of magnitude in both strain rate and pressure, aresufficient to determine the stress exponent. Stress exponent can be usedto define the superplasticity of a material. The variations in stressexponent reflect the changes that may take place when the substructuregenerated at high strain rate approaches equilibrium condition.[190]

Nanofracture Toughness. Fracture toughness, KIc of a mate-rial is a measure of its resistance to the propagation of cracks, and theratio H/KIc is an index of brittleness, where H is the hardness.Indentation fracture toughness is a simple technique for determina-tion of fracture toughness.[18][79][81][82][88][134][172][174][220][232] In-dentation cracking method is especially useful for measurement offracture toughness of thin films, or small volumes. This method isquite different from conventional methods, in that no special


specimen geometry is required. Rather, the method relies on the factthat when indented with a sharp indenter, most brittle materials formradial cracks, and the lengths of the surface traces of the radial cracks(for definition of crack length, see Fig. 14) have been found tocorrelate reasonably well with fracture toughness. Using simpleempirical equations, fracture toughness can then be determined fromsimple measurement of crack length.

Figure 14. Schematic of Vickers indentation with radial cracks.

In microindentation, cracks at relatively high indentation loadsof several hundred grams are on the order of 100 m in length, andcan be measured optically. However, to measure toughness of verythin films or small volumes, much smaller indentations are required.However, a problem exists in extending the method to nanoindentationregime in that there are well defined loads, called cracking thresh-olds, below which indentation cracking does not occur in most brittlematerials.[169] For a Vickers indenter, cracking thresholds in mostceramics are about 25 g. Pharr, et al.[232] have found that Berkovichindenter, (a three-sided pyramid) with the same depth-to-area ratio asa Vickers indenter, (a four-sided pyramid) has a cracking of thethresholds very similar to that of the Vickers indenter. They showedthat cracking thresholds can be substantially reduced by using sharpindenters, i.e., indenters with smaller included tip angles, such as athree-sided indenter with the geometry of the corner of a cube.Studies using a three-sided indenter with the geometry of a corner of


a cube have revealed that cracking thresholds can be reduced to loadsas small as 0.5 g, for which indentations and crack lengths in mostmaterials are submicron in dimension.

Based on fracture mechanics analysis, Lawn, et al.[174] devel-oped a mathematical relationship between fracture toughness andindentation crack length given as,

Eq. (21)

= 2/3

2/1

c

WHEBK IC

where W is the applied load and B is an empirical constant dependingupon the geometry of the indenter, (also see Refs. 172 and 232).Antis, et al.[18] conducted a study on a number of brittle materialschosen to span a wide range of toughness. They indented with aVickers indenter at several loads, and measured crack length opti-cally. They found a value of B = 0.016 to give good correlationbetween the toughness values measured from the crack length, andthe ones obtained using more conventional methods. Mehrotra andQuinto[196] used a Vickers indenter to measure fracture toughness ofthe coatings. Pharr, et al.[232] tested several bulk ceramics listed inTable 4 using Vickers, Berkovich, and cube corner indenters. Theyfound that the fracture toughness equation can be applied for the dataobtained with all three indenters, provided a different empiricalconstant was used for a cube corner indenter. The constant B forVickers and Berkovich indenter was found to be about 0.016 and forcube corner it was about 0.032. Pharr, et al.[232] further reported thatpredominant cracks formed with Vickers or Berkovich indenters arecone cracks, and with cube corner indenter, predominant cracks wereradial cracks, Fig. 15.


Chantikul et al.[79] developed a relationship between fracturetoughness and the indentation fracture strength and the applied load

Eq. (22)43

318

1

= W

HE

cK fcI

where is the fracture strength after indentation at a given load andc is an empirical constant (0.59). Advantage of this analysis is thatthe measurement of crack length is not required. Mecholsky et al.[194]used this analysis to calculate fracture toughness of diamond filmson silicon. They indented the films at various indentation loads of 3to 9 kg, and then fractured in four point flexure to measure fracturestrength. The data was then used to get fracture toughness. Equation(22) was found to hold for the measurements. They reported afracture toughness of 6 and 12 m thick diamond films on silicon onthe order of 2 MPa m .

Chaing et al.[81] developed a relationship for fracture toughnessof the coating/substrate interface, which can be used as a measure ofindentation adhesion of the coatings. This analysis is presented lateron in the section on adhesion measurements.

