Preparation, Modeling, and Optimization of Mechanical Properties of Epoxy/HIPS/Silica Hybrid Nanocomposite Using Combination of Central Composite Design and Genetic Algorithm. Part 1. Study of Damping and Tensile Strengths
Brittle nature and poor resistance in front of vibrational waves despite of good mechanical strength have limited widespread use of epoxy resins in industry. In current study a new combination of thermoplastic and particulate nanofiller is used as modifier to enhance simultaneously tensile strengths...
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| Cite this: | Preparation, Modeling, and Optimization of Mechanical Properties of Epoxy/HIPS/Silica Hybrid Nanocomposite Using Combination of Central Composite Design and Genetic Algorithm. Part 1. Study of Damping and Tensile Strengths / Y. Rostamiyan, A.B. Fereidoon // Проблемы прочности. — 2013. — № 5. — С. 146-165. — Бібліогр.: 47 назв. — англ. |
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Rostamiyan, Y. Fereidoon, A.B. 2017-01-25T10:44:20Z 2017-01-25T10:44:20Z 2013 Preparation, Modeling, and Optimization of Mechanical Properties of Epoxy/HIPS/Silica Hybrid Nanocomposite Using Combination of Central Composite Design and Genetic Algorithm. Part 1. Study of Damping and Tensile Strengths / Y. Rostamiyan, A.B. Fereidoon // Проблемы прочности. — 2013. — № 5. — С. 146-165. — Бібліогр.: 47 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/112651 539.4 Brittle nature and poor resistance in front of vibrational waves despite of good mechanical strength have limited widespread use of epoxy resins in industry. In current study a new combination of thermoplastic and particulate nanofiller is used as modifier to enhance simultaneously tensile strengths and damping properties in first and second modes of epoxy-based nanocomposite. High impact polystyrene (HIPS) as thermoplastic phase and silica nanoparticles as particulate phases incorporately used to obtain ternary epoxy-based nanocomposite. In current study solution blending as dispersion mechanism is used to prepare homogenous mixture and brings good molecular level of mixing. Tensile and damping properties in first and second modes were the two different mechanical tests investigated in order to achieve higher toughness strengths without attenuating desired mechanical properties. Also central composite design is employed to present mathematical models for predict mechanical behaviors of epoxy/HIPS/silica nanocomposite as function of physical factors. The effective parameters investigated were HIPS, SiO₂, and hardener contents. Based on mathematical functions obtained from central composite design model, the genetic algorithm as one of powerful optimization tools is applied to find optimum values of mentioned mechanical properties. From the results it can be found that combination of HIPS and silica nanoparticles significantly increased tensile and damping strengths of epoxy resin up to 69, 42, and 91%, respectively. The morphology of fracture surface is also studied by scanning electron microscopy Значительная хрупкость и низкие характеристики сопротивления волновым нагрузкам, несмотря на высокую механическую прочность, обусловили недостаточно широкое промышленное применение эпоксидных смол. В работе используется новое сочетание термопластичных и дисперсных нанонаполнителей в качестве модификатора для одновременного повышения прочности на разрыв и демпфирующих свойств нанокомпозита на эпоксидной основе при нагружении по первой и второй моде. Для получения трехкомпонентного нанокомпозита на эпоксидной основе используются ударопрочный полистирол в качестве термопластичной фазы и наночастицы из кремнезема в качестве дисперсной фазы. Для реализации дисперсионного механизма применяется метод перемешивания раствора для приготовления однородной смеси, обеспечивающий адекватное перемешивание на молекулярном уровне. Прочность на разрыв и демпфирующие свойства материала при его нагружении по первой и второй моде оценивали при проведении двух различных механических испытаний с целью достижения более высокой прочности и ударной вязкости без ухудшения требуемых механических свойств. При создании математических моделей для прогнозирования механического поведения нанокомпозита из эпоксидной смолы, ударопрочного полистирола и кремнезема как функции физических факторов используется центральный композиционный план. В качестве эффективных параметров исследовалось процентное содержание ударопрочного полистирола, кремнезема и эпоксидного отвердителя. На основе математических функций, полученных с помощью модели центрального композиционного плана, был использован генетический алгоритм, как одно из мощных средств оптимизации, для определения оптимальных значений механических свойств. Полученные результаты показывают, что сочетание наночастиц ударопрочного полистирола с кремнеземом значительно увеличивает предел прочности на разрыв и характеристики демпфирования эпоксидной смолы на 69, 42 и 91% соответственно. Морфологию поверхностей разрушения изучали с помощью сканирующего электронного микроскопа Значна крихкість і низькі характеристики опору хвильовій напрузі, незважаючи на високу механічну міцність, обумовили недостатньо широке промислове використання епоксидних смол. Використовується нове поєднання термопластичних і дисперсних наповнювачів як модифікатора для одночасного підвищення міцності на розрив і демпфірувальних властивостей нанокомпозита на епоксидній основі при навантаженні за першою і другою модою. Для отримання трикомпонентного нанокомпозита на епоксидній основі використовуються удароміцний полістирол як термопластична фаза і наночастинки з кремнезему як дисперсна фаза. Для реалізації дисперсійного механізму використовується метод перемішування розчину для приготування однорідної суміші, що забезпечує адекватне перемішування на молекулярному рівні. Міцність на розрив і демпфірувальні властивості матеріалу при його навантаженні за першою і другою модою оцінювали при проведенні двох різних механічних випробувань із метою досягнення більш високої міцності й ударної в’язкості без погіршення необхідних механічних властивостей. При розробці математичних моделей для прогнозування механічної поведінки нанокомпозита з епоксидної смоли, удароміцного полістирола і кремнезему як функції фізичних чинників використовується центральний композиційний план. За ефективні параметри брали процентний вміст удароміцного полістирола, кремнезему й епоксидного затверджувача. На основі математичних функцій, отриманих за допомогою моделі центрального композиційного плану, було використано генетичний алгоритм, як один із потужних засобів оптимізації, для визначення оптимальних значень механічних властивостей. Отримані результати свідчать, що поєднання наночастинок удароміцного полістирола з кремнеземом значно збільшує границю міцності на розрив і характеристики демпфірування епоксидної смоли на 69, 42 і 91% відповідно. Морфологію поверхонь руйнування вивчали за допомогою сканувального електронного мікроскопа. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Preparation, Modeling, and Optimization of Mechanical Properties of Epoxy/HIPS/Silica Hybrid Nanocomposite Using Combination of Central Composite Design and Genetic Algorithm. Part 1. Study of Damping and Tensile Strengths Компоновка, моделирование и оптимизация механических свойств гибридного нанокомпозита из эпоксидной смолы, ударопрочного полистирола и кремнезема с использованием центрального композиционного плана и генетического алгоритма. Сообщение 1. Исследование демпфирования и прочности на разрыв Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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Preparation, Modeling, and Optimization of Mechanical Properties of Epoxy/HIPS/Silica Hybrid Nanocomposite Using Combination of Central Composite Design and Genetic Algorithm. Part 1. Study of Damping and Tensile Strengths |
