characterisation of the scratch deformation mechanisms for poly(methylmethacrylate) using surface...

Polymer International 43 (1997) 359È367

Characterisation of the ScratchDeformation Mechanisms for

Poly(methylmethacrylate) using SurfaceOptical Reflectivity*

B. J. Briscoe,¹ E. Pelillo & S. K. Sinha

Department of Chemical Engineering and Chemical Technology, Imperial College of Science, Technology and Medicine, PrinceConsort Road, London SW7 2BY, UK

(Received 29 October 1996 ; revised version received 10 December 1996 ; accepted 24 January 1997)

Abstract : A novel technique using surface local optical reÑectivity measurementsfor characterising the modes of surface mechanical damage of polymers isdescribed. The technique utilises the sensed laser reÑectivity of polymer surfaces,after damage, as a means of measuring the relative extent of brittle and plasticdeformation modes for polymers. The polymeric surface used in this paper is acommercial poly(methylmethacrylate). The surface damage is produced byscratching with rigid conical indenters under di†erent contact conditions ofstrain and load. The results show that the local optical reÑectivity of a surfacedepends upon the topography of the surfaces, which varies for di†erent modes ofdeformation. The reÑectivity of a brittle fractured surface is signiÐcantly lower incomparison with that for a plastically deformed surface.

Polym. Int. 43, 359È367 (1997)No. of Figures : 10 No. of Tables : 0 No. of References : 11

Key words : scratching technique, laser reÑectivity, deformation mechanisms.

INTRODUCTION

The uses of polymers for optical purposes such aslenses, wind panels, casings, smooth and glossy surfacesare very numerous. The optical properties required forsuch applications are transparency and reÑectivity,which depend upon the bulk intrinsic optical propertiesof the material and the topographical features on thesurface, such as the roughness and the presence ofscratches. The optical working life of these polymersoften depends entirely upon the surface mechanicalproperties, such as the scratch resistance and the modesof possible material deformation. The scratch resistance

* Presented at “The Cambridge Polymer Conference : Partner-ship in PolymersÏ, Cambridge, UK, 30 SeptemberÈ2 October1996.¤ To whom all correspondence should be addressed.

indicates the ability of the material to withstand abra-sive interactions with another body. The mode of defor-mation indicates the type of deformation, mainly brittleor plastic, that may occur on the surface of the polymerduring such interactions. Polymers show a very widerange of deformation modes within a relatively narrowrange of contact variables such as temperature, strain,strain rate and severity of the contact deformation.Generally, brittle fracture on the surface causes mostdamage to the material, in terms of its optical features,in comparison with plastic deformation. This impliesthat a brittle scratch makes the surface more unevenand fragmented owing to the production of fractures1and this results in a rather pronounced scattering e†ectof the light from the surface. In contrast, plastic deform-ation produces less severe damage and a fairly evensurface is observed after the contact. Thus, the opticalreÑectivity of the surface changes according to the type

3591997 SCI. Polymer International 0959È8103/97/$17.50 Printed in Great Britain(

360 B. J. Briscoe, E. Pelillo, S. K. Sinha

of deformation produced during scratching. Hence, theoptical reÑectivity data from the surface of a polymermay be used to identify and, to a large extent, quantifythe mode of deformation the material has undergoneduring any surface interaction. This procedure may alsobe used to monitor the optical life of a polymer com-ponent or to study the optical behaviour of a polymerwhen it is in contact with another relatively hardmaterial. Information on the factors inÑuencing theductile to brittle transition is also required for estimat-ing the mechanical working life of polymer componentsused for engineering applications and, in particular, intribological applications.

In this paper, a reÑectivity measurement technique ispresented for identifying and quantifying the modes ofdeformation on a commercial grade poly(methyl-methacrylate) (PMMA) when the surface of the PMMAis scratched by rigid conical indenters of varyingincluded angle, a, and under di†erent normal loads (Fig.1). This polymer experiences a change in the deforma-tion mode from brittle fracture to ductile ploughingwhen the indenter included angle is increased or whenthe applied normal load is decreased. The mode ofdeformation during scratching depends primarily uponthe attack angle, h, and the depth of the scratch, h (seeFig. 1). The reÑectivity data obtained from the scratchedsurface region are analysed using an established sta-tistical method.

