Polymer International 43 (1997) 359È367 Characterisation of the Scratch Deformation Mechanisms for Poly(methylmethacrylate) using Surface Optical Reflectivity* B. J. Briscoe,¹ E. Pelillo & S. K. Sinha Department of Chemical Engineering and Chemical Technology, Imperial College of Science, Technology and Medicine, Prince Consort 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 measurements for characterising the modes of surface mechanical damage of polymers is described. The technique utilises the sensed laser reÑectivity of polymer surfaces, after damage, as a means of measuring the relative extent of brittle and plastic deformation modes for polymers. The polymeric surface used in this paper is a commercial poly(methylmethacrylate). The surface damage is produced by scratching with rigid conical indenters under di†erent contact conditions of strain and load. The results show that the local optical reÑectivity of a surface depends upon the topography of the surfaces, which varies for di†erent modes of deformation. The reÑectivity of a brittle fractured surface is signiÐcantly lower in comparison 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. indicates the ability of the material to withstand abrasive interactions with another body. The mode of deformation indicates the type of deformation, mainly brittle or plastic, that may occur on the surface of the polymer during such interactions. Polymers show a very wide range of deformation modes within a relatively narrow range of contact variables such as temperature, strain, strain rate and severity of the contact deformation. Generally, brittle fracture on the surface causes most damage to the material, in terms of its optical features, in comparison with plastic deformation. This implies that a brittle scratch makes the surface more uneven and fragmented owing to the production of fractures1 and this results in a rather pronounced scattering e†ect of the light from the surface. In contrast, plastic deformation produces less severe damage and a fairly even surface is observed after the contact. Thus, the optical reÑectivity of the surface changes according to the type INTRODUCTION The uses of polymers for optical purposes such as lenses, wind panels, casings, smooth and glossy surfaces are very numerous. The optical properties required for such applications are transparency and reÑectivity, which depend upon the bulk intrinsic optical properties of the material and the topographical features on the surface, such as the roughness and the presence of scratches. The optical working life of these polymers often depends entirely upon the surface mechanical properties, such as the scratch resistance and the modes of possible material deformation. The scratch resistance * Presented at “The Cambridge Polymer Conference : Partnership in PolymersÏ, Cambridge, UK, 30 SeptemberÈ2 October 1996. ¤ To whom all correspondence should be addressed. 359 ( 1997 SCI. Polymer International 0959È8103/97/$17.50 Printed in Great Britain 360 of deformation produced during scratching. Hence, the optical reÑectivity data from the surface of a polymer may be used to identify and, to a large extent, quantify the mode of deformation the material has undergone during any surface interaction. This procedure may also be used to monitor the optical life of a polymer component or to study the optical behaviour of a polymer when it is in contact with another relatively hard material. Information on the factors inÑuencing the ductile to brittle transition is also required for estimating the mechanical working life of polymer components used for engineering applications and, in particular, in tribological applications. In this paper, a reÑectivity measurement technique is presented for identifying and quantifying the modes of deformation on a commercial grade poly(methylmethacrylate) (PMMA) when the surface of the PMMA is scratched by rigid conical indenters of varying included angle, a, and under di†erent normal loads (Fig. 1). This polymer experiences a change in the deformation mode from brittle fracture to ductile ploughing when the indenter included angle is increased or when the applied normal load is decreased. The mode of deformation during scratching depends primarily upon the attack angle, h, and the depth of the scratch, h (see Fig. 1). The reÑectivity data obtained from the scratched surface region are analysed using an established statistical method. Laser profilometry and reflectivity measurements The reÑectivity of an interface separating two di†erent media may be deÐned as the property by which it reÑects any incident light back into the same medium. The amount and the characteristics of the spatial reÑected light depend upon the wavelength, the polarisation and the angle of incidence of the incident beam, as well as 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, polished metals (e.g. silver, aluminium, gold) are the best reÑectors and may reÑect nearly 100% of incident light beams along a predictable and focused direction. This is Fig. 1. A schematic section through the central axis of a scratch to deÐne the various contact mechanics variables : a \ cone angle ; h \ depth of penetration ; h \ attack angle. B. J. Briscoe, E. Pelillo, S. K. Sinha found to be associated with their ability to