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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
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
¤ To whom all correspondence should be addressed.
( 1997 SCI. Polymer International 0959È8103/97/$17.50
Printed in Great Britain
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.
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.
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¡).
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
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.
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
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.
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
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.
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
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
C \ C(I ) \ 0
where *I is the range of the reÑectivity intensity (class
interval) which is constructed from a certain number of
data or frequency, " , obtained from the material
surface. " is the total number of data points analysed
(population). The area under the cumulative curve may
then be deÐned as follows :
; (*I " )
i i
100 *I
t\ ;
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
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.
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
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 )
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
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 :
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
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.
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 mean central line) and R (root mean square of the
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.
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
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.
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.).
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,
11 Briscoe, B. J., Pelillo, E. & Sinha, S. K., Polym. Eng. Sci. 36 :24,
Dec 1996.
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