U. ÖZMEN, B. OKUTAN BABA: PREDICTION OF THE ELASTIC MODULUS OF CHICKEN-FEATHER-REINFORCED PLA ...
141–146
PREDICTION OF THE ELASTIC MODULI OF
CHICKEN-FEATHER-REINFORCED PLA AND A COMPARISON
WITH EXPERIMENTAL RESULTS
NAPOVEDOVANJE MODULOV ELASTI^NOSTI PLA, OJA^ANEGA
S PI[^AN^JIM PERJEM IN PRIMERJAVA Z
EKSPERIMENTALNIMI REZULTATI
Uður Özmen, Buket Okutan Baba
Celal Bayar University, Engineering Faculty, Mechanical Engineering Department, 45140 Muradiye/Manisa, Turkey
u.ozmen@hotmail.com
Prejem rokopisa – received: 2014-08-07; sprejem za objavo – accepted for publication: 2015-03-04
doi:10.17222/mit.2014.182
The purpose of this study is to obtain the elastic moduli, the key material property, of random discontinuous fiber composites
with experiments and micromechanical models and to compare them. The proposed study makes it possible to assess the elastic
moduli of chicken-feather fiber (CFF)/PLA green composites with different CFF mass fractions and to determine the feasibility
of the micromechanical models for the CFF/PLA composites. For this purpose, initially, CFF/PLA composites including 2, 5 or
10 % chicken-feather mass fractions were extruded and standard tensile specimens for ISO 527 were formed with the
injection-molding method. Tensile tests were carried out in accordance with the standards and the elastic moduli were calculated
using the stress-strain curve. Then, using six different micromechanical models, the elastic moduli of the CFF/PLA composites
with different mass fractions were calculated and compared with the experimental results. The results of the experiments and the
models indicated that the presence of chicken feather increased the elastic moduli of all the composites in comparison with the
pure PLA. According to the experimental data, the maximum increase in the elastic moduli of the composites with the presence
of CFF was found to be 5.4 %. The maximum error in the prediction is about 16.8 % for the composite with a chicken-feather
rate of 10 % when Manera’s model is used. Among the micromechanical models, the ones that gave more converging results for
the prediction of the elastic moduli of the CFF/PLA composites are Pan’s 2-D, IROM (the inverse rule of mixtures),
Nielsen-Chen and Halpin-Tsai models. A comparison of the results of these six models shows that the maximum deviation (the
percentage error in prediction) is the smallest (1.4 %) for the Nielsen-Chen model. Therefore, the Nielsen-Chen model is the
most appropriate model for the prediction of the elastic moduli of the CFF/PLA composites.
Keywords: chicken feather, PLA, green composite, micromechanical models
Namen te {tudije je dobiti module elasti~nosti kot glavne lastnosti materiala, kompozitov z naklju~nimi vlakni, z eksperimenti in
z mikromehanskimi modeli ter njihova primerjava. Predlagana {tudija bo omogo~ila dolo~itev modula elasti~nosti kompozita iz
vlaken pi{~an~jega perja (CFF)/PLA, z razli~nim masnim dele`em CFF in ugotoviti izvedljivost mikromehanskih modelov za
CFF/PLA kompozite. V ta namen so bili najprej kompoziti CFF/PLA z 2 %, 5 % in 10 % pi{~an~jih peres, ekstrudirani in
izdelani so bili standardni natezni preizku{anci po ISO 527, z metodo brizganja v formo. Natezni preizkusi so bili izvr{eni v
skladu s standardom in modul elasti~nosti je bil izra~unan iz krivulje napetost-raztezek. Nato so bili izra~unani moduli
elasti~nosti kompozita CFF/PLA, z uporabo {estih razli~nih mikromehanskih modelov in primerjani z rezultati preizkusov.
