Modeling of the mechanical behavior of composite at different relative humidities
The moisture diffusion and mechanical response in shear of a laminate constituted of 12 layers of glass fabric fiber/epoxy resin were evaluated. The experimental analysis of the moisture absorption of the specimens conditioned at different relative humidities, 0, 60, and 96% RH at 60°C was to...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2009
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Naceri, A. 2013-08-19T12:09:59Z 2013-08-19T12:09:59Z 2009 Modeling of the mechanical behavior of composite at different relative humidities / A. Naceri // Проблемы прочности. — 2009. — № 4. — С. 133-140. — Бібліогр.: 9 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/48399 539.4 The moisture diffusion and mechanical response in shear of a laminate constituted of 12 layers of glass fabric fiber/epoxy resin were evaluated. The experimental analysis of the moisture absorption of the specimens conditioned at different relative humidities, 0, 60, and 96% RH at 60°C was to determine the two parameters characteristic of the Fick diffusion law (the diffusion coefficient D and the maximum quantity of water of saturation Mm) which admits the reversibility of the phenomenon. The analysis of the mechanical response in shear of the specimens oriented at 45° tested in uniaxial tension at constant imposed displacement rates, has permitted to show that the influence of the moisture concentration for the composite is very important at 96% RH. The proposed simple model permits to specify the influence of water absorption on the mechanical behavior in shear. Для дванадцятишаруватого ламіната з матрицею з епоксидної смоли і скловолокон досліджено закономірності абсорбції вологи і механічної поведінки в умовах зсуву. Експериментальні дослідження абсорбції вологи зразками з ламіната за різних значень вологості повітря (0, 60 і 96%) при температурі 60°C дозволили визначити два параметри (коефіцієнт дифузії D і максимальну кількість вологи при насиченні M m), що характеризують закон дифузії Фіка, який припускає зворотність процесу. Аналіз механічної поведінки при зсуві, що забезпечується одновісним розтягом ламіната з волокнами, орієнтованими під кутом 45° до осі розтягу, при постійних швидкостях переміщення показав, що при вологості 96% концентрація вологи в композиті грає особливо важливу роль. Запропоновано просту модель, яка дозволяє описати вплив абсорбції вологи на механічну поведінку ламіната при зсуві. Для 12-слоистого ламината с матрицей из эпоксидной смолы и стекловолокон исследованы закономерности абсорбции влаги и механического поведения в условиях сдвига. Экспериментальные исследования абсорбции влаги образцами из ламината при различных значениях влажности воздуха (0, 60 и 96%) при температуре 6WC позволили определить два параметра (коэффициент диффузии D и максимальное количество влаги при насыщении Mm), характеризующих закон диффузии Фика, который предполагает обратимость процесса. Анализ механического поведения при сдвиге, обеспечиваемом одноосным растяжением ламината с волокнами, ориентированными под углом 45° к оси растяжения, при постоянных скоростях перемещения показал, что при влажности 96% концентрация влаги в композите играет особенно важную роль. Предложена простая модель, позволяющая описать влияние абсорбции влаги на механическое поведение ламината при сдвиге. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Modeling of the mechanical behavior of composite at different relative humidities Моделирование механического поведения композита при различных значениях относительной влажности Article published earlier |
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| title |
Modeling of the mechanical behavior of composite at different relative humidities |
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Modeling of the mechanical behavior of composite at different relative humidities Naceri, A. Научно-технический раздел |
| title_short |
Modeling of the mechanical behavior of composite at different relative humidities |
| title_full |
Modeling of the mechanical behavior of composite at different relative humidities |
| title_fullStr |
Modeling of the mechanical behavior of composite at different relative humidities |
| title_full_unstemmed |
Modeling of the mechanical behavior of composite at different relative humidities |
| title_sort |
modeling of the mechanical behavior of composite at different relative humidities |
| author |
Naceri, A. |
| author_facet |
Naceri, A. |
| topic |
Научно-технический раздел |
| topic_facet |
Научно-технический раздел |
| publishDate |
2009 |
| language |
English |
| container_title |
Проблемы прочности |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| format |
Article |
| title_alt |
Моделирование механического поведения композита при различных значениях относительной влажности |
| description |
The moisture diffusion and mechanical response
in shear of a laminate constituted of
12 layers of glass fabric fiber/epoxy resin
were evaluated. The experimental analysis
of the moisture absorption of the specimens
conditioned at different relative humidities,
0, 60, and 96% RH at 60°C was to determine
the two parameters characteristic of the Fick
diffusion law (the diffusion coefficient D
and the maximum quantity of water of saturation
Mm) which admits the reversibility of
the phenomenon. The analysis of the mechanical
response in shear of the specimens
oriented at 45° tested in uniaxial tension at
constant imposed displacement rates, has
permitted to show that the influence of the
moisture concentration for the composite is very important at 96% RH. The proposed simple
model permits to specify the influence of water
absorption on the mechanical behavior in shear.
