Microhardness of PEEK/ceramic micro- and nanocomposites:
Correlation with Halpin–Tsai model
R.K. Goyal a,∗ , A.N. Tiwari b , Y.S. Negi c
a
Centre for Materials for Electronics Technology, Department of Information Technology, Government of India, Panchwati,
Off Pashan Road, Pune 411008, India
b Department of Metallurgical Engineering and Materials Science, Indian Institute of Technology, Bombay Powai,
Mumbai 400076, India
c Polymer Science and Technology Laboratory, Department of Paper Technology, Indian Institute of Technology Roorkee,
Saharanpur campus, Saharanpur 247001, U.P., India
Abstract
Microhardness of high performance PEEK matrix composites reinforced with micro- and nanosize ceramic particles of aluminum nitride
and alumina was evaluated with Vickers hardness tester. The microhardness of composites increases with increasing ceramic particle loading.
The microhardness of PEEK/AlN composites is higher than that of PEEK/Al2 O3 composites. For a given volume fraction, the improvement in
microhardness of nanocomposites is higher than that of microcomposites. For the first time, the Halpin–Tsai equation was applied to correlate
the microhardness. It was found that the adjustable parameter, i.e. ξ, is different for both particles. The value of ξ is higher for nanocomposites
compared to microcomposites.
Keywords: Particle-reinforced composites; Polymer-matrix composites; Hardness; Scanning electron microscopy
1. Introduction
Micohardness testing is widely used in industry and laboratory as a useful tool for determining the mechanical properties
of materials because it provides an easy, inexpensive, and
nondestructive method of characterizing properties from small
volumes of materials. Due to these advantages, Vickers indentation has been used to characterize residual stresses, yield
strength, and Young’s modulus of polymeric materials [1–3].
Recently, microhardness testing has been used for studying; the
trend of the elastic properties in functionally graded epoxy composites [4] and relative creep resistance of polymers [5]. The
microhardness of many polymer composites such as acrylic
polymer/TiO2 [6], high density polyethylene (HDPE)/Kaolin
[7], poly(ether-ether-ketone) (PEEK)/SiO2 [8], PEEK/Al2 O3
[8], and epoxy/SiC [4] has been evaluated and correlated with
simple rule of mixtures (ROM), also known as Rice model [9].
The extrapolated hardness values of TiO2 , SiC, and Kaolin par-
ticles, which are obtained by extrapolating the graph between
experimental hardness and volume fraction, Vf = 1, could not
be obtained close to the theoretical hardness of the reinforcing particle, respectively. This is due to the fact that rule of
mixture does not include the size and shape of the particles,
and the interaction between the particle and polymer matrix.
In the low particle-loading region, the resistance to indention
is resulted from the particle–matrix interaction thus the property of the composites is linearly dependent on the particle
loading. As the particle loading is high, there will also be
the particle–particle interaction in addition to particle–polymer
interaction, which increases significantly the resistance to flow
of materials thus causing deviation from linearity [5]. Moreover, the maximum packing fraction of the particles depends
on the size distribution and shape of the particles, which is not
considered in the ROM. Hence, a factor such as strengthening
efficiency factor was included in the ROM [8]. Nevertheless, the ROM obeys well for the polymer and copolymer
blends because their hardness values are close to each other
[10].
In view of above, microhardness of high performance PEEK
matrix composites containing both micro- and nanoparticles of
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AlN and Al2 O3 using hot press was evaluated and correlated with
ROM, modified-ROM, and Halpin–Tsai semi-empirical equation. For the first time, the Halpin–Tsai equation was correlated
with hardness data.
2. Experimental procedure
2.1. Materials
The commercial PEEK (Grade 5300PF) donated by Gharda
Chemicals Ltd. India under the trade name GATONETM PEEK
was used as matrix. The ceramic particles, viz. micro-AlN,
micro-Al2 O3 and nano-Al2 O3 (39 nm) purchased from Aldrich
Chemical Company, and nano-AlN (10–20 nm) purchased from
Alfa Chemical Company were used as received. The differential distribution of micro-Al2 O3 and AlN particles size was
determined on a GALAI CIS-1 laser particle size analyzer.