conduct electricity.2 On the other hand, very rough surfaces may show scatter and multiple reÑection e†ects,3 which disperse part of the beam along di†erent directions. However, regular reÑection, that is reÑection in the absence of scattering e†ects, is encountered on surfaces where the geometrical irregularities (roughness, waviness, etc.) are small compared with the wavelength of the light. Polymers show a range of common optical properties such as transparency, translucency, opaqueness and reÑectivity. Because of this variety in optical response of polymers, they are used for many optical purposes. If we consider the case of a fairly rough sample, at a microscopic level of observation this is characterised by a number of grooves on the surface. A transverse section would therefore show a series of irregular peaks and valleys characterised by di†erent slopes. According to the grade of roughness, the slopes may vary frequently and dramatically along the surface proÐle considered. If such a rough surface is impinged normally by a light beam, single rays may be reÑected along di†erent directions, each particular slope region behaving, at a microscopic level, as a single reÑecting surface. In this case, some of the light is back-scattered directly towards the source and a fraction is scattered o† the incident direction (see Fig. 2). Thus, a partial loss in reÑectivity, along the incident direction, is observed. In conclusion, the reÑectivity of a surface is a function of the local topography at a microscopic level and it therefore varies from point to point, according to the spatial resolution of the scanner and the wavelength of the beam. The net surface reÑectivity may be readily expressed in statistical terms of average topographical quantities and cumulative distributions for the entire Fig. 2. The phenomenon of multiple scattering of a light beam 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 variety of the topographical features over a selected area of the surface. In general, mechanical damage on a surface, such as plastic deformation and brittle fracture, changes the topography and, therefore, the reÑectivity of the surface. Other intrinsic optical properties of the material might be changed because of such mechanical damage. The present paper is, however, focused upon the analysis of changes in surface reÑectivity of polymers due to scratching deformations. Laser proÐlometry measures the surface topography of materials and involves the use of a non-contacting infrared laser beam, which is focused normally upon the surface to be scanned. Usually, the sample is moved beneath the laser beam. The beam creates a light spot of a certain diameter, which depends upon the type of emitter and the numerical aperture of the lens ; the value is typically c. 1 km. The laser beam is reÑected back from the surface onto a detector (see Fig. 3). A piezoelectric motion system identiÐes the lens position, with respect to the reÑecting surface, which gives the highest spatial back-reÑection of the laser beam. The auto-focus system, usually comprising moving lenses, adjusts the focus on the surface by sensing the maximum reÑected light and the optical position is registered and used as the measuring signal. These instruments record both the topographical proÐle and the 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. POLYMER INTERNATIONAL VOL. 43, NO. 4, 1997 361 The main di†erences between a laser proÐlometer and the mechanical stylus techniques adopted for traditional surface metrological studies arise from the nondestructive nature of the laser beam. Thus the common problems encountered in the mechanical devices, such as the wear of the stylus tip, the local damage of the surfaces, tip vibrations and the low rates of data collection, are avoided. However, the stylus methods usually have a better resolution in the vertical direction. One of the functional aspects that distinguishes a laser proÐlometer from any other non-optical stylus is the capability to measure the reÑectivity of the scanned surface, point by point, in terms of the percentage of the back-scattered beam intensity. The laser proÐlometer system also di†ers from other reÑectance techniques which are commonly adopted to measure the haze of abraded plastics (see, for example, Ref. 4) or, in general, the optical scattering behaviour of surfaces.5 The optical followers are usually limited to a relatively narrow receiver solid angle, ), of c. 24¡ (^12¡) for the present system, which is formed by the cone of the reÑected rays back-scattered from the focusing spot subtended by the receive aperture stop. Other reÑectance devices, such as the widely adopted optical photogoniometers, usually cover the whole range of possible light reÑection (180¡). However, they are limited to a lower resolution and to a planar angle of collection (see Fig. 4), according to the type of detector installed. Such optical devices are usually based upon a static collimated light/laser source incident at a certain angle onto the sample surface and with a detector unit which is rotated around the sample, from 0¡ to 180, with speed to the normal to the sample. Because of the simplicity of these devices, an optical photogoniometer does not allow the scanning of large surfaces in relatively short lengths of time, and detailed interrelationships between local surface topography (e.g. within single microscopic scratch grooves) and the corresponding reÑectivity are not easily obtainable. The static nature of the laser emitter and detector in the laser proÐlometry method is, therefore, an advantage for the examination of localised changes in the surface reÑectivity. Fig. 4. Schematic comparison of the collection range of a dynamic photogoniometer (c \ 180¡) and a laser proÐlometer () \ 24¡). 