Для дванадцятишаруватого ламіната з матрицею з епоксидної смоли і скловолокон
досліджено закономірності абсорбції вологи і механічної поведінки
в умовах зсуву. Експериментальні дослідження абсорбції вологи зразками з
ламіната за різних значень вологості повітря (0, 60 і 96%) при температурі
60°C дозволили визначити два параметри (коефіцієнт дифузії D і максимальну
кількість вологи при насиченні M m), що характеризують закон
дифузії Фіка, який припускає зворотність процесу. Аналіз механічної поведінки
при зсуві, що забезпечується одновісним розтягом ламіната з волокнами,
орієнтованими під кутом 45° до осі розтягу, при постійних швидкостях
переміщення показав, що при вологості 96% концентрація вологи в композиті
грає особливо важливу роль. Запропоновано просту модель, яка дозволяє
описати вплив абсорбції вологи на механічну поведінку ламіната при зсуві.
Для 12-слоистого ламината с матрицей из эпоксидной смолы и стекловолокон исследованы
закономерности абсорбции влаги и механического поведения в условиях сдвига. Экспериментальные
исследования абсорбции влаги образцами из ламината при различных значениях
влажности воздуха (0, 60 и 96%) при температуре 6WC позволили определить два параметра
(коэффициент диффузии D и максимальное количество влаги при насыщении Mm), характеризующих
закон диффузии Фика, который предполагает обратимость процесса. Анализ
механического поведения при сдвиге, обеспечиваемом одноосным растяжением ламината с
волокнами, ориентированными под углом 45° к оси растяжения, при постоянных скоростях
перемещения показал, что при влажности 96% концентрация влаги в композите играет
особенно важную роль. Предложена простая модель, позволяющая описать влияние абсорбции
влаги на механическое поведение ламината при сдвиге.
|
| issn |
0556-171X |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/48399 |
| citation_txt |
Modeling of the mechanical behavior of composite at different relative humidities / A. Naceri // Проблемы прочности. — 2009. — № 4. — С. 133-140. — Бібліогр.: 9 назв. — англ. |
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AT naceria modelingofthemechanicalbehaviorofcompositeatdifferentrelativehumidities AT naceria modelirovaniemehaničeskogopovedeniâkompozitaprirazličnyhznačeniâhotnositelʹnoivlažnosti |
| first_indexed |
2025-11-26T00:06:42Z |
| last_indexed |
2025-11-26T00:06:42Z |
| _version_ |
1850591333310267392 |
| fulltext |
UDC 539.4
Modeling of the Mechanical Behavior of Composite at Different Relative
Humidities
A. N aceri
Mohammed Boudiaf University, M’sila, Algeria
УДК 539.4
Моделирование механического поведения композита при различных
значениях относительной влажности
А. Н асери
Университет им. Мохаммеда Будиафа, г. Мсила, Алжир
Для 12-слоистого ламината с матрицей из эпоксидной смолы и стекловолокон исследованы
закономерности абсорбции влаги и механического поведения в условиях сдвига. Эксперимен
тальные исследования абсорбции влаги образцами из ламината при различных значениях
влажности воздуха (0, 60 и 96%) при температуре 6WC позволили определить два параметра
(коэффициент диффузии D и максимальное количество влаги при насыщении M m), характе
ризующих закон диффузии Фика, который предполагает обратимость процесса. Анализ
механического поведения при сдвиге, обеспечиваемом одноосным растяжением ламината с
волокнами, ориентированными под углом 45° к оси растяжения, при постоянных скоростях
перемещения показал, что при влажности 96% концентрация влаги в композите играет
особенно важную роль. Предложена простая модель, позволяющая описать влияние абсорб
ции влаги на механическое поведение ламината при сдвиге.
