Study of the Effect of Water Intake by the Matrix on the Optimization of the Fiber Matrix Interface Damage for a Composite Material by Genetic Algorithms
The objective of this paper is study the influence of the matrix swelling due to water on the damage of the fiber matrix interface of a composite material. The results obtained by a genetic approach based on Weibull probabilistic model, show good agreement between the simulation and the actual...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
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| Cite this: | Study of the Effect of Water Intake by the Matrix on the Optimization of the Fiber Matrix Interface Damage for a Composite Material by Genetic Algorithms / Lahouari H. Temimi, M. Allel, N. Belkaid, A. Boutaous, R. Bnuamrane // Проблемы прочности. — 2013. — № 6. — С. 142-151. — Бібліогр.: 16 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1126692025-02-10T01:41:55Z Study of the Effect of Water Intake by the Matrix on the Optimization of the Fiber Matrix Interface Damage for a Composite Material by Genetic Algorithms Исследование влияния поглощения воды смолой на оптимизацию повреждения поверхности раздела между волокном и матрицей в композитном материале с помощью генетических алгоритмов Temimi Lahouari, H. Allel, M. Belkaid, N. Boutaous, A. Bnuamrane, R. Научно-технический раздел The objective of this paper is study the influence of the matrix swelling due to water on the damage of the fiber matrix interface of a composite material. The results obtained by a genetic approach based on Weibull probabilistic model, show good agreement between the simulation and the actual behavior of the two materials T300/914 and PEEK/APC2. Also the absorption of water by the matrix increases significantly the interface damage. Исследовано влияние набухания смолы (матрицы) вследствие поглощения воды на повреждение поверхности раздела между волокном и матрицей в композитном материале. Результаты, полученные с помощью генетического алгоритма на основе вероятностной модели Вейбулла, показали хорошее соответствие между процессом моделирования и фактическим поведением двух материалов (T300/914 и PEEK/APC2). Более того, абсорбция воды смолой (матрицей) значительно увеличивает повреждение поверхности раздела. Досліджено вплив набухання смоли (матриці) внаслідок поглинання води на пошкодження поверхні поділу між волокном і матрицею в композитному матеріалі. Результати, що отримані за допомогою генетичного алгоритму на основі імовірнісної моделі Вейбулла, показали хорошу відповідність між процесом моделювання і фактичною поведінкою двох матеріалів (Т300/914 і PEEK/APC2). Більш того, абсорбція води смолою (матрицею) значно збільшує пошкодженість поверхні поділу. 2013 Article Study of the Effect of Water Intake by the Matrix on the Optimization of the Fiber Matrix Interface Damage for a Composite Material by Genetic Algorithms / Lahouari H. Temimi, M. Allel, N. Belkaid, A. Boutaous, R. Bnuamrane // Проблемы прочности. — 2013. — № 6. — С. 142-151. — Бібліогр.: 16 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/112669 539.4 en Проблемы прочности application/pdf Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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English |
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Научно-технический раздел Научно-технический раздел |
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Научно-технический раздел Научно-технический раздел Temimi Lahouari, H. Allel, M. Belkaid, N. Boutaous, A. Bnuamrane, R. Study of the Effect of Water Intake by the Matrix on the Optimization of the Fiber Matrix Interface Damage for a Composite Material by Genetic Algorithms Проблемы прочности |
| description |
The objective of this paper is study the influence
of the matrix swelling due to water on the
damage of the fiber matrix interface of a composite
material. The results obtained by a genetic
approach based on Weibull probabilistic
model, show good agreement between the simulation
and the actual behavior of the two