362 Scratching of polymers The scratching of a surface of a material by sharp rigid indenters induces complex and localised deformations. The value of the scratch hardness, which may be variously deÐned, is often used as a measure of the resistance of a material to mechanically induced surface damage ; it is a common and long-established testing procedure (see, for example, Refs 6È9). This technique is carried out by drawing a rigid indenter of a speciÐed shape over the surface of a softer material under an applied normal load, and the scratch hardness is usually taken as the ratio of normal load to a contact area estimated from the permanent deformation produced on the surface. The numerical value of the scratch hardness is primarily a measure of the plastic Ñow characteristics and it does not incorporate a description of the kinds of damage the material may undergo at the surface. The study of the nature of the damage characteristics is generally carried out by examining the damaged areas using optical or scanning electron microscopy. Through a subjective assessment of the nature of the damage, deformation maps may be constructed which describe the damage characteristics as a function of the contact variables.6 These deformation maps are extremely useful for study of the origins of the damage processes which occur in polymers, and where a wide range of deformation characteristics may be produced during scratching. EXPERIMENTAL PROCEDURE The PMMA system used in this study was a commercial grade of cast Perspex' (ICI Acrylics, UK). The average molecular weight of this system is in the order of 1 ] 106 and the glass transition temperature, T , is c. g 110¡C ; no solvent was utilised in the casting process. The experimental procedure used in this study was as follows. The PMMA samples were mounted on the stage of a scratching machine and levelled (see later). Scratches were produced on the surface of the PMMA samples (initial roughness c. 0É1 km) using various rigid steel cones and under di†erent normal loading conditions. No lubricant was applied to the interface between the indenter and the surface. The samples were cleaned with commercial detergents and no surface polishing was carried out. After scratching, the specimens were coated with a layer of gold using vacuum evaporation, and were placed beneath the laser proÐlometer for the measurement of their topography and optical reÑectivity. The gold coating was applied to all samples before reÑectivity measurement in order to suppress any light di†usion into the bulk of the material. A smooth gold surface gives c. 99% reÑectivity, and hence the reÑectivity data obtained from the gold-coated surface B. J. Briscoe, E. Pelillo, S. K. Sinha was a characteristic of the surface features only and independent of the intrinsic optical properties of the material. The reÑectivity data for the areas inside and outside the scratch groove were analysed separately, as they exhibit di†erent modes of deformation during the scratching process and hence provide di†erent contributions to the optical response of the surface. Scratching machine The scratching machine consisted of a pivoted lever arm system upon which the indenters were Ðxed, and a motion stage where the specimens were mounted.1 The stage was moved horizontally below the indenters at a constant linear velocity of 0É2 mm s~1 using an electric motor. 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 was allowed to indent the polymer specimens before the specimen was moved. After a static indentation period which was maintained for 10 s, the stage which held the specimen was moved to produce the scratches on the polymer surface. The normal loads used for the tests varied between 0É03 and 2 N ; these loads were maintained constant during each experiment. Scratch profiles and reflectivity The optical reÑectivity of the surface was measured using a commercial laser proÐlometer system (Rhodenstock, Germany). This machine provides data for surface roughness, as well as the percentage of the light incident upon the detector system from the surface of the specimen after reÑection. As was explained earlier, the measurements obtained by this non-contact means are based on the record of the displacement of an automatically focusing laser beam. The beam spot diameter is c. 1 km and the wavelength is 780 nm. The beam encounters the specimen sample (which is coated with gold) at a working distance of 10 mm and a detector records the intensity of the fraction of the beam reÑected back from the surface within a solid angle of c. 24¡. The detector monitors any beam which reaches the detecting lenses in a single (specular surfaces) or multiscattered mode of reÑection (external di†usion). The latter e†ect is peculiar to rough surfaces. However, the contribution of multi-scattered light