| spellingShingle |
Preparation, Modeling, and Optimization of Mechanical Properties of Epoxy/HIPS/Silica Hybrid Nanocomposite Using Combination of Central Composite Design and Genetic Algorithm. Part 1. Study of Damping and Tensile Strengths Rostamiyan, Y. Fereidoon, A.B. Научно-технический раздел |
| title_short |
Preparation, Modeling, and Optimization of Mechanical Properties of Epoxy/HIPS/Silica Hybrid Nanocomposite Using Combination of Central Composite Design and Genetic Algorithm. Part 1. Study of Damping and Tensile Strengths |
| title_full |
Preparation, Modeling, and Optimization of Mechanical Properties of Epoxy/HIPS/Silica Hybrid Nanocomposite Using Combination of Central Composite Design and Genetic Algorithm. Part 1. Study of Damping and Tensile Strengths |
| title_fullStr |
Preparation, Modeling, and Optimization of Mechanical Properties of Epoxy/HIPS/Silica Hybrid Nanocomposite Using Combination of Central Composite Design and Genetic Algorithm. Part 1. Study of Damping and Tensile Strengths |
| title_full_unstemmed |
Preparation, Modeling, and Optimization of Mechanical Properties of Epoxy/HIPS/Silica Hybrid Nanocomposite Using Combination of Central Composite Design and Genetic Algorithm. Part 1. Study of Damping and Tensile Strengths |
| title_sort |
preparation, modeling, and optimization of mechanical properties of epoxy/hips/silica hybrid nanocomposite using combination of central composite design and genetic algorithm. part 1. study of damping and tensile strengths |
| author |
Rostamiyan, Y. Fereidoon, A.B. |
| author_facet |
Rostamiyan, Y. Fereidoon, A.B. |
| topic |
Научно-технический раздел |
| topic_facet |
Научно-технический раздел |
| publishDate |
2013 |
| language |
English |
| container_title |
Проблемы прочности |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| format |
Article |
| title_alt |
Компоновка, моделирование и оптимизация механических свойств гибридного нанокомпозита из эпоксидной смолы, ударопрочного полистирола и кремнезема с использованием центрального композиционного плана и генетического алгоритма. Сообщение 1. Исследование демпфирования и прочности на разрыв |
| description |
Brittle nature and poor resistance in front of vibrational waves despite of good mechanical strength have limited widespread use of epoxy resins in industry. In current study a new combination of thermoplastic and particulate nanofiller is used as modifier to enhance simultaneously tensile strengths and damping properties in first and second modes of epoxy-based nanocomposite. High impact polystyrene (HIPS) as thermoplastic phase and silica nanoparticles as particulate phases incorporately used to obtain ternary epoxy-based nanocomposite. In current study solution blending as dispersion mechanism is used to prepare homogenous mixture and brings good molecular level of mixing. Tensile and damping properties in first and second modes were the two different mechanical tests investigated in order to achieve higher toughness strengths without attenuating desired mechanical properties. Also central composite design is employed to present mathematical models for predict mechanical behaviors of epoxy/HIPS/silica nanocomposite as function of physical factors. The effective parameters investigated were HIPS, SiO₂, and hardener contents. Based on mathematical functions obtained from central composite design model, the genetic algorithm as one of powerful optimization tools is applied to find optimum values of mentioned mechanical properties. From the results it can be found that combination of HIPS and silica nanoparticles significantly increased tensile and damping strengths of epoxy resin up to 69, 42, and 91%, respectively. The morphology of fracture surface is also studied by scanning electron microscopy
Значительная хрупкость и низкие характеристики сопротивления волновым нагрузкам, несмотря на высокую механическую прочность, обусловили недостаточно широкое промышленное применение эпоксидных смол. В работе используется новое сочетание термопластичных и
дисперсных нанонаполнителей в качестве модификатора для одновременного повышения прочности на разрыв и демпфирующих свойств нанокомпозита на эпоксидной основе при нагружении по первой и второй моде. Для получения трехкомпонентного нанокомпозита на эпоксидной основе используются ударопрочный полистирол в качестве термопластичной фазы и
наночастицы из кремнезема в качестве дисперсной фазы. Для реализации дисперсионного
механизма применяется метод перемешивания раствора для приготовления однородной смеси,
обеспечивающий адекватное перемешивание на молекулярном уровне. Прочность на разрыв и
демпфирующие свойства материала при его нагружении по первой и второй моде оценивали
при проведении двух различных механических испытаний с целью достижения более высокой
прочности и ударной вязкости без ухудшения требуемых механических свойств. При создании
математических моделей для прогнозирования механического поведения нанокомпозита из
эпоксидной смолы, ударопрочного полистирола и кремнезема как функции физических факторов используется центральный композиционный план. В качестве эффективных параметров
исследовалось процентное содержание ударопрочного полистирола, кремнезема и эпоксидного
отвердителя. На основе математических функций, полученных с помощью модели центрального композиционного плана, был использован генетический алгоритм, как одно из мощных
средств оптимизации, для определения оптимальных значений механических свойств. Полученные результаты показывают, что сочетание наночастиц ударопрочного полистирола с
кремнеземом значительно увеличивает предел прочности на разрыв и характеристики демпфирования эпоксидной смолы на 69, 42 и 91% соответственно. Морфологию поверхностей
разрушения изучали с помощью сканирующего электронного микроскопа
Значна крихкість і низькі характеристики опору хвильовій напрузі, незважаючи на високу механічну міцність, обумовили недостатньо широке промислове використання епоксидних смол. Використовується нове поєднання термопластичних і дисперсних наповнювачів як модифікатора для одночасного
підвищення міцності на розрив і демпфірувальних властивостей нанокомпозита на епоксидній основі при навантаженні за першою і другою модою. Для
отримання трикомпонентного нанокомпозита на епоксидній основі використовуються удароміцний полістирол як термопластична фаза і наночастинки з
кремнезему як дисперсна фаза. Для реалізації дисперсійного механізму використовується метод перемішування розчину для приготування однорідної
суміші, що забезпечує адекватне перемішування на молекулярному рівні.
Міцність на розрив і демпфірувальні властивості матеріалу при його навантаженні за першою і другою модою оцінювали при проведенні двох різних
механічних випробувань із метою досягнення більш високої міцності й ударної в’язкості без погіршення необхідних механічних властивостей. При розробці математичних моделей для прогнозування механічної поведінки нанокомпозита з епоксидної смоли, удароміцного полістирола і кремнезему як
функції фізичних чинників використовується центральний композиційний
план. За ефективні параметри брали процентний вміст удароміцного полістирола, кремнезему й епоксидного затверджувача. На основі математичних
функцій, отриманих за допомогою моделі центрального композиційного
плану, було використано генетичний алгоритм, як один із потужних засобів
оптимізації, для визначення оптимальних значень механічних властивостей.
Отримані результати свідчать, що поєднання наночастинок удароміцного
полістирола з кремнеземом значно збільшує границю міцності на розрив і
характеристики демпфірування епоксидної смоли на 69, 42 і 91% відповідно.