materials T300/914 and PEEK/APC2. Also the
absorption of water by the matrix increases significantly
the interface damage. |
| format |
Article |
| author |
Temimi Lahouari, H. Allel, M. Belkaid, N. Boutaous, A. Bnuamrane, R. |
| author_facet |
Temimi Lahouari, H. Allel, M. Belkaid, N. Boutaous, A. Bnuamrane, R. |
| author_sort |
Temimi Lahouari, H. |
| title |
Study of the Effect of Water Intake by the Matrix on the Optimization of the Fiber Matrix Interface Damage for a Composite Material by Genetic Algorithms |
| title_short |
Study of the Effect of Water Intake by the Matrix on the Optimization of the Fiber Matrix Interface Damage for a Composite Material by Genetic Algorithms |
| title_full |
Study of the Effect of Water Intake by the Matrix on the Optimization of the Fiber Matrix Interface Damage for a Composite Material by Genetic Algorithms |
| title_fullStr |
Study of the Effect of Water Intake by the Matrix on the Optimization of the Fiber Matrix Interface Damage for a Composite Material by Genetic Algorithms |
| title_full_unstemmed |
Study of the Effect of Water Intake by the Matrix on the Optimization of the Fiber Matrix Interface Damage for a Composite Material by Genetic Algorithms |
| title_sort |
study of the effect of water intake by the matrix on the optimization of the fiber matrix interface damage for a composite material by genetic algorithms |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| publishDate |
2013 |
| topic_facet |
Научно-технический раздел |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/112669 |
| citation_txt |
Study of the Effect of Water Intake by the Matrix on the Optimization of the Fiber Matrix Interface Damage for a Composite Material by Genetic Algorithms / Lahouari H. Temimi, M. Allel, N. Belkaid, A. Boutaous, R. Bnuamrane // Проблемы прочности. — 2013. — № 6. — С. 142-151. — Бібліогр.: 16 назв. — англ. |
| series |
Проблемы прочности |
| work_keys_str_mv |
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2025-12-02T12:50:47Z |
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| fulltext |
UDC 539.4
Study of the Effect of Water Intake by the Matrix on the Optimization
of the Fiber Matrix Interface Damage for a Composite Material by
Genetic Algorithms
H. Temimi Lahouari,
1
M. Allel, N. Belkaid, A. Boutaous, and R. Bouamrane
Mohamed Boudiaf University of Science and Technology of Oran, Oran, Algeria
1 husseintemimi@yahoo.fr
ÓÄÊ 539.4
Èññëåäîâàíèå âëèÿíèÿ ïîãëîùåíèÿ âîäû ñìîëîé íà îïòèìèçàöèþ
ïîâðåæäåíèÿ ïîâåðõíîñòè ðàçäåëà ìåæäó âîëîêíîì è ìàòðèöåé â
êîìïîçèòíîì ìàòåðèàëå ñ ïîìîùüþ ãåíåòè÷åñêèõ àëãîðèòìîâ
Õ. Òåìèìè Ëàõîóàðè, Ì. Àëëåë, Í. Áåëêàèä, À. Áóòàó, Ð. Áîóàìðàíå
Óíèâåðñèòåò íàóêè è òåõíèêè èì. Ìóõàìåäà Áîóäèàôà, Îðàí, Àëæèð
Èññëåäîâàíî âëèÿíèå íàáóõàíèÿ ñìîëû (ìàòðèöû) âñëåäñòâèå ïîãëîùåíèÿ âîäû íà ïîâðåæ-
äåíèå ïîâåðõíîñòè ðàçäåëà ìåæäó âîëîêíîì è ìàòðèöåé â êîìïîçèòíîì ìàòåðèàëå. Ðåçóëü-
òàòû, ïîëó÷åííûå ñ ïîìîùüþ ãåíåòè÷åñêîãî àëãîðèòìà íà îñíîâå âåðîÿòíîñòíîé ìîäåëè
Âåéáóëëà, ïîêàçàëè õîðîøåå ñîîòâåòñòâèå ìåæäó ïðîöåññîì ìîäåëèðîâàíèÿ è ôàêòè÷åñêèì
ïîâåäåíèåì äâóõ ìàòåðèàëîâ (T300/914 è PEEK/APC2). Áîëåå òîãî, àáñîðáöèÿ âîäû ñìîëîé
(ìàòðèöåé) çíà÷èòåëüíî óâåëè÷èâàåò ïîâðåæäåíèå ïîâåðõíîñòè ðàçäåëà.
Êëþ÷åâûå ñëîâà: ãðàíèöà ðàçäåëà, âîëîêíî, ìàòðèöà, ïîâðåæäåíèå, íàáóõà-
íèå, âîäà, ãåíåòè÷åñêèé àëãîðèòì.
Introduction. According Aytac et al. [1] damage is the main cause of
phenomena leading to failure by progressive loss of stiffness of material. It affects
all final physical properties. The damage of material results into an irreversible
change in the microstructure. This results in a variation of the elastic properties at
the macroscopic level (relaxation of material, reduced Young’s modulus). For
Lemaitre and Chaboche [2], the theory describes the evolution of damage
phenomena between the pristine and the initiation of macroscopic crack. The
plastic ductile damage accompanies large plastic deformations, damage macro-
fragile can be caused by stress monotonous without significant permanent
deformation.
