Flexural Fatigue Behavior of Cross-Ply Laminates: An Experimental Approach
Within an experimental approach we describe the mechanical behavior of different resin-epoxy laminates reinforced with cross-ply Kevlar and glass fibers under the conditions of static and cyclic three-point bending. In static tests, we consider the effect of stacking sequence, the thickness of...
Збережено в:
| Дата: | 2003 |
|---|---|
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут проблем міцності ім. Г.С. Писаренко НАН України
2003
|
| Назва видання: | Проблемы прочности |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/46964 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Flexural Fatigue Behavior of Cross-Ply Laminates: An Experimental Approach / A.R. Bezazi, A El Mahi, J.-M. Berthelot, B. Bezzazi // Проблемы прочности. — 2003. — № 2. — С. 66-83. — Бібліогр.: 43 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-46964 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-469642013-08-31T12:53:25Z Flexural Fatigue Behavior of Cross-Ply Laminates: An Experimental Approach Bezazi, A.R. Mahi, A.El Berthelot, J.-M. Bezzazi, B. Научно-технический раздел Within an experimental approach we describe the mechanical behavior of different resin-epoxy laminates reinforced with cross-ply Kevlar and glass fibers under the conditions of static and cyclic three-point bending. In static tests, we consider the effect of stacking sequence, the thickness of 90°-oriented layers, reinforcement type on the mechanical behavior of laminates under loading and on realization of various damage modes leading to rupture. Cyclic loading studies have been performed in two steps. In the first stage, we inquire into the dependence of the behavior and durability of four glass fiber- reinforced laminate-types on the stacking sequence; the second stage is devoted to studying the dependence of cyclic strength and fatigue behavior of laminates on the reinforcement type. Fatigue tests are carried out in load-control regime for glass and hybrid (Kevlar + glass) fiber laminates. Fatigue curves are constructed in coordinates “stress - number of cycles until fracture” from the criteria corresponding to a drop in stiffness by 5 and 10%. Analysis of the results obtained permits evaluation of the effect of the stacking sequence and the reinforcement type on the behavior of cross-ply laminates in cyclic loading. The presence of Kevlar fibers accounts for nonlinear behavior of laminates in static tests and for low cyclic strength in fatigue tests under three-point bending. В рамках экспериментального подхода описано механическое поведение различных ламинатов с матрицей из эпоксидной смолы, перекрестно-армированных кевларовыми волокнами и стекловолокнами, в условиях статического и циклического трехточечного изгиба. При статических испытаниях рассматриваются последовательность укладки слоев и волокон, толщины слоев, ориентированных под углом 90° и влияние типа армирования на механическое поведение ламинатов в процессе нагружения, а также на реализацию различных режимов повреждения, приводящих к разрушению. Исследования при циклическом нагружении состоят из двух этапов. На первом этапе изучается влияние последовательности укладки слоев и волокон на поведение и долговечность четырех типов ламинатов, армированных стекловолокнами, на втором этапе - влияние типа армирования на циклическую прочность и сопротивление ламинатов при циклическом нагружении. Усталостные испытания выполнены в мягком режиме нагружения для ламинатов, армированных стекловолокнами и гибридными волокнами (кевлар+стекло). Кривые усталости были построены в координатах напряжение - число циклов до разрушения на основе критериев снижения жесткости на 5 и 10%. Анализ полученных результатов позволяет оценить влияние последовательности укладки слоев и типа армирования на поведение перекрестно-армированных ламинатов при циклическом нагружении. Наличие кевларовых волокон в ламинатах обеспечивает их нелинейное поведение при статических испытаниях и низкую циклическую прочность при усталостных испытаниях в условиях трехточечного изгиба. У рамках експериментального підходу описано механічну поведінку різних ламінатів із матрицею з епоксидної смоли, що перехресноармовані кевларо- вими волокнами і скловолокнами, в умовах