Modeling and Analysis of the Tensile and Flexural Properties of a FiberOrientated Hybrid Nanocomposite Using Taguchi Methodology
Оценено влияние трех независимых параметров (ориентация волокон, весовая доля наночастиц глинозема и кремнезема) на прочностные характеристики гибридного нанокомпозита из эпоксидной смолы, армированной углепластиковыми волокнами, с нанодобавками глинозема и кремнезема при растяжении и изгибе. Для пл...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2015
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| Цитувати: | Modeling and Analysis of the Tensile and Flexural Properties of a FiberOrientated Hybrid Nanocomposite Using Taguchi Methodology / Y. Rostamiyan // Проблемы прочности. — 2015. — № 6. — С. 49-65. — Бібліогр.: 34 назв. — англ. |
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Rostamiyan, Y. 2020-12-02T16:15:24Z 2020-12-02T16:15:24Z 2015 Modeling and Analysis of the Tensile and Flexural Properties of a FiberOrientated Hybrid Nanocomposite Using Taguchi Methodology / Y. Rostamiyan // Проблемы прочности. — 2015. — № 6. — С. 49-65. — Бібліогр.: 34 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/173394 539.4 Оценено влияние трех независимых параметров (ориентация волокон, весовая доля наночастиц глинозема и кремнезема) на прочностные характеристики гибридного нанокомпозита из эпоксидной смолы, армированной углепластиковыми волокнами, с нанодобавками глинозема и кремнезема при растяжении и изгибе. Для планирования экспериментов использовали ортогональный набор согласно методике Тагучи. Для оценки функции отклика было изготовлено и испытано 16 образцов при запланированных комбинациях вышеуказанных параметров. Оцінено вплив трьох незалежних параметрів (орієнтація волокон, вагова частка наночастинок глинозему і кремнезему) на міцнісні характеристики гібридного нанокомпозиту з епоксидної смоли, армованої вуглепластиковими волокнами, з нанодобавками глинозему і кремнезему при розтязі та згині. Для планування експеримент ів використовували ортогональний набір згідно з методикою Тагучі. Для оцінки функції відклику було виготовлено і випробувано 16 зразків при запланованих комбінаціях вищевказаних параметрів. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Modeling and Analysis of the Tensile and Flexural Properties of a FiberOrientated Hybrid Nanocomposite Using Taguchi Methodology Моделирование и расчет характеристик прочности армированного волокнами гибридного нанокомпозита при растяжении и изгибе по методике Тагучи Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Modeling and Analysis of the Tensile and Flexural Properties of a FiberOrientated Hybrid Nanocomposite Using Taguchi Methodology |
| spellingShingle |
Modeling and Analysis of the Tensile and Flexural Properties of a FiberOrientated Hybrid Nanocomposite Using Taguchi Methodology Rostamiyan, Y. Научно-технический раздел |
| title_short |
Modeling and Analysis of the Tensile and Flexural Properties of a FiberOrientated Hybrid Nanocomposite Using Taguchi Methodology |
| title_full |
Modeling and Analysis of the Tensile and Flexural Properties of a FiberOrientated Hybrid Nanocomposite Using Taguchi Methodology |
| title_fullStr |
Modeling and Analysis of the Tensile and Flexural Properties of a FiberOrientated Hybrid Nanocomposite Using Taguchi Methodology |
| title_full_unstemmed |
Modeling and Analysis of the Tensile and Flexural Properties of a FiberOrientated Hybrid Nanocomposite Using Taguchi Methodology |
| title_sort |
modeling and analysis of the tensile and flexural properties of a fiberorientated hybrid nanocomposite using taguchi methodology |
| author |
Rostamiyan, Y. |
| author_facet |
Rostamiyan, Y. |
| topic |
Научно-технический раздел |
| topic_facet |
Научно-технический раздел |
| publishDate |
2015 |
| language |
English |
| container_title |
Проблемы прочности |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| format |
Article |
| title_alt |
Моделирование и расчет характеристик прочности армированного волокнами гибридного нанокомпозита при растяжении и изгибе по методике Тагучи |
| description |
Оценено влияние трех независимых параметров (ориентация волокон, весовая доля наночастиц глинозема и кремнезема) на прочностные характеристики гибридного нанокомпозита из эпоксидной смолы, армированной углепластиковыми волокнами, с нанодобавками глинозема и кремнезема при растяжении и изгибе. Для планирования экспериментов использовали ортогональный набор согласно методике Тагучи. Для оценки функции отклика было изготовлено и испытано 16 образцов при запланированных комбинациях вышеуказанных параметров.
Оцінено вплив трьох незалежних параметрів (орієнтація волокон, вагова частка наночастинок глинозему і кремнезему) на міцнісні характеристики гібридного нанокомпозиту з епоксидної смоли, армованої вуглепластиковими волокнами, з нанодобавками глинозему і кремнезему при розтязі та згині. Для планування експеримент ів використовували ортогональний набір згідно з методикою Тагучі. Для оцінки функції відклику було виготовлено і випробувано 16 зразків при запланованих комбінаціях вищевказаних параметрів.