The micro-Al2 O3 and AlN particle size ranges from 3–15 to
1.5–9.6 ␮m, respectively as shown in Fig. 1. The mean particle
size of micro-Al2 O3 and AlN particle is 7.8 and 4.8 ␮m, respectively. An ethanol was used as received from Merck company
for mixing the ceramic and the PEEK powder.
2.2. Procedure for composite preparation
PEEK matrix composites containing ceramic (AlN/Al2 O3 )
particles were fabricated by a simple method as reported in our
previous paper [11,12]. Dried PEEK and ceramic powder were
well premixed through magnetic stirring in an ethanol medium
for 8 h and then the homogeneous slurry was dried in a vacuum oven at 120 ◦ C for 10 h and finally hot pressed at 350 ◦ C
and 15 MPa. The micro-AlN or Al2 O3 particles were reinforced
up to 60 wt% whereas their nanoparticles were reinforced up
to 30 wt%. All samples have experimental density close to the
theoretical density [11–13].
2.3. Characterization
Scanning electron microscopy (SEM) (Philips XL-30) and
SEM (Hitachi S3400) were used to investigate the micro- and
nanoparticles distribution in the PEEK matrix, respectively.
Polished sample of microcomposites and fractured (in liquid
nitrogen) samples of nanocomposites were coated with a thin
layer of gold using gold sputter coater (Polaron SC 7610) to
minimize charging effects. The morphology of the micro-AlN
and Al2 O3 powder was also examined. Transmission electron
microscopy (TEM) (Philips CM 30) operated at an accelerating
voltage of 200 kV was used to examine the morphology of nanoAlN and Al2 O3 particles. For this, nanoparticles suspended in
an ethanol were dispersed on 200-mesh copper grids.
The microhardness of well-polished samples was determined using Vickers hardness tester (Future-Tech Corp FM-700,
Tokyo, Japan) at a constant load of 100 g and dwell time
of 15 s. Average values of six readings were reported as the
microhardness of the samples. Since properties depend on the
volume fraction of the reinforcing particles added to the matrix.
Therefore, volume fraction of the ceramic particles for a given
weight fraction was determined from Eq. (1) and shown in
Table 1.
Vf = Wf /[Wf + (1 − Wf )ρf /ρm ]
(1)
where, Vf is the volume fraction of particles, Wf is the weight
fraction of particles, ρf is the density of the particles, and ρm is
the density of the PEEK matrix.
Table 1
Weight (volume) percentage of Al2 O3 and AlN particles in the PEEK matrix
Fig. 1. Differential distribution of: (a) micro-Al2 O3 particle size (mean particle
size: 7.8 ␮m) and (b) micro-AlN particle size (mean particle size: 4.8 ␮m).
Al2 O3 : wt% (vol.%)
AlN: wt% (vol.%)
5 (1.67)
10 (3.46)
20 (7.46)
30 (12.14)
50 (24.39)
60 (32.60)
5 (2.04)
10 (4.21)
20 (9.00)
30 (14.50)
50 (28.35)
60 (37.25)
The density of the PEEK, Al2 O3 , and AlN is 1.29, 3.98, and 3.26 g/cm3 , respectively.
232
Fig. 2. SEM micrographs of: (a) micro-Al2 O3 and (b) micro-AlN powder; scale bar: 10 ␮m.