статичного і циклічного три- точкового згину. При статичних випробуваннях розглядаються послідовність укладення шарів і волокон, товщини орієнтованих під кутом 90° шарів і вплив типу армування на механічну поведінку ламінатів у процесі навантаження, а також на реалізацію різних режимів пошкодження, що призводить до руйнування. Дослідження при циклічному навантаженні складається з двох етапів. На першому етапі розглядається вплив послідовності укладення шарів і волокон на поведінку і довговічність чотирьох типів армованих скловолокнами ламінатів, на другому етапі - вплив типу армування на циклічну міцність і опір ламінатів при циклічному навантаженні. Випробування на втому виконано у м ’якому режимі навантаження для армованих скловолокнами і гібридними волокнами (кевлар + скло) ламінатів. На основі критеріїв зниження жорсткості на 5 і 10% в координатах напруження - число циклів до руйнування побудовано криві утоми. Аналіз отриманих результатів дозволяє оцінити вплив послідовності укладення шарів і типу армування на поведінку перехресноармованих ламінатів при циклічному навантаженні. Наявність кевларових волокон у ламінатах запезчує їх нелінійну поведінку при статичних випробуваннях і низьку циклічну міцність при випробуваннях на втому в умовах триточкового згину. 2003 Article Flexural Fatigue Behavior of Cross-Ply Laminates: An Experimental Approach / A.R. Bezazi, A El Mahi, J.-M. Berthelot, B. Bezzazi // Проблемы прочности. — 2003. — № 2. — С. 66-83. — Бібліогр.: 43 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/46964 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Научно-технический раздел Научно-технический раздел |
| spellingShingle |
Научно-технический раздел Научно-технический раздел Bezazi, A.R. Mahi, A.El Berthelot, J.-M. Bezzazi, B. Flexural Fatigue Behavior of Cross-Ply Laminates: An Experimental Approach Проблемы прочности |
| description |
Within an experimental approach we describe
the mechanical behavior of different resin-epoxy
laminates reinforced with cross-ply Kevlar
and glass fibers under the conditions of static
and cyclic three-point bending. In static tests,
we consider the effect of stacking sequence, the
thickness of 90°-oriented layers, reinforcement
type on the mechanical behavior of laminates
under loading and on realization of various damage
modes leading to rupture. Cyclic loading
studies have been performed in two steps. In
the first stage, we inquire into the dependence
of the behavior and durability of four glass fiber-
reinforced laminate-types on the stacking
sequence; the second stage is devoted to studying
the dependence of cyclic strength and fatigue
behavior of laminates on the
reinforcement type. Fatigue tests are carried out
in load-control regime for glass and hybrid
(Kevlar + glass) fiber laminates. Fatigue curves
are constructed in coordinates “stress - number
of cycles until fracture” from the criteria corresponding
to a drop in stiffness by 5 and 10%.
Analysis of the results obtained permits evaluation
of the effect of the stacking sequence and
the reinforcement type on the behavior of
cross-ply laminates in cyclic loading. The presence
of Kevlar fibers accounts for nonlinear behavior
of laminates in static tests and for low
cyclic strength in fatigue tests under three-point
bending. |
| format |
Article |
| author |
Bezazi, A.R. Mahi, A.El Berthelot, J.-M. Bezzazi, B. |
| author_facet |
Bezazi, A.R. Mahi, A.El Berthelot, J.-M. Bezzazi, B. |
| author_sort |
Bezazi, A.R. |
| title |
Flexural Fatigue Behavior of Cross-Ply Laminates: An Experimental Approach |
| title_short |
Flexural Fatigue Behavior of Cross-Ply Laminates: An Experimental Approach |
| title_full |
Flexural Fatigue Behavior of Cross-Ply Laminates: An Experimental Approach |
| title_fullStr |
Flexural Fatigue Behavior of Cross-Ply Laminates: An Experimental Approach |
| title_full_unstemmed |
Flexural Fatigue Behavior of Cross-Ply Laminates: An Experimental Approach |
| title_sort |
flexural fatigue behavior of cross-ply laminates: an experimental approach |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| publishDate |
2003 |
| topic_facet |
Научно-технический раздел |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/46964 |
| citation_txt |
Flexural Fatigue Behavior of Cross-Ply Laminates: An Experimental