Rezultati preizkusov in modelov so pokazali, da prisotnost pi{~an~jih peres pove~a modul elasti~nosti vseh kompozitov, v
primerjavi s ~istim PLA. Eksperimentalni podatki so pokazali, da je najve~je pove~anje modula elasti~nosti kompozita s CFF za
5,4 %. Pri uporabi Manera modela je bila najve~ja napovedana napaka okrog 16,8 % pri kompozitu z 10 % dele`em pi{~an~jega
perja. Med mikromehanskimi modeli, ki imajo najve~ji raztros rezultatov pri napovedovanju modula elasti~nosti CFF/PLA
kompozitov so Pan’s 2-D, IROM (Inverse Rule of Mixtures), Nielsen-Chen in Halpin-Tsai model. Primerjava rezultatov teh
{estih modelov ka`e, da je najve~je odstopanje (odstotek pri napovedi) najmanj{e (1,4 %) pri Nielsen-Chen modelu. Torej je
Nielsen-Chen model najbolj primeren za napovedovanje modula elasti~nosti CFF/PLA kompozitov.
Klju~ne besede: pi{~an~je perje, PLA, zelen kompozit, mikromehanski modeli
1 INTRODUCTION
Since the straw-reinforced cement in the antique
ages, random discontinuous short-fiber-reinforced com-
posites have always existed.1 A lot of experimental
studies have been done on this subject. Many are about
natural-fiber-reinforced ones because of the structure of
natural fibers that cannot be converted into long fibers.
Waste-based,2 synthetic-based,3 plant-based4–7 and ani-
mal-based8–12 fibers have been studied by many
researchers. Experimental studies are substantially
important to get the highest efficiency from the random
discontinuous short-fiber-reinforced composites. Experi-
mental studies are still hard to perform, as
time-consuming and costly tests need to be done to
characterize the composite materials.13 Therefore,
researchers developed certain micromechanical models
for calculating the properties of the composites to avoid
a great number of tests. Modelling of the random
discontinuous short-fiber-reinforced composites is quite
hard compared to the long and oriented ones. For the
situations where the well-known method named the rule
of mixtures for predicting the elastic moduli of com-
posite materials could not provide proper predictions,
Materiali in tehnologije / Materials and technology 50 (2016) 1, 141–146 141
UDK 66.017:620.168 ISSN 1580-2949
Professional article/Strokovni ~lanek MTAEC9, 50(1)141(2016)
Christensen and Waals,14 Pan,15 Manera,16 Nielsen-
Chen17 and Halpin-Tsai18,19 proposed new models based
on the rule of mixtures. While for some models the range
of validity is limited to specific mass fractions, other
models are different. Although each of these models was
developed for all the random discontinuous short-fiber-
reinforced composites, they may give unexpected results
for some of the composites.
The purpose of this study is to predict the elastic mo-
duli of the composites with different chicken-feather
mass content via the models developed for random dis-
continuous short-fiber-reinforced composites. The volu-
me fractions, with which these models express their sen-
sitive results, were investigated and the volume-fraction
range for these composite materials was determined.
2 EXPERIMENTAL WORK
Two materials were used for the composites, poly
lactic acid (PLA) as the matrix and chicken-feather
fibers (CFFs) as the reinforcement. The CFFs were
procured from a local company in Manisa/Turkey. The
CFFs (or barbs) were separated from the rachis (Figure
1a). They were washed with hot water for sterilization
and kept in water for 24 h. Then, the CFFs were kept in
an oven at 60 °C for 6 h in order to dehumidify them.
The lengths of the CFFs varied from 10 mm to 30 mm.
Their diameters were measured to be approximately
20–40 μm using a light microscope (Figure 1b). The
PLA was purchased from Resinex BMY AS in Istan-
bul/Turkey. The type of the PLA was NatureWorks
3052D with a density of 1.24 g/cm3.