3. Results and discussion
3.1. Morphology
Fig. 2a and b shows the SEM of pure micro-Al2 O3 and AlN
particles, respectively. The micro-Al2 O3 particles have platelet
shape with smooth surface morphology whereas micro-AlN particles have irregular shape morphology. Fig. 3a and b shows the
TEM of pure nano-Al2 O3 and AlN particles, respectively. The
nano-Al2 O3 particles are almost spherical in shape with sizes
less than 100 nm approximately. The nano-AlN particles are
polygonal in shape with sizes seem to be less than that of nanoAl2 O3 . Fig. 4a–d shows the SEM of polished PEEK composites
reinforced with 30 wt% micro-Al2 O3 , 60 wt% micro-Al2 O3 ,
30 wt% micro-AlN, and 60 wt% micro-AlN, respectively. It
can be seen that microparticles are almost uniformly dispersed
in the PEEK matrix. However, particle aggregates consisting
of few AlN or Al2 O3 primary particles are also observed in
some regions. The aggregate formation may be attributed to the
particle–particle interactions due to the decrease in interparticle
distance with increasing particle loading. Fig. 5a and b shows
SEM of fractured surface of PEEK nanocomposites reinforced
with 30 wt% nano-Al2 O3 and nano-AlN, respectively. It could
be seen that nano-Al2 O3 or AlN particles were almost uniformly
distributed in the PEEK matrix. However, some aggregates of
about 100 nm size were also observed with individual nanoparticles in the PEEK matrix. This was expected due to the higher
surface energy of nanoparticles and decreased average interparticle distance with nanoparticles content. This is similar to the
results reported by Bikiaris et al. [14].
3.2. Microhardness
Fig. 6a and b shows the microhardness of PEEK/Al2 O3
micro- and nanocomposites as a function of Al2 O3 content,
respectively. The hardness of composite at 30 wt% Al2 O3
increases from 24 kg/mm2 for the pure PEEK to 28.33 kg/mm2
for microcomposite and 32.45 for nanocomposite. The hardness
of microcomposite at 60 wt% Al2 O3 increases to 34.9 kg/mm2 .
The increase in microhardness might be attributed to higher
microhardness of Al2 O3 (2000 kg/mm2 ) compared to PEEK
(24 kg/mm2 ). Moreover, relatively uniform distribution of
Al2 O3 particles and decrease in interparticle distance with
increasing particle loading in the matrix results in increase of
Fig. 3. TEM micrographs of: (a) nano-Al2 O3 and (b) nano-AlN powder; scale bar: 200 nm.
233
Fig. 4. SEM micrographs of PEEK composites containing (a) 30 wt% micro-Al2 O3 , (b) 60 wt% micro-Al2 O3 , (c) 30 wt% micro-AlN, and (d) 60 wt% micro-AlN;
scale bar: 50 ␮m.
resistance to indentation of PEEK matrix. For a given volume
fraction, nanoparticles are much closer to each other compared
to microparticles in the matrix, and hence, nanoparticles will
resist more strongly the penetration of the indentation in the
matrix. For example, in 12 vol.% Al2 O3 filled PEEK composite,
the Al2 O3 nanoparticles have interparticle distance about 30 nm
whereas microparticles have about 6 ␮m. This results in higher
microhardness for nanocomposites than that of microcomposites
at a constant volume fraction of particles. Composite hardness
has been predicted by a rule of mixtures (ROM) as shown in Eq.
(1).
Hc = Hf Vf + Hm Vm
(1)
where, Hc , Hf , and Hm are the hardness of composite, particle,
and matrix, respectively.
As shown in Fig. 6, a wide gap exists between the experimental and the microhardness predicted from the ROM. This can be
attributed to the surface coating of Al2 O3 particles with a film
of matrix and hence, preventing direct particle–particle contact.
Due to this, hard Al2 O3 particles are pressed into the comparatively soft PEEK matrix rather than being plastically deformed
under the applied load during the indentation test [4]. Moreover,
due to much lower maximum packing factor of the Al2 O3 particles under applied pressure, micro- or nanocomposites could
not resist the indent penetration in proportion of Al2 O3 content.
It is worth noting that maximum packing of the particles varies
with the size distribution and shape of the particles. Hence, a factor such as strengthening efficiency factor should be included in
Eq. (1). After introducing a factor, the modified-ROM can be
presented as
Hc = βHf Vf + Hm Vm
(2)
The β is the strengthening efficiency factor, which depends upon
the aspect ratio and distribution of the reinforcements in the
matrix. The value of β for the random distributed glass fiber is
0.2 [15]. This value can be extended to less than 0.2 for the particles reinforced polymer composite. Moreover, it can safely be
assumed less than or equal to 0.1 since the Vickers hardness of
the polycrystalline dense Al2 O3 is 2000 kg/mm2 , which is about
83 times of pure PEEK (24 kg/mm2 ). Furthermore, Al2 O3 hardness decreases approximately by one order of magnitude as the
volume fraction of the porosity in Al2 O3 increases to 40% [16].