Figure 15. Indentations in fused quartz made with the cube corner indentershowing radial cracking at indentation loads of (a) 12 g and (b) 0.45 g.[232]


Nanofatigue. Delayed fracture resulting from extended serviceis called fatigue. Fatigue fracturing progresses through a material viachanges within the material at the tip of a crack, where there is a highstress intensity. There are several situations: cyclic fatigue, stresscorrosion, and static fatigue. Cyclic fatigue results from cyclic load-ing of machine components, e.g., the stresses cycle from tension, andcompression occurs in a loaded rotating shaft. Fatigue also can occurwith fluctuating stresses of the same sign, as occurs in a leaf spring,in a dividing board. In a low flying slider in a head-disk interface,isolated asperity contacts occur during use, and the fatigue failureoccurs in the multilayered thin-film structure of the magnetic disk.[38]Asperity contacts can be simulated using a sharp diamond tip in anoscillating contact with the thin-film disk.

Li and Chu[177] developed a indentation fatigue test, calledimpression fatigue. In this test, a cylindrical indenter with a flat endwas pressed onto the surface of the test material with a cyclic loadand the rate of plastic zone propagation was measured.

Wu et al.[307] developed a nanoindentation fatigue test by modi-fying their Nanoindenter. The cyclic indentation was implementedby servo controlling the PZT stack to drive the indenter so that theloadcell output followed a 0.1 Hz sinusoidal loading pattern, and thelatter was specified by the cyclic frequency, and the lower and upperlimits for the desired load range. The lower limit for all the tests wasset at about 0.2 mN to perform a full load cycle indentation fatigue. Anonzero limit was required in order to activate the load cell servocontrol mode. Several maximum loads, namely 4, 16, and 24 mNwere used. Following results can be obtained: (i) endurance limit,i.e., the maximum load below which there is no coating failure for apreset number of cycles, (ii) number of cycles at which the coatingfailure occurs, and (iii) changes in contact stiffness measured byusing the unloading slope of each cycle which can be used to monitorthe propagation of the interfacial cracks during cyclic fatigue pro-cess. They used a conical diamond indenter with a nominal 1 m tip.Applied load and penetration depth were simultaneously monitoredduring the entire test.


Typical nanoindentation fatigue results for a 0.11-m DCplanar magnetron sputtered amorphous carbon films on (100) siliconsubstrate deposited at argon pressure of 30 m torr is shown in Fig.16.[307] The test was run at a maximum cyclic load of 4 mN and 0.1Hz for a total of 105 cycles with fracture in the 93rd cycle. SEMmicrograph of the damaged zone (Fig. 16c) shows that the plasticdeformation attributed primarily to the silicon substrate, occurred inthe central indent area, and moreover, the carbon coating spalledaround the indent, and resulted in several isolated carbon flakes aswell as cantilevered flakes. Wu et al. reported that in a singleindentation test, the critical indentation load required to crack thecarbon coating was about 6 mN. The critical indentation load wasextracted by using the criterion of the applied load at which a loaddrop appeared along a loading curve. Evidently, the endurance limitcan be significantly lower than the critical load of a single indenta-tion. This scenario is analogous to the fatigue strength versus tensilestrength in macrotests. Wu et al. further reported that the carbonfilms deposited at a argon pressure of 6 m torr exhibited endurancelimit of about 24 mN, about a factor of six higher than the filmdeposited at 30 m torr. Scratch resistance of the film at 30 m torr wasalso poorer as compared to that deposited at 6 m torr.[302][305][306]

Adhesion Strength Measurements. For measurement of ad-hesion strength of the coating-substrate interface using indentationmethod, the coating sample is indented at various loads. At lowloads, the coating deforms with the substrate. However, if the load issufficiently high, a lateral crack is initiated and propagated along thecoating-substrate interface. The lateral crack length increases with theindention load. The minimum load at which the coating fracture isobserved is called the critical load, and is employed as the measure ofcoating adhesion (Fig. 17). For relatively thick films, the indentationis generally made using Brinell hardness tester with a diamond sphereof 20 m radius,[278] Rockwell hardness tester with a Rockwell C120o cone with a tip radius of 200 m,[196] or a Vickers pyramidalindenter.[5][81][180] However, for extremely thin films, a Berkovichindenter,[263] or a conical diamond indenter with a tip radius of 5 mmand 30 of included angle,[285] is used in a nanoindenter.


Figure 16. Typical microindentation fatigue results from 0.11-m thick dcsputtered amorphous carbon on (100) Si, (a) the direct outputs from a strip chartrecorder of applied load (LC) and indenter position (IND) (Maximum load = 4mN, frequency = 0.1 Hz), (b) a plot of the indentation fatigue loading curveversus total penetration depth (the plot includes only the load cycles from 91 to100; note the abrupt depth increase started from the 93rd cycle) and (c) SEMmicrograph of the fatigue indent.[307]

Figure 17. Schematic illustration of the indentation method for adhesionmeasurement.