К л ю ч е в ы е с л о в а : абсорбция влаги, композит с упрочнением стекловолок
нами, стекло, эпоксидная смола, механическое поведение
Introduction . The combination o f moisture and temperature has previously
been found [1, 2] to degrade the m echanical properties o f com posite materials by
enhancing damage growth. Moisture absorption is characterized by the migration
o f m olecules down the concentration gradient, w hich occurs through diffusion. The
properties o f the matrix (resin) can also change significantly during exposure to an
aquaous environment [3, 4]. Furthermore, the water can diffuse between the fibers
and the matrix, weakening or destroying the bond at the fiber/matrix interface. The
amount o f moisture absorption during o f specific period o f time (t) depends on the
diffusion coefficients o f the individual component in the plastic/com posite. For
fiber-reinforced plastic com posites, the diffusion coefficien t depends on the
fo llow ing three factors: volum e or w eight fraction o f fibers, diffusion coefficient
o f the matrix (base resin) and temperature [5, 6]. The driving force for moisture
diffusion is the gradient in the moisture concentration. For hom ogeneous materials,
the moisture diffusion follow s the Fick diffusion law. It was observed [7] that
moisture absorption in fiber-reinforced plastics correlated very w ell w ith the Fick
diffusion law. In this study, w e have estim ated characteristics o f moisture absorption
© A. NACERI, 2009
ISSN 0556-171X. Проблемы прочности, 2009, № 4 133
A. Naceri
behavior by assuming one-dim ensional diffusion. The main assumption involved is
that moisture diffusion can be described by the Fick diffusion law. Additionally,
diffusivity is assumed to depend only on temperature and to be independent o f
moisture concentration or the stress levels inside the material.
I f the initial temperature and moisture content in the specim en are uniform,
and i f the geom etry allows for the assumption o f a one-dim ensional diffusion
through the tickness, then the percent moisture content (by weight). The relative
moisture absorption can be described by the follow ing equation [8]:
G =
m — m i
m m — m i (1)
8
G = 1— z ï zn 2 j= J(2j + 1)'
exp
(2 j + 1)2 n 2 D xt
(2)
where mt is the initial w eight o f the moisture in the material, m m is the w eight o f
moisture in the material when the material is fully saturated, in equilibrium with its
environment, and D x is the mass diffusivity in the composite. This is an effective
diffusivity since all the heterogeneities o f the com posites have been neglected.
Here h is thickness o f specim en and t is the time. The moisture content is
measured by finding the w eight gain o f the material.
The percent moisture content o f the com posite as a function o f time was
measured according to mass gain, using the follow ing formula [9]:
M (%) =
W — W ,wet dry
W
100,
dry
(3)
where the w et and dry w eights are denoted by Wwet and W dry, respectively. By
solving the diffusion equation for w eight o f the moisture, and rearranging in terms
o f percent moisture content, the follow ing relation is obtained
D = n
h
4 M m
( s!o p e )z (4)
s lo p e =
M b — M a 4 M ,
hV n
4 d , (5)
where M m is the equilibrium moisture content o f the specimen. U sing the weight
gain data o f the material w ith respect to time, a graph o f percent moisture content
o f the material vs square root o f time is plotted.