to the total reÑected light sensed by the detector is generally low.3 The calibration of the laser detector was performed considering the reÑectivity of a smooth, perfectly cleaned mirror as giving 100% reÑectivity. A plane glass Ðlter was utilised for this purpose. The thickness of the glass Ðlter was varied until the laser detector recorded 100% reÑectivity for a commercial mirror. A statistical approach, described in the next section, was employed to analyse the reÑectivity data, in order to obtain a suitable parameter to evaluate the interrelationship POLYMER INTERNATIONAL VOL. 43, NO. 4, 1997 Characterisation of scratch deformation mechanisms between the reÑectivity of the surfaces and the topography of the scratch deformations. The proÐlometric scans were performed in a direction orthogonal to the scratching vector at various locations along the length of scratch in order to obtain a representative description of the surface. Each scan was taken from the whole width of the scratch grooves and the horizontal topographical resolution (scanning step) was maintained constant at 1 km. STATISTICAL ANALYSIS The data recorded from the reÑectivity of the scanned surface were in the format of the percentage of the initial intensity of the incident laser beam received by the detector at the point of focus, that is at the maximum reÑectivity. The statistical analysis adopted for interpreting the reÑectivity data obtained from differently 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 that the roughness of a surface is primarily responsible for the level of its “optical glossÏ ; a lower value of the surface roughness allows more light to be reÑected from the surface along a single direction (determined by the symmetry of the incident direction). A very rough surface scatters the light along di†erent directions, resulting in a lower intensity of the back-scattered light observed by a detector ; and a greater amount of diffused light. The reÑectivity of scratches produced under di†erent experimental conditions, in terms of its intensity, was investigated along the surface within the scratch grooves and also outside the grooves, thus characterising the whole surface where any deformations due to the scratching process were detectable. For each scratch, the surface spatial distribution of the frequencies of the reÑected laser intensity was analysed over the whole reÑectivity range (0È100%). The data for the running sum of the relative frequencies of the increasing reÑectivities give results which are usually denoted as the relative cumulative frequency polygons or percentage ogives.10 The following analysis has been applied to the cumulative polygons, which can be generated from the frequency distributions of the surface reÑectivity over a chosen part of the surface. In general, a point on a relative cumulative frequency curve gives the percentage of surface (or data) which has been found to have reÑectivity intensity equal to or lower than a certain value which is read on the abscissae. Therefore, the area bound by the cumulative curve at a certain value of its abscissa gives a quantiÐcation of the surface which is characterised as having a reÑectivity not higher than the value indicated by the abscissa. The trend of cumulative curves constructed for di†erent surfaces, and therefore, the magnitude of the POLYMER INTERNATIONAL VOL. 43, NO. 4, 1997 363 areas under the curves, may be considered as a means of evaluating the weight that certain ranges of frequencies, obtained from the detected reÑectivity intensity, have in the whole range of the reÑectivity spectrum. The statistical data analysis presented in the previous paragraphs may be explained more clearly by the schematic diagrams described in the following. Figure 5 illustrates the histogram distributions of the laser reÑectivities of a very rough surface (emery paper, grade 100) and for a very smooth, highly reÑecting surface (a commercial mirror). In both cases the scan length was c. 10 mm. The frequency distribution relative to the emery paper, though slightly skewed to the right, is relatively spread, since the reÑectivity of the surface is not characterised by a single value of the intensity, but close values of the intensities may be found for each class interval. The relative cumulative polygon for this distribution is shown in Fig. 6. The data for emery paper in the cumulative curve show a greater slope in the lower intensity regions. This indicates that the majority of the data collected belong to the lower percentile reÑectivity ranges. The second distribution, shown in Fig. 5, is the frequency distribution for the highly reÑectant mirror surface. The whole histogram shows a J-shaped frequency distribution, which is dominated by the very high frequency range obtained from the interval relative to the 100% laser reÑectivity value. In this case, the cumulative curve shows a very low slope before reaching the maximum value of intensity. The area covered by the cumulative curve in this case is found to be comparatively smaller than in the case of the rough abrasive paper surface. The two Ðgures illustrate two extreme cases, where a high surface roughness decreases the mean value of the reÑectivity, while a smooth highly “shinyÏ surface gives nearly the physical maximum percentage of reÑected light. Fig. 5. Histograms of the number of data with di†erent percentages of reÑectivity obtained for a mirror and emery paper. 