Approach / A.R. Bezazi, A El Mahi, J.-M. Berthelot, B. Bezzazi // Проблемы прочности. — 2003. — № 2. — С. 66-83. — Бібліогр.: 43 назв. — англ. |
| series |
Проблемы прочности |
| work_keys_str_mv |
AT bezaziar flexuralfatiguebehaviorofcrossplylaminatesanexperimentalapproach AT mahiael flexuralfatiguebehaviorofcrossplylaminatesanexperimentalapproach AT berthelotjm flexuralfatiguebehaviorofcrossplylaminatesanexperimentalapproach AT bezzazib flexuralfatiguebehaviorofcrossplylaminatesanexperimentalapproach |
| first_indexed |
2025-07-04T06:31:13Z |
| last_indexed |
2025-07-04T06:31:13Z |
| _version_ |
1836696914401165312 |
| fulltext |
UDC 539.4
Flexural Fatigue Behavior of Cross-Ply Laminates: An Experimental
Approach
A. R. B ezazi,a A. E l M ah i,b J.-M . B erthelo t,b and B. Bezzazic
a Laboratoire de Mécanique et de Structure (LMS), Université 08 Mai 1945, Guelma,
Algeria
b Institute of Acoustic and Mechanics Group of Composite and Mechanical Structures,
University of Le Mans, Le Mans, France
c Institute of the Materials of Constructions, University of Boumerdes, Boumerdes,
Algeria
УДК 539.4
Сопротивление усталости перекрестно-армированных ламинатов
при изгибе
А. Р. Б езази а, А. Э ль М ахи6, Дж.-М . Б ертело6, Б . Б еззази в
а Университет г. Гуэльма, Алжир
6 Университет г. Ле Манс, Франция
в Университет г. Бумэрди, Алжир
В рамках экспериментального подхода описано механическое поведение различных лами
натов с матрицей из эпоксидной смолы, перекрестно-армированных кевларовыми волокнами
и стекловолокнами, в условиях статического и циклического трехточечного изгиба. При
статических испытаниях рассматриваются последовательность укладки слоев и волокон,
толщины слоев, ориентированных под углом 90° и влияние типа армирования на механи
ческое поведение ламинатов в процессе нагружения, а также на реализацию различных
режимов повреждения, приводящих к разрушению. Исследования при циклическом нагру
жении состоят из двух этапов. На первом этапе изучается влияние последовательности
укладки слоев и волокон на поведение и долговечность четырех типов ламинатов, армиро
ванных стекловолокнами, на втором этапе - влияние типа армирования на циклическую
прочность и сопротивление ламинатов при циклическом нагружении. Усталостные испы
тания выполнены в мягком режиме нагружения для ламинатов, армированных стекло
волокнами и гибридными волокнами (кевлар+стекло). Кривые усталости были построены в
координатах напряжение - число циклов до разрушения на основе критериев снижения
жесткости на 5 и 10%. Анализ полученных результатов позволяет оценить влияние после
довательности укладки слоев и типа армирования на поведение перекрестно-армированных
ламинатов при циклическом нагружении. Наличие кевларовых волокон в ламинатах обеспе
чивает их нелинейное поведение при статических испытаниях и низкую циклическую проч
ность при усталостных испытаниях в условиях трехточечного изгиба.
К лю чевы е сл о ва : ламинаты, кевларовые волокна, гибридные волокна,
эпоксидная матрица, трехточечный изгиб, усталость, повреждение, кривые
усталости.
© A. R. BEZAZI, A. EL MAHI, J.-M. BERTHELOT, B. BEZZAZI, 2003
66 ISSN 0556-171X. Проблемы прочности, 2003, N 2
Flexural Fatigue Behavior o f Cross-Ply Laminates
In tro d u c tio n . M odem aerospace, aeronautical, naval, motor, and railway
technologies require materials w ith high m echanical properties. However, the
experience acquired in the use o f homogeneous traditional materials showed their
lim ited potential applications. Fortunately, the alternative appeared with
composite materials whose properties are very interesting: lightness, high
directional stiffness, good resistance to fatigue, the absence o f corrosion for
nonmetallic constituents, ease o f fabrication, etc. Such materials, despite the
misunderstanding o f certain aspects o f their behavior, have stimulated a great
interest in several industrial applications. Over the last three decades, several
investigations have been carried out on the fatigue behavior o f composite
materials with organic matrices (epoxy, polyester, etc.) and continuous fibers
(glass, aramide, carbon, etc.) The prediction o f their fatigue life, however, is still
difficult to achieve thus necessitating a better understanding o f many damage
mechanisms that m ay lead to total rupture.