Laser profilometry and reflectivity measurements

The reÑectivity of an interface separating two di†erentmedia may be deÐned as the property by which it re-Ñects any incident light back into the same medium.The amount and the characteristics of the spatial reÑect-ed light depend upon the wavelength, the polarisationand the angle of incidence of the incident beam, as wellas the material properties of the second medium (e.g.the characteristic velocity of light within that medium,electrical conductivity) and the geometry of the surface(e.g. gloss, lustre, roughness). For example, polishedmetals (e.g. silver, aluminium, gold) are the best reÑec-tors and may reÑect nearly 100% of incident lightbeams along a predictable and focused direction. This is

Fig. 1. A schematic section through the central axis of ascratch to deÐne the various contact mechanics variables :a \ cone angle ; h\ depth of penetration ; h \ attack angle.

found to be associated with their ability to conduct elec-tricity.2 On the other hand, very rough surfaces mayshow scatter and multiple reÑection e†ects,3 which dis-perse part of the beam along di†erent directions.However, regular reÑection, that is reÑection in theabsence of scattering e†ects, is encountered on surfaceswhere the geometrical irregularities (roughness, wavi-ness, etc.) are small compared with the wavelength ofthe light.

Polymers show a range of common optical propertiessuch as transparency, translucency, opaqueness andreÑectivity. Because of this variety in optical response ofpolymers, they are used for many optical purposes.

If we consider the case of a fairly rough sample, at amicroscopic level of observation this is characterised bya number of grooves on the surface. A transverse sec-tion would therefore show a series of irregular peaks andvalleys characterised by di†erent slopes. According tothe grade of roughness, the slopes may vary frequentlyand dramatically along the surface proÐle considered.If such a rough surface is impinged normally by a lightbeam, single rays may be reÑected along di†erent direc-tions, each particular slope region behaving, at a micro-scopic level, as a single reÑecting surface. In this case,some of the light is back-scattered directly towards thesource and a fraction is scattered o† the incident direc-tion (see Fig. 2). Thus, a partial loss in reÑectivity, alongthe incident direction, is observed.

In conclusion, the reÑectivity of a surface is a functionof the local topography at a microscopic level and ittherefore varies from point to point, according to thespatial resolution of the scanner and the wavelength ofthe beam. The net surface reÑectivity may be readilyexpressed in statistical terms of average topographicalquantities and cumulative distributions for the entire

Fig. 2. The phenomenon of multiple scattering of a lightbeam upon an ideal rough surface ; the slopes are exaggerated

compared with real roughness.

POLYMER INTERNATIONAL VOL. 43, NO. 4, 1997

Characterisation of scratch deformation mechanisms 361

variety of the topographical features over a selectedarea of the surface.

In general, mechanical damage on a surface, such asplastic deformation and brittle fracture, changes thetopography and, therefore, the reÑectivity of the surface.Other intrinsic optical properties of the material mightbe changed because of such mechanical damage. Thepresent paper is, however, focused upon the analysis ofchanges in surface reÑectivity of polymers due toscratching deformations.

Laser proÐlometry measures the surface topographyof materials and involves the use of a non-contactinginfrared laser beam, which is focused normally upon thesurface to be scanned. Usually, the sample is movedbeneath the laser beam. The beam creates a light spot ofa certain diameter, which depends upon the type ofemitter and the numerical aperture of the lens ; the valueis typically c. 1 km. The laser beam is reÑected backfrom the surface onto a detector (see Fig. 3). Apiezoelectric motion system identiÐes the lens position,with respect to the reÑecting surface, which gives thehighest spatial back-reÑection of the laser beam. Theauto-focus system, usually comprising moving lenses,adjusts the focus on the surface by sensing themaximum reÑected light and the optical position isregistered and used as the measuring signal. Theseinstruments record both the topographical proÐle andthe percentage of light reÑected back from the surface ;the devices are usually described as “optical followersÏ.3

Fig. 3. Schematic diagram of the laser proÐlometer system.

The main di†erences between a laser proÐlometerand the mechanical stylus techniques adopted for tradi-tional surface metrological studies arise from the non-destructive nature of the laser beam. Thus the commonproblems encountered in the mechanical devices, suchas the wear of the stylus tip, the local damage of thesurfaces, tip vibrations and the low rates of data collec-tion, are avoided. However, the stylus methods usuallyhave a better resolution in the vertical direction.