For Ladevese [3, 4] the damage is the degradation more or less progressive
material due to the emergence and development of microcracks and microvoids.
The damage mechanics modelling of these phenomena depend of design of
structures. For composite, there are not one, but several mechanisms of damage,
and they are highly anisotropic. The idea is that the deterioration of a material can
be described by its effects on elastic properties. Changes in elastic stiffness are
© H. TEMIMI LAHOUARI, M. ALLEL, N. BELKAID, A. BOUTAOUS, R. BOUAMRANE, 2013
142 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6
indicators of the level of damage in the material. For the particular case of a
unidirectional composite subjected to uniaxial tensile stress in the fiber direction,
there is in general:
1. Rupture of fibers: boot from a default, if the fiber–matrix is low, it initiates
a separation of the interface (interfacial failure). If the fiber breaks in an area where
the matrix is already cracked, there may be transverse propagation of the crack.
2. Rupture of the matrix: initiation and propagation of a fault. When the crack
reaches the fiber–matrix interface, there may be fiber breakage encountered, stress
at the crack tip is important. At this meeting, there may be a change in direction of
crack propagation in the matrix.
3. Degradation of the interface, which is the result of excess stress shear,
tension or both. Decohesion of interface usually accompanies a broken fiber or
crack propagation in the matrix.
Some matrices increase in volume when exposed to ambient humidity, under
the effect of water absorption. This swelling, opposed, induces stress as would a
thermal expansion. But in opposed thermal expansion, constraints (hydrostatic
pressure when the swelling is isotropic) have an influence on the amount of water
that can be absorbed [5–8]. The process of water absorption into the polymeric
materials is described by Fig. 1. The first portion of the curve (from t �0 to
t t� 1) is governed by the law of diffusion of water in the polymer to reach
saturation for t tending towards infinity or pseudo saturation [9, 10]. Mass gain
can then be stabilized as shown in Fig. 1, or increase after a latency, or continue to
gradually increase depending on the material studied [11].
The diffusion of water depends on the amount of cavities and their size.
During the diffusion, water molecules move from one site to the other with an
activation energy (Fig. 2). Water is then considered as liquid water or free water [5,
6].
Fig. 1. Kinetics of diffusion of water into a polymeric material.
Fig. 2. Theories of free volumes.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6 143
Study of the Effect of Water Intake by the Matrix ...
The high water absorption capacity of epoxy resins results from the presence
on the epoxide chain of OH groups attracting polar water molecules. The diffusion
of water is along the polar groups present on the polymer chains. The hydrophilic
sites present in the material bind doubly (and sometimes triply) with the molecules
or groups of molecules of water by means of hydrogen bonds. Diffusion is then
performed by a trapping process. The water molecule linked to a site acquires
sufficient energy Ea to be freed and move to a new site [6] (Fig. 3).
Brun [5] shows that the water absorbed in the resin usually interacts with the
polar groups by hydrogen bonds and that these interactions are completely
reversible.
In this study, we will show the effect of water intake by the matrix on the
damage of the interface fiber-matrix of a composite. We will use the Weibull model
to determine the damage of the interface, Cox model to determine the objective
function to optimize, and finally the laws relating to the linear diffusion of the
water in the matrix.
1. Review of Analytical Models.
1.1. Absorption Model Diffusion. Diffusion models describe the first phase of
water absorption in the material (t �0 to t t� 1) in Fig. 1. The kinetics of water
diffusion in epoxy resins has been studied in many works [5, 6], all based on Fick’s
law in one dimension, that is diffusion is controlled by the concentration gradient
of water between the environment and the material until saturation.
To simplify the analysis of diffusion, the following hypotheses have been
considered:
(i) the diffusion coefficient D is independent of the water concentration C ;
(ii) the diffusion profile is linear in the x direction.
We can write
�
�
�
�
C
t
D
C
x
�
2
2
, (1)
where C is concentration and D is diffusion coefficient.
Considering that the highest water concentration is at the surface and does not
change during the absorption [6]. The absorption profile is continuous.
Monophase absorption model is described by Marque [6]. They developed
equations to describe the behavior during conditioning. A first step corresponding
to the diffusion phase involves the free water molecules and using Fick’s second
Fig. 3. Approach molecular.