364 B. J. Briscoe, E. Pelillo, S. K. Sinha tially is the area bound by the cumulative curves obtained from the laser reÑectivity, may be a convenient means for characterising the scattering e†ect of di†erent surfaces or the change in the reÑectivity due to various mechanical deformations and changes in the original specular reÑection of certain material surfaces, such as PMMA. A general expression for a relative cumulative frequency polygon may be written as follows : Fig. 6. Relative cumulative frequencies of the percentage of reÑectivity obtained for a mirror and emery paper. When the frequencies, relative to the lower values of reÑectivity, are higher in number than those representing the higher reÑectivity data, the cumulative distribution curve will exhibit an increasing trend (and therefore a greater area) and show a decrease in the slope, when the curve is accounting for the higher values of reÑectivity for the lower frequencies. The situation is the converse when higher frequencies are recorded for the higher reÑectivity intensities. For this case, the cumulative curve has a lower slope in the lower frequency range, accounting for low reÑectivity, and greater slope in the high frequency range, accounting for high reÑectivity. The extreme cases which may theoretically be encountered in a statistical analysis which utilises the relative cumulative frequency distributions are the following. The sample may have an extremely rough surface which scatters the laser beam in various directions over the detecting limits of the apparatus. In this case, the histogram distribution is a reverse J-shape and presents one column on the low-frequency side of the chart ; this indicates that the whole population of data (relative to the scanned surface) is concentrated at the very Ðrst class interval of intensity (around 0%) and the relative cumulative curve has a step-like shape, where the step has a 100% amplitude. The other extreme may be encountered when the reÑectivity of smooth mirrorlike surfaces is analysed (see a similar case in Figs 5 and 6). In this case, the entire surface may reÑect all the scanning beam back to the detector and the histogram is moved towards the upper limit of reÑectivity (100% of specular scattering) concentrated in one frequency. Therefore, the reÑective cumulative curve is zero until it reaches the maximum value of the reÑectivity ; there it reaches the 100% value. From Figs 5 and 6 it appears that the evaluation of the extent of the cumulative distribution, which essen- i ; (*I " ) i i C \ C(I ) \ 0 100 (1) i " t where *I is the range of the reÑectivity intensity (class i interval) which is constructed from a certain number of data or frequency, " , obtained from the material i surface. " is the total number of data points analysed t (population). The area under the cumulative curve may then be deÐned as follows : 1 2 i/100 ; (*I " ) i i i/100 i/0 100 *I t\ ; i " t i/0 (2) RESULTS AND DISCUSSION Figures 7a and 7b show a typical scratch topographical proÐle and the corresponding percentage of reÑectivity plot for a scratch produced by a 60¡ cone, under an applied normal load of 0É3 N for PMMA. Figure 7a shows the cross-sectional roughness proÐle of the scratch ; note that the scales di†er by a factor of two. A scanning electron microscopy (SEM) study of this scratch showed that, together with a visible plastic ploughing e†ect, the deformation characteristic noted inside the scratch was primarily brittle in nature, with the presence of a signiÐcant number of cracks. This results in a low percentage of laser reÑectivity detected in the surface region within the scratch groove. The reÑectivity of an undeformed part of the PMMA specimen, which was gold-coated prior to the proÐlometric study, is equal to c. 99%, as the surface of the sample used in this study was optically smooth. Also, adjacent to the sides of the scratch, cracks and brittle fracture were observed. This e†ect may be seen both in the scratch proÐle (Fig. 7a) and in the reÑectivity data (Fig. 7b) plots. In the present paper, the analysis of the reÑectivity data is carried out only for the PMMA surface region “insideÏ the scratch track. A statistical analysis (see previous section) of the percentage of the reÑectivity detected within the scratches is presented in Fig. 8. This Ðgure shows three relative cumulative polygons for scratches produced by cones of included angles 45¡, 60¡ and 75¡ for a normal load of 0É3 N. The ordinate shows the percentage of the data (relative cumulative frequency) for a particular scan of POLYMER INTERNATIONAL VOL. 43, NO. 4, 1997 Characterisation of scratch deformation mechanisms Fig. 7. (a) ProÐle of a scratch produced on a PMMA surface using a 60¡ cone indenter. (b) Percentage of reÑectivity of the scratched surface shown in (a). The percentage of reÑectivity is c. 100 for the undeformed surface and considerably lower than 100 for the scratch. Fig. 8. Relative cumulative frequencies as a function of the percentage of reÑectivity for the data obtained from the scratches produced on PMMA using various cones. The normal load was 0É3 N. POLYMER INTERNATIONAL VOL. 43, NO. 4, 1997 365 the