One of the functional aspects that distinguishes alaser proÐlometer from any other non-optical stylus isthe capability to measure the reÑectivity of the scannedsurface, point by point, in terms of the percentage of theback-scattered beam intensity. The laser proÐlometersystem also di†ers from other reÑectance techniqueswhich are commonly adopted to measure the haze ofabraded plastics (see, for example, Ref. 4) or, in general,the optical scattering behaviour of surfaces.5 Theoptical followers are usually limited to a relativelynarrow receiver solid angle, ), of c. 24¡ (^12¡) for thepresent system, which is formed by the cone of thereÑected rays back-scattered from the focusing spot sub-tended by the receive aperture stop. Other reÑectancedevices, such as the widely adopted optical photogonio-meters, usually cover the whole range of possible lightreÑection (180¡). However, they are limited to a lowerresolution and to a planar angle of collection (see Fig.4), according to the type of detector installed. Suchoptical devices are usually based upon a static colli-mated light/laser source incident at a certain angle ontothe sample surface and with a detector unit which isrotated around the sample, from 0¡ to 180, with speedto the normal to the sample. Because of the simplicity ofthese devices, an optical photogoniometer does notallow the scanning of large surfaces in relatively shortlengths of time, and detailed interrelationships betweenlocal surface topography (e.g. within single microscopicscratch grooves) and the corresponding reÑectivity arenot easily obtainable. The static nature of the laseremitter and detector in the laser proÐlometry method is,therefore, an advantage for the examination of localisedchanges in the surface reÑectivity.

Fig. 4. Schematic comparison of the collection range of adynamic photogoniometer (c\ 180¡) and a laser proÐlometer

()\ 24¡).



Scratching of polymers

The scratching of a surface of a material by sharp rigidindenters induces complex and localised deformations.The value of the scratch hardness, which may be vari-ously deÐned, is often used as a measure of the resist-ance of a material to mechanically induced surfacedamage ; it is a common and long-established testingprocedure (see, for example, Refs 6È9). This technique iscarried out by drawing a rigid indenter of a speciÐedshape over the surface of a softer material under anapplied normal load, and the scratch hardness is usuallytaken as the ratio of normal load to a contact area esti-mated from the permanent deformation produced onthe surface. The numerical value of the scratch hardnessis primarily a measure of the plastic Ñow characteristicsand it does not incorporate a description of the kinds ofdamage the material may undergo at the surface. Thestudy of the nature of the damage characteristics is gen-erally carried out by examining the damaged areasusing optical or scanning electron microscopy. Througha subjective assessment of the nature of the damage,deformation maps may be constructed which describethe damage characteristics as a function of the contactvariables.6 These deformation maps are extremelyuseful for study of the origins of the damage processeswhich occur in polymers, and where a wide range ofdeformation characteristics may be produced duringscratching.

EXPERIMENTAL PROCEDURE

The PMMA system used in this study was a com-mercial grade of cast (ICI Acrylics, UK). ThePerspex'

average molecular weight of this system is in the orderof 1 ] 106 and the glass transition temperature, is c.Tg ,110¡C; no solvent was utilised in the casting process.The experimental procedure used in this study was asfollows. The PMMA samples were mounted on thestage of a scratching machine and levelled (see later).Scratches were produced on the surface of the PMMAsamples (initial roughness c. 0É1 km) using various rigidsteel cones and under di†erent normal loading condi-tions. No lubricant was applied to the interface betweenthe indenter and the surface. The samples were cleanedwith commercial detergents and no surface polishingwas carried out. After scratching, the specimens werecoated with a layer of gold using vacuum evaporation,and were placed beneath the laser proÐlometer for themeasurement of their topography and optical reÑect-ivity. The gold coating was applied to all samplesbefore reÑectivity measurement in order to suppress anylight di†usion into the bulk of the material. A smoothgold surface gives c. 99% reÑectivity, and hence thereÑectivity data obtained from the gold-coated surface

was a characteristic of the surface features only andindependent of the intrinsic optical properties of thematerial. The reÑectivity data for the areas inside andoutside the scratch groove were analysed separately, asthey exhibit di†erent modes of deformation during thescratching process and hence provide di†erent contribu-tions to the optical response of the surface.

