Prediction by a Genetic Algorithm of the Fiber-Matrix Interface Damage for Composite Material. Part 1. Study of Shear Damage in Two Composites T300/914 and PEEK/APC2
We have conducted research on the effect of fiber arrangement on the optimization of the damage to the interface, recently published. We develop in this paper the evolution of the damage in the shearing direction by genetic algorithm. The results obtained by varying the shear rate of the interface o...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
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| Zitieren: | Prediction by a Genetic Algorithm of the Fiber-Matrix Interface Damage for Composite Material. Part 1. Study of Shear Damage in Two Composites T300/914 and PEEK/APC2 / A. Mokaddem, M. Alami, B. Doumi, A. Boutaoush // Проблемы прочности. — 2014. — № 4. — С. 123-129. — Бібліогр.: 18 назв. — англ. |
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irk-123456789-1731282020-11-24T01:26:49Z Prediction by a Genetic Algorithm of the Fiber-Matrix Interface Damage for Composite Material. Part 1. Study of Shear Damage in Two Composites T300/914 and PEEK/APC2 Mokaddem, A. Alami, M. Doumi, B. Boutaoush, A. Научно-технический раздел We have conducted research on the effect of fiber arrangement on the optimization of the damage to the interface, recently published. We develop in this paper the evolution of the damage in the shearing direction by genetic algorithm. The results obtained by varying the shear rate of the interface of the two materials studied T300 and PEEK, show a good agreement between our genetic approach and the mathematical models presented by Cox and Weibull. Для композитных материалов, армированных волокнами, актуальной является оптимизация размещения последних, что обеспечивает минимальное повреждение на стыке волокон и матрицы. Исследована кинетика развития повреждений в направлении действия максимальных сдвиговых напряжений с помощью генетического алгоритма, ранее разработанного авторами. Для двух композитов типа T300 и PEEK с использованием предложенного генетического подхода получены расчетные данные для различных скоростей сдвиговых деформаций на стыке волокон и матрицы, которые хорошо согласуются с полученными на основании математических моделей Кокса и Вейбулла. В дальнейших исследованиях планируется изучение влияния термомеханического нагружения на сдвиговое повреждение зоны стыка волокон и матрицы. Для композитних матеріалів, армованих волокнами, актуальною є оптимізація розміщення останніх, що забезпечує мінімальне пошкодження на стику волокон і матриці. Досліджено кінетику розвитку пошкоджень у напрямку дії максимальних зсувних напружень за допомогою раніше розробленого авторами генетичного алгоритму. Для двох композитів типу Т300 і PEEK з використанням запропонованого генетичного підходу отримано розрахункові дані для різної швидкості зсувних деформацій на стику волокон і матриці, які добре узгоджуються з отриманими на основі математичних моделей Кокса і Вейбулла. У подальших дослідженнях планується вивчення впливу термомеханічного навантаження на зсувне пошкодження зони стику волокон і матриці. 2014 Article Prediction by a Genetic Algorithm of the Fiber-Matrix Interface Damage for Composite Material. Part 1. Study of Shear Damage in Two Composites T300/914 and PEEK/APC2 / A. Mokaddem, M. Alami, B. Doumi, A. Boutaoush // Проблемы прочности. — 2014. — № 4. — С. 123-129. — Бібліогр.: 18 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/173128 539.4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Научно-технический раздел Научно-технический раздел |