|
| issn |
0556-171X |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/173394 |
| citation_txt |
Modeling and Analysis of the Tensile and Flexural Properties of a FiberOrientated Hybrid Nanocomposite Using Taguchi Methodology / Y. Rostamiyan // Проблемы прочности. — 2015. — № 6. — С. 49-65. — Бібліогр.: 34 назв. — англ. |
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2025-11-26T08:40:51Z |
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| fulltext |
UDC 539.4
Modeling and Analysis of the Tensile and Flexural Properties of a Fiber-
Orientated Hybrid Nanocomposite Using Taguchi Methodology
Y. Rostamiyan
a,b
a Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran
b Department of Mechanical Engineering, Semnan University, Semnan, Iran
yasser.rostamiyan@iausari.ac.ir
ÓÄÊ 539.4
Ìîäåëèðîâàíèå è ðàñ÷åò õàðàêòåðèñòèê ïðî÷íîñòè àðìèðîâàííîãî
âîëîêíàìè ãèáðèäíîãî íàíîêîìïîçèòà ïðè ðàñòÿæåíèè è èçãèáå ïî
ìåòîäèêå Òàãó÷è
ß. Ðîñòàìèÿí
à,á
à Èñëàìñêèé óíèâåðñèòåò Àçàä, Ñàðè, Èðàí
á Óíèâåðñèòåò ã. Ñåìíàí, Èðàí
Îöåíåíî âëèÿíèå òðåõ íåçàâèñèìûõ ïàðàìåòðîâ (îðèåíòàöèÿ âîëîêîí, âåñîâàÿ äîëÿ íàíî-
÷àñòèö ãëèíîçåìà è êðåìíåçåìà) íà ïðî÷íîñòíûå õàðàêòåðèñòèêè ãèáðèäíîãî íàíîêîìïîçèòà
èç ýïîêñèäíîé ñìîëû, àðìèðîâàííîé óãëåïëàñòèêîâûìè âîëîêíàìè, ñ íàíîäîáàâêàìè ãëèíîçåìà
è êðåìíåçåìà ïðè ðàñòÿæåíèè è èçãèáå. Äëÿ ïëàíèðîâàíèÿ ýêñïåðèìåíòîâ èñïîëüçîâàëè
îðòîãîíàëüíûé íàáîð ñîãëàñíî ìåòîäèêå Òàãó÷è. Äëÿ îöåíêè ôóíêöèè îòêëèêà áûëî èçãî-
òîâëåíî è èñïûòàíî 16 îáðàçöîâ ïðè çàïëàíèðîâàííûõ êîìáèíàöèÿõ âûøåóêàçàííûõ ïàðà-
ìåòðîâ. Âûÿâëåí îáðàòíûé ýôôåêò âëèÿíèÿ âõîäíûõ ïàðàìåòðîâ íà ñîîòâåòñòâóþùèå
îòêëèêè, ïðè÷åì ïîëó÷åííûå äâóõìåðíûå ãðàôèêè ïîêàçûâàþò, ÷òî âàðüèðîâàíèå òàêèìè
äâóìÿ ïàðàìåòðàìè, êàê îðèåíòàöèÿ âîëîêîí – äîëÿ íàíî÷àñòèö ãëèíîçåìà è îðèåíòàöèÿ
âîëîêîí – äîëÿ íàíî÷àñòèö êðåìíåçåìà, ñóùåñòâåííî âëèÿåò íà ïðî÷íîñòíûå õàðàêòåðèñ-
òèêè ïðè ðàñòÿæåíèè è èçãèáå, â òî âðåìÿ êàê âàðüèðîâàíèå ïàðàìåòðàìè äîëÿ íàíî÷àñòèö
êðåìíåçåìà – äîëÿ íàíî÷àñòèö ãëèíîçåìà íå îêàçûâàåò çíà÷èòåëüíîãî âëèÿíèÿ íà âûøå-
óêàçàííûå õàðàêòåðèñòèêè. Ïîëó÷åííûå äèàãðàììû íàïðÿæåíèå–äåôîðìàöèÿ ïîêàçûâàþò,
÷òî ãèáðèäíûå íàíîêîìïîçèòû ñ ðàçëè÷íîé îðèåíòàöèåé âîëîêîí èìåþò áîëåå âûñîêèå
ïðî÷íîñòíûå õàðàêòåðèñòèêè ïðè ðàñòÿæåíèè è èçãèáå, áîëüøèå óäëèíåíèÿ ïðè ðàçðóøåíèè è
ìåíüøèå ìîäóëè óïðóãîñòè, ÷åì êîìïîçèòû èç ýïîêñèäíîé ñìîëû êàê áåç íàíîäîáàâîê, òàê è ñ
íàíîäîáàâêàìè ãëèíîçåìà èëè êðåìíåçåìà.
Êëþ÷åâûå ñëîâà: óãëåïëàñòèêîâûå âîëîêíà, ëàìèíàò, ãèáðèä, ìåõàíè÷åñêèå ñâîéñòâà,
ìåòîäèêà Òàãó÷è.