Scratching machine

The scratching machine consisted of a pivoted lever armsystem upon which the indenters were Ðxed, and amotion stage where the specimens were mounted.1 Thestage was moved horizontally below the indenters at aconstant linear velocity of 0É2 mm s~1 using an electricmotor. Normal loads were applied on the indenters(steel conical indenters of included angles 45¡, 60¡, 75¡and 90¡) attached to the lever arm; the indenter wasallowed to indent the polymer specimens before thespecimen was moved. After a static indentation periodwhich was maintained for 10 s, the stage which held thespecimen was moved to produce the scratches on thepolymer surface. The normal loads used for the testsvaried between 0É03 and 2 N; these loads were main-tained constant during each experiment.

Scratch profiles and reflectivity

The optical reÑectivity of the surface was measuredusing a commercial laser proÐlometer system(Rhodenstock, Germany). This machine provides datafor surface roughness, as well as the percentage of thelight incident upon the detector system from the surfaceof the specimen after reÑection. As was explainedearlier, the measurements obtained by this non-contactmeans are based on the record of the displacement of anautomatically focusing laser beam. The beam spotdiameter is c. 1 km and the wavelength is 780 nm. Thebeam encounters the specimen sample (which is coatedwith gold) at a working distance of 10 mm and a detect-or records the intensity of the fraction of the beamreÑected back from the surface within a solid angle of c.24¡. The detector monitors any beam which reaches thedetecting lenses in a single (specular surfaces) or multi-scattered mode of reÑection (external di†usion). Thelatter e†ect is peculiar to rough surfaces. However, thecontribution of multi-scattered light to the total reÑect-ed light sensed by the detector is generally low.3

The calibration of the laser detector was performedconsidering the reÑectivity of a smooth, perfectlycleaned mirror as giving 100% reÑectivity. A plane glassÐlter was utilised for this purpose. The thickness of theglass Ðlter was varied until the laser detector recorded100% reÑectivity for a commercial mirror. A statisticalapproach, described in the next section, was employedto analyse the reÑectivity data, in order to obtain a suit-able parameter to evaluate the interrelationship



between the reÑectivity of the surfaces and the topo-graphy of the scratch deformations.

The proÐlometric scans were performed in a directionorthogonal to the scratching vector at various locationsalong the length of scratch in order to obtain a repre-sentative description of the surface. Each scan wastaken from the whole width of the scratch grooves andthe horizontal topographical resolution (scanning step)was maintained constant at 1 km.

STATISTICAL ANALYSIS

The data recorded from the reÑectivity of the scannedsurface were in the format of the percentage of theinitial intensity of the incident laser beam received bythe detector at the point of focus, that is at themaximum reÑectivity. The statistical analysis adoptedfor interpreting the reÑectivity data obtained from dif-ferently produced scratches was as follows.

The principle of the surface analysis of the reÑectivity,which was used in this study, is based upon the fact thatthe roughness of a surface is primarily responsible forthe level of its “optical glossÏ ; a lower value of thesurface roughness allows more light to be reÑected fromthe surface along a single direction (determined by thesymmetry of the incident direction). A very roughsurface scatters the light along di†erent directions,resulting in a lower intensity of the back-scattered lightobserved by a detector ; and a greater amount of dif-fused light.

The reÑectivity of scratches produced under di†erentexperimental conditions, in terms of its intensity, wasinvestigated along the surface within the scratchgrooves and also outside the grooves, thus character-ising the whole surface where any deformations due tothe scratching process were detectable. For eachscratch, the surface spatial distribution of the fre-quencies of the reÑected laser intensity was analysedover the whole reÑectivity range (0È100%). The data forthe running sum of the relative frequencies of theincreasing reÑectivities give results which are usuallydenoted as the relative cumulative frequency polygonsor percentage ogives.10 The following analysis has beenapplied to the cumulative polygons, which can be gener-ated from the frequency distributions of the surfacereÑectivity over a chosen part of the surface.