(b) (c)

(a)


It should be noted that the measured critical load Wcr is afunction of hardness and fracture toughness in addition to the adhe-sion of coatings. Chiang et al.[81] have related the measured cracklength during indentation, the applied load and critical load (at whichcoating fracture is observed) to the fracture toughness of the sub-strate-coating interface. A semianalytical relationship derived be-tween the measured crack length c and the applied load W:

Eq. (23) 4/12/1

1 WWW

c cr

=

where ( )interface2/12/3

12

Ic

c

KHt

=

1 is a numerical constant, tf is the coating thickness, H is the meanhardness and (KIc)interface is the fracture toughness of the substrate-coating interface. Mehrotra and Quinto[196] used this analysis tocalculate fracture toughness of the interface.

Marshall and Oliver[184] estimated adhesion of composites bymeasuring the magnitude of shear (friction) stresses at fiber/matrixinterfaces in composites. They used a Berkovich indenter to push onthe end of an individual fiber and measured the resulting displace-ment of the surface of the fiber below the matrix surface (due tosliding). The shear stress was calculated from the force-displacementrelation obtained by analysis of the frictional sliding. The force anddisplacement measurements were obtained only at the peak of theload cycle, and the sliding analysis was based on sliding at constantshear resistance at the interface. These experiments provided mea-surements of average shear stresses at individual fibers.


2.5 Scratch Resistance/Adhesion Measurements

Macro-, micro-, and nanoscratch techniques are used to mea-sure scratch resistance of surfaces from bulk materials to a fewnanometer thick films. Adhesion describes the sticking together oftwo materials. Adhesion strength, in practical sense, is the stressrequired to remove a coating from a substrate. Indentation, describedearlier, and scratch on micro-and nanoscales are the two commonlyused techniques to measure adhesion of thin hard films with goodadhesion to the substrate (>70 MPa).[37][46][60][76][199]

Scratching the surface with a fingernail, or a knife, is probablyone of the oldest methods for determining the adhesion of paints andother coatings. Scratch tests to measure adhesion of films was firstintroduced by Heavens.[139] A smoothly round chrome-steel styluswith a tungsten carbide, or Rockwell C diamond tip (in the form of120 cone with a hemispherical tip of 200 mm radius),[196][223][224][261][287] or Vickers pyramidal indenter,[70][73] for macro-andmicroscratching a conical diamond indenter (with a 1 m or 5 m oftip radius and 60 of included angle), for nanoscratching[56][131][132][302][305][306] is drawn across the coating surface. A vertical load isapplied to the scratch tip, and is gradually increased during scratch-ing until the coating is completely removed. The minimum or criticalload at which the coating is detached or completely removed is usedas a measure of adhesion.[2][30][70][73][76][80][119][147][149][153][170][196][199][223][225][253][261][287][288][299][301][302][305][306]

It is a most com-monly used technique to measure adhesion of hard coatings withstrong interfacial adhesion (>70 MPa).

For a scratch geometry shown in Fig. 18, surface hardness H isgiven by

Eq. (24) 2aWH cr

=

and adhesion strength t is given by[30]


Eq. (25a) t = H tan

( )

= 21222 /cr

aRa

a

W

or

Eq. (25b) aRRaWcr >> if =

where Wcr is the critical normal load, a is the contact radius and R isthe stylus radius.

Figure 18. Geometry of the scratch.

Burnett and Rickerby,[73] and Bull and Rickerby[70] analyzedscratch test of a coated sample in terms of three contributions: (i) aploughing contribution, which will depend on the indentation stressfield, and the effective flow stress in the surface region, (ii) anadhesive friction contribution due to interactions at the indenter-sample interface, and (iii) an internal stress contribution since anyinternal stress will oppose the passage of the indenter through thesurface, thereby effectively modifying the surface flow stress. Theyderived a relationship between the critical normal load Wcr and thework of adhesion Wad


Eq. (26)21

2 22

=

t

EWaW adc

where E is the Youngs modulus of elasticity and t is the coatingthickness. Plotting of Wc as a function of a2/t1/2 should give a straightline of the slope (2EWad/t)1/2/2 from which Wad can be calculated.Bull and Rickerby suggested that either the line slope (interfacetoughness) or Wad could be used as a measure of adhesion.

An accurate determination of critical load Wcr sometimes isdifficult. Several techniques, such as (i) microscopic observation(optical or scanning electron microscope) during the test, (ii) chemi-cal analysis of the bottom of the scratch channel, (with electronmicroprobes) and (iii) acoustic emission, have been used to obtainthe critical load.[149][223][224][253][261][287][302][306] The acoustic-emis-sion technique has been reported to be very sensitive in determiningcritical load. Acoustic emission starts to increase as soon as cracksbegin to form perpendicular to the direction of the moving stylus. Insome instruments, tangential (or friction), force is measured duringscratching.[16][55][57][131][133][147][287][301][302][306] An instant increasein the friction force during scratch has also been used as an indicatorof a damage event.