The CFF/PLA composites with CFF mass fractions
of (2, 5 and 10) % were manufactured by extrusion. Ini-
tially, the PLA granules and the CFFs were mixed with a
mechanical mixer. The mixtures were extruded using a
U. ÖZMEN, B. OKUTAN BABA: PREDICTION OF THE ELASTIC MODULUS OF CHICKEN-FEATHER-REINFORCED PLA ...
142 Materiali in tehnologije / Materials and technology 50 (2016) 1, 141–146
Figure 1: a) Parts of a chicken feather, b) light-microscope image of
the barb
Slika 1: a) Deli pi{~an~jega peresa, b) svetlobni posnetek str`ena
peresa in perja
Table 1: Tensile-test specimens of composites with different chicken-feather mass fractions
Tabela 1: Natezni preizku{anci kompozitov z razli~nim masnim dele`em pi{~an~jega perja
Pure PLA
Tensile specimens containing 2 % of chicken feather
Tensile specimens containing 5 % of chicken feather
Tensile specimens containing 10 % of chicken feather
Figure 2: Specimen during the tensile test
Slika 2: Vzorec med nateznim preizkusom
ThermoFisher Scientific EuroLab 16 XL twin-screw
extruder. The barrel temperature-zone profile and the
screw speed were 165/175/185/195/205 °C and 150
min–1, respectively. Following the extrusion process, the
composites were chopped, with a pelletizer, into pieces
with a length of 0.3 cm. Then, the granules were manu-
factured as the tensile specimens in line with the ISO
527 standards, with a PERMAK injection-molding
machine. The barrel temperatures and pressure were
154/160/154 °C and 147 bar, respectively. The tensile
specimens are shown in Table 1.
The length of the tensile specimens was 88 mm, the
width of the narrow and wide sections was 5 and 10 mm,
respectively. The thickness of the specimens was 4 mm
and the gage length was 40 mm. The tensile test was
conducted to determine the elastic moduli of the
composites. Each specimen was tested at a speed of
1 mm/min, using a 100 kN Shimadzu Autograph testing
machine (Figure 2). At least five identical specimens
were tested per specimen type.
3 MICROMECHANICAL MODELS
The micromechanical models that can predict the
elastic moduli of random discontinuous fiber composites
are presented below.
The fiber volume fraction (Vf) used in the equations
is calculated as follows:13
V
M
M M Mf
f
f
f
f
c f
m
=
+
−

 
(1)
where Mf and f indicate the mass and the density of the
fiber material. Mc indicates the mass of the composite
material and m indicates the density of the matrix.
3.1 Christensen-Waals model
Christensen and Waals14 investigated a composite-
material system whose random fiber orientation has three
dimensional directions. They considered both the fiber
orientation and the fiber/matrix interaction. They cal-
culated the elastic moduli of the composite materials
with low fiber fractions for the plane stress using the
formula below:
E
c
E c E= + +
3
1f m( ) c < 0.2 (2)
where E indicates the elastic modulus of the composite
material, Ef indicates the elastic modulus of the fiber
material, Em indicates the elastic modulus of the matrix
material and c indicates the fiber volume fraction.
3.2 Pan’s model
Pan15 put forward a new approach for the prediction
of the elastic moduli of the randomly oriented fiber com-
posites. First, he used the rule of mixtures for the parts
where the fibers were not unidirectional; he used the
relationship between the fiber volume fraction and the
fiber-area ratio. He obtained the equations below for 2-
and 3-dimensional cases:
E E V E V2
1
1
1D
f f m f= + −
⎛
⎝
⎜
⎞
⎠
⎟π π
(3)
E E V E V3
1
2
1
1D
f f m f= + −
⎛
⎝
⎜
⎞
⎠
⎟π 2π
(4)
where, E indicates the elastic modulus of the composite
material, Ef indicates the elastic modulus of the fiber
material, Em indicates the elastic modulus of the matrix
material and Vf indicates the fiber volume fraction.
3.3 Inverse rule of mixtures (IROM)
The rule-of-mixtures model is frequently used to pre-
dict the elastic moduli of the composite materials with
continuous and unidirectional fibers. Since the inverse
rule of mixtures indicates that the loading is perpendi-
cular to the fibers, it is used to predict the elastic moduli
of the random discontinuous short-fiber-reinforced
composites in this study.13 The inverse rule of mixtures is
expressed as:
E
V
E
V
E
= +
−⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
−
f
f
f
m
1
1
(5)
where E indicates the elastic modulus of the composite
material, Ef indicates the elastic modulus of the fiber
material, Em indicates the elastic modulus of the matrix
material and Vf indicates the fiber volume fraction.
3.4 Manera’s model
Manera16 developed a new equation by making some
assumptions on Puck’s micromechanical model and
simplifying it. These assumptions include a high fiber
orientation ratio, two-dimensional random-fiber range,
and he also considered the randomly oriented discon-
tinuous fibers as the laminate of an unlimited number of
layers. Manera’s equation is as follows:
E V E E E= +⎛
⎝
⎜
⎞
⎠
⎟ +f f m m
16
45
2
8
9
(6)
where E indicates the elastic modulus of the composite
material, Ef indicates the elastic modulus of the fiber
material, Em indicates the elastic modulus of the matrix
material and Vf indicates the fiber volume fraction.