In general, a point on a relative cumulative frequencycurve gives the percentage of surface (or data) which hasbeen found to have reÑectivity intensity equal to orlower than a certain value which is read on the abscis-sae. Therefore, the area bound by the cumulative curveat a certain value of its abscissa gives a quantiÐcation ofthe surface which is characterised as having a reÑect-ivity not higher than the value indicated by the ab-scissa. The trend of cumulative curves constructed fordi†erent surfaces, and therefore, the magnitude of the

areas under the curves, may be considered as a means ofevaluating the weight that certain ranges of frequencies,obtained from the detected reÑectivity intensity, have inthe whole range of the reÑectivity spectrum.

The statistical data analysis presented in the previousparagraphs may be explained more clearly by the sche-matic diagrams described in the following. Figure 5illustrates the histogram distributions of the laser reÑec-tivities of a very rough surface (emery paper, grade 100)and for a very smooth, highly reÑecting surface (a com-mercial mirror). In both cases the scan length was c.10 mm. The frequency distribution relative to the emerypaper, though slightly skewed to the right, is relativelyspread, since the reÑectivity of the surface is not charac-terised by a single value of the intensity, but close valuesof the intensities may be found for each class interval.The relative cumulative polygon for this distribution isshown in Fig. 6. The data for emery paper in the cumu-lative curve show a greater slope in the lower intensityregions. This indicates that the majority of the data col-lected belong to the lower percentile reÑectivity ranges.

The second distribution, shown in Fig. 5, is the fre-quency distribution for the highly reÑectant mirrorsurface. The whole histogram shows a J-shaped fre-quency distribution, which is dominated by the veryhigh frequency range obtained from the interval relativeto the 100% laser reÑectivity value. In this case, thecumulative curve shows a very low slope before reach-ing the maximum value of intensity. The area coveredby the cumulative curve in this case is found to be com-paratively smaller than in the case of the rough abrasivepaper surface. The two Ðgures illustrate two extremecases, where a high surface roughness decreases themean value of the reÑectivity, while a smooth highly“shinyÏ surface gives nearly the physical maximum per-centage of reÑected light.

Fig. 5. Histograms of the number of data with di†erent per-centages of reÑectivity obtained for a mirror and emery paper.



Fig. 6. Relative cumulative frequencies of the percentage ofreÑectivity obtained for a mirror and emery paper.

When the frequencies, relative to the lower values ofreÑectivity, are higher in number than those represent-ing the higher reÑectivity data, the cumulative distribu-tion curve will exhibit an increasing trend (and thereforea greater area) and show a decrease in the slope, whenthe curve is accounting for the higher values of reÑec-tivity for the lower frequencies. The situation is the con-verse when higher frequencies are recorded for thehigher reÑectivity intensities. For this case, the cumula-tive curve has a lower slope in the lower frequencyrange, accounting for low reÑectivity, and greater slopein the high frequency range, accounting for high reÑec-tivity.

The extreme cases which may theoretically beencountered in a statistical analysis which utilises therelative cumulative frequency distributions are the fol-lowing. The sample may have an extremely roughsurface which scatters the laser beam in various direc-tions over the detecting limits of the apparatus. In thiscase, the histogram distribution is a reverse J-shape andpresents one column on the low-frequency side of thechart ; this indicates that the whole population of data(relative to the scanned surface) is concentrated at thevery Ðrst class interval of intensity (around 0%) and therelative cumulative curve has a step-like shape, wherethe step has a 100% amplitude. The other extreme maybe encountered when the reÑectivity of smooth mirror-like surfaces is analysed (see a similar case in Figs 5 and6). In this case, the entire surface may reÑect all thescanning beam back to the detector and the histogramis moved towards the upper limit of reÑectivity (100%of specular scattering) concentrated in one frequency.Therefore, the reÑective cumulative curve is zero until itreaches the maximum value of the reÑectivity ; there itreaches the 100% value.

From Figs 5 and 6 it appears that the evaluation ofthe extent of the cumulative distribution, which essen-

tially is the area bound by the cumulative curvesobtained from the laser reÑectivity, may be a convenientmeans for characterising the scattering e†ect of di†erentsurfaces or the change in the reÑectivity due to variousmechanical deformations and changes in the originalspecular reÑection of certain material surfaces, such asPMMA.