Apparatuses For Scratch Measurements On Macroscale.Several macroscratch testers are commercially available, such as theTaber shear/scratch tester model 502 with a no. 13958 diamondcutting tool (manufactured by Teledyne Taber, North Tonawanda,NY) for thick films, Revetest automatic scratch tester (manufac-tured by Centre Suisse dElectronique et de Microtechnique S.A.,CH-2007, Neuchatel, Switzerland), and scratch tester with frictionforce attachment (manufactured by VTT, Technical Research Centerof Finland, Espoo, Finland) for thin films.[223][224][253][261][288] Of allthe macroscratch testers available commercially, Revetest is usedmost extensively by numerous research groups to study the adhesioncharacteristics of hard coatings.


Revetest automatic scratch tester is shown schematically inFig. 19. This tester has a Rockwell C diamond tip with a cone angleof 120, and a tip radius of about 200 m. Normal load is appliedthrough a spring loaded arm in steps of 1 N up to a maximum of 200N. This tester was further modified by replacing-loaded arm with anelectromagnetic coil to operate at lower load of 10 mN to 30 N witha detection sensitivity of 10 mN. This tester is equipped with anacoustic emission detector, and a device which enables the tangentialforce in the direction of displacement to be measured. Damage at thecoating-substrate interface usually results in an increase in frictionforce, and a generation of an acoustic emission signal.

Figure 19. Schematic illustration of the scratch method for adhesion measurement.

An example of a scratch test, optical micrographs of typicalfailure mode of sputtered TiN coating on a steel substrate are pre-sented in Fig. 20a. The acoustic emission curves showing the maxi-mum and minimum signals are plotted as a function of stylus load inFig. 20b. As the stylus load was increased to 7.8 N, the coatingstarted to crack perpendicular to the steel surface at the edge of thechannel. The onset of coating damage was accompanied by a suddenincrease in acoustic emission at loads greater than 7.8 N (region b inFig. 20b). The very high normal load can cause the detached coatingparticles either to the completely pressed back into the substrate or bepartially removed, thus leaving a smooth surface within the channel.


Figure 20. (a) Optical micrographs of channels produced during scribing fromright to left under various stylus loads in Crofer 1700 coated with sputteredTiN about 1.5 m thick. (b) Acoustic emission signal maxima and minimataken from the curves recorded within the scratch channel length between 0.5and 2.5 mm.[149]

(b)

(a)


Apparatuses For Scratch Measurement On Microscale. Inprinciple, the microscratch testers are quite similar to those used formacroscratch but only with a difference in the normal load and sizeand radius of the diamond tip. In the microscratch testers, usually thenormal load ranges from a few hundred N to a few tens of mN andtips radii varies from about 100 nm to a couple of microns. Aprototype microscratch tester was developed by Wu et al.[307] at IBMAlmaden Research Center by modifying a nanoindenter. With thisinstrument, following measurements can be made simultaneouslyduring a scratch test: applied load and tangential load along thescratch length (coefficient of friction), critical load, i.e., appliednormal load corresponding to an event of coating failure during ascratch process, total and plastic depth along the scratch length, theaccumulated acoustic emission (AE) counts versus the scratch length.The commercially available Nanoindenter, described earlier, hasalso been modified for making microscratch measurements.

We describe the microscratch and tangential force attachmentsof Nanoindenter which allows making of the scratches of variouslengths at programmable loads. Tangential (friction) forces can alsobe measured simultaneously.[16][56] The additional hardware for thetangential force option includes a set of proximity (capacitance)probes for measurement of lateral displacement or force in the twolateral directions along x and y, and a special scratch collar whichmounts around the indenter shaft with hardness indenter, Fig. 21.The scratch collar consists of an aluminum block, mounted aroundthe indenter shaft, with four prongs descending from its base. Two ofthese prongs hold the proximity probes, and the set screws set themin place, while the other two prongs hold position screws (andcorresponding set screws). The position screws serve a dual purpose;they are used to limit the physical deflection of the indenter shaft,and they are used to lock the indenter shaft in place during tip changeoperations. A scratch block is mounted on the end of the indentershaft, in line with the proximity probes and the positioning screws.Finally, the scratch tip itself is mounted on the end of the indentershaft, covering the scratch tip. The scratch tip is attached to the


scratch block with two Allen head screws. The scratch tip can be aBerkovich indenter, or a conventional conical diamond tip with a tipradius of about 1 to 20 m, and an included angle of 60 to 90(typically 1 m or 5 m of tip radius with 60 of includedangle.)[56][131][133][302][306] The tip radius does not have to be verysmall as it will get blunt readily.