scratch, while the abscissa shows the percentage reÑectivity. Hence, any point, A, on a cumulative curve (see, for example, A in Fig. 8) shows that 40% of the total data of the scanned surface has a percentage of reÑectivity less than 30. The cumulative curves presented in Fig. 4 show di†erent trends for di†erent cone angles. Data for the lower angled cones (45¡ and 60¡) show a steep rise of the curves in the lower range of percentage of reÑectivity before they reach the 100% data value. In contrast, the curves for the higher angled cone (75¡) show a greater percentage of the data in the higher reÑectivity region. This indicates that the frequency of low reÑectivity data is higher for the lower angle cones, while the reverse is true for the high included angle cones. In terms of the surface roughness, this means that the roughness of the scratched surface is higher for low angle cones than it is for high angle cones. This has been found to be the case in SEM studies of the same deformed surfaces. Low angle cones produce brittle fractures and cracks during scratching and hence the scratched surfaces are rougher in comparison with the surfaces of scratches produced by the high angle cones, where the mode of deformation is predominantly one of plastic ploughing. In Fig. 8 it is also seen that the area encompassed by the cumulative curve on the percentile reÑectivity axis is an indication of the weight of the data frequency of the percentage reÑectivity. 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 reÑectivity (plastically deformed). Now, if t is assumed as 0 the maximum area theoretically encompassed by a cumulative curve on the percentage reÑectivity axis in the case of a zero percentage reÑectivity level for all data, and t is the area covered by any particular cumulative curve on the same axis, then a new parameter, m, may be deÐned as follows : m \ (1 [ t/t ) (3) 0 The parameter m can vary between 0 and 1 and may be termed a “statistical index of reÑectivityÏ. For m \ 1, the surface features a “mirror-likeÏ optical reÑectivity, or 100% reÑectivity for all the data analysed. For m \ 0, the material surface does not reÑect specularly any fraction of the laser beam, indicating the presence of a high degree of roughness. In terms of the modes of deformation, the predominant deformation regime changes from the brittle to the plastic mode as the value of m increases from 0 to 1. Figure 9 illustrates a plot of the calculated values of m against the applied normal load for scratches produced on PMMA surfaces ; the surfaces were gold-coated after deformation prior to the reÑectivity characterisation. This Ðgure shows clear trends for the data obtained from di†erent cones. In all cases, the value of m reduces with the increase of the normal load. However, these slopes of the curves also depend upon the cone angle of 366 B. J. Briscoe, E. Pelillo, S. K. Sinha the decreasing trends shown by the data for every geometry of indenter for increasing loads are subjected to a dramatic change in the slope within and below the transitional zone. These facts may be considered as conÐrmation of the hypothesis that PMMA surfaces show the lowest values of cumulative reÑectivity in the case of brittle deformation. The same data for the statistical index of reÑectivity are plotted against the computed values of the contact pressure during scratching (see Fig. 10). By analogy with the normal indentation mechanics, the contact pressure was evaluated from the proÐlometric average values of the scratch width, according to the following expression : P\ Fig. 9. Statistical index of reÑectivity, m, as a function of normal load for the scratches produced on PMMA using cones of various included angles (…, 45¡ ; K, 60¡ ; >, 75¡ ; L, 90¡). The data are produced for the surface inside the scratches. The map shows a region of brittle scratch deformation, a region of ductile deformation and a transitional zone (shaded area). The areas are constructed from the SEM assessment of the deformations. the indenter. A decrease in the value of m with load indicates that the scratched surfaces are rougher as the applied normal load is increased. This implies that a change occurs in the deformation mechanism from one of ductile Ñow to one of brittle fracture with the increase of the load. This trend has been found to be the case in SEM observations.6 Figure 9 also shows that for a similar normal loading condition, the value of m is low for low cone angles. A ductile to brittle transition zone is indicated in Fig. 9 as the shaded area. The ductile to brittle transition zone has been assumed to occur for those scratches where the statistical reÑectivity index is in the range m \ 0É22 to 0É33. One of the trends which is observed in Fig. 9 is that the value of m also decreases signiÐcantly in the ductile deformation regime. For example, in the case of the scratches produced with the 90¡ cones, there is a gradual loss of the cumulative reÑectivity of the surface for increasing loads, even though the deformation was observed to be wholly ductile using SEM imaging. This fact indicates that there are some changes in the surface features, such as the creation of very minute cracks and irregular plastic Ñow behaviour of the material, with the change in the experimental parameters, which are