Морфологію поверхонь руйнування вивчали за допомогою сканувального
електронного мікроскопа.
|
| issn |
0556-171X |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/112651 |
| citation_txt |
Preparation, Modeling, and Optimization of Mechanical Properties of Epoxy/HIPS/Silica Hybrid Nanocomposite Using Combination of Central Composite Design and Genetic Algorithm. Part 1. Study of Damping and Tensile Strengths / Y. Rostamiyan, A.B. Fereidoon // Проблемы прочности. — 2013. — № 5. — С. 146-165. — Бібліогр.: 47 назв. — англ. |
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UDC 539.4
Preparation, Modeling, and Optimization of Mechanical Properties of
Epoxy/HIPS/Silica Hybrid Nanocomposite Using Combination of Central
Composite Design and Genetic Algorithm. Part 1. Study of Damping
and Tensile Strengths
Y. Rostamiyan
1
and A. B. Fereidoon
Semnan University, Semnan, Iran
1 y.rostamiyan@yahoo.com
ÓÄÊ 539.4
Êîìïîíîâêà, ìîäåëèðîâàíèå è îïòèìèçàöèÿ ìåõàíè÷åñêèõ ñâîéñòâ
ãèáðèäíîãî íàíîêîìïîçèòà èç ýïîêñèäíîé ñìîëû, óäàðîïðî÷íîãî
ïîëèñòèðîëà è êðåìíåçåìà ñ èñïîëüçîâàíèåì öåíòðàëüíîãî
êîìïîçèöèîííîãî ïëàíà è ãåíåòè÷åñêîãî àëãîðèòìà. Ñîîáùåíèå 1.
Èññëåäîâàíèå äåìïôèðîâàíèÿ è ïðî÷íîñòè íà ðàçðûâ
ß. Ðîñòàìèÿí, À. Á. Ôåðåéäóí
Óíèâåðñèòåò ã. Ñåìíàí, Èðàí
Çíà÷èòåëüíàÿ õðóïêîñòü è íèçêèå õàðàêòåðèñòèêè ñîïðîòèâëåíèÿ âîëíîâûì íàãðóçêàì, íå-
ñìîòðÿ íà âûñîêóþ ìåõàíè÷åñêóþ ïðî÷íîñòü, îáóñëîâèëè íåäîñòàòî÷íî øèðîêîå ïðîìûøëåí-
íîå ïðèìåíåíèå ýïîêñèäíûõ ñìîë.  ðàáîòå èñïîëüçóåòñÿ íîâîå ñî÷åòàíèå òåðìîïëàñòè÷íûõ è
äèñïåðñíûõ íàíîíàïîëíèòåëåé â êà÷åñòâå ìîäèôèêàòîðà äëÿ îäíîâðåìåííîãî ïîâûøåíèÿ ïðî÷-
íîñòè íà ðàçðûâ è äåìïôèðóþùèõ ñâîéñòâ íàíîêîìïîçèòà íà ýïîêñèäíîé îñíîâå ïðè íàãðó-
æåíèè ïî ïåðâîé è âòîðîé ìîäå. Äëÿ ïîëó÷åíèÿ òðåõêîìïîíåíòíîãî íàíîêîìïîçèòà íà ýïîêñèä-
íîé îñíîâå èñïîëüçóþòñÿ óäàðîïðî÷íûé ïîëèñòèðîë â êà÷åñòâå òåðìîïëàñòè÷íîé ôàçû è
íàíî÷àñòèöû èç êðåìíåçåìà â êà÷åñòâå äèñïåðñíîé ôàçû. Äëÿ ðåàëèçàöèè äèñïåðñèîííîãî
ìåõàíèçìà ïðèìåíÿåòñÿ ìåòîä ïåðåìåøèâàíèÿ ðàñòâîðà äëÿ ïðèãîòîâëåíèÿ îäíîðîäíîé ñìåñè,
îáåñïå÷èâàþùèé àäåêâàòíîå ïåðåìåøèâàíèå íà ìîëåêóëÿðíîì óðîâíå. Ïðî÷íîñòü íà ðàçðûâ è
äåìïôèðóþùèå ñâîéñòâà ìàòåðèàëà ïðè åãî íàãðóæåíèè ïî ïåðâîé è âòîðîé ìîäå îöåíèâàëè
ïðè ïðîâåäåíèè äâóõ ðàçëè÷íûõ ìåõàíè÷åñêèõ èñïûòàíèé ñ öåëüþ äîñòèæåíèÿ áîëåå âûñîêîé
ïðî÷íîñòè è óäàðíîé âÿçêîñòè áåç óõóäøåíèÿ òðåáóåìûõ ìåõàíè÷åñêèõ ñâîéñòâ. Ïðè ñîçäàíèè
ìàòåìàòè÷åñêèõ ìîäåëåé äëÿ ïðîãíîçèðîâàíèÿ ìåõàíè÷åñêîãî ïîâåäåíèÿ íàíîêîìïîçèòà èç
ýïîêñèäíîé ñìîëû, óäàðîïðî÷íîãî ïîëèñòèðîëà è êðåìíåçåìà êàê ôóíêöèè ôèçè÷åñêèõ ôàêòî-
ðîâ èñïîëüçóåòñÿ öåíòðàëüíûé êîìïîçèöèîííûé ïëàí.  êà÷åñòâå ýôôåêòèâíûõ ïàðàìåòðîâ
èññëåäîâàëîñü ïðîöåíòíîå ñîäåðæàíèå óäàðîïðî÷íîãî ïîëèñòèðîëà, êðåìíåçåìà è ýïîêñèäíîãî
îòâåðäèòåëÿ. Íà îñíîâå ìàòåìàòè÷åñêèõ ôóíêöèé, ïîëó÷åííûõ ñ ïîìîùüþ ìîäåëè öåíòðàëü-
íîãî êîìïîçèöèîííîãî ïëàíà, áûë èñïîëüçîâàí ãåíåòè÷åñêèé àëãîðèòì, êàê îäíî èç ìîùíûõ
ñðåäñòâ îïòèìèçàöèè, äëÿ îïðåäåëåíèÿ îïòèìàëüíûõ çíà÷åíèé ìåõàíè÷åñêèõ ñâîéñòâ. Ïîëó-
÷åííûå ðåçóëüòàòû ïîêàçûâàþò, ÷òî ñî÷åòàíèå íàíî÷àñòèö óäàðîïðî÷íîãî ïîëèñòèðîëà ñ
êðåìíåçåìîì çíà÷èòåëüíî óâåëè÷èâàåò ïðåäåë ïðî÷íîñòè íà ðàçðûâ è õàðàêòåðèñòèêè äåìï-
ôèðîâàíèÿ ýïîêñèäíîé ñìîëû íà 69, 42 è 91% ñîîòâåòñòâåííî. Ìîðôîëîãèþ ïîâåðõíîñòåé
ðàçðóøåíèÿ èçó÷àëè ñ ïîìîùüþ ñêàíèðóþùåãî ýëåêòðîííîãî ìèêðîñêîïà.