Figure 21. Schematic of the tangential force option hardware (not to scale andthe front and rear prongs not shown).[16]

During scratching, a load is applied up to a specified indenta-tion load or up to a specified indentation depth, and the lateral motionof the sample is measured. In addition, of course, load and indenta-tion depth are monitored. Scratches can be made either at the con-stant load, or at ramp up load. Measurement of lateral force allowsthe calculations of coefficient of friction during scratching. Theresolution of the capacitance proves to measure tangential load isabout 50 N, therefore, a minimum load of about 0.5 mN can bemeasured, or a minimum normal load of about 5 mN should be usedfor a sample with coefficient of friction of about 0.1. Microscopy ofthe scratch produced at ramp up load allows the measurement ofcritical load required to break up of the film (if any) and scratchwidth, and general observations of scratch morphology. Additional


parameters which are used to control the scratch are scratch length(m), draw acceleration (m/s2), and draw velocity (m/s). Thelatter parameters control the speed with which the scratch is per-formed. The default values of 10 m/s2 and 10 m/s provide saferates for performing the scratch. Draw velocity is limited by themaximum rate of data acquisition (during a scratch the maximumrate is approximately 2/s) and the length of the desired scratch. Thus,a scratch with a desired 20 points over 1 mm must have a drawvelocity no greater than 100 m/s.

Wu[302] has used the scratch technique to study the adhesion ofdiamondlike carbon and zirconia films deposited on Si(100) sub-strates. Figure 22 shows the scratch morphology at increasing nor-mal loads, and typical scratch data (normal load, tangential load andacoustic emission, as well as calculated apparent coefficient offriction). We note that all three monitored outputs (LC, TG, and AE),detected the first spallation event of the carbon coating by showingsudden changes in their output signals. Correlation between thedelamination pattern and the sudden change in the scratch loading isclearly observed.

Figure 22. Scratch morphology and scratch loading curves of 0.11-m thickd-c sputtered diamondlike carbon film on a Si substrate.[302]


Gupta and Bhushan[132] measured scratch depths duringscratching and residual depth after scratching. The surface profile ofthe coated surface was first obtained by translating the sample at alow load of about 1.5 mN, which is insufficient to damage the samplesurface. The actual scratches were made by translating the samplewhile ramping the loads on the conical tip over different loads, forinstance ranging from 1.5 mN to 45 mN. The actual depth duringscratching was obtained by subtracting the initial profile from thescratch depth measured during scratching. In order to measure per-manent depth, the scratched surface was profiled at a low load of 1.5mN and was subtracted from the surface profile before scratching. Atypical scratch experiment consisted of seven subsequent steps:

1. Approaching the surface.2. Indent into sample surface by loading the tip to

1.5 mN.3. Translating the sample at a constant load of 1.5 mN

at a speed of 5 microns per second.4. Translating the sample in the opposite direction at

ramping load to a load ranging from 1.5 to 45 mN ata speed of 5 micron per second.

5. Unloading of the tip to 1.5 mN.6. Translating the sample at constant load of 1.5 mN

at a speed of 5 micron per second.7. Final unloading of the tip.

The 500-micron long scratch at ramping normal load was madeduring the fourth step, and surface profiles before and after scratchwere obtained during the third and sixth steps, respectively. Thescratch depth profiles obtained during and after the scratch of 20 nmthick carbon coatings deposited on silicon by cathodic arc, andsputtering are plotted with respect to initial profile after thecylindrical curvature is removed, Fig. 23. Reduction in scratchdepth after scratching is observed in Fig. 23. The reduction inscratch depth after scratching is attributed to an elastic recovery


after the removal of the normal load. It appears that the scratch depthafter scratching indicates the final depth which reflects the extent ofpermanent damage and ploughing of the tip into the sample surface.We believe that the scratch depths after scratching are probably morerelevant for visualizing the damage that can occur in real applica-tions. The abrupt increase in the coefficient of friction and scratchdepth is associated with damage to the coating. The cathodic arccoating exhibits an almost constant low coefficient of friction ofabout 0.10.15 during the initial stages and an abrupt increase infriction when normal load exceeds the critical load, the load suffi-cient to damage the coating. Sputtered carbon coating exhibits agradual increase in the coefficient of friction with increasing normalload from the beginning of the scratch.

Figure 23. Coefficient of friction profile during scratching and scratch depthduring and after scratching as a function of normal load for scratches made on20 nm thick carbon coatings deposited on silicon by cathodic arc and sputteringdeposition techniques.[132]


Bulk Si exhibits a very low coefficient of friction of 0.05 at thebeginning of a scratch at 2 mN, Fig. 24. The coefficient of frictionremains constant up to 4 mN. The coefficient of friction increasesabruptly from 0.05 to 0.15, and then gradually increases to 0.25, asthe normal load increased from 4 to 18 mN, and to 0.9 when the loadexceeded 18 mN. Particulate debris of submicron size was observedwhen the normal load exceeded 18 mN. First abrupt increase infriction corresponds to an initiation of ploughing of the siliconsurface by the tip, whereas the second abrupt increase in frictioncorresponds to a catastrophic damage of the surface.