We perform the analysis o f m echanical response o f a laminate constituted o f
12 layers o f glass fiber fabric/epoxy resin saturated at different relative humidities
0, 60, and 96% RH at 60oC.
2h
2
134 ISSN 0556-171X. npoôëeMbi npounocmu, 2009, N9 4
Modeling o f the Mechanical Behavior o f Composite
The first part o f this study consist to determine the two parameters
characteristic o f the Fick diffusion law (the diffusion coefficient D and the
m aximum quantity o f water saturation M m) w hich admits the reversibility o f the
phenom enon and the second part consist in testing the specim ens oriented at 45° in
uniaxial tension until the failure at constant im posed displacement rates.
E xperim ental. M a teria l. The material used was a laminate constituted o f 12
layers o f glass fiber/epoxy resin in one sequence [± 4 5 ]3s. The physical properties
o f w oven fabric com posite (glass fiber fabric/epoxy resin) studied are presented in
Table 1. The test is carried out on specimen with a length 200 mm, thickness 3.2 mm
and width o f 30 mm.
T a b l e 1
Physical Properties of Woven Fabric Composite
Composite Thickness (mm) Density (g/cm3) Fiber volume fraction (in %)
Fabric composite 3.2 1.94 55
E n viro n m en ta l C o n d itio n in g . A fter total drying in a vacuum oven, the
specim ens were exposed to various m oist environments in an environmental
conditioning chamber. A periodic w eighing allowed to ensure that a physical
equilibrium had been reached before testing. The experimental analysis o f the
kinetics o f moisture absorption o f the specim ens conditioned in w et medium at
different relative humidities, 0, 60, and 96% RH at 60°C was carried out by a
measurement o f resumption o f w eight (gravimetric method) according to the
duration o f conditioning with an aim o f determining the two parameters
characteristic o f the Fick diffusion law (the diffusion coefficient D and the
maximum quantity o f water o f saturation M m w hich admits the reversibility o f
the phenomenon. The equilibrium moisture level o f saturation o f material was
reached about six months. The aim is to study the environmental behavior
(moisture absorption) o f glass fiber fabric/resin epoxy. This method is used to
calculate the diffusivity D and the maximum moisture content M m o f the w oven
fabric composite.
M e ch a n ic a l Test. The [±45]3s laminate w as tested in off-axis configuration.
Each specim en (200 X 30 X 3.2 mm) w as equipped with aluminum end-tabs and
three-directional rosettes. A ll the specim ens were carefully conditioned: after prior
total drying, the specim ens were exposed to various m oist environments. A
periodic w eighing allowed to ensure that a physical equilibrium had been reached
before testing. The test itse lf was performed in a temperature- and moisture-
controlled environmental chamber. Both conditioning and testing were carried on
at 60°C, value chosen to enhance matrix influence on the material behavior. The
test was a tensile loading up to failure at constant im posed displacement rates.
R esults and D iscussion . M o is tu re D iffu sion . The influence o f environmental
conditions (absorbed moisture) for the lamina (glass fiber fabric/epoxy resin) is
discussed. Table 2 shows the experimental results o f moisture absorption o f
com posite (fabric glass/epoxy resin).
The w eight gain depends m ainly on three parameters: time (t), equilibrium
moisture content (M m), and diffusion coefficient (D). The values (characteristic
parameters) o f the kinetics o f moisture absorption (M m and D ) obtained by the
ISSN 0556-171X. npoôëeMbi npounocmu, 2009, N 4 135
A. Naceri
experimental moisture conditioning method confirms clearly the principal remarks
observed: the diffusion coefficient D depends not only on the temperature but also
o f the relative humidity and the equilibrium moisture content M m depends
strongly on the relative humidity.