144 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6
H. Temimi Lahouari, M. Allel, N. Belkaid, et al.
law in one dimension. It is shown by Brun [5] that in this model, the weight gain
M (%) caused by the absorption can be expressed in terms of the diffusion
coefficient D and the increase in mass to saturation M s (%):
M M
h
Dts�
4
�
, (2)
where h is thickness of the sample (in m) and t is conditioning time. (This
equation is valid when Dt h 2 � 0.05. This is for low conditioning time. After this
phase of diffusion, the curve stabilizes.)
1.2. Model Based on the Micromechanical Approach. For a single fiber
surrounded by matrix, many analytical solutions have been proposed by Cox [12],
which provides the shape of the shear stress along the fiber length as the following
form:
�
�
� ��
E a
th l
f
2
21 1( ). (3)
To simplify calculations, we take
�1
2
2
2
�
G
E r R r
m
f f fln( )
,
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 relating to the components of a composite material (fiber and
matrix) are all taken into account through the formula (3). Therefore these
variables will allow us to appreciate the result sets of genetic algorithm [13].
1.3. Model Based on the Statistical Approach. Damage to the matrix, when
the stress is uniform, is given by formula (4) [14]:
D Vm m
m
T
m
mm
�
�
�
�
�
�
�
�
�
��
�
�
�
��
1
0
exp ,
� �
�
(4)
where � is applied stress, � m
T is heat stress, Vm is the volume of the matrix, and
mm and � 0m are the Weibull parameters.
After the 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). At each crack of 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 breaks are calculated. All blocks which
break reaches 0.5 give rise to new cracks.
A broken fiber is discharged along its entire length. That is to say it can not
break once. The rupture follows a law similar to that described for the matrix:
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6 145
Study of the Effect of Water Intake by the Matrix ...
D A Lf f eq
f
f
m f
�
�
�
�
�
�
�
�
�
��
�
�
�
��
1
0
exp ,
max�
�
(5)
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.
2. Damage to the Interface (D).
Lemaitre and Chaboche consider a damaged solid in which an element of
finite volume (Fig. 4) a notch large enough relative to heterogeneities is defined as
follows [2]: 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 , characterizes the state of damage defined, the macroscopic elastic behavior
of the damaged material can be calculated using D through the stiffness [13, 15,
16].
3. Numerical Simulation by a Genetic Algorithm (GA).
3.1. Development. Our job is to study the influence of water absorption on the
damage to the fiber matrix interface of a composite material. To do this, we chose
to use a genetic optimization to evolve in the variation of moisture [Eqs. (1) and
(2)]. This requires a set of mathematical and analytical tools defined by the Cox
model, the theorem probabilistic Weibull model and linear laws of diffusion of
water in a polymer. The principle begins by randomly generating an initial
population and the selection of D (diffusion coefficient), then change this
population (the number 100 with a maximum of 50 equal to generation as stopping
criterion) by a set of genetic operators (selection, crossover and mutation) and in
each case calculating the diffusion coefficient of water in the matrix. The
population is composed of chromosome genes represent the following variables:
the mechanical stress which is between 80, 100, and 120 N, Young’s module of the
two materials, the shear modulus of the matrix, the fiber diameter, and distance R.
The evaluation of each generation is made by an objective function derived from
the Cox model, which includes all the variables defined at the beginning of the
Fig. 4. Representative volume element.
146 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6
H. Temimi Lahouari, M. Allel, N. Belkaid, et al.
algorithm (mechanical properties of each component of the composite, the distance
R and the radius). To exploit the maximum tensile stresses and see the progress of
our genetic algorithm, we chose a roulette selection and mutation selected value
equal to 0.3. Calculation by iteration values C and D were performed according
to the principle of Fick’s law, which has allowed the optimization of the results of
our genetic model.
3.2. The Materials Used. Our choice to focus on composite materials
T300/914 [thermosetting matrix composites (epoxy)] and PEEK/APC2
[thermoplastic composites-poly(ether ether ketone)], materials that we have used
by Boutaous [13], and whose main characteristics of the carbon fiber are shown in
Table 1. The index f means that the parameter refers to a fiber.
3.3. The Flowchart of Genetic Algorithm (shown in Fig. 5).
4. Simulation Results. A calculation was performed on two types of
composite materials T300/914 and PEEK/APC2. We examined the variation of
mechanical stress for different load values (� �80, 100, and 120 N), and see the
influence of the moisture by the water absorption on the damage to the interface.