Figure 24. SEM images of various regions and coefficient of friction profiles asa function of normal load for 500 m long scratches made on single-crystalsilicon (111) at 2 to 20 mN.[56]


The dependence of coefficient of friction on increasing normalload and shape and size of debris generated during scratching can beused to obtain important information regarding the adhesion of thecoating with the substrate, and how the coating or sample surface isdamaged during scratching.

Apparatuses For Scratch Measurement On Nanoscale.Nanoscratch measurements were made by Bhushan et al.[53] andBhushan[40] using a modified commercial AFM/ FFM (NanoscopeIII from Digital Instruments, Inc. Santa Barbara, Calif.). The modi-fied AFM/ FFM will be described later on in the next section, on themeasurements of friction and wear on nanoscale. The scratches weremade by a three-sided pyramidal diamond tip with a tip radius ofabout 100 nm at normal loads ranging from 10 to 100 N. Samplesurfaces were scanned before and after the scratch to obtain theinitial and the final surface topography at a load of about 0.05 N,over an area larger than the scratches region. AFM images of scratchesmade on (111) silicon, PECVD-oxide coated silicon, dry-oxidizedsilicon, and C+ implanted (1 10-17 ions cm-2 at 100 keV) silicon areshown in Fig. 25.[51] As expected, the scratch depth increases with anincrease in normal load. The depths of scratches at 40 N onPECVD-oxide coated silicon and (111) silicon are about 5 and 20nm, respectively. PECVD-oxide coated silicon has the largest scratchresistance followed by dry-oxidized silicon and ion-implanted sili-con. Ion implantation showed no improvements on scratch resis-tance because the depth of the scratches is lower than the depth ofimplanted zone beneath the surface.

This study demonstrates that scratches with a depth of a fewnanometers can be made at very low loads using AFM/ FFM. Thishelp characterizing the scratch resistance/ adhesion of top few toptens of monolayers of bulk materials or coating of the order of a fewnanometers thickness.


Figure 25. Surface profiles for scratched (a) (111) single-crystal silicon, (b)PECVD-oxide coated Si, (c) dry-oxidized Si and (d) C+-implanted Si. The loadsused for various scratches at ten cycles are indicated in the plot.[51]


3.0 MEASUREMENT OF FRICTION AND WEAR

Friction and wear between two moving surfaces depends onmechanical properties of the mating materials such as: hardness, elasticmodulus, fracture toughness; other physical and chemical propertiessuch as: thermal conductivity, surface energy, adsorption character-istics, chemical reactivity; surface conditions such as: roughness andapparent area of contact; and operating conditions such as: load, speed,interface temperature, and environment. Various friction mecha-nisms such as adhesion and ploughing, that contribute to friction andwear, are strongly affected by the properties of mating surfaces andoperating conditions. Surface roughness of mating surfaces and areaof contact between these surfaces play a key role in deciding friction.For instance, rigid thin-film magnetic disk are deliberately rough-ened to reduce the area of contact to obtain lower friction between ahead slider and the magnetic disk. The friction and wear tests shouldbe performed under the close-to-ideal conditions. The conditions andtest geometry for friction and wear tests should be selected on thebasis of the actual operating conditions of the components.

With the advent of new surface imaging tools like atomic forcemicroscope (AFM), friction force microscope (FFM), and pointcontact microscope (PCM), it is possible to perform friction tests atultra small loads of a couple of N against a sharp tip of about 10 to100 nm tip-radius which simulates a single-asperity contact condi-tions.[39][40][58] Sliding tests with a single-asperity contact are moreclose-to-ideal conditions of micromechanical devices, and help un-derstand the failure mechanisms.

In this section, we present the apparatuses used for friction andwear measurements on macro- to nanoscales.

3.1 Friction and Wear Measurements on Macroscale

Accelerated friction and wear tests on macroscale are con-ducted to rank the friction and wear resistance of coatings, or bulkmaterials to optimize their selection or development for specificapplications. After these coatings or bulk materials have been rankedby accelerated friction and wear tests, the most promising candidates


(typically from one to three), should be tested in the actual machineunder the actual operating conditions (functional tests). Acceleratedfriction and wear tests should accurately simulate the operatingconditions to which the material pair will be subjected. If these testsare properly simulated, an acceleration factor between the simulatedtest, and the functional tests can be empirically determined so thatthe subsequent functional tests can be minimized, saving consider-able test time. Standardization, repeatability, short testing time, andsimple measuring and ranking techniques are desirable in theseaccelerated tests. The coefficient of friction of a material, or acoating depends not only on the counterface materials, but on theoperating conditions such as speed, load, lubrication, and environ-ment. Shown in Table 1 are a couple of examples of coefficients offriction and wear rate for various bulk material and coating combina-tions. We note that with a proper selection of materials and operatingconditions, one can achieve as low coefficient of friction as 0.02between two solid materials without using any lubricant. In thissection, we will present the design methodology and typical testgeometries for friction and wear tests.