Êëþ÷åâûå ñëîâà: ýïîêñèäíàÿ ñìîëà, âÿçêîñòü ðàçðóøåíèÿ, óäàðîïðî÷íûé
ïîëèñòèðîë, êðåìíåçåì, ðàñòÿæåíèå, äåìïôèðîâàíèå, öåíòðàëüíûé êîìïîçèöè-
îííûé ïëàí, ãåíåòè÷åñêèé àëãîðèòì, ñêàíèðóþùèé ýëåêòðîííûé ìèêðîñêîï.
© Y. ROSTAMIYAN, A. B. FEREIDOON, 2013
146 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 5
Introduction. Epoxy polymer is one of the most applicable thermoset matrices
used for reinforced composite materials, due to its high elastic modulus, considerable
rupture strength, low creep and good performance at elevated temperature[1–3].
Despite the above improved characteristics, epoxy materials have a brittle nature,
low toughness, and poor damping characteristics[4]. Blending of various kinds of
thermoplastic polymers [5, 6] or microphase dispersed rubber [7–9] has been a
conventional way to increase impact strength of epoxy matrices for many years. In
applications of rubber and thermoplastic phases aimed at improval of impact
strength, in view of dramatic effects on other mechanical properties, quite popular
is the material toughening by engineering thermoplastic, such as polysulfone [10],
polyether amide [11], ABS [12], and polyethersulfone [13]. Although, in many
cases, presence of elastomeric phase in epoxy matrix enhances toughness and,
consequently, damping properties, but on the other hand, it provides an increase in
viscosity and drastic reduction of strength, elastic modulus and stiffness [14–17].
In the last years, one of the well-known proposed ways to increase the material
stiffness implied usage of rigid inorganic particles with glass or ceramic base,
having diameter between 4 to 100 �m [18, 19], but due to large size of these
particles, the viscosity of the epoxy resin was also increased, which made the
product processing quite problematic [20]. In the last decade, application of
nanophase structures in polymer matrices, in order to improve mechanical properties,
such as tensile, compressive and flexural strength, have opened new horizons, in
comparison with conventional composite materials [20]. Usage of nanoparticles
such as silica, resulted in no considerable viscosity enhancement, due to their small
sizes [21]. The distinction between nano- and microparticles is mainly due to their
high specific surface (relation of the surface to the mass) [22–24]. Previous studies
have shown that addition of relatively cost-effective nanosilica into epoxy matrix
can considerably improve the mechanical strength [20, 25]. It is noteworthy that
addition of nanoparticles may strongly affect the mechanical strength, it has no
considerable effect on impact strength improvement of epoxy-based composites
[26]. Also some studies have shown that usage of both soft particles, and rigid
fillers in epoxy resin as a hybrid composite, may enhance simultaneously the
strength and toughness. For instance, adding micron-size glass spheres, including
rubber particles into epoxy matrices, has shown a synergistic toughening effect
with acceptable strength enhancement [27, 28]. In order to study the mechanical
properties and hybrid mechanism of epoxy-based nanocomposite, the effective
quantitative factors must be introduced. Conventionally, based on numerous
studies [29–31], it can be found that the weight percentage of reinforcement such
as toughening agent and nanofiller is the most critical parameter, which controls
the mechanical behavior of epoxy-based nanocomposites. Another important factor
in epoxy/thermoplastic/nanoparticle sample preparation is a weight percentage of
hardener. Although determination of appropriate amount of this factor is based on
stoichiometric ratio, one can expect that presence of thermoplastic phase as
toughening agent, as well as of nanofiller in epoxy resin, would dramatically
reduce the probability of complete mixture of epoxy monomers and hardener, and
hence hinder the complete polymerization. Mirmohseni and Zavareh [12] have
determined the optimum amount of hardener according to the maximum tensile and
impact strength of the prepared epoxy samples. This type of optimization is called
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OVAT (one variable at a time) [32]. Leardi [32] concluded in his research that 93%
of scientific publications on optimization, development, and improvement of these
materials was based on the OVAT model. Due to the fact that in many approaches
the optimized variables are interrelated with each other, these interrelations need to
be determined, but the OVAT model cannot guarantee that the real optimum point
is reached [32]. Moreover, prediction of the nonlinear effect of each parameter
requires availability of at least three experimental points as parameter levels, which
increases the number of required experiments for model prediction and,
consequently, increases the costs. The central composite design (CCD), which was
introduced by Box and Wilson [33], is one of very useful types of sequential
second-order experimental design, with provides simultaneous reduction of the
number of experiments, predicts a probable nonlinear effect of each parameter, as
well as interrelations of coupled parameters. Within framework of the mathematical
model, one of optimization methods should be used to predict the optimum values.
Based on the famous research of Charles Darwin, genetic algorithm has been
applied as a powerful tool for solving complex problems [34]. Many researchers
used this method for optimization of numerous case studies in engineering [34–36].
Genetic algorithm is a global optimization method, which codes the design
variables by individual genes or chromosomes [35]. The result based on this
algorithm has feeble associations with the original problem. This method can find
the answer to a wide range of problems and can govern a large number of
responses at the same time. This feature reduces the possibility that the algorithm is
being trapped in the local optimum points. This algorithm is easily applied for
solving problems that have a large number of variables. Moreover, the genetic
algorithm is simple, needs no auxiliary information like derivative of the objective
function, and can be used for optimization of intricate objective functions,
discontinuous or non-differentiable function or systems which have no specific
mathematical definition [34].
In the current work, addition of the combination of thermoplastic (HIPS) and
particulate nanofiller (silica) to epoxy matrix is provided, in order to ensure
simultaneous improvement of tensile strength and damping characteristics. Central
composite design is applied for elaboration of a model for predicting the mechanical
behavior of the above nanocomposite. Based on the obtained mathematical function
from CCD, the genetic algorithm is employed to find the optimum conditions. In
addition, the authors tried to use inorganic nanofillers and commercial thermoplastic
to reduce the total costs of sample preparation and concurrently achieve a
considerable enhancement of the mechanical properties. Morphological and
structural characteristics of the hybrid mechanism are investigated using scanning
electron microscopy (SEM).
1. Experimental.
1.1. Materials. Epoxy resin utilized in current study was an undiluted clear
difunctional bisphenol A, Epon 828 provided by Shell Chemicals Co. with epoxide
equivalent weight 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 spherical silica nanoparticles with
average particle size 10–15 nm and SSA (specific surface area) 180–270 m2/g
were supplied from TECNAN Ltd. The high impact polystyrene used in this study
148 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 5
Y. Rostamiyan and A. B. Fereidoon
was purchased from Tabriz petrochemical Company in Iran. The solvent used was
tetrahydrofuran (THF) with purity (GC) more than 99% provided by Merck Co
(Germany).
1.2. Sample Preparation. In order to prepare a homogenous mixture, all of
reinforcement-adding procedures into resin were conducted in a proper solvent.