Figures 6–11 and 12–17, respectively, show each value of � and humidity for the
level of damage to the interface of two materials: T300/914 and PEEK/APC2.
4.1. T300/914. Figures 6, 8, and 10 show 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.
Figures 7, 9, and 11 show that the damage “D” interface starts at 0.3 for
humidity H �0 and then increases to a maximum value of 0.9 for humidity
H �60%.
4.2. PEEK/APC2. Figures 12, 14, and 16 show 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.
Figures 13, 15, and 17 show that the damage “D” interface starts this time at
0.1 for humidity H �0, then increases to a maximum value of 0.7 for humidity
H �60%.
We can say that the stress concentration along the length of the fiber and
humidity create 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.
T a b l e 1
Characteristiñs of the Carbon Fiber
Properties of the carbon fiber Symbol [unit] Value
Density p f , kg/m3 1760
Diameter u, m 10
Young’s modulus E f , GPa 231
Shear modulus G f , GPa 92.1
Compression modulus K f , GPa 123
Poisson’s ratio � f 0.2
Coefficient of thermal expansion � f , � C 1 19 10 5. �
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6 147
Study of the Effect of Water Intake by the Matrix ...
NB: We also observed that the humidity increases the damage level of 0.2 for
both materials that have been the subject of study (T300: 0.7 to 0.9; PEEK: 0.5 to
0.7).
Conclusions. The results obtained by genetic algorithm calculation show that
the level of damage is related to the mechanical stress applied for both materials
that were studied the T300 and PEEK and indicate that the rate of absorption of
water has a substantial influence on the gradual degradation of the interface.
Numerical simulation compared with the result obtained by genetic algorithm
for T300 and PEEK show that the level of damage in a humid environment is more
important to a dry environment. We can therefore say that the model properly took
into account the phenomenon of damage to a unidirectional composite. It would be
interesting to see the effect of thermal stress on the damage interface of fiber
polymer matrix composite material.
Fig. 5. The flowchart of genetic algorithm.
148 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6
H. Temimi Lahouari, M. Allel, N. Belkaid, et al.
Ð å ç þ ì å
Äîñë³äæåíî âïëèâ íàáóõàííÿ ñìîëè (ìàòðèö³) âíàñë³äîê ïîãëèíàííÿ âîäè íà
ïîøêîäæåííÿ ïîâåðõí³ ïîä³ëó ì³æ âîëîêíîì ³ ìàòðèöåþ â êîìïîçèòíîìó
ìàòåð³àë³. Ðåçóëüòàòè, ùî îòðèìàí³ çà äîïîìîãîþ ãåíåòè÷íîãî àëãîðèòìó íà
Fig. 6. Damage to the interface
in a dry environment (� � 80 N).
Fig. 7. Damage to the interface
in a wet environment (� � 80 N).
Fig. 8. Damage to the interface
in a dry environment (� �100 N).
Fig. 9. Damage to the interface
in a wet environment (� �100 N).
Fig. 10. Damage to the interface
in a dry environment (� �120 N).
Fig. 11. Damage to the interface
in a wet environment (� �120 N).
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Study of the Effect of Water Intake by the Matrix ...
îñíîâ³ ³ìîâ³ðí³ñíî¿ ìîäåë³ Âåéáóëëà, ïîêàçàëè õîðîøó â³äïîâ³äí³ñòü ì³æ
ïðîöåñîì ìîäåëþâàííÿ ³ ôàêòè÷íîþ ïîâåä³íêîþ äâîõ ìàòåð³àë³â (Ò300/914 ³
PEEK/APC2). Á³ëüø òîãî, àáñîðáö³ÿ âîäè ñìîëîþ (ìàòðèöåþ) çíà÷íî çá³ëü-
øóº ïîøêîäæåí³ñòü ïîâåðõí³ ïîä³ëó.
Fig. 12. Damage to the interface
in a dry environment (� � 80 N).
Fig. 13. Damage to the interface
in a wet environment (� � 80 N).
Fig. 14. Damage to the interface
in a dry environment (� �100 N).
Fig. 15. Damage to the interface
in a wet environment (� �100 N).
Fig. 16. Damage to the interface
in a dry environment (� �120 N).
Fig. 17. Damage to the interface
in a wet environment (� �120 N).
150 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6
H. Temimi Lahouari, M. Allel, N. Belkaid, et al.
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Received 20. 05. 2013
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