A general expression for a relative cumulative fre-quency polygon may be written as follows :

C\ C(Ii) \

;0

i(*I

i"

i)

"t100 (1)

where is the range of the reÑectivity intensity (class*Ii

interval) which is constructed from a certain number ofdata or frequency, obtained from the material"

i,

surface. is the total number of data points analysed"t(population). The area under the cumulative curve maythen be deÐned as follows :

t\ ;i/0

i/1001

;i/0

i/100(*I

i"

i)

"t100

2*I

i(2)

RESULTS AND DISCUSSION

Figures 7a and 7b show a typical scratch topographicalproÐle and the corresponding percentage of reÑectivityplot for a scratch produced by a 60¡ cone, under anapplied normal load of 0É3 N for PMMA. Figure 7ashows the cross-sectional roughness proÐle of thescratch ; note that the scales di†er by a factor of two. Ascanning electron microscopy (SEM) study of thisscratch showed that, together with a visible plasticploughing e†ect, the deformation characteristic notedinside the scratch was primarily brittle in nature, withthe presence of a signiÐcant number of cracks. Thisresults in a low percentage of laser reÑectivity detectedin the surface region within the scratch groove. ThereÑectivity of an undeformed part of the PMMA speci-men, which was gold-coated prior to the proÐlometricstudy, is equal to c. 99%, as the surface of the sampleused in this study was optically smooth. Also, adjacentto the sides of the scratch, cracks and brittle fracturewere observed. This e†ect may be seen both in thescratch proÐle (Fig. 7a) and in the reÑectivity data (Fig.7b) plots. In the present paper, the analysis of the reÑec-tivity data is carried out only for the PMMA surfaceregion “insideÏ the scratch track.

A statistical analysis (see previous section) of the per-centage of the reÑectivity detected within the scratchesis presented in Fig. 8. This Ðgure shows three relativecumulative polygons for scratches produced by cones ofincluded angles 45¡, 60¡ and 75¡ for a normal load of0É3 N. The ordinate shows the percentage of the data(relative cumulative frequency) for a particular scan of



Fig. 7. (a) ProÐle of a scratch produced on a PMMA surfaceusing a 60¡ cone indenter. (b) Percentage of reÑectivity of thescratched surface shown in (a). The percentage of reÑectivity isc. 100 for the undeformed surface and considerably lower than

100 for the scratch.

Fig. 8. Relative cumulative frequencies as a function of thepercentage of reÑectivity for the data obtained from thescratches produced on PMMA using various cones. The

normal load was 0É3 N.

the scratch, while the abscissa shows the percentagereÑectivity. Hence, any point, A, on a cumulative curve(see, for example, A in Fig. 8) shows that 40% of thetotal data of the scanned surface has a percentage ofreÑectivity less than 30. The cumulative curves present-ed in Fig. 4 show di†erent trends for di†erent coneangles. Data for the lower angled cones (45¡ and 60¡)show a steep rise of the curves in the lower range ofpercentage of reÑectivity before they reach the 100%data value. In contrast, the curves for the higher angledcone (75¡) show a greater percentage of the data in thehigher reÑectivity region. This indicates that the fre-quency of low reÑectivity data is higher for the lowerangle cones, while the reverse is true for the highincluded angle cones. In terms of the surface roughness,this means that the roughness of the scratched surface ishigher for low angle cones than it is for high anglecones. This has been found to be the case in SEMstudies of the same deformed surfaces. Low angle conesproduce brittle fractures and cracks during scratchingand hence the scratched surfaces are rougher in com-parison with the surfaces of scratches produced by thehigh angle cones, where the mode of deformation is pre-dominantly one of plastic ploughing. In Fig. 8 it is alsoseen that the area encompassed by the cumulative curveon the percentile reÑectivity axis is an indication of theweight of the data frequency of the percentage reÑec-tivity. If we designate the magnitude of this area as t,then t has a high value for the low reÑectivity surfaces(brittle) and a low value for surfaces with high reÑec-tivity (plastically deformed). Now, if is assumed ast0the maximum area theoretically encompassed by acumulative curve on the percentage reÑectivity axis inthe case of a zero percentage reÑectivity level for alldata, and t is the area covered by any particular cumu-lative curve on the same axis, then a new parameter, m,may be deÐned as follows :

m \ (1[ t/t0) (3)

The parameter m can vary between 0 and 1 and may betermed a “statistical index of reÑectivityÏ. For m \ 1, thesurface features a “mirror-likeÏ optical reÑectivity, or100% reÑectivity for all the data analysed. For m \ 0,the material surface does not reÑect specularly any frac-tion of the laser beam, indicating the presence of a highdegree of roughness. In terms of the modes of deforma-tion, the predominant deformation regime changes fromthe brittle to the plastic mode as the value of m increasesfrom 0 to 1.