3.5 Nielsen-Chen model
Nielsen and Chen built a new model for the predic-
tion of the elastic moduli of the composite materials
using the rule of mixtures and the inverse rule of
mixtures:17
U. ÖZMEN, B. OKUTAN BABA: PREDICTION OF THE ELASTIC MODULUS OF CHICKEN-FEATHER-REINFORCED PLA ...
Materiali in tehnologije / Materials and technology 50 (2016) 1, 141–146 143
E E E= +∏ ⊥
3
8
5
8
(7)
where;
E E V E V∏ = + −f f m f( )1 (8)
E
E E
E V V E⊥
=
− +
f m
f f f m( )1
(9)
and E indicates the elastic modulus of the composite
material, Ef indicates the elastic modulus of the fiber
material, Em indicates the elastic modulus of the matrix
material and Vf indicates the fiber volume fraction.
3.6 Halpin-Tsai model
The Halpin-Tsai model is quite complicated in
comparison with the other micromechanical models.18,19
Its consideration of the aspect ratio is the most important
advantage of this model. Therefore, the Halpin-Tsai
model converges better to the experimental results. The
Halpin-Tsai model is as follows:
E E
v
v
=
+
−m
f
f
1
1


(10)
where  and  are:


=
−
E
E
E
E
f
m
f
m
1
(11)
 =
2L
D
(12)
and E indicates the elastic modulus of the composite
material, Ef indicates the elastic modulus of the fiber
material, Em indicates the elastic modulus of the matrix
material and Vf indicates the fiber volume fraction. L
and D indicate the fiber length and diameter, respec-
tively.
4 RESULTS AND DISCUSSION
The elastic moduli of PLA and CFF/PLA composites
were obtained with tensile testing and the results are
shown in Table 2. The elastic modulus of PLA was
experimentally measured as 3004 MPa. The chicken-
feather addition increased the elastic modulus by
approximately 2.6 % for the mass fraction of 2 %, while
increasing the elastic modulus by 2.4 % for the mass
U. ÖZMEN, B. OKUTAN BABA: PREDICTION OF THE ELASTIC MODULUS OF CHICKEN-FEATHER-REINFORCED PLA ...
144 Materiali in tehnologije / Materials and technology 50 (2016) 1, 141–146
Figure 3: Comparison of the elastic moduli of the composite materials
obtained with different micromechanical models
Slika 3: Primerjava modulov elasti~nosti kompozitnih materialov,
dobljenih iz razli~nih mikromehanskih modelov
Table 3: Elastic moduli of composite materials obtained with micro-
mechanical models
Tabela 3: Moduli elasti~nosti kompozitnih materialov iz mikro-
mehanskih modelov
C
hi
ck
en
-f
ea
th
er
m
as
s
fr
ac
ti
on
s
(w
/%
)
C
hr
is
te
ns
en
-W
aa
ls
M
od
el
IR
O
M
Pa
n’
s
M
od
el
(2
-D
)
Pa
n’
s
M
od
el
(3
-D
)
M
an
er
a’
s
M
od
el
N
ie
ls
en
-C
he
n
M
od
el
H
al
pi
n-
T
sa
i
M
od
el
2 3130(1.7)
3034
(1.6)
3019
(2.1)
3317
(7.6)
2882
(6.3)
3040
(1.4)
3034
(1.6)
5 3315(7.8)
3079
(0.1)
3040
(1.2)
3319
(7.9)
3194
(3.8)
3092
(0.5)
3079
(0.1)
10 3614(14.1)
3153
(0.4)
3074
(2.9)
3322
(4.9)
3697
(16.8)
3179
(0.4)
3153
(0.4)
*The values given in the parentheses are percentage differences
between the elastic moduli obtained with the micromechanical models
and experiments.