Solution blending is a liquid-state powder processing method that ensures a good
molecular level of mixing and is widely used in material preparation and processing
[25]. Some of the limitations of melt mixing can be overcome if both the polymer
and the nanoparticles are dissolved or dispersed in solution and recovered after
mixing. In order to avoid various solvents’ effects, as well as to achieve the
comparable results, the authors employed THF as an appropriate solvent for
dissolving all mixture components such as epoxy resin, silica and, especially, high
impact polystyrene. For preparing neat epoxy samples, in order to ensure equal
conditions and comparability with other specimens, liquid epoxy resin was poured
into adequate amount of THF solvent and after 30 min mixing by magnetic stirrer
the mixture was poured into vacuum vessel and the solvent evaporated completely
under vacuum conditions using the vacuum pump. At this step, the stoichiometry
ratio of cycloaliphatic polyamine as hardener, i.e., 23 phr was added and mixed
uniformly for 15 min and degassed by a vacuum pump to remove the air bubbles.
The mixture was poured into silicon mould and cured for 24 h at room temperature,
which was followed by post-curing from 50 to 90�C each 2 h at 20�C temperature
enhancement interval and at 120�C for 2 h to ensure complete curing. In order to
prepare epoxy/HIPS/SiO2 samples, desired amount of the reinforcements was
dissolved in adequate amount of mentioned solvent and mixed via magnetic stirrer
for 30 min. In the current study, the mixture was homogenized by ultrasonic
treatment (Ultrasonic SONOPULS-HD3200, 50% amplitude, 20 kHz, and pulsation;
on for 10 s and off for 3 s) for 30 min. The required amount of epoxy resin with
the same procedure as mentioned before was added to this mixture and mixed
mechanically at high speed for 2.5 h, and subsequently the mixture was subjected
to ultrasonic treatment by the same procedure for 30 min. The same protocol was
used for the neat epoxy, whereas stoichiometric ratio of hardener content was
varied for each hybrid sample.
1.3. Characterization. The tensile tests were conducted according to ASTM
D638 at room temperature. This test method covers the determination of the tensile
properties of reinforced plastics in the form of standard dumbbell-shaped test
specimens. The dimensions of specimens were chosen according to the type I of
this standard test method. The rate of motion of the driven grip when the testing
machine was running was 5 mm/min. For each sample five specimens were tested.
All of tensile tests are conducted via STM-150 universal testing machine from
Santam Company (Iran) with load capacity 150 kN. For the specimens of damping
test the authors used izod impact unnotched samples according to ASTM D256
with the dimensions of 63.5, 12.7, and 7.2 mm as indicated in standard. The laser
doppler vibrometer OMETRON VH300+, which is shown in Fig. 1, was used for
measuring vibrations. In the current test, calculation of damping coefficients is
based on stochastic subspace identification–data (SSI-data) method, which was
introduced by Van Overschee and De Moor [37] and modified by Peeter and
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Preparation, Modeling, and Optimization of Mechanical Properties ...
Brinker [38, 39]. Based on this method, the specimen was treated as cantilevered
beam with environmental excitation. All time-dependent responses were accumulated
in Block Henkel Matrix and converted into individual Past and Future matrices. At
this step, in order to make connection between responses, the future matrix was
projected on past matrix and created the projection matrix [37–39]. By severance
singular value decomposition (SVD) of projection matrix, observability matrix and
Kalman states are calculated, and the collection of polar system matrix is achieved.
At this step, as it is shown in Fig. 2, in order to calculate damping coefficients and
natural frequencies, the stabilization diagram is used. The stabilization diagram is a
tool to shows polars of systems of different order [33–35]. To display and analyze
the measurement results on a workstation, the Polytec Vibrometer Software
(VibSoft) was optionally used. A scanning electron microscope (SEM 1530) from
TECNAN was utilized to observe the dispersion of fracture surfaces of the cured
composites. The fracture surface was gold-coated prior to SEM studies, in order to
avoid charging, and was examined at 15 kV accelerating voltage.
1.4. Design of Experiment. In order to present the mathematical model,
central composite design is used as one of the well-known experimental designs
[40, 41]. Based on this type of design, N experiments should be executed for f
factors, according to the following formulation:
150 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 5
Y. Rostamiyan and A. B. Fereidoon
a b
Fig. 1. Vibration measurement by laser doppler vibrometer OMETRON VH300+ (a) and specimen (b).
Fig. 2. Example of stabilization diagram in SSI-data method for neat epoxy.
N N N Nf a� � � 0 , (1)
where N f
f�2 represents two-level full factorial points and N fa �2 corresponds
to extra star points located at � � from the center of the experimental domain.
Also N 0 is the number of experiments repeated at the center of the design carried
out to provide an independent estimation of the “pure” experimental error variance.
This value must be calculated by considering the rotatability and orthogonality of
the design. If the variance of responses for all variables at distance � from the
center of the experimental domain is constant, a design would be rotatable [40].
The required value � for rotatability is calculated via the following equation:
���( ) ./N f
1 4
(2)
The STATISTICA software as statistical package version 7.0 (Stat Soft Inc.,
Tulsa, USA) was used for experimental design analysis and data processing. In
current study, the CCD is employed to predict models for tensile and damping
properties of epoxy-based hybrid nanocomposite. The input variables investigated
were HIPS, SiO2 and Hardener contents. Actual and coded levels of the design
parameters are described in Table 1.
As shown in Table 2, 16 samples with different compositions for 3 factors
with 2 replications at the center point have been designed. Noteworthy is that, in
order to avoid random errors, all treatments were set in a random order. The
responses obtained from mechanical tests including coded value are presented in
Table 2. According to central composite design model, the result should be fitted to
the following basic second-order polynomial equation:
Y b b x b x b x xi i ii i ij i j
i
f
i
f
i
f
i
f
� � � �
��
�
��
0
2
11
1
11
, (3)
where b0 is constant, bi shows the linear effect of x i , bii shows the quadratic
nonlinear effect of x i , and bij indicates the interaction between parameters. Also
in central composite design analysis of variance (ANOVA) is used to determine the
significance of model terms. After elaboration of the mathematical model, different
optimization algorithms can be used to optimize the results. In order to validate the
optimized results, the optimum condition should be satisfied.
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Preparation, Modeling, and Optimization of Mechanical Properties ...
T a b l e 1
Actual and Coded Levels of the Design Parameters
Factors Levels Star points � �168179.
Low (�1) Central (0) High (�1) �� ��
(X1) HIPS content (wt.%) 4.0 7.0 10.0 2 12
(X 2) SiO2 content (wt.%) 2.8 5.5 8.2 1 10
(X 3) hardener content (Phr) 23.0 26.0 29.0 21 13
2. Results and Discussion.
2.1. Statistical Modeling. As it was mentioned before, in order to reduce the
number of experiments, required for elaboration of the mathematical model and
final optimization of the results, the CCD method was used, and the results of
tensile and damping tests in the first and second modes were obtained and
tabulated in Table 2. The important fact is each treatment response was replicated
five times, the average values being listed in Table 2. Using STATISTICA software
for predicting responses, the following equations were proposed:
Y X X X X1 1 1
2
2 263 626 6 490 2 248 5 442 3 839� � � � �. . ( ) . ( ) . ( ) . ( )2
35 019� �. ( )X
� � � �1895 1875 2125 0 6253
2
1 2 1 3 2 3. ( ) . ( ) . ( ) . ( ),X X X X X X X (4)
Y X X X X2 1 1
2
2 2
23 51 0 26 0126 0 03 0 073 0� � � � � �. . ( ) . ( ) . ( ) . ( ) .344 3( )X �
� � � �0133 0 0187 0 0762 0 04373
2
1 2 1 3 2 3. ( ) . ( ) . ( ) . ( )X X X X X X X , (5)
152 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 5
Y. Rostamiyan and A. B. Fereidoon
T a b l e 2
Experimental Design and Corresponding Responses
Run
No.