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Научно-технический раздел Научно-технический раздел Mokaddem, A. Alami, M. Doumi, B. Boutaoush, A. Prediction by a Genetic Algorithm of the Fiber-Matrix Interface Damage for Composite Material. Part 1. Study of Shear Damage in Two Composites T300/914 and PEEK/APC2 Проблемы прочности |
| description |
We have conducted research on the effect of fiber arrangement on the optimization of the damage to the interface, recently published. We develop in this paper the evolution of the damage in the shearing direction by genetic algorithm. The results obtained by varying the shear rate of the interface of the two materials studied T300 and PEEK, show a good agreement between our genetic approach and the mathematical models presented by Cox and Weibull. |
| format |
Article |
| author |
Mokaddem, A. Alami, M. Doumi, B. Boutaoush, A. |
| author_facet |
Mokaddem, A. Alami, M. Doumi, B. Boutaoush, A. |
| author_sort |
Mokaddem, A. |
| title |
Prediction by a Genetic Algorithm of the Fiber-Matrix Interface Damage for Composite Material. Part 1. Study of Shear Damage in Two Composites T300/914 and PEEK/APC2 |
| title_short |
Prediction by a Genetic Algorithm of the Fiber-Matrix Interface Damage for Composite Material. Part 1. Study of Shear Damage in Two Composites T300/914 and PEEK/APC2 |
| title_full |
Prediction by a Genetic Algorithm of the Fiber-Matrix Interface Damage for Composite Material. Part 1. Study of Shear Damage in Two Composites T300/914 and PEEK/APC2 |
| title_fullStr |
Prediction by a Genetic Algorithm of the Fiber-Matrix Interface Damage for Composite Material. Part 1. Study of Shear Damage in Two Composites T300/914 and PEEK/APC2 |
| title_full_unstemmed |
Prediction by a Genetic Algorithm of the Fiber-Matrix Interface Damage for Composite Material. Part 1. Study of Shear Damage in Two Composites T300/914 and PEEK/APC2 |
| title_sort |
prediction by a genetic algorithm of the fiber-matrix interface damage for composite material. part 1. study of shear damage in two composites t300/914 and peek/apc2 |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| publishDate |
2014 |
| topic_facet |
Научно-технический раздел |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/173128 |
| citation_txt |
Prediction by a Genetic Algorithm of the Fiber-Matrix Interface Damage for Composite Material. Part 1. Study of Shear Damage in Two Composites T300/914 and PEEK/APC2 / A. Mokaddem, M. Alami, B. Doumi, A. Boutaoush // Проблемы прочности. — 2014. — № 4. — С. 123-129. — Бібліогр.: 18 назв. — англ. |
| series |
Проблемы прочности |
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2025-07-15T09:39:53Z |
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2025-07-15T09:39:53Z |
| _version_ |
1837705351116357632 |
| fulltext |
UDC 539.4
Prediction by a Genetic Algorithm of the Fiber–Matrix Interface Damage for
Composite Material. Part 1. Study of Shear Damage in Two Composites
T300/914 and PEEK/APC2
A. Mokaddem,
a,1
M. Alami,
b
B. Doumi,
c
and A. Boutaous
b
a Houari Boumediene University of Science and Technology, USTHB, Algiers, Algeria
b Mohamed Boudiaf University of Science and Technology of Oran, USTO, Oran, Algeria
c University of Dr. Moulay Tahar, Saida, Algeria
1 mokaddem.allel@gmail.com
ÓÄÊ 539.4
Ïðîãíîçèðîâàíèå ïîâðåæäåíèÿ êîìïîçèòà íà ñòûêå ìàòðèöû è âîëîêîí
ñ ïîìîùüþ ãåíåòè÷åñêîãî àëãîðèòìà. Ñîîáùåíèå 1. Àíàëèç ïîâðåæäåíèé
îò ñäâèãîâûõ íàïðÿæåíèé â äâóõ êîìïîçèòàõ T300/914 è PEEK/APC2
À. Ìîêàääåì
à,1
, Ì. Àëàìè
á
, Á. Äîóìè
â
, À. Áóòàó