Figure 9 illustrates a plot of the calculated values of magainst the applied normal load for scratches producedon PMMA surfaces ; the surfaces were gold-coated afterdeformation prior to the reÑectivity characterisation.This Ðgure shows clear trends for the data obtainedfrom di†erent cones. In all cases, the value of m reduceswith the increase of the normal load. However, theseslopes of the curves also depend upon the cone angle of



Fig. 9. Statistical index of reÑectivity, m, as a function ofnormal load for the scratches produced on PMMA usingcones of various included angles 45¡ ; 60¡ ; 75¡ ;(…, K, >, L,90¡). The data are produced for the surface inside thescratches. The map shows a region of brittle scratch deforma-tion, a region of ductile deformation and a transitional zone(shaded area). The areas are constructed from the SEM assess-

ment of the deformations.

the indenter. A decrease in the value of m with load indi-cates that the scratched surfaces are rougher as theapplied normal load is increased. This implies that achange occurs in the deformation mechanism from oneof ductile Ñow to one of brittle fracture with theincrease of the load. This trend has been found to be thecase in SEM observations.6 Figure 9 also shows that fora similar normal loading condition, the value of m is lowfor low cone angles. A ductile to brittle transition zoneis indicated in Fig. 9 as the shaded area. The ductile tobrittle transition zone has been assumed to occur forthose scratches where the statistical reÑectivity index isin the range m \ 0É22 to 0É33.

One of the trends which is observed in Fig. 9 is thatthe value of m also decreases signiÐcantly in the ductiledeformation regime. For example, in the case of thescratches produced with the 90¡ cones, there is agradual loss of the cumulative reÑectivity of the surfacefor increasing loads, even though the deformation wasobserved to be wholly ductile using SEM imaging. Thisfact indicates that there are some changes in the surfacefeatures, such as the creation of very minute cracks andirregular plastic Ñow behaviour of the material, with thechange in the experimental parameters, which are notreadily detected by the SEM imaging process and itssubjective assessment.

Other features which may be observed in the plot ofFig. 9 are that the transitional zone (as observed bySEM) appears at the lowest values of the index and that

the decreasing trends shown by the data for everygeometry of indenter for increasing loads are subjectedto a dramatic change in the slope within and below thetransitional zone. These facts may be considered as con-Ðrmation of the hypothesis that PMMA surfaces showthe lowest values of cumulative reÑectivity in the case ofbrittle deformation.

The same data for the statistical index of reÑectivityare plotted against the computed values of the contactpressure during scratching (see Fig. 10). By analogy withthe normal indentation mechanics, the contact pressurewas evaluated from the proÐlometric average values ofthe scratch width, according to the following expres-sion :

P\ W(nd2/8)

(4)

where W is the normal load and d the scratch width,assuming a fully plastic deformation of the material andneglecting any signiÐcant elastic recovery of thematerial behind the moving indenter.11

Figure 10 was also calibrated against the SEMimaging assessment. The ductile to brittle transitionzone, as deduced from the SEM study, falls within thesame range of m values, that is between 0É22 and 0É33.The plot illustrates that the contact pressure does notvary signiÐcantly with increasing loads if the deforma-tion is conÐned within the ductile region, whilst the stat-istical index of reÑectivity may change dramaticallyeven for similar values of contact pressure. Further-

Fig. 10. Statistical index of reÑectivity, m, as a function ofcontact pressure for the scratches produced on PMMA usingcones of various included angles 45¡ ; 60¡ ; 75¡ ;(…, K, >, L,90¡). The data are produced for the surface inside thescratches. The contact pressure is evaluated from the pro-Ðlometric measurements of the scratches. The map shows aregion of brittle scratch deformation, a region of ductile defor-mation and a transitional zone (shaded area). The areas are

constructed from the SEM assessment of the deformations.



more, the decreasing trends of the statistical reÑectivityindex, m, become steeper than in Fig. 9. In Fig. 10 thecontact pressure varies with the load within the transi-tional brittle zones. This may be explained by assumingthat the friction energy involved in brittle fracture ismostly spent by the system in cracking the surfacerather than in plastically deforming it, and the evalu-ated load-supporting areas are smaller. However, brittledeformations correspond to the lower values of m.