Introduction. Composite materials have been used in a wide range of industry fields
like: aerospace, sports, automobile and etc. In recent decades because of their
environmentally friendly nature, economical efficiency properties and superior mechanical
and thermal properties compare with other kind of materials [1]. For example composites
have demonstrated weight savings for aircraft structures and outstanding corrosion and
fatigue-damage resistance [2]. In recent years, approximately all of the research done in the
field of composite materials has focused on improving their mechanical and thermal
properties by adding various additives. Different types of materials can be added to
composite materials in order to achieve considered properties such as fibers, macro-,
© Y. ROSTAMIYAN, 2015
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6 49
micro-, and nanomaterials. The most applicable thermoset matrices used for reinforcing
composite materials are epoxy resins due to their low price, superior mechanical properties
and chemical stability [3–8]. Mechanical properties of epoxy resins can be improved by
adding rigid inorganic nanoparticles without affecting the glass transition temperature of
the epoxy [9]. In many studies, the epoxy resin performance was improved by
incorporating thermoplastic fillers, rubber agents, diluents, and nanoparticles into the
epoxy, in addition to inorganic nanoparticles being used as reinforcing materials due to
their low cost, ease of fabrication, and environmentally friendly nature [10]. Various
nanofillers, such as silica (SiO2) [9], clay, carbon nanotube (CNT), alumina (Al2O3) [11],
and titania (TiO2) [12] can be employed for this purpose. Mirmohseni and Zavareh [13]
reported that adding 2.5 wt.% organically modified clay into the epoxy resin increased the
tensile modulusand impact strength compared to those of the neat epoxy. Xu and Hoa [14]
showed 38% improvement in flexural strength achieved by adding a low weight percentage
of nanoclay to the fiber/epoxy composites. Akbari et al. [15] used liquid carboxyl-
terminated butadiene acrylonitrile (CTBN) for toughening epoxy resin and 26%
improvement in tensile strength was reported when 5 phr (per hundred resins) CTBN was
added. Becker et al. [16] added Nanomer I.30E nanoclay into epoxy resin, which resulted
in the increased fracture toughness and elastic modulus. Liu et al. [17] founded that adding
nanoclay to a nanocomposite increased the fracture toughness and elastic modulus of the
epoxy system without decreasing its compressive strength. Yasmin et al. [18] filled DGEBA
resin with nanoclay and produced a specimen with a lower tensile strength and a higher
elastic modulus compare to the neat epoxy. Ragosta et al. [19] found that adding 10 wt.%
silica in to the epoxy matrix improved mechanical properties. Zheng et al. [9] added 3 wt.%
of nanosilica to the epoxy matrix and described that the tensile strength increased by about
115%, and the impact strength increased by about 56%. Rosso et al. [20] filled epoxy resin
with 11 wt.% of silica nanoparticles and an improvement in the tensile modulus and
fracture toughness was reported.
As mentioned above, various additives can be added to composite materials. Fibers
are such additives, that provide stress redistribution throughout the restoration and improve
the structural properties of the material by acting as crack stoppers [21]. Glass fiber is the
most commonly used fiber compared to other kinds of fibers and can improve the in-plane
mechanical properties much better than the others. Panthapulakkal and Sain [22] evaluated
mechanical and thermal properties of hemp/glass fiber-polypropylene composite and
showed that adding glass fiber into hemp-polypropylene composite improved thermal
properties. Eronat et al. [23] studied effects of glass fiber layering on the flexural strength
of microfill and hybrid composites and reported that glass fiber layering of microfill and
hybrid composites showed higher flexural strength, and veneering of hybrid composite with
microfill composite increased the resistance of restoration. Using carbon fiber as
reinforcement improves the mechanical properties of epoxy and other material matrices
because of specific strength and modulus. Godara et al. [24] reinforced carbon nanotubes
(CNTs) with carbon fibers and showed that the viscosity profile of the epoxy matrix
reinforced with different types of CNTs indicated a strong dependency on the type of
CNTs. There was also a substantial increase of over 80% in fracture toughness Mode-I for
the pristine multi-walled CNTs in combination with the epoxy resin which was modified by
using a compatibilizer. Bekyarova et al. [25] used carbon fiber/epoxy reinforced with
carbon nanotubes and reported a great laminar strength (~ 50 MPa).
Using two or more kinds of micro- or nanoparticles as reinforcement creates hybrid
nanocomposites. These kinds of composites provide higher mechanical properties and
crack propagation resistance compared to those with one kind of reinforcement [26]. A
large number of researches have been carried out on hybrid nanocomposites. Rostamyian et
al. [27] used multi-walled carbon nanotube in present of high impact polystyrene and
showed that mechanical properties such as tensile, compression and impact were improved.
Y. Rostamiyan
50 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6
Rostamiyan et al. [6] reported that adding nanoclay as a nanoreinforcement and HIPS as a
thermoplastic phase into the epoxy resin creates synergistic effects on mechanical properties.
Their results showed that new ternary nanocomposite possessing tensile, compressive, and
impact strengths were improved up to 60, 64, and 402%, respectively. Geisler and Kelley
[28] filled epoxy resin with alumina (Al2O3) and rubber particles and reported that obtained
toughness values were 25% higher than those of epoxy systems having only alumina
(Al2O3) or rubber particles. Mirmohseni and Zavareh [29] showed that by adding 2% clay
and 20% polyamide, the material toughness increased by 115% and also impact strength
improved as compared to neat epoxy. Kinloch et al. [30] added nanosilica and rubber
microparticles to epoxy resin. They described a significant increase in toughness.
Rostamyian et al. [31] used nanosilica and high impact poly styrene as reinforcement in
epoxy-based hybrid nanocomposite. They reported that new ternary nanocomposite
improved ultimate tensile, compression and impact strength up to 59.5, 45, and 414%,
respectively, compared to those of the neat epoxy resin. Mirmohseni and Zavareh [29]
showed that adding ABS, nanoclayand TiO2 into the epoxy improved impact strength
compared to neat epoxy. Rostamiyan et al. [6] also filled epoxy resin with nanoclay as a
nanoreinforcement and HIPS as a thermoplastic phase and reported that impact, tensile and
compression and strengths were improved by up to 402, 60, and 64%, respectively, as
compared to those of the pure epoxy.
As follows from the above considerations, the mechanical properties of hybrid
nanocomposites can be affected by many factors, one of which is the weight percentage of
reinforcement, such as toughening agent and nanofiller [29]. The other important factor is
weight percentage of a hardener. Although determination of the appropriate amount of this
factor is based on the stochiometric ratio, this expectation is not far, especially in the
presence of thermoplastic phase as toughening agent and also nanofiller in the epoxy resin.