á
à Íàó÷íî-òåõíîëîãè÷åñêèé óíèâåðñèòåò èì. Õóàðè Áóìåäüåíà, Àëæèð, Àëæèð
á Íàó÷íî-òåõíîëîãè÷åñêèé óíèâåðñèòåò èì. Ìóõàìåäà Áîóäèàôà, Îðàí, Àëæèð
â Óíèâåðñèòåò Ìóëàé Òàõàð, Ñàèäà, Àëæèð
Äëÿ êîìïîçèòíûõ ìàòåðèàëîâ, àðìèðîâàííûõ âîëîêíàìè, àêòóàëüíîé ÿâëÿåòñÿ îïòèìèçàöèÿ
ðàçìåùåíèÿ ïîñëåäíèõ, ÷òî îáåñïå÷èâàåò ìèíèìàëüíîå ïîâðåæäåíèå íà ñòûêå âîëîêîí è ìàò-
ðèöû. Èññëåäîâàíà êèíåòèêà ðàçâèòèÿ ïîâðåæäåíèé â íàïðàâëåíèè äåéñòâèÿ ìàêñèìàëüíûõ
ñäâèãîâûõ íàïðÿæåíèé ñ ïîìîùüþ ãåíåòè÷åñêîãî àëãîðèòìà, ðàíåå ðàçðàáîòàííîãî àâòî-
ðàìè. Äëÿ äâóõ êîìïîçèòîâ òèïà T300 è PEEK ñ èñïîëüçîâàíèåì ïðåäëîæåííîãî ãåíåòè-
÷åñêîãî ïîäõîäà ïîëó÷åíû ðàñ÷åòíûå äàííûå äëÿ ðàçëè÷íûõ ñêîðîñòåé ñäâèãîâûõ äåôîð-
ìàöèé íà ñòûêå âîëîêîí è ìàòðèöû, êîòîðûå õîðîøî ñîãëàñóþòñÿ ñ ïîëó÷åííûìè íà îñíî-
âàíèè ìàòåìàòè÷åñêèõ ìîäåëåé Êîêñà è Âåéáóëëà.  äàëüíåéøèõ èññëåäîâàíèÿõ ïëàíèðóåòñÿ
èçó÷åíèå âëèÿíèÿ òåðìîìåõàíè÷åñêîãî íàãðóæåíèÿ íà ñäâèãîâîå ïîâðåæäåíèå çîíû ñòûêà
âîëîêîí è ìàòðèöû.
Êëþ÷åâûå ñëîâà: ñòûê, ñäâèãîâîå ïîâðåæäåíèå, âîëîêíî, ìàòðèöà, êîìïîçèò, ãåíå-
òè÷åñêèé àëãîðèòì.
Introduction. Nowadays the enormous use of polymer materials is attributed to their
extraordinary combination of properties, low weight and ease of processing. However for
improvement of some properties such as thermal and mechanical stability, large numbers of
additives were added to polymeric matrix and formed polymer matrix composite [1, 2].
A composite is defined as a combination of two or more materials with different
physical and chemical properties and distinguishable interface. Composite materials have
a wonderful and different range of applications. Important advantages of composites over
many metal compounds are high specific stiffness and specific strength, high toughness,
corrosion resistance, low density and thermal insulation [1–3].
In most composite materials, one phase is usually continuous and called the matrix,
while the other phase called the dispersed phase. On the basis of the nature of the matrices,
composites can be classified into four major categories [3, 4]:
© A. MOKADDEM, M. ALAMI, B. DOUMI, A. BOUTAOUS, 2014
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 4 123
1. Polymer matrix composite.
2. Metal matrix composite.
3. Ceramic matrix composite.
4. Carbon matrix composite [4, 5].
Polymer matrix composite can be processed at a much lower temperature, compared
to other composite. Depending on the types of polymer matrices, polymer matrix composite
are classified as thermosetting composites and thermoplastic composites [6, 7].
Lemaitre and Chaboche [8] consider a damaged solid in which an element of finite
volume a notch large enough relative to heterogeneities is defined as follows: S is area
representative volume element identified by its norm n, S e is effective resistance area (if
S Se � ), and S d is damaged area, S S Sd e� � .
The mechanical measurement of local damage in relation to n is then characterized
by D S Sd� .
If D� 0, the material is in a pristine or not damaged.
If D� 1, the volume element is broken into two parts along the plane normal n.
If 0 1� �D , D characterizes the state of damage defined, the macroscopic elastic
behavior of the damaged material can be calculated using D through the stiffness.
In this study, we present a genetic approach of shear damage to the interface of two
composites materials T300/914 and PEEK/APC2, using the Weibull probability model.
This model accounts for the damage of the two main constituent fibers and matrix, the
results are compared with those obtained by the Cox model.
Reminder on Analytical Models.