In present PEEK/Al2 O3 composite system, for approximation
the presence of PEEK may be assumed as porosity in the Al2 O3
matrix since PEEK hardness is much lower than that of Al2 O3 .
Therefore, in present study strengthening efficiency factor may
safely be assumed less than 0.1 along with dense Al2 O3 hardness
of 2000 kg/mm2 . For PEEK/Al2 O3 system, modified-ROM with
β = 0.03 and 0.05 fits well the experimental data of microcomposites and nanocomposites, respectively. Kuo et al correlated
the theoretical and experimental microhardness of PEEK/Al2 O3
nanocomposites up to 10 wt% (3.5 vol.%) Al2 O3 content, and
found that β = 0.1 underestimate the microhardness [8].
Halpin–Tsai [17] equation has shown good fitting for the
modulus because it takes into account the aspect ratio of the
reinforcing particles. Zamfirova et al. reported that modulus of
ultra high molecular weight polyethylene increased with increasing microhardness. In view of this, Halpin–Tsai equation was
234
microcomposite at 60 wt% AlN increases to 44 kg/mm2 . The
microhardness increases with increasing AlN content due to
the increase in crystallinity of the PEEK fraction in composite
[18] and higher microhardness of AlN (1200 kg/mm2 ) compared
to pure PEEK (24 kg/mm2 ). Similar to PEEK/Al2 O3 system,
a wide gap exists between the experimental and the values
predicted from the rule of mixture due to the reasons as mentioned above. However, modified-rule of mixture with β = 0.065
and 0.12 fits well the experimental data of PEEK/AlN microcomposites and nanocomposites, respectively. The Halpin–Tsai
equation with ξ = 0.5 and 3 fit well the data for microcomposites
and nanocomposites, respectively. For PEEK/AlN nanocomposites, the value of ξ is highest among the studied composites.
Table 2 shows the summary of strengthening efficiency factor and adjustable parameter of composites. It can be seen
that the values of strengthening efficiency factor and adjustable
parameter are higher for PEEK/AlN composites than that of
PEEK/Al2 O3 composites.
Fig. 5. SEM micrographs of PEEK nanocomposites containing (a) 30 wt% nanoAl2 O3 and (b) 30 wt% nano-AlN particle; scale bar: 2 ␮m.
applied for microhardness by replacing symbol of modulus with
hardness as shown in Eq. (3):
1 + ξηVf
(3)
H c = Hm
1 − ηVf
where η = [(Hf /Hm − 1)/(Hf /Hm + ξ)] and ξ is an adjustable
parameter. The upper bound is obtained when ξ = infinite and
lower bound when ξ = 0. The value of ξ depends on the geometry and packing of the particles as well as on the direction
of the load relative to the orientation of anisotropic particles.
For PEEK/Al2 O3 composites ξ = 0.05 and ξ = 2 fit well the data
for microcomposites and nanocomposites, respectively. Nevertheless, the ξ is an adjustable or curve fitting parameter, and
hence fits well the data. The value of ξ for nanocomposites is
much higher, i.e. 40-fold than that of microcomposites. It can
be seen from Fig. 6 that the microhardness predicted from the
Halpin–Tsai equation and modified-rule of mixture fit well for
both micro- and nanocomposites.
Fig. 7a and b shows the microhardness of PEEK/AlN microand nanocomposites as a function of AlN content, respectively. The hardness of composite at 30 wt% AlN increases
from 24 kg/mm2 for the pure PEEK to 32 kg/mm2 for microcomposite and 38 kg/mm2 for nanocomposite. The hardness of
Fig. 6. Correlation of experimental and predicted microhardness for
PEEK/Al2 O3 (a) microcomposites and (b) nanocomposites.
235
Fig. 8. Microhardness of PEEK matrix composites as a function of vol.%
ceramic particles (points are experimental data and lines are trends).
Fig. 7. Correlation of experimental and predicted microhardness for PEEK/AlN
(a) microcomposites and (b) nanocomposites.