Experimental factors (coded value) Responses of mechanical tests
HIPS
content
SiO2
content
Hardener
content
Tensile
strength
(MPa)
First mode
damping
(%)
Second mode
damping
(%)
1 (C) 0 0 0 65 4� 3 49 0 22. .� 4 35 013. .�
2 �1.68179 0 0 68 5� 3 67 0 09. .� 4 33 016. .�
3 �1.00000 1.00000 1.00000 63 2� 3 69 012. .� 4 44 0 08. .�
4 1.00000 1.00000 1.00000 50 3� 3 35 016. .� 3 98 0 05. .�
5 (C) 0 0 0 62 5� 3 53 0 04. .� 4 42 019. .�
6 �1.00000 �1.00000 1.00000 68 3� 3 68 0 07. .� 4 52 0 06. .�
7 1.00000 1.00000 �1.00000 33 4� 2 47 019. .� 3 40 0 24. .�
8 0 0 �1.68179 52 2� 2 58 0 24. .� 3 79 016. .�
9 0 1.68179 0 43 3� 3 31 016. .� 4 18 011. .�
10 �1.00000 �1.00000 �1.00000 62 1� 3 28 0 08. .� 4 22 0 09. .�
11 1.00000 �1.00000 �1.00000 48 4� 2 56 0 05. .� 2 81 018. .�
12 0 �1.68179 0 64 2� 3 30 015. .� 3 75 016. .�
13 0 0 1.68179 66 2� 3 69 0 26. .� 4 54 0 22. .�
14 1.00000 �1.00000 1.00000 62 1� 3 40 019. .� 3 39 015. .�
15 1.68179 0 0 48 5� 2 64 0 27. .� 2 76 012. .�
16 �1.00000 1.00000 �1.00000 55 4� 2 98 013. .� 4 03 0 21. .�
Note. C is central point.
Y X X X X3 1 1
2
2 2
24 386 0 459 0 3 0119 0151 0� � � � � �. . ( ) . ( ) . ( ) . ( ) . ( )229 3X �
� � � �0 081 0181 0 056 0 01373
2
1 2 1 3 2 3. ( ) . ( ) . ( ) . ( ),X X X X X X X (6)
where Y1 , Y2 , and Y3 correspond to the ultimate tensile strength (UTS), damping
ratio at first and second modes of epoxy-based ternary nanocomposite, respectively.
At this stage, in order to demonstrate the effectiveness of each parameter, the
ANOVA tables listed Table 3 should be used. Based on the ANOVA results, the
confidence level was determined at 95% and the significance of each parts of
model was evaluated based on their probability (P-value). If the terms have a
significant effect on response, the probability value will be less than 0.05 and the
null hypothesis ( )H 0 will be rejected [40]. The terms having no significant effect
(i.e., with P-value higher than 0.05) are eliminated from the final equation of the
model. The final results that illustrate the effective or non-effective terms are
presented in the form of pareto charts and are shown in Fig. 3. After determining
the effective terms, Eqs. (4)–(6) are reduced to the following forms:
� . . ( ) . ( ) . ( ) . (Y X X X X1 1 1
2
2 263 626 6 490 2 248 5 442 3 839� � � � � )2 �
� � � �5 019 1895 1875 21253 3
2
1 2 1 3. ( ) . ( ) . ( ) . ( ),X X X X X X (7)
� . . ( ) . ( ) . ( )Y X X X2 1 1
2
2
23 51 0 26 0126 0 073� � � � �
� � �0 344 0133 0 07623 3
2
1 3. ( ) . ( ) . ( ),X X X X (8)
� . . ( ) . ( ) . ( ) . ( )Y X X X X3 1 1
2
2 2
24 386 0 459 0 3 0119 0151� � � � � �
� � � �0 229 0 081 0181 0 0563 3
2
1 2 1 3. ( ) . ( ) . ( ) . ( ).X X X X X X (9)
Another criterion for evaluating the ability of reduced model to predict results
is coefficient of determination (R 2). When this value is close to 100%, the model
provides an accurate estimate of the results. The value of (R 2) related to each
model is shown in the predicted-observed diagram for each model in Fig. 4. Using
STATISTICA software, the 3D and contour graphs related to mechanical behavior
of nanocomposite depending on variable parameters were plotted in Figs. 5–7.
2.2. Optimization of the Mechanical Properties. In this study, one of the main
goals is to optimize the effective factors to obtain the best content of new hybrid
epoxy-based nanocomposite. One of the common techniques for achieving the
optimum conditions within framework of the central composite design is usage of
profiles for predicted values and desirability functions shown in Fig. 8 , which are
provided by STATISTICA software that can be a proper tool for controlling the
behavior of each parameter and its effect on responses. But in this study upon
elaboration of the final mathematical model for each mechanical property, a
genetic algorithm provided by Matlab software is used to find more accurate
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154 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 5
Y. Rostamiyan and A. B. Fereidoon
conditions on content instead of those provided by the desirability function. At
first, genetic algorithm starts working with a population of chromosomes, which
are randomly selected. In order to obtain better generation, genetic operators are
applied to the population. Reproduction, mutation and crossover are the most
common genetic operators, which can be described as follows. Reproduction
operator selects a couple of people that will produce the next generation. Persons
with higher fitness have more chances for reproduction, but chance of being
selected is also given to persons who have lower fitness conditions because they
may have valuable genes. Crossover operator is applied to the two selected
chromosomes so that they share their structure based on a specified probable value.
This operation creates a pair of new chromosomes that includes characterization of
their parents. After reproduction and crossover, mutation operator is applied to each
of the produced chromosomes. When the above algorithm is applied to the problem
under study, the following maximal mechanical properties for the optimal
conditions were obtained: for the ultimate tensile strength, HIPS content of 4.54%,
SiO2 content of 4.15%, and hardener content of 28.6 phr. These optimal condition
values for damping ratio in the first mode are 4.87% for HIPS, 5.5% for nanosilica
and 29.25 phr for hardener. Finally, the best concentrations of modifiers and
hardener for damping ratio in the second mode are: 5.05% for HIPS, 5.51% for
nanosilica, and 29.56% phr for hardener. The maximal values of mechanical
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 5 155
Preparation, Modeling, and Optimization of Mechanical Properties ...
a b
c
Fig. 3. Pareto chart of standardized effects: (a) tensile; (b) damping ratio-first mode; (c) damping
ratio-second mode.