Modeling of the Interface. D12 and D22 internal variables of damage [9–11], D12
is the shear and D22 for transverse traction.
Once the elastic deformation energy of damage is established, the dual variables
YD12
and YD22
, variables of damage D12 and D22, and evolution variables are
Y Y bYeq D D� �
12 22
.
Laws of damage are
�
�
�
�
12
22
12
22
�
�
�
�
f Y
h Y
i ( ),
( ).
(1)
The interface has the following behavior:
(i) linear elastic, brittle, tensile, transverse;
(ii) elastic, damageable, shear.
Two new damage variables are introduced: �12 and �22. The same way as the
matrix, the elastic strain energy and damage variables associated YD12
and YD22
are
defined and, finally, the laws of evolution [9–11]. For a single fiber surrounded by matrix,
many analytical solutions have been proposed. One of the first [12] provides the shape of
the shear stress along the fiber length as the form [13, 14]
�
�
�
E a
th l
f
2
2( ). (2)
To simplify calculation, we put:
2
2
2
�
G
E r R r
m
f f fln( )
,
A. Mokaddem, M. Alami, B. Doumi, and A. Boutaous
124 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 4
where Gm is shear modulus of the matrix, E f is the Young modulus of the fiber, � is
deformation, a is radius of the fiber, R is distance between fibers, and � is shear stress of
the interface.
These variables related to the components of a composite material (fiber and matrix)
are all taken into account through formula (2). These variables allow us therefore to
appreciate the resulting sets of genetic algorithm.
Model Based on the Statistical Approach. Damage to the matrix, when the stress is
uniform, is given by [15]:
D Vm m
m
T
m
mm
� � �
��
�
�
�
�
�
�
�
�
�
�
1
0
exp ,
� �
�
(3)
where � is applied stress, � m
T is heat stress, Vm is the ratio volume of the matrix, and
� 0m and mm are the Weibull parameters.
After creation of a crack, a fragment of length L will give rise to two fragments of
size L L� 1 and L XL X2 1� �( ) (X being a random number between 0 and 1) [16, 17].
At each crack up a fiber, a fiber–matrix debonding length 2l will occur with a corollary
decrease of creating a new crack in part because the matrix unloaded. At each increment of
stress, the break is calculated. All blocks which break reaches 0.5 give rise to new cracks.
[16, 17].
A broken fiber is discharged along its entire length. That is to say, it can not break at
once. The rupture follows a law similar to that described for the matrix
D A Lf f eq
f
f
mf
� � �
�
�
�
�
�
�
�
�
�
�
�
1
0
exp ,
max�
�
(4)
where � max
f is the maximum stress applied and Leq is the length of the fibers would have
the same break in a consistent manner.
Numerical Simulation by the Genetic Algorithm (GA).
Development. Our work involves modeling the damage in shear D12 interface fiber
matrix of a composite material. To do so, we chose to use a genetic optimization which
allows us to see the evolution of the damage along the fiber.
This approach is based on the probabilistic model of Weibull. The principle begins
with a random generation of an initial population and the choice of Dm and D f as two
random variables, then it is necessary to change this population (numbering 100 with a
maximum generation equal to 50 as a stop criterion) by a set of genetic operators (selection,
crossover and mutation) and each time is varied the shear rate of the interface to determine
the damage D12. The population is composed of the genes on chromosome represent the
following variables: the shear rate � which is between 80 and 120 N as defined by the
maximum value of stress tests, the Dm and D f . These three variables allow us to locate
the shear damage D12 interface, this one compare to damage transverse D22, and find the
optimum value of the damage [18].
The evaluation of each generation is made by an objective function after the Cox and
Weibull model reflecting all the variables set at the beginning of the algorithm (the
mechanical properties of each constituent of the composite) by a shear damage interface.
Figure 1 presents the flowchart of genetic algorithm.
Simulation Results. A calculation was performed on two types of composite materials
T300/914 and PEEK/APC2. We examined the variation of shear rate for different load
values (�� 80, 100, and 120 N), which allowed us to calculate the shear damage of the
Prediction by a Genetic Algorithm ... Part 1 ...