Table 2: Experimental data for the elastic moduli of CFF/PLA com-
posites
Tabela 2: Eksperimentalni podatki za module elasti~nosti CFF/PLA
kompozita
Chicken-feather
mass fractions,
(w/%)
Chicken-feather
volume fractions,
(Vf /%)
Elastic modulus
(E/MPa)
0 0 3004 (255)
2 2.76 3083 (83)
5 6.83 3076 (309)
10 13.4 3166 (132)
*The values given in the parentheses are standard deviations.
fraction of 5 %. Similarly, its increase for the composite
materials with a chicken-feather mass fraction of 10 %
was 5.4 %. The increasing CFF content raised the elastic
modulus as expected. This increase in the elastic modu-
lus validated the predictions made with the micro-
mechanical models.
A comparison of the elastic moduli obtained with the
models and tests for the composite materials including
the chicken-feather mass fractions of (2, 5 and 10) % is
shown in Table 3. To show the differences between the
results of the models and the tests, the elastic moduli
from Table 3 are plotted as shown in Figure 3. Accord-
ing to the literature, the Christensen-Waals model gives
accurate results for some composite materials containing
a mass fraction of up to 20 %. In this study, the
CFF/PLA composites having a mass fraction of 2 %
show a deviation of 1.7 %, which is a close to the experi-
mental results, as mentioned above. The materials
including mass fractions of 5 and 10 % show deviations
of 7.8 % and 14.1 %, respectively, which means that the
results diverge from the experimental data when the
mass fraction of the material increases. Consequently,
the Christensen-Waals model does not predict the elastic
modulus very well for a fiber mass fraction of more than
2 %.
IROM shows a deviation of 1.6 % from the predic-
tion of the elastic modulus of the composites including a
2 % chicken-feather content when compared with the
experimental results. IROM produces accurate values
converging by more than 99 % to the prediction of the
elastic moduli of the composites having mass fractions
of 5 and 10 %. Pan’s 2-D model shows the results close
to the experimental elastic-modulus values of the com-
posites including (2, 5 and 10) % of CFF. Their devi-
ations are (2.1, 1.2 and 2.9) %, respectively. On the other
hand, the elastic modulus found with Pan’s 3-D model is
higher than the test data even at low fiber mass fractions.
Manera’s model fails to give good predictions of the
elastic modulus for high fiber mass fractions. Therefore,
it is not possible to use Manera’s model for the predic-
tion of the elastic moduli of the composites including
high fiber contents. However, the model gives reasonable
predictions for the fiber mass fractions of about 5 %.
Manera’s model exhibits a deviation of 3.8 % for the
composite including a mass fraction of 5 %.
Another elastic-modulus-prediction model is the
Nielsen-Chen model. The predictions of this model are
close to the test data. It exhibits deviations of (1.4, 0.5
and 0.4) % for the elastic moduli of the composites
including (2, 5 and 10) % of the CFF content, respec-
tively, when compared with the experimental results.
Hence, the Nielsen-Chen model is the best model
producing the closest and most reliable results among the
models investigated in this study. As seen in Figure 2,
the Halpin-Tsai model exhibits the results similar to
IROM and its deviations are very close to the ones found
with IROM. The Halpin-Tsai model is also one of the
most appropriate models to predict the elastic moduli of
the CFF/PLA composites.
5 CONCLUSION
In this study, the elastic moduli of the composites
including mass fractions of (2, 5 and 10) % of chicken-
feather fibers were predicted using six different micro-
mechanical models and the results were compared with
the experimental data. The results are given below:
Although the Christensen-Waals model gives good
predictions for low fiber mass fractions, it does not fit
well the test data for high fiber mass fractions. Pan’s 3-D
model and Manera’s model do not produce reliable
results when used to predict the elastic moduli of the
CFF/PLA composites.
The comparison with the experimental results shows
that Pan’s 2-D model, the inverse rule of mixtures and
the Halpin-Tsai model can be used to predict the elastic
moduli of the CFF/PLA composites.
From the comparison, it can be seen that the Niel-
sen-Chen model gives the best predictions of the elastic
modulus of the CFF/PLA composites. Consequently, the
most appropriate model to predict the elastic moduli of
the CFF/PLA composites is the Nielsen-Chen model.
Acknowledgements
This project was supported by the Celal Bayar
University Research Funds 2013/35.
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146 Materiali in tehnologije / Materials and technology 50 (2016) 1, 141–146