T a b l e 2
Experimental Results of Moisture Absorption of Composite (Fabric Glass/Epoxy Resin)
Humidity RH (%) 60 96
D (cm2/s • 10-8) 1.20 0.21
Mm (%) 0.18 1.10
M e ch a n ic a l R esp o n se . The analysis o f the m echanical and acoustic behavior
in shear o f the specim ens (Table 3), conditioned at different relative humidities 0,
60, and 96% RH at 60oC, tested in uniaxial tension at constant imposed displacement
rates, has allowed to show that the influence o f the moisture concentration for the
specim ens oriented at 450 is very important at 96% RH. This effect is particularly
observed for the specim ens oriented at 450 through the evolutions o f the tangent
shear modulus (G 06), the ultimate shear stress (o 6u), and the ultimate shear strain
(Y 6u) w ith the variation o f the quantity o f water absorbed by the composite.
T a b l e 3
Mechanical Responses at Different Relative Humidities
RH (%)
at 600C
0
(dry)
60
(wet)
96
(wet)
Mm (%) 0 0.17 1.10
G06 (GPa) 6.08 5.55 3.49
06u (MPa) 145 128 100
Y 6u (%) 15.83 11.00 9.80
From the preceding study it follow s that it is reasonable to m odel the lamina
(glass fiber fabric/epoxy resin) behavior by a definite shear modulus-shear strain
relationship. We propose here the follow ing exponential law:
G 6 - G i f Y 6
G = exp [- ^ “G 06 G 1 \ Y 06
(6)
The asymptotic value Gi o f expression (6) is not easy to determine from
experimental plots, due to its nature. However, it can be assumed to fall within the
range 0 .1 -0 .2 GPa and w ill be determined w ith more sensitivity by fitting the
computed laminate response to the experimental curves, as the sequel w ill show.
Nevertheless, choosing any value in the range 0 .1 -0 .2 GPa has no great influence
on the values o f G 06 and y 06 obtained in plotting ln(G 6 - G 1) versus y 6 - We
admit that the agreement is acceptable in the first approximation between the
136 ISSN 0556-171X. npo6n.eMH npounocmu, 2009, N 4
Modeling o f the Mechanical Behavior o f Composite
proposed m odel and the experimental data. Table 4 summarizes o f G 06, G j, and
y 06 derived from tests on [ ± 4 5 ^ for various humidities. From the data in Table 3,
two main features can be pointed out:
(i) the different methods used to determine the shear modulus correspond to
different m echanical states o f the lamina, and the evolution o f the shear modulus
governed by the value o f y 06 depends on that m echanical state;
(ii) humidity both reduces the initial shear m odulus, especially beyond 60%
(the decrease from dry to 96% RH specim ens is 43%, and activates its decrease,
w ith y 06 varying from 31% for [± 4 5 ]3s).
T a b l e 4
Results of the Principal Parameters of the Model Proposed
Humidity RH (%) G1 (GPa) G06 (GPa) V 06 (%)
0 0.080 6.08 0.62
60 0.180 5.55 0.55
96 0.200 3.49 0.43
Thus, environmental conditions prove to have a prominent influence on the
m echanical behavior o f epoxy-based com posites. The comparison between
experimental and computed stress-strain responses o f [± 4 5 ]3s are shown in Fig. 1,
where there is a good fit for all moisture contents.
8
0
0 1 2 3 4
Shear strain (%)
Fig. 1. Comparison between experimental and computed responses for [±45]3i specimen [(■) expe
rimental, (♦ ) modeling].
A good agreement between the plotted curves (m odeled and experimental) o f
the m odel proposed o f behavior in shear justifies a good control o f the nonlinearity
o f the m echanical response in shear o f material tested (Fig. 1).
The straight line o f the curve (Fig. 2) representing the initial tangent shear
modulus versus characteristic strain by taking account o f the maxim um quantity o f
water retained at the saturation (M m) for the conditioned specim ens with various
relative humidities (0, 60, and 96% RH at 60°C), made it possible to propose a
sim ple m odel o f the straight line obtained allow ing for the sensitivity o f behavior
in shear to the moisture and at the stressed state.