Fig. 8 shows the microhardness of PEEK matrix composites
as a function of volume fraction of AlN and Al2 O3 particles. It can be seen that PEEK/AlN nanocomposites show
highest microhardness among the studied composites at a
given volume fraction whereas PEEK/Al2 O3 microcomposites show lowest microhardness. This is despite lower intrinsic
hardness of AlN (1200 kg/mm2 ) than Al2 O3 (2000 kg/mm2 ).
Moreover, the microhardness of nanocomposites containing
less than about 3 vol.% nanoparticles is slightly higher than
the trends. This is probably due to the dominant role of
increased crystallinity [18] and PEEK morphology in the vicinity of the nanoparticles of nanocomposites [19]. In general,
the addition of micro- or nanoparticles to polymer matrices
significantly increases the mechanical properties, particularly
modulus and hardness, of the composites if the particles are
strongly bonded to the polymer matrix [20–21]. Recently,
Misra et al. studied the effect of morphology on the scratch
hardness of polymer/clay nanocomposites [22]. They reported
that scratch hardness of polypropylene (PP)/clay nanocomposite increases with increasing clay nanoparticles due to an
increase in crystallinity and lamellar thickness, and decrease
in spherulite size. An increase in lamellae thickness plays an
important role for controlling hardness property of the particle filled polymer composites [23]. They investigated that the
clay nanoparticles influence strongly the micromechanism of
scratch deformation and reduce the extent of plastic deformation
whereas the mineral microparticles did not influence significantly. For example, the scratch deformation mechanism was
changed strongly from periodic ripples in neat PP to zig-zag and
shallow ploughing in PP/clay nanocomposites compared to the
high density polyethylene (HDPE)/calcium carbonate (CaCO3 )
microcomposite. Hence, a higher resistance to scratch deformation for PP/clay nanocomposites was found compared to
PP/wollastonite [20] and HDPE/CaCO3 microcomposites [23].
As per the ROM composites should have shown the microhardness in proportion of the constituent’s volume fraction. This
discrepancy may be attributed to the different particle packing
Table 2
Reinforcing efficiency factor and adjustable parameter of composites
Type of composite system
Reinforcing efficiency factor (β)
Adjustable parameter (ξ)
PEEK/AlN
Microcomposites
Nanocomposites
0.065
0.12
0.50
3.00
PEEK/Al2 O3
Microcomposites
Nanocomposites
0.03
0.05
0.05
2.00
236
factor and nature of the interactions between the ceramic particles and the matrix. Recently, we have reported that there is
good interactions between the AlN particles and PEEK matrix
[11] whereas poor interactions between the Al2 O3 particles and
PEEK matrix [13]. However, a detailed study is needed to see
the effect of interactions between the particles and the polymer
matrix on the hardness.
4. Conclusions
High performance PEEK matrix composites reinforced with
micro- and nanosize ceramic particles of aluminum nitride and
alumina were fabricated by a simple method consisting dispersion of ceramic particles in PEEK matrix followed by hot
pressing at 350 ◦ C and 15 MPa. The microhardness of composites increases with increasing ceramic particles loading. For a
given volume fraction, the improvement in microhardness of
nanocomposites is higher than that of microcomposites. The
microhardness of PEEK/AlN composites is higher than that
of PEEK/Al2 O3 composites. Modified-rule of mixture with an
appropriate value of strengthening efficiency (β) can be used to
predict the microhardness. The value of β vary between 0.03
and 0.12 for the composites. The nanocomposites have higher β
value than that of microcomposites. The Halpin–Tsai equation
with an appropriate value of adjustable parameter (ξ) fits well
the microhardness data of all composites and hence, it may be
useful for predicting the microhardness of composites. The ξ
depends on the type and size of particles. The values of β and ξ
is higher for nanocomposites compared to microcomposites.
Acknowledgements
We thank Dr. P.D. Trivedi, Polymer Division, Gharda Chemicals Ltd., India for providing PEEK powder for this work and are
grateful to Dr. T.L. Prakash, Executive Director of C-MET for his
interest in this work. RKG is thankful to Professor Mr. Sandeep
Butee, College of Engineering, Pune for unlimited access to
Vickers microhardness tester.
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