The probability of complete mixture of epoxy monomers and hardener would dramatically
deteriorate and hence prevent a complete polymerization. The OVAT (one variation at time)
is the conventional method for analyzing effective parameters of an experiment. This
method can only analyze one variable at a time, while in most experimental designs,
variables depend on each other and also the effect of interactions between them is
important, so this method is not instrumental for deriving the truly optimum point. Leardi
[32] claimed that 93% of the published papers in 2009 with general titles containing
“optimization,” “development,” “improvement” or “effect of,” employed the OVAT model.
Predicting the nonlinear effect of each parameter is the important feature, which requires at
least three points as parameter levels, which directly increases the number of the required
experiments for model prediction and consequently increases the time and cost. There are a
numerous mathematical methods of design of experiments (DOE). These methods provide
the ability to evaluate the joint effect of two parameters and also the nonlinear effect of
selected parameters. Also these methods can optimize the results and provide the optimum
levels of each factor, in order to achieve the best result based on the desired goal. The
response surface design is one of the most widespread mathematical and statistical methods
for analyzing multiple factors at a time, evaluating nonlinear effect of parameters, studying
the effect of interaction between factors and finally optimizing the response [33]. The
Taguchi design is a section of DOE methods, which uses an orthogonal array,
signal-to-noise (S/N) ratio and analyses of variance (ANOVA) for analyzing the results and
determining the significant parameters and how they affect the corresponding response.
This method reduces the number of generated experiments and thus reduces their
conduction time and cost. For measuring the quality characterization deviating from the
desired values, the Taguchi design transforms into the S/N ratio. A higher S/N ratio
indicates a better experimental response of characteristics (the optimal level of the process
parameter). Analyses of variance should be done to evaluate the effect of each input
parameter on the response. Moreover, the ANOVA table can reveal, which particular
Modeling and Analysis of the Tensile and Flexural Properties ...
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6 51
parameter has a significant effect on the result [34]. The Taguchi method is widely used in
the field of engineering. In the current study, the Taguchi method was selected for
analyzing flexural and tensile strength of epoxy/carbon fiber/nanoclay/nanosilica quadratic
hybrid nanocomposite. The weight percentage of nanoclay and nanosilica and also the
orientation of carbon fiber were selected as independent input variables and the effect of
these parameters on flexural and tensile strength properties was investigated.
1. Experimental.
1.1. Materials. The epoxy resin utilized in this study was an undiluted clear
difunctional bisphenol A, Epon 828 and provided by Shell Chemicals Co. Its epoxide
equivalent weight was 185–192 g/eq. Epon 828 is basically DGEBA (Diglycidyl ether of
bisphenol-A). The curing agent was a nominally cycloaliphatic polyamine, Aradur® 42
supplied by Huntsman Co. The organoclay Cloisite 30B was purchased from Southern Clay
Products (Gonzales, TX, USA). The spherical silica nanoparticles with average particle size
10–15 nm and SSA (specific surface area) 180–270 m2/g were supplied by TECNAN Ltd.
The solvent used was Tetrahydrofuran (THF) with purity (GC) of more than 99% provided
from Merck Co (Germany).
1.2. Specimen Preparation. The laminate plates were prepared with 16 layers and
different fiber orientations based on the generated experiments using the Taguchi design.
For preparing each specimen carbon fiber was hand laid-up with the specific steps. In order
to create homogenous mixture, the whole procedure of reinforcing the resin was carried out
in a suitable solvent. Tetrahydrofuran was selected as solvent for all the mixture
components, including nanosilica, epoxy resin, and nanoclay. Liquid epoxy resin was
poured into an adequate amount of THF solvent, so the comparable neat epoxy specimens
could be mixed using of magnetic stirrer at least 2 h with 2000 rpm. Then the solvent was
completely evaporated using a vacuum Erlenmeyer. In the next stage, the mixture was
homogenized by ultrasonicating (ultrasonic SONOPLUS-HD3200, 50% amplitude, 20 kHz
and pulsation; on for 10 s and off for 3 s) for 8 min. At this step, 23 phr of cycloaliphatic
polyamine was added as hardener according to the stoichiometric ratio. Then the mixture
was degassed using the vacuum pump to remove the air bubbles. All specimens were
prepared using the handy lay-up method and cured at room temperature for 24 h with the
following post-curing from 20 to 130�C every 2 h with a 20�C temperature enhancement
interval. Figure 1 depicts a symmetric laminate composite ply structure, while Fig. 2
displays a laminated composite specimen prepared for the current study.
52 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6
Y. Rostamiyan
Fig. 1. Laminate stacking of plies [(��) 2] sym.
1.3. Characterization. Tensile tests in the current study were conducted according to
the ASTM D: 3039. Specimens with 0 and 90� unidirectional fibers were prepared with
dimensions of 15 250 1� � and 25 175 2� � mm, respectively. Other specimens were prepared
with dimensions of 25 250 2 5� � . mm, according to the above standard. These mechanical
tests were conducted using an STM-150 universal testing machine from Santam Company
(Tehran, Iran) with a load capacity of 150 kN. In addition, flexural tests were conducted
based on the 3-point bending loading scheme according to the ASTM: D790. This test
method covers the determination of the flexural properties of reinforced plastics, including
high-modulus composites. The dimensions of the specimens were 127 12 7 3 2� �. . mm.