156 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 5
Y. Rostamiyan and A. B. Fereidoon
a b
c
Fig. 4. Predicted vs observed data for tensile (a), damping ratio-first mode (b), and damping ratio-
second mode (c).
a b c
Fig. 5. 3D and contour plots of UTS at HIPS ��0 82. (a), SiO2 ��0 5. (b), hardener � 0 87. (c).
properties predicted by the model at the optimal values of variables were, as follows:
69.8 MPa for UTS, 3.79% for damping ratio in the first mode, and 4.67% for
damping ratio in the second mode. Upon preparation of samples, according to the
optimal conditions, they were tested, in order to provide verification of the
predicted results. By using five replications for each experiment, the following
average results have been obtained: 68.5 MPa for UTS, 3.75% for damping ratio in
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Preparation, Modeling, and Optimization of Mechanical Properties ...
a b c
Fig. 6. 3D and contour plots of damping ratio-first mode at HIPS ��0 71. (a), SiO2 � 0 (b), hardener
�109. (c).
a b c
Fig. 7. 3D and contour plots of damping ratio-second mode at HIPS ��0 65. (a), SiO2 � 0 (b),
hardener �119. (c).
the first mode, and 4.61% for damping ratio in the second mode. Analysis of the
results obtained shows that the experimental values have a close fit with those
predicted by the model. Similar to results of previous studies, it was found that
simultaneous addition of nano- and thermoplastic phases to epoxy resin results in
higher toughness of the material. Mirmohseni and Zavareh [42] have shown that by
adding 2% clay and 20% polyamide, the material toughness can be increased up to
115%. Mirmohseni and Zavareh [43] demonstrated that with incorporation of 2.5%
clay nanolayered and 4 phr ABS into epoxy matrix, 133% improvement was
observed for impact strength.
158 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 5
Y. Rostamiyan and A. B. Fereidoon
b
a
2.3. 3D and Contour Plots for Mechanical Behavior of Epoxy-Based Hybrid
Nanocomposite. In this study, in order to show the dependence of mechanical
properties of epoxy-based hybrid nanocomposite on such effective parameters as
design factors, the 3D response surface and contour plots are employed.
2.3.1. Effect of Hardener and Silica Loading on Mechanical Properties.
Figures 5a, 6a, and 7a present 3D response surface and 2D contour plots of the
ultimate tensile strength and damping ratio at the first and second modes of epoxy/
HIPS/SiO2 ternary nanocomposite as a function of hardener and silica nano-
particles contents, while HIPS factor was at its optimal concentration for each
property. As one can see from the results, in similar cases silica content and
hardener loading have significant effects on the measured mechanical properties.
The tensile and damping values in the first and second modes increased with
increasing silica content to some extent and decreased with higher loading. This
amount varied between 4.15–5.51%. As Mirmohseni and Zavareh reported in [43],
the above figures indicate that the best concentration of hardener in hybrid
mechanism does not correspond to stoichiometric ratio (23 phr), whereas the
optimal loading for hardener occurs in the range of 28.40–29.56 phr. Also it can be
concluded that hardener and silica nanoparticles provide no significant interaction
effect on the results. A possible reason for these phenomena may be attributed to
the fact that due to small size and low concentration of silica nanoparticles, these
particles cannot inhibit the performance of hardener in polymerization of epoxy
monomers.
2.3.2. Effect of Hardener and HIPS Loading on Mechanical Properties.
Figures 5b, 6b, and 7b depict the response surface and contour plots, which
demonstrate the effects of HIPS and hardener factors on the ultimate tensile
strength, damping ratio at the first and second modes of epoxy/HIPS/silica hybrid
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 5 159
Preparation, Modeling, and Optimization of Mechanical Properties ...
c
Fig. 8. Profiles for predicted values and desirability function for UTS (a), damping ratio-first mode (b),
damping ratio-second mode (c).
nanocomposite, whereas the SiO2 loading is fixed at its best concentration for each
property. It is seen from the figures that the hardener behavior is similar to that
described in the previous section. It seems that the main processing defects in
epoxy-based nanocomposites are related to the entrained voids and incomplete cure
during the cross-linking phase. Noteworthy is that HIPS loading yields the
optimal mechanical strength values at different contents. The optimal amount of
HIPS for tensile loading is 4.54%, for damping ratio at the first mode – 4.87% and
finally, for damping ratio at the second mode – 5.05%. In these results, the main
feature is a considerable interaction effect between HIPS and hardener for the
ultimate tensile strength and lower interaction for damping ratios at the first and
second modes, as compare to that in tensile mode. This behavior may be related to
the large size of HIPS particles that inhibit complete involvement of epoxy
monomers by hardener and reduce the chance of all epoxy monomers to participate
in polymerization and network forming that lead poor strength of epoxy. But
insofar as rigidity is a negative parameter from the standpoint of damping
properties, this interaction has a feeble effect on the latter.
2.3.3. Effect of HIPS and SiO2 Loading on Mechanical Properties. The effect
of HIPS and nano-SiO2 contents upon mechanical strength of epoxy-based nano-
composite is depicted in Figs. 5c, 6c, and 7c. As it follows from the results, they
are strongly affected by these factors. Increase in toughness by usage of
thermoplastic particles results in the matrix shear bonding and matrix dilation from
the plastic zone in front of the crack tip [8, 9, 44, 45], which provide the
improvement of damping properties. A localized plastic zone during vibration can
absorb these waves, limiting the high local stresses and thereby can reduce the
probability of vibration growth. Also this strategy may ensure absorption of more
energy than it would be required for the equivalent propagation in brittle materials.
Noteworthy is that interaction between HIPS and SiO2 affects the tensile and
damping strength values at the second mode, whereas this interaction is not
observed in case of damping at the first mode. This behavior may be attributed to
the fact that the simultaneous presence of HIPS and SiO2 increases the viscosity
and decreases the possibility of homogeneous mixture formation. This may lead to
agglomeration of SiO2 nanoparticles and formation of large particles, which cannot
absorb the energy of vibration in the material.
The results obtained indicate that the ultimate tensile strength of epoxy/
HIPS/SiO2 ternary nanocomposite is increased up to 69% for the optimal levels of
parameters The damping ratio at the first mode, in comparison with neat epoxy
sample, is enhanced by 42%, while damping ratio at the second mode can be
increased by 91%. This result shows the synergistic effect of silica and HIPS
modifiers on damping strength of hybrid nanocomposite. These results indicate
that addition of rigid nanoparticles (silica) enhances tensile strength, whereas
addition of HIPS, as a thermoplastic phase, improves the vibration-absorbing
ability of composite. In general, it may be concluded that simultaneous addition of
HIPS as a thermoplastic modifier and silica as a nanoparticulate material can
considerably improve the mechanical and damping strength values concurrently.
The micrograph depicting the fracture surface of tensile specimen at the optimal
amount of HIPS, SiO2 and hardener is shown in Fig. 9. In epoxy materials,
cross-link density plays a vital role in achievement of good mechanical properties.
160 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 5
Y. Rostamiyan and A. B. Fereidoon
As seen from Fig. 9, good dispersion of silica nanoparticles and high impact
polystyrene as thermoplastic phase with small-scale agglomeration takes place.