not readily detected by the SEM imaging process and its subjective assessment. Other features which may be observed in the plot of Fig. 9 are that the transitional zone (as observed by SEM) appears at the lowest values of the index and that W (nd2/8) (4) where W is the normal load and d the scratch width, assuming a fully plastic deformation of the material and neglecting any signiÐcant elastic recovery of the material behind the moving indenter.11 Figure 10 was also calibrated against the SEM imaging assessment. The ductile to brittle transition zone, as deduced from the SEM study, falls within the same range of m values, that is between 0É22 and 0É33. The plot illustrates that the contact pressure does not vary signiÐcantly with increasing loads if the deformation is conÐned within the ductile region, whilst the statistical index of reÑectivity may change dramatically even for similar values of contact pressure. Further- Fig. 10. Statistical index of reÑectivity, m, as a function of contact pressure for the scratches produced on PMMA using cones of various included angles (…, 45¡ ; K, 60¡ ; >, 75¡ ; L, 90¡). The data are produced for the surface inside the scratches. The contact pressure is evaluated from the proÐlometric measurements of the scratches. The map shows a region of brittle scratch deformation, a region of ductile deformation and a transitional zone (shaded area). The areas are constructed from the SEM assessment of the deformations. POLYMER INTERNATIONAL VOL. 43, NO. 4, 1997 Characterisation of scratch deformation mechanisms more, the decreasing trends of the statistical reÑectivity index, m, become steeper than in Fig. 9. In Fig. 10 the contact pressure varies with the load within the transitional brittle zones. This may be explained by assuming that the friction energy involved in brittle fracture is mostly spent by the system in cracking the surface rather than in plastically deforming it, and the evaluated load-supporting areas are smaller. However, brittle deformations correspond to the lower values of m. The data and the statistical analyses presented in this paper have shown that the optical reÑectivity from a surface is a characteristic of the topographical features present. Since di†erent modes of surface deformation produce di†erent types of topography, these modes of deformation can be correlated with the optical reÑectivity of the surface. Here, it may be argued that, if the variations in the topography are the result of changes with modes of deformation, then a topographical parameter may be used for distinguishing the di†erent deformation modes. The topographical parameters such as R (average of the distances of peaks and valleys from a a mean central line) and R (root mean square of the q distances of peaks and valleys from a mean central line) do not di†erentiate between the types of roughness ; for instance, between a very irregular and a wavy surface. In contrast, in the reÑectivity measurement such di†erences are clearly detected since the light-scattering properties of irregular and wavy surfaces are di†erent. Hence, the reÑectivity method of surface characterisation is more discriminatory when characterising the surface topographical features which are important for the identiÐcation of the deformation mode. CONCLUSIONS The local optical reÑectivity was measured using a laser proÐlometer for PMMA surfaces scratched by conical indenters of varying cone angles and under di†erent normal loads. The reÑectivity data were analysed using a statistical approach. The following conclusions are drawn from this work. The topographical features on a scratched polymer surface are characteristic of the mode of deformation the surface undergoes during deformation. The surfaces of scratches with di†erent topography have di†erent POLYMER INTERNATIONAL VOL. 43, NO. 4, 1997 367 optical reÑectivity when exposed to light, and hence the reÑective property of the surface may be related to the modes of surface deformation for polymers. The statistical analysis adopted in this study provides a parameter which may be used as a quantitative measure of the relative extents of the various modes of surface scratch deformations. Therefore, the reÑectivity measurement may be used to determine the ductile to brittle transition and also optical usefulness of a surface with respect to resistance to mechanical damage. In this case, the statistical parameter, m, which takes into account the cumulative variation of the scatter e†ect of scratched surfaces upon the local reÑectivity, seems to be more useful than the subjective assessment of the SEM images. The value of the statistical reÑectivity index varies signiÐcantly even within the ductile regime, where the surface is plastically deformed without major topographical changes. In the brittle regime, the index data evaluated follow a fairly constant trend at the lower values, indicating a prevailing e†ect of the brittle nature of the deformation upon the general optical response of the surface. ACKNOWLEDGEMENTS The authors acknowledge the Ðnancial help provided by EPSRC (UK) for the purchase of the laser proÐlometer system, and Dow Chemical Company (USA) for the provision 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. McGrawHill, 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.