Figure 3 shows the delamination process of the specimen under flexural test, while Fig. 4
shows a delaminated specimen under tensile test.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6 53
Modeling and Analysis of the Tensile and Flexural Properties ...
Fig. 2. Laminated nanocomposite prepared for tests.
Fig. 3. Delamination process of specimen under flexural test.
Fig. 4. Delaminated specimen under tensile test.
2. Design of Experiment. The Taguchi design is a lucrative method for the design of
experiments and is known as “orthogonal array design.” It provides a simple and effective
way of analyzing and allows one to produce high-quality products with a low
manufacturing cost and in less time. This method requires only a fraction of the full
factorial combinations. An orthogonal array means that the design is balanced so that factor
levels are weighted equally. Because of this, each factor can be evaluated independently of
all the other factors, so the effect of one factor does not influence the estimation of another.
This method decreases the number of experiments, as compared to other DOE methods
such as full factorial design or response surface design. In this study, carbon fiber
orientation, nanoclay wt.% and nanosilica wt.% were selected as input parameters and the
effectiveness of each factor on tensile and flexural properties of hybrid quaternary
nanocomposite was investigated. By using this method the number of experiments carried
out was reduced to 16 sets instead of 64 (4 4 4� � for full factorial design). The steps of the
Taguchi experimental design are as follows:
(i) determining the number of levels for each parameter;
(ii) selecting the appropriate orthogonal array;
(iii) arrangement of operation parameters to the orthogonal array;
(iv) conducting experiments based on the arrangement of the orthogonal array;
(v) analysis of results usingthe signal-to-noise ratio (S/N) and analysis of variance
(ANOVA).
The Taguchi method selects the optimum condition so the effect of uncontrollable
factors (noise) on response attains the minimum. The Taguchi method utilizes ANOVA to
determine the influence of any parameter on response and to interpret the percentage of
contribution of each experimental variable. One aim of this study was to specify the most
effective factors, in order to achieve the maximum enhancement of tensile and flexural
properties of the mentioned quaternary nanocomposite. Three factors, such as carbon fiber
orientation, nanoclay wt.%, and nanosilica wt.% with four different levels were selected for
the design of experiments. Table 1 shows the independent factors and the selected levels for
each of these factors. The L16 orthogonal array (shown in Table 2) was selected for this
study according to the number of factors and their levels. Responses of the designed
experiments were set to the maximum flexural and tensile strength values. The Minitab
software v.16.244 was used for analyzing the results.
3. Results and Discussion. As it was mentioned above, the independent input
parameters selected for the current study were carbon fiber orientation, nanoclay wt.% and
nanosilica wt.% which are designated in the analysis of variance as parameters A, B, and C,
respectively, whereas the selected responses were tensile and flexural properties of hybrid
quaternary nanocomposite. Table 3 displays the details of 16 generated experiments using
the Taguchi design and the levels of each factor in different run numbers, as well as
experimental results obtained from tensile and flexural tests. According to this table, the
maximum tensile and flexural strength values were obtained for the design level 2 with
magnitudes of 470.3 and 26.6 MPa, respectively. The related value of input parameters for
54 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6
Y. Rostamiyan
T a b l e 1
Factors and Levels Selected for Taguchi Design
Level A. Fiber orientation (deg) B. Nanoclay (wt.%) C. Nanosilica (wt.%)
1
2
3
4
0
30
60
90
0.5
1.5
2.5
3.5
0.5
1.0
1.5
2.0
this level were 0� of fiber orientation, 1.5 wt.% of nanoclay and 1 wt.% of nanosilica. The
minimum value of tensile strength occurred in design level 16 with a magnitude of 69.5 MPa
and input parameters of 90� of fiber orientation, 3.5 wt.% of nanoclay and 0.5 wt.% of
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Modeling and Analysis of the Tensile and Flexural Properties ...
T a b l e 2
L16 Orthogonal Array Used for Experimental Design
Experimental
No.
Factor levels
Aa Bb Cc
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
1
1
1
1
2
2
2
2
3
3
3
3
4
4
4
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
2
1
4
3
3
4
1
2
4
3
2
1
T a b l e 3
Experimental Design and Corresponding Responses
Experimental
No.
Experimental factors Responses
Fiber
orientation
(deg)
Clay
content
(wt.%)
Silica
content
(wt.%)
Tensile
strength
(MPa)
Flexural
strength
(MPa)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
0
0
0
0
30
30
30
30
60
60
60
60
90
90
90
90
0.5
1.5
2.5
3.5
0.5
1.5
2.5
3.5
0.5
1.5
2.5
3.5
0.5
1.5
2.5
3.5
0.5
1.0
1.5
2.0
1.0
0.5
2.0
1.5
1.5
2.0
0.5
1.0
2.0
1.5
1.0
0.5
420.1
470.3
465.4
359.2
250.6
245.3
215.1
227.4
195.6
171.2
159.1
180.3
74.7
88.2
95.3
69.5
21.3
26.6
22.8
18.1
12.5
12.2
10.3
11.1
5.2
6.8
7.5
7.3
2.8
3.9
4.1
3.3
nanosilica. Also the minimum value of flexural strength was 2.8 MPa which occurred in
design level 13 with 90� of fiber orientation, 0.5 wt.% of nanoclay and 2 wt.% of nanosilica
respectively.
3.1. Signal to Noise (S/N) Ratio. The Taguchi method recommends the use of S/N
ratio which is measured by the deviation of characteristics from their target value. In this
case the aim is to improve and increase the obtained value of tensile and flexural strength
and, so it seems that a larger response is better and the S/N ratio will be defined as follows:
S/N ��
�
�
�
�
�10
1 1
2
1
log ,
n yii
n
where n is the trial repetition and yi is the result of the ith experiment for each trial.