Moreover, phase separation of nano- and microparticles in epoxy-rich matrix is
observed. Thus, modifier with homogenous dispersion can act as crack stopper
and reinforcement, enhancing the mechanical strength [46, 47].
Conclusions. A new combination of thermoplastic-nanofiller as a modifier for
epoxy-based composite is proposed. In this study, tensile and damping properties at
the first and second modes have been investigated. The central composite model is
applied for prediction and optimization of the results. A genetic algorithm is used
to optimize the models provided by CCD. In addition, the effects of parameters on
mechanical strength of epoxy/HIPS/SiO2 ternary nanocomposite are described by
3D response surface and 2D contour plots. As follows from the results obtained,
combination of HIPS and silica nanoparticles significantly increases the epoxy
resin tensile strength, as well as damping properties at the first and second modes
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 5 161
Preparation, Modeling, and Optimization of Mechanical Properties ...
a b
c d
Fig. 9. Scanning electron micrographs of fracture surface for specimens: neat (a), with 3.5 wt.% SiO2
and 4 wt.% HIPS (b, c, d).
by 69, 42, and 91%, respectively. Correlation between morphology and mechanical
properties is observed via the SEM technique.
Ð å ç þ ì å
Çíà÷íà êðèõê³ñòü ³ íèçüê³ õàðàêòåðèñòèêè îïîðó õâèëüîâ³é íàïðóç³, íåçâà-
æàþ÷è íà âèñîêó ìåõàí³÷íó ì³öí³ñòü, îáóìîâèëè íåäîñòàòíüî øèðîêå ïðîìèñ-
ëîâå âèêîðèñòàííÿ åïîêñèäíèõ ñìîë. Âèêîðèñòîâóºòüñÿ íîâå ïîºäíàííÿ òåðìî-
ïëàñòè÷íèõ ³ äèñïåðñíèõ íàïîâíþâà÷³â ÿê ìîäèô³êàòîðà äëÿ îäíî÷àñíîãî
ï³äâèùåííÿ ì³öíîñò³ íà ðîçðèâ ³ äåìïô³ðóâàëüíèõ âëàñòèâîñòåé íàíîêîìïî-
çèòà íà åïîêñèäí³é îñíîâ³ ïðè íàâàíòàæåíí³ çà ïåðøîþ ³ äðóãîþ ìîäîþ. Äëÿ
îòðèìàííÿ òðèêîìïîíåíòíîãî íàíîêîìïîçèòà íà åïîêñèäí³é îñíîâ³ âèêîðèñ-
òîâóþòüñÿ óäàðîì³öíèé ïîë³ñòèðîë ÿê òåðìîïëàñòè÷íà ôàçà ³ íàíî÷àñòèíêè ç
êðåìíåçåìó ÿê äèñïåðñíà ôàçà. Äëÿ ðåàë³çàö³¿ äèñïåðñ³éíîãî ìåõàí³çìó âèêî-
ðèñòîâóºòüñÿ ìåòîä ïåðåì³øóâàííÿ ðîç÷èíó äëÿ ïðèãîòóâàííÿ îäíîð³äíî¿
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̳öí³ñòü íà ðîçðèâ ³ äåìïô³ðóâàëüí³ âëàñòèâîñò³ ìàòåð³àëó ïðè éîãî íàâàíòà-
æåíí³ çà ïåðøîþ ³ äðóãîþ ìîäîþ îö³íþâàëè ïðè ïðîâåäåíí³ äâîõ ð³çíèõ
ìåõàí³÷íèõ âèïðîáóâàíü ³ç ìåòîþ äîñÿãíåííÿ á³ëüø âèñîêî¿ ì³öíîñò³ é óäàð-
íî¿ â’ÿçêîñò³ áåç ïîã³ðøåííÿ íåîáõ³äíèõ ìåõàí³÷íèõ âëàñòèâîñòåé. Ïðè ðîç-
ðîáö³ ìàòåìàòè÷íèõ ìîäåëåé äëÿ ïðîãíîçóâàííÿ ìåõàí³÷íî¿ ïîâåä³íêè íàíî-
êîìïîçèòà ç åïîêñèäíî¿ ñìîëè, óäàðîì³öíîãî ïîë³ñòèðîëà ³ êðåìíåçåìó ÿê
ôóíêö³¿ ô³çè÷íèõ ÷èííèê³â âèêîðèñòîâóºòüñÿ öåíòðàëüíèé êîìïîçèö³éíèé
ïëàí. Çà åôåêòèâí³ ïàðàìåòðè áðàëè ïðîöåíòíèé âì³ñò óäàðîì³öíîãî ïîë³ñòè-
ðîëà, êðåìíåçåìó é åïîêñèäíîãî çàòâåðäæóâà÷à. Íà îñíîâ³ ìàòåìàòè÷íèõ
ôóíêö³é, îòðèìàíèõ çà äîïîìîãîþ ìîäåë³ öåíòðàëüíîãî êîìïîçèö³éíîãî
ïëàíó, áóëî âèêîðèñòàíî ãåíåòè÷íèé àëãîðèòì, ÿê îäèí ³ç ïîòóæíèõ çàñîá³â
îïòèì³çàö³¿, äëÿ âèçíà÷åííÿ îïòèìàëüíèõ çíà÷åíü ìåõàí³÷íèõ âëàñòèâîñòåé.
Îòðèìàí³ ðåçóëüòàòè ñâ³ä÷àòü, ùî ïîºäíàííÿ íàíî÷àñòèíîê óäàðîì³öíîãî
ïîë³ñòèðîëà ç êðåìíåçåìîì çíà÷íî çá³ëüøóº ãðàíèöþ ì³öíîñò³ íà ðîçðèâ ³
õàðàêòåðèñòèêè äåìïô³ðóâàííÿ åïîêñèäíî¿ ñìîëè íà 69, 42 ³ 91% â³äïîâ³äíî.
Ìîðôîëîã³þ ïîâåðõîíü ðóéíóâàííÿ âèâ÷àëè çà äîïîìîãîþ ñêàíóâàëüíîãî
åëåêòðîííîãî ì³êðîñêîïà.
1. M. M. Shokrieh, M. A. Torabizadeh, and A. Fereidoon, “A new method for
evaluation of mechanical properties of glass/epoxy composites at low
temperatures,” Strength Mater., 44, No. 1, 87–99 (2012).
2. M. M. Shokrieh, M. A. Torabizadeh, and A. Fereidoon, “Progressive failure
analysis of glass/epoxy composites at low temperatures,” Strength Mater., 44,
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3. A. V. Buketov, P. D. Stukhlyak, V. V. Levyts’kyi, et al., “A study of creep of
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162 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 5
Y. Rostamiyan and A. B. Fereidoon
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/SVE <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>
/ENU (Use these settings to create Adobe PDF documents for quality printing on desktop printers and proofers. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /NoConversion
/DestinationProfileName ()
/DestinationProfileSelector /NA
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure true
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles true
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /NA
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /LeaveUntagged
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|