Design Methodology. Design methodology of a friction andwear test consists of four basic elements: simulation, acceleration,specimen preparation, and friction and wear measurements. Simula-tion is most critical, but no other elements should be overlooked.

Proper simulation ensures that the behavior experienced in thetest is identical to that of the actual system. A successful simulationrequires the similarity between the functions of actual system, andthose of the test system, i.e., similarity of inputs and outputs, and ofthe functional input-output relations. To obtain this similarity, firstthe mating materials, the lubricant, and the operating conditions ofthe test should be the same as the actual system requirements.Selection of the contact geometry depends on the geometry of thefunction to be simulated. Other factors besides contact type thatsignificantly influence the success of a simulation include type ofmotion, load, speed, and operating environment (contamination,lubrication, temperature, and humidity). Specimen preparation playsa key role in obtaining repeatable/reproducible results.


Table 1. Typical Values of Coefficients of Friction for SelectedMaterials and Coatings in the Ambient Environments (~ 22C, 50%RH) Unless Otherwise Specified[46][64][142][227]

Materials pairBulk Counterface material Coefficient of frictionmaterial/Coatingand Substrate

Bulk materials

Aluminum Aluminum 1.0

Copper Copper 0.8

Silver Silver 0.9

Brass Brass 0.4Cast iron Cast iron 0.6

Mild steel 0.4Brass 0.25Bronze 0.25Copper 0.3

Mild steel Mild steel 0.8Aluminum 0.5Nickel 0.7Silver 0.5Copper 0.8Brass 0.3Bronze 0.3Babbitt 0.3Graphite 0.15PTFE 0.1

Tool steel Tool steel 0.4Brass 0.25Polyethylene 0.25PTFE 0.1

Nickel Nickel 1.1

Chromium Chromium 0.4

Silicon nitride Silicon nitride 0.3 (Contd.)


The coefficient of friction is generally measured during a weartest. It is calculated from the ratio of friction force to applied normalforce. The stationary member of the material pair is mounted on aflexible member, and the frictional force is measured using the straingauges or displacement gauges.[36][38] Common wear measurementsare weight loss, volume loss, or displacement scar width or depth, orother geometric measures, and indirect measurements such as, time

Table 1. (Contd.)

Materials pairBulk Counterface material Coefficient of frictionmaterial/Coatingand SubstrateTungsten carbide Tungsten carbide 0.35

Steel 0.4Natural diamond Natural diamond 0.05

PTFE PTFE 0.05Coatings/Surfacetreatments

MoS2 (Sputtered) Steel 0.050.1 (Ambient)WC-Co 0.02 (Vacuum)

Graphite (air sprayed) Steel 0.10.2 (Ambient)0.40.6 (Dry)

PTFE (Air sprayed) Steel 0.030.1Silver/Gold (Sputtered) Steel 0.10.25Al2O3 (CVD) Steel 0.20.5TiN (Sputtered) Steel 0.150.5TiC(Sputtered) Steel 0.20.5Diamond(HFCVD)/Si Steel 0.10.2a-C:H (Sputtered) Steel 0.150.3a-C:H (PEPVD) Steel 0.150.3


required to wear through a coating or load required to cause severewear, or a change in the surface finish, size of indentation marks, orwidth and depth of scratches. Scanning electron microscopy of wornsurfaces is commonly used to measure microscopic wear. Other lesscommonly used techniques include radioactive decay, scanning tun-neling microscopy (STM), and atomic force microscopy (AFM).The resolution of various macroscopic wear measurement tech-niques are compared in Table 2.

Table 2. Resolution of Several Macroscopic Wear MeasurementTechniques

Typical Test Geometries. The choice of a test geometrydepends on the wear situation to be simulated. In this section, we willpresent a few most commonly used test geometries to rank coatingsand materials in terms of their resistance to sliding wear, and rollingcontact fatigue wear. However, depending on the requirements, testscan be performed with replicas and facsimiles of the actual devices.Many accelerated test apparatuses are commercially available thatallow control of such factors as sample geometry, applied load,sliding velocity, ambient temperature, and humidity. Bayer,[24][27]


Benzing et al.[31] Bhushan,[37][38] Bhushan and Gupta,[46] Clauss,[87]Nicoll,[209] and Yust and Bayer[313] have reviewed the various fric-tion and wear testers that have been used in various tribologicalapplications.