Results of the mean S/N ratios for the three input factors at their designed levels are
shown in Table 4. Figure 5 shows the S/N graph for different levels of the three selected
factors.
3.2. Analysis of Variance for S/N Ratio. The Taguchi method uses analysis of
variance for estimating the effect of input parameters on corresponding response. For this
purpose Taguchi method evaluates the significance of each parameter according to its
probability value (P-value). In the current study, the ANOVA analysis was carried out
based on confidence level �� 0.05. So the terms with probability P � 95% (�� 0.05) are
significant and those with P-value less than 95% (�� 0.05) are not considered effective on
the selected response. Table 5 displays the ANOVA results for tensile and flexural strength
properties. As seen the fiber orientation was the most effective parameter on both responses
with a probability value of P � 99%. Nanoclay wt.% was significant on tensile and flexural
56 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6
Y. Rostamiyan
T a b l e 4
Magnitudes of S/N Ratio
Experimental
No.
Experimental factors S/N ratio
Fiber
orientation
(deg)
Clay
content
(wt.%)
Silica
content
(wt.%)
Tensile
strength
Flexural
strength
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
0
0
0
0
30
30
30
30
60
60
60
60
90
90
90
90
0.5
1.5
2.5
3.5
0.5
1.5
2.5
3.5
0.5
1.5
2.5
3.5
0.5
1.5
2.5
3.5
0.5
1.0
1.5
2.0
1.0
0.5
2.0
1.5
1.5
2.0
0.5
1.0
2.0
1.5
1.0
0.5
52.46
53.44
53.34
51.19
47.95
47.78
46.64
47.12
45.80
44.65
44.02
45.10
37.38
38.88
39.55
36.77
26.56
28.49
26.92
25.10
21.93
21.58
20.00
20.82
13.97
16.65
17.50
17.26
8.29
11.82
12.25
10.37
strength with P-value 96%. Moreover nanosilica wt.% affected both tensile and flexural
strength with P-values of 96 and 98% respectively. So it can generally be concluded that
variation in weight percentage of nanosilica had a greater effect on the flexural strength
than tensile.
3.3. Main Effect Plot for S/N Ratio. Figures 6 and 7 display the main effect plot of
S/N ratio on tensile and flexural strength properties respectively. These types of plots
determine how a parameter affects the corresponding response. According to Fig. 6, the
tensile strength decreased while continuously increasing the degree of fiber orientation and
had a small increase with increasing the weight percentage of nanoclay and nanosilica and
then decreased slightly. From Fig. 7 it is obvious that nanosilica wt.% and nanoclay wt.%
had a similar effect on flexural strength and the nanosilica wt.% decreased the magnitude of
flexural strength more than tensile, also increasing in the degree of fiber orientation
decreased the flexural strength. Comparing the effect of nanoclay wt.% in both graphs, it
shows that the magnitude of tensile strength at level 4 was higher than level 1, while the
flexural strength at level 4 was lower than that at level 1.
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T a b l e 5
Analysis of Variance for S/N Ratio for Tensile and Flexural Strengths
Source DF Seq SS Adj SS Adj MS F P
Tensile strength
A
B
C
Residual error
Total
3
3
3
6
15
431.566
3.060
7.023
1.211
442.860
431.566
3.060
7.023
1.211
–
143.855
1.020
2.341
0.202
–
712.62
5.05
11.60
–
–
0
0.044
0.007
–
–
Flexural strength
A
B
C
Residual error
Total
3
3
3
6
15
562.532
8.807
13.031
3.626
587.966
562.532
8.807
13.031
3.626
–
187.511
2.936
4.344
0.604
–
310.32
4.86
7.19
–
–
0
0.048
0.021
–
–
a b
Fig. 5. Plot of S/N ratio as a function input parameters for tensile (a) and flexural (b).
3.4. Normal Probability Plot for S/N Ratio. Figure 8 depictss the normal probability
plot of S/N ratio obtained from the analysis of variance for tensile and flexural properties
respectively. These types of plots help us to determine whether a particular distribution fits
collected data and allows the comparison of different specimen distributions. Falling of the
plotted points close to the fitted distribution line and close together means that the selected
distribution has a good and acceptable fitness. From two parts of this figure it can be seen
that the plotted points for both responses have fallen close together and also close to the
fitted distribution line, so the selected distribution fitness is good for both tensile and
flexural strength but it is more fitted for tensile as opposed to flexural as seen in Fig. 8.
3.5. Plot of Residuals versus Fitted Values for S/N Ratio. Plot of residuals versus
fitted values for tensile and flexural strength properties is shown in Fig. 9. From this figure
it can be generally obtained that the residuals for both responses had scattered on the
display randomly, therefore the model proposed was adequate and there were no reasons to
suspect any violation of the independence or constant variance assumption. As seen the
dispersion of residuals for the flexural strength was better than tensile.
3.6. 2D Contour Plots for Tensile and Flexural Strength Properties. At this stage,
2D contour plots have been used in order to evaluate the effect of interaction between
parameters on flexural and tensile strength properties of desired hybrid quaternary
nanocomposite. These plots are also useful for comparing the effect of main factors with
the results obtained from analysis of variance and main effect plots. The graph shows how
58 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6
Y. Rostamiyan
Fig. 6. Main effect plot of S/N ratio for tensile strength.
Fig. 7. Main effect plot of S/N ratio for flexural strength.