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 4 125
126 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 4
A. Mokaddem, M. Alami, B. Doumi, and A. Boutaous
Fig. 1. The genetic algorithm flowchart.
a b
c
Fig. 2. Influence of shear stress on the damage to the interface by GA for T300/914 composite:
(a) � � 80 N; (b) � � 100 N; (c) � � 120 N.
interface. Figures 2 and 3 show each value of � for the level of shear damage to the
interface of two materials.
T300/914. Figure 2 shows that the damage D interface starts at 0.3 for �� 80 N,
then increases to a maximum value of 0.7 for �� 120 N, we note the presence of a
symmetry of the damage to the interface. This damage is zero in the middle of the fiber and
dense at the ends. One can say that the stress concentration along the length of the fiber
creates a strong degradation of the interface and which is greater at the ends relative to the
center.
PEEK/APC2. Figure 3 shows that the damage D interface starts this time at 0.1 for
�� 80 N, then increases to a maximum value of 0.5 for �� 120 N, we note the presence of
a symmetry of the damage to the interface, zero in the middle of the fiber and dense at the
ends. We can say that the stress concentration along the length of the fiber creates a strong
degradation of the interface most important at the ends relative with the middle; values are
lower compared to those found for the T300.
Conclusions. The results obtained in this study via the genetic algorithm coincide
perfectly with the results at the meso level of Ladevèze, which showed that the shear rate
leads to a significant reduction in the degradation of the interface. These results show that
the level of damage in shear of interface is more important than the level of the transverse
damage for both materials studied T300 and PEEK, which provides a good agreement
between the numerical simulation and the actual behavior of the two materials. Numerical
simulation shows that the PEEK is stronger than the T300. We can therefore say that the
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 4 127
Prediction by a Genetic Algorithm ... Part 1 ...
ba
c
Fig. 3. Influence of shear stress on the damage to the interface by GA for PEEK/APC2 composite:
(a) � � 80 N; (b) � � 100 N; (c) � � 120 N.
model is applicable to the phenomenon of damage of a unidirectional composite as a
function of applied stress. Finally, we can conclude that the shear loading of interface is
dominant compared to transverse loading. In future studies we’ll analyze the thermo-
mechanical effect on shear damage of interface.
Ð å ç þ ì å
Äëÿ êîìïîçèòíèõ ìàòåð³àë³â, àðìîâàíèõ âîëîêíàìè, àêòóàëüíîþ º îïòèì³çàö³ÿ ðîçì³-
ùåííÿ îñòàíí³õ, ùî çàáåçïå÷óº ì³í³ìàëüíå ïîøêîäæåííÿ íà ñòèêó âîëîêîí ³ ìàòðèö³.
Äîñë³äæåíî ê³íåòèêó ðîçâèòêó ïîøêîäæåíü ó íàïðÿìêó 䳿 ìàêñèìàëüíèõ çñóâíèõ
íàïðóæåíü çà äîïîìîãîþ ðàí³øå ðîçðîáëåíîãî àâòîðàìè ãåíåòè÷íîãî àëãîðèòìó. Äëÿ
äâîõ êîìïîçèò³â òèïó Ò300 ³ PEEK ç âèêîðèñòàííÿì çàïðîïîíîâàíîãî ãåíåòè÷íîãî
ï³äõîäó îòðèìàíî ðîçðàõóíêîâ³ äàí³ äëÿ ð³çíî¿ øâèäêîñò³ çñóâíèõ äåôîðìàö³é íà
ñòèêó âîëîêîí ³ ìàòðèö³, ÿê³ äîáðå óçãîäæóþòüñÿ ç îòðèìàíèìè íà îñíîâ³ ìàòå-
ìàòè÷íèõ ìîäåëåé Êîêñà ³ Âåéáóëëà. Ó ïîäàëüøèõ äîñë³äæåííÿõ ïëàíóºòüñÿ âèâ÷åí-
íÿ âïëèâó òåðìîìåõàí³÷íîãî íàâàíòàæåííÿ íà çñóâíå ïîøêîäæåííÿ çîíè ñòèêó
âîëîêîí ³ ìàòðèö³.
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