The data and the statistical analyses presented in thispaper have shown that the optical reÑectivity from asurface is a characteristic of the topographical featurespresent. Since di†erent modes of surface deformationproduce di†erent types of topography, these modes ofdeformation can be correlated with the optical reÑec-tivity of the surface. Here, it may be argued that, if thevariations in the topography are the result of changeswith modes of deformation, then a topographicalparameter may be used for distinguishing the di†erentdeformation modes. The topographical parameters suchas (average of the distances of peaks and valleys fromRaa mean central line) and (root mean square of theRqdistances of peaks and valleys from a mean central line)do not di†erentiate between the types of roughness ; forinstance, between a very irregular and a wavy surface.In contrast, in the reÑectivity measurement such di†er-ences are clearly detected since the light-scatteringproperties of irregular and wavy surfaces are di†erent.Hence, the reÑectivity method of surface character-isation is more discriminatory when characterising thesurface topographical features which are important forthe identiÐcation of the deformation mode.

CONCLUSIONS

The local optical reÑectivity was measured using a laserproÐlometer for PMMA surfaces scratched by conicalindenters of varying cone angles and under di†erentnormal loads. The reÑectivity data were analysed usinga statistical approach. The following conclusions aredrawn from this work.

The topographical features on a scratched polymersurface are characteristic of the mode of deformationthe surface undergoes during deformation. The surfacesof scratches with di†erent topography have di†erent

optical reÑectivity when exposed to light, and hence thereÑective property of the surface may be related to themodes of surface deformation for polymers.

The statistical analysis adopted in this study providesa parameter which may be used as a quantitativemeasure of the relative extents of the various modes ofsurface scratch deformations.

Therefore, the reÑectivity measurement may be usedto determine the ductile to brittle transition and alsooptical usefulness of a surface with respect to resistanceto mechanical damage. In this case, the statisticalparameter, m, which takes into account the cumulativevariation of the scatter e†ect of scratched surfaces uponthe local reÑectivity, seems to be more useful than thesubjective assessment of the SEM images. The value ofthe statistical reÑectivity index varies signiÐcantly evenwithin the ductile regime, where the surface is plasticallydeformed without major topographical changes. In thebrittle regime, the index data evaluated follow a fairlyconstant trend at the lower values, indicating a prevail-ing e†ect of the brittle nature of the deformation uponthe general optical response of the surface.

ACKNOWLEDGEMENTS

The authors acknowledge the Ðnancial help provided byEPSRC (UK) for the purchase of the laser proÐlometersystem, and Dow Chemical Company (USA) for theprovision of a bursary to one of the authors (E.P.).

REFERENCES

1 Briscoe, B. J. & Evans, P. D. W ear, 133 (1989) 47.2 Jenkins, F. A. & White, H. E., Fundamentals of Optics. McGraw-

Hill, New York, 1950.3 Whitehouse, D. J., Handbook of Surface Metrology. Institute of

Physics, Bristol (UK), 1994.4 ASTM D 673-70, 1982.5 ASTM E 1392-90, 1991.6 Briscoe, B. J., Evans, P. D., Pelillo, E. & Sinha, S. K., W ear 200 :

1È2 (1996) 137.7 Bernhardt, E. C., Modern Plastics, Oct. (1948) 123.8 Briscoe, B. J., Evan, P. D., Biswas, S. W. & Sinha, S. K., T rib. Int.,

29 : 2 (1996) 93.9 Williams, J. A., T rib. Int., 29 : 8 (1996) 675.

10 ChatÐeld, C., Statistics for T echnology. Chapman & Hall, London,1983.

11 Briscoe, B. J., Pelillo, E. & Sinha, S. K., Polym. Eng. Sci. 36 :24,Dec 1996.


characterisation of the scratch deformation mechanisms for poly(methylmethacrylate) using surface...

Documents