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Modeling and Analysis of the Tensile and Flexural Properties ...
a
b
Fig. 8. Normal probability plot of S/N ratio for tensile (a) and flexural (b) strengths.
a
b
Fig. 9. Plot of residuals versus fitted values for S/N ratio for tensile (a) and flexural (b) strengths.
the selected parameter changes the response: the color varies with variation of the response
magnitudes, while the range of this variation can be seen in the graph legend.
3.6.1. Effect of Fiber Orientation and Nanoclay. Figure 10 depicts the 2D contour
plots for evaluating the effect of fiber orientation and nanosilica on corresponding
responses which are indicated as A and B, respectively. As seen, an increase in the degree
of fiber orientation results in the reduction of both tensile and flexural strength values,
while an increase in wt.% of nanoclay provides a slight increase in the flexural strength
followed by its reduction, whereas the tensile strength exhibits a continuous reduction.
More, a significant interaction between fiber orientation and nanoclay is observed, while a
simultaneous increase of both variables reversely affected two interested responses, according
to Fig. 10.
3.6.2. Effect of Fiber Orientation and Nanosilica. Figure 11 depicts the 2D contour
plots drawn for the effect of fiber orientation and nanosilica. From these graphs it can be
obtained that the fiber orientation had a continuous reverse effect on both responses, while
an increase in the nanosilica wt.% resulted in an initial slight increase of the flexural and
tensile values and their further reduction. Moreover, a simultaneous increase in the
magnitudes of both parameters decreased the tensile and flexural strength properties, which
is similar to the effect of fiber orientation and nanoclay. The interaction between fiber
orientation and nanosilica was significant.
3.6.3. Effect of Nanoclay and Nanosilica. Figure 12 displays the 2D contour plots for
nanosilica and nanoclay for tensile and flexural strength, respectively. As is seen, the
increased value of each factor decreased both the required responses, but simultaneous
60 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6
Y. Rostamiyan
a b
Fig. 10. 2D contour plots for fiber orientation and nanoclay for tensile (a) and flexural (b) strengths.
a b
Fig. 11. 2D contour plots for fiber orientation and nanosilica for tensile (a) and flexural (b) strengths.
increase in the magnitudes of both factors had no obvious effect on the tensile and flexural
properties.
From the above discussion it can be concluded that increasing the levels of all input
parameters has reverse effects on both of the studied responses and reduces the response of
obtained values. Therefore, in order to achieve higher magnitudes of tensile and flexural
strengths, lower degrees of fiber orientation and lower contents of nanosilica and nanoclay
should be incorporated for preparing the required hybrid nanocomposite.
3.7. Stress–Strain Plots. Stress–strain plots were generated and the mechanical
properties of desired hybrid nanocomposite were measured with simple nanocomposites
and pure epoxy. Hybrid nanocomposite specimens were prepared with different fiber
orientations, weight percentage of nanoclay and weight percentage of nanosilica and
compared with nanocomposites with single nanoparticle and neat epoxy.
Figure 13a displays the stress–strain dependence for design level 2 with 0� of fiber
orientation. 1.5 wt.% of nanoclay and 1 wt.% of nanosilica. Two single nanoparticle
nanocomposites were considered with 1.5 wt.% of nanoclay and 1 wt.% of nanosilica. It
can be seen that, pure epoxy had the lowest value of tensile strength and the hybrid
nanocomposite showed a higher value of tensile strength and elongation at break compare
to the two other nanocomposites mentioned. Also it failed at a higher value of tensile
strength compared to others. Moreover hybrid nanocomposite specimen had a lower elastic
modulus compared to other specimens according to the gradient of stress–strain graphs.
Figure 13b depicts the stress–strain dependence for design level 6 with 30� of fiber
orientation. 1.5 wt.% of nanoclay and 0.5 wt.% of nanosilica. Two single nanoparticle
nanocomposites were prepared 1.5 wt.% of nanoclay and 0.5 wt.% of nanosilica. From this
section it can be seen that, the hybrid nanocomposite had a higher value of tensile strength
and elongation at rupture, as compared to nanoclay-epoxy, nanosilica-epoxy, and pure
epoxy. Moreover, the hybrid nanocomposite specimen exhibited a lower elastic modulus, as
compared to other specimens, according to the gradient of stress–strain graphs, and failed at
a higher value of tensile strength.
Stress–strain graphs for design level 12 with 60� of fiber orientation. 3.5 wt.% of
nanoclay and 1 wt.% of nanosilica are shown in Fig. 13c. As seen, the values of tensile
strength for hybrid nanocomposite were higher than those of nanosilica-epoxy;
nanoclay-epoxy and pure epoxy, while they had lower elastic moduli, as compared to three
other composites, according to the gradient of graphs. They also failed at higher values of
the tensile strength, similar to the earlier described cases. In general, the results discussed
of this section demonstrate the reverse effect of studied factors on the tensile properties and
are in agreement with observation made during the analysis of variance and results of 2D
contour plots.
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Modeling and Analysis of the Tensile and Flexural Properties ...
a b
Fig. 12. 2D contour plots for nanosilica and CNT for tensile (a) and flexural (b) strengths.