ISSN 0556-171X. npoôëeMbi npounocmu, 2009, N 4 137
A. Naceri
Characteristic strain (
Fig. 2. Initial tangent shear modulus G06 vs characteristic strain y 06.
The proposed equation for the straight line is as follows:
G 06 _ aY 06 b > (7)
where a is the slope o f the straight line o f the function in linear scale, and b is
the initial value (intersection o f the straight line w ith the y-axis for y 06 = 0) o f the
modulus o f rigidity o f the function in linear scale.
The graduation o f the straight line (Fig. 2) in linear scale o f M m which
corresponds to a w ell-defined scale, allows us to specify the value o f the initial
tangent initial shear modulus and the characteristic strain for each quantity o f
water absorbed.
Fig. 3. Characteristic strain y og vs maximum quantity of water retained at the saturation M m
The plotted curve (Fig. 3) representing the characteristic strain versus the
m aximum quantity o f water retained at the saturation by fabric com posite makes it
possible to determine the coefficients a' and b' according to the equation
obtained
138 ISSN 0556-171X. Проблемы прочности, 2009, N 4
Modeling o f the Mechanical Behavior o f Composite
Y 06 = b ' ~ a 'M m , (8)
where M m is the m aximum quantity o f water retained at the saturation (%), a' is
the slope o f the straight line o f the function in linear scale, and b' is the initial
value (intersection o f the straight line w ith the j -a x is for M m = 0) o f the
characteristic strain o f the function in linear scale.
This m odel describes the influence o f water absorption on the mechanical
behavior in shear.
C onclusions. Experimental results for laminate constituted o f 12 layers o f
glass fiber/epoxy resin having fiber orientation at [± 4 5 ]зs exposed to humid
environm ent (absorbed moisture) and m echanical tests have been presented.
M oisture absorption takes place through o f a diffusion process, in w hich water
m olecules are transported from areas w ith moisture concentration. The amount o f
moisture absorption during the hygrothermal conditioning depends on the diffusion
coefficients o f the component in the plastic/com posite. For fiber reinforced plastic
com posites, the diffusion coefficient depends on the follow ing three factors:
diffusion coefficient o f the matrix (resin), temperature and volum e or weight
fraction o f fibers. The moisture diffusion process is h ighly dependent on the
temperature and relative humidity. The analysis o f the m echanical behavior in
shear o f the specim ens, conditioned at different relative humidities 0, 60, and 96%
RH at 60°C, tested in uniaxial tension at constant im posed displacement rates has
permitted allowed to show that the influence o f the moisture concentration for the
specim ens oriented at 45° is very important at 96% RH. This effect is particulary
observed for the specim ens oriented at 45° through the evolutions o f the shear
modulus and the shear stress with the variation o f the quantity o f water absorbed
by the composite. The proposed sim ple m odel permits to specify the influence o f
water absorption on the m echanical behavior in shear.
Р е з ю м е
Для дванадцятишаруватого ламіната з матрицею з епоксидної смоли і скло
волокон дослідж ено закономірності абсорбції вологи і механічної поведінки
в умовах зсуву. Експериментальні дослідження абсорбції вологи зразками з
ламіната за різних значень вологості повітря (0, 60 і 96%) при температурі
60°C дозволили визначити два параметри (коефіцієнт диф узії D і макси
мальну кількість вологи при насиченні M m), що характеризують закон
дифузії Фіка, який припускає зворотність процесу. Аналіз механічної пове
дінки при зсуві, що забезпечується одновісним розтягом ламіната з волок
нами, орієнтованими під кутом 45° до осі розтягу, при постійних швидкостях
переміщення показав, що при вологості 96% концентрація вологи в композиті
грає особливо важливу роль. Запропоновано просту модель, яка дозволяє
описати вплив абсорбції вологи на механічну поведінку ламіната при зсуві.
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Received 20. 12. 2007
140 ISSN 0556-171X. npoôneMbi npoHHocmu, 2009, № 4
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