Sliding Friction And Wear Tests. In the sliding wear testconfigurations, ball, pin, cylinder, or ring of one material slides overthe disk, block, or cylinder of another material in the presence orabsence of a lubricant. The most commonly used interface geom-etries used to rank coatings and materials in terms of their resistanceto sliding wear are schematically shown in Fig. 26, and are comparedin Table 3. With these test geometries, static, or dynamic loading canbe applied, and the tests can be performed either in the presence orabsence of a lubricant. In the pin-on-disk test apparatus (Fig. 26a),the pin is held stationary, and the disk rotates or oscillates. The pincan be a non rotating ball, a hemispherically tipped rider, a flat-endedcylinder, or even a rectangular parallelepiped. In the pin-on-flat testapparatus (Fig. 26b), a flat moves relative to a stationary pin inreciprocating motion, such as in a Bowden Leben apparatus. Thepin-on-cylinder test apparatus (Fig. 26c), is similar to the pin-on-diskapparatus, except that loading of the pin is perpendicular to the axisof rotation or oscillation. In the thrust-washer test apparatus (Fig.26d), the flat surface of a washer (disk or cylinder) rotates oroscillates on the flat surface of a stationary washer, such as in theAlpha model LFW-3. In the pin-into-bushing test apparatus (Fig. 26e),the axial force necessary to press an oversized pin into a bushing ismeasured, such as in the Alpha model LFW-4. The normal (axial)force acts in the radial direction, and tends to expand the bushing; theradial force can be calculated from the material properties, theinterference, and the change in the bushings outer diameter. Divid-ing the axial force by the radial force gives the coefficient of friction.In the rectangular flat, on a rotating cylinder test apparatus (Fig. 26f),two rectangular flats are loaded perpendicular to the axis of rotationor oscillation of the disk. The crossed cylinders test apparatus (Fig.26g), consists of a hollow (water cooled) or solid cylinder as thestationary wear member and a solid cylinder as the rotating or


oscillating wear member that operated at 90o to the stationary mem-ber, such as in Reichert wear tester. The four ball test apparatus (Fig.26h), also called the Shell four-ball tester, consists of four ball in theconfiguration of an equilateral tetrahedron. The upper ball rotatesand slides against the lower three balls, which are held in a fixedposition. This test configuration is extensively used to study liquidlubricants.

Figure 26. Schematic illustration of typical interface geometries used for slidingfriction and wear tests: (a) pin-on-disk, (b) pin-on-flat, (c) pin-on-cylinder, (d)thrust washer, (e) pin-into-bushing, (f) rectangular flats on rotating cylinder, (g)crossed cylinders and (h) four ball.[46]


Rolling-Contact Fatigue Wear Tests. A number of rolling-contact fatigue (RCF) tests are used for testing materials and lubri-cants for rolling-contact applications such as rolling element bear-ings, and gears. In RCF test apparatus, basically a pair of drivenrollers are pressed against one another, and the surface damage onroller surfaces is monitored with the number of cycles. The surfacedamage could be the appearance of cracks, change in surface textureor roughness, or spalling of material. In general, rolling-contactfatigue (RCF) wear is compared in terms of number of cyclessufficient to result a specific damage on the rollers. The most com-monly used interface geometries used to rank coatings and materialsin terms of their resistance to rolling-contact fatigue wear are sche-matically shown in Fig. 27. The disk-on-disk test apparatus (Fig.27a) uses two disks or a ball-on-disk rotating against each otheron their outer surfaces (edge loaded). The rotating four ball test

Table 3. Details of Typical Test Geometries for Sliding Friction andWear Testing


apparatus (Fig. 27b) consists of four balls in the configuration of anequilateral tetrahedron. The rotating upper ball is deadweight loadedagainst the three supporting balls (positioned 120 apart), whichorbit the upper ball in rotating contact. The rolling-element-on-flattest apparatus consists of three balls or rollers equispaced by a retainerthat are loaded between a stationary flat washer and a rotatinggrooved washer (Fig. 27c). The rotating washer produces ball mo-tion, and serves to transmit load to the ball and the flat washer.[42]

Figure 27. Schematic illustration of typical interface geometries used forrolling-contact fatigue wear tests: (a) disk-on-disk, (b) rotating four ball, (c)balls-on-flat.[46]

3.2 Friction and Wear Measurements on Micro- and Nanoscale

Friction and wear measurements on a micro-to nanoscale canbe performed using a nanoindenter in scratch mode which wasdescribed earlier, or an atomic force microscope, or friction force


microscope.[41][58][185] The coefficient of friction can be measuredusing a nanoindenter in the scratch mode by monitoring the frictionforce during scratching at low loads on the order of a few hundredmicroNewtons. The selection of the normal load should be such t

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Mechanical Systems Design Handbook