62 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 6
Y. Rostamiyan
a b
c
Fig. 13. Stress–strain plots for different fiber orientation: (a) 0�; (b) 30�; (c) 60�.
a b
Fig. 14. Plot of flexural strength for different fiber orientation: (a) 0�; (b) 30�; (c) 60�.
c
Figure 14 display the plots of flexural strength for 0, 60, and 90� of fiber orientation
and feature the design levels used for preparing hybrid and simple nanocomposites. The
analysis of three plots in Fig. 14 implies that the hybrid nanocomposite exhibits the
highest flexural strength, whereas the epoxy-nanosilica and epoxy-nanoclay nanocomposites
are the next in the respective decreasing order. Thus, the epoxy-nanosilica nanocomposite
was more effective than epoxy-nanoclay one, which fact is in agreement with earlier
observations made during the analysis of variance in previous sections. Also, a pure
epoxy had the lowest value of flexural strength. Moreover, reduction of magnitude of
all mentioned nanocomposites can be observed with increase in the fiber orientation
value.
Conclusions. In this study, the effect of three independent parameters on tensile and
flexural properties of hybrid quaternary nanocomposite was evaluated. Input selected
variables were carbon fiber orientation, weight percentage of nanoclay and weight
percentage of nanosilica. The Taguchi orthogonal array design was selected for designing
the experiments and 16 specimens were prepared and tested based on designed levels for
each response. Main effect plot and also analysis of variance for S/N ratio indicated that the
most effective parameter was carbon fiber orientation which decreased both responses
continuously. Nanosilica and nanoclay contents decreased the tensile strength and flexural
strength properties. Also the analysis of variance showed that nanoclay and nanosilica
affected the tensile strength more than the flexural one due to related probability values.
Moreover, from 2D contour plots it was obtained that two component interactions between
fiber orientation and nanosilica and also between fiber orientation and nanoclay were
effective for both responses, whereas interaction between nanoclay and nanosilica was not
an effective term. In addition, stress–strain plots indicate that hybrid nanocomposites with
different fiber orientations manifest higher values of tensile strength, as compared to those
of epoxy-nanosilica, epoxy-nanoclay composites and pure epoxy, and generally have higher
values of tensile strength and elongation at rupture, but lower elastic moduli. Finally, the
flexural strength of a hybrid nanocomposite is higher than that obtained for epoxy-
nanoclay and epoxy-nanosilica nanocomposites, whereas the pure epoxy has the lowest
value of flexural strength.
Ð å ç þ ì å
Îö³íåíî âïëèâ òðüîõ íåçàëåæíèõ ïàðàìåòð³â (îð³ºíòàö³ÿ âîëîêîí, âàãîâà ÷àñòêà
íàíî÷àñòèíîê ãëèíîçåìó ³ êðåìíåçåìó) íà ì³öí³ñí³ õàðàêòåðèñòèêè ã³áðèäíîãî íàíî-
êîìïîçèòó ç åïîêñèäíî¿ ñìîëè, àðìîâàíî¿ âóãëåïëàñòèêîâèìè âîëîêíàìè, ç íàíî-
äîáàâêàìè ãëèíîçåìó ³ êðåìíåçåìó ïðè ðîçòÿç³ òà çãèí³. Äëÿ ïëàíóâàííÿ åêñïå-
ðèìåíò³â âèêîðèñòîâóâàëè îðòîãîíàëüíèé íàá³ð çã³äíî ç ìåòîäèêîþ Òàãó÷³. Äëÿ
îö³íêè ôóíêö³¿ â³äêëèêó áóëî âèãîòîâëåíî ³ âèïðîáóâàíî 16 çðàçê³â ïðè çàïëàíîâàíèõ
êîìá³íàö³ÿõ âèùåâêàçàíèõ ïàðàìåòð³â. Âèÿâëåíî çâîðîòíèé åôåêò âïëèâó âõ³äíèõ
ïàðàìåòð³â íà â³äïîâ³äí³ â³äêëèêè, ïðè÷îìó îòðèìàí³ äâîâèì³ðí³ ãðàô³êè ïîêàçóþòü,
ùî âàð³þâàííÿ òàêèìè äâîìà ïàðàìåòðàìè, ÿê îð³ºíòàö³ÿ âîëîêîí – ÷àñòêà íàíî-
÷àñòèíîê ãëèíîçåìó é îð³ºíòàö³ÿ âîëîêîí – ÷àñòêà íàíî÷àñòèíîê êðåìíåçåìó, ³ñòîòíî
âïëèâຠíà õàðàêòåðèñòèêè ì³öíîñò³ ïðè ðîçòÿç³ òà çãèí³, â òîé ÷àñ ÿê âàð³þâàííÿ
ïàðàìåòðàìè ÷àñòêà íàíî÷àñòèíîê êðåìíåçåìó – ÷àñòêà íàíî÷àñòèíîê ãëèíîçåìó íå
ìຠçíà÷íîãî âïëèâó íà âèùåçãàäàí³ õàðàêòåðèñòèêè. Îòðèìàí³ ä³àãðàìè íàïðó-
æåííÿ–äåôîðìàö³ÿ ïîêàçóþòü, ùî ã³áðèäí³ íàíîêîìïîçèòè ç ð³çíîþ îð³ºíòàö³ºþ
âîëîêîí ìàþòü á³ëüø âèñîê³ õàðàêòåðèñòèêè ïðè ðîçòÿç³ òà çãèí³, âåëèê³ ïîäîâæåííÿ
ïðè ðóéíóâàíí³ ³ ìåíø³ ìîäóë³ ïðóæíîñò³, í³æ êîìïîçèòè ç åïîêñèäíî¿ ñìîëè ÿê áåç
íàíîäîáàâîê, òàê ³ ç íàíîäîáàâêàìè ãëèíîçåìó àáî êðåìíåçåìó.
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Received 06. 04. 2015
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Modeling and Analysis of the Tensile and Flexural Properties ...
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