A great num ber o f studies are reported in the literature on the traction and
flexural fatigue o f composite materials. The influence o f fatigue behavior o f the
components o f those materials was studied by several authors [1-3]. M andell [4]
described the process o f rupture in fatigue in the case o f tensile tests o f glass fiber
composites. It was shown that rupture depends only on the properties o f the fibers
independently o f the matrix. In a review paper, Talreja [5] summarized various
interpretations o f damage mechanisms in fatigue o f plastic matrix composites.
Kim and Ebert [6] studied the influence o f cycling frequency, via 4-point
bending, on unidirectional glass fiber composites; they found that an increase in
frequency leads to a rise in the m aterial temperature without significant effects on
fundamental fatigue mechanisms. They also put into evidence the influence o f the
distance between supporting points, l, on the rupture mechanisms. D jebar et al.
[7] studied, via 3-point bending, the influence o f the ratio l/h (where h is the
specimen thickness) on the fatigue o f glass/epoxy composites. Several other
studies o f composite materials and their damage behavior via 3- and 4-point
bending and tension were also reported in [8-26].
Aramide (Kevlar) fibers possess high m echanical properties being 4 to 6
times cheaper than carbon fibers. Nevertheless, Kevlar fiber laminates have
various weaknesses (weak compressive resistance to bending, to buckling, etc.)
These weaknesses are generally attributed to a bad fiber-matrix adherence [27].
To overcome such a problem, hybrid composites (glass-Kevlar, carbon-Kevlar)
are used. Only few investigations [28-33] are reported on Kevlar fibers and
hybrids. In this context, we carry out an investigation in static and cyclic fatigue,
using 3-point bending, on different cross-ply laminates made o f epoxy resin and
glass fibers, Kevlar fibers, and hybrid (glass-Kevlar) fibers.
Static tests are carried out on various lam inated composites allowing the
analysis o f stacking sequence effects, o f (0o- and 90°-oriented) layer thickness
ratios, and o f the reinforcement type on the behavior and on different types o f
damages up to laminate rupture. Fatigue investigations consist o f two parts: (i) the
influence o f the stacking sequence on both the behavior and fatigue life o f four
types o f glass-fiber laminates and (ii) determination o f the reinforcement type
effects on the laminate behavior and endurance. Hence, several glass fiber
laminates and various loading ratios R are considered. Moreover, the endurance
tests are perform ed not only with displacement control but also with load control
ISSN 0556-171X. npoôëeMbi npounocmu, 2003, N 2 67
A. R. Bezazi, A. E l Mahi, J.-M. Berthelot, B. Bezzazi
for Kevlar and glass fiber lam inates. Stress vs num ber o f cycles (S- N) endurance
diagrams (Wu,hler’s curves) are plotted using the criteria o f fatigue life N 5 and
N 10 corresponding, respectively, to 5% and 10% reduction in stiffness with
respect to the initial value.
1. M ateria ls an d Tests.
1.1. M ateria ls. D ifferent cross-ply laminates were prepared by vacuum
moulding from continuous glass fibers, Kevlar fibers, hybrid (glass-Kevlar)
fibers, and epoxy resin. The obtained laminates differ by (i) the reinforcement
type; (ii) the stacking sequence, and (iii) the (0o- and 90°-oriented) layer thickness
ratios. N ine glass fiber laminates (GFL) consisting o f 16 plies each and
designated by GFL 1 to GFL 9 were investigated. A hybrid glass and Kevlar fiber
laminate (HGKFL) consists o f 8 plies o f glass and 4 plies o f Kevlar, and
Kevlar-fiber laminate (KFL) consists o f 8 plies. The choice o f the num ber o f glass
and Kevlar plies is dictated by the necessity o f keeping the specimen thickness
almost constant. The ensemble o f these laminates and their stacking sequences are
grouped in Table 1. The important characteristics o f laminate constituents are
given in Tables 2 and 3 for epoxy resin SR 1500/SD 2505 and continuous fibers,
respectively.
T a b l e 1
Investigated Materials
GFL 1 GFL 2 GFL 3 GFL 4 GFL 5 GFL 6
(9O4/O4X (04/904)s (906/02)s (06/902)s [(02/902)s]s [(0/90)4],
GFL 7 GFL 8 GFL 9 HGKFL KFL
[(02/902)2]s (902/06)s (02/906)s (02v/0k/902v/90k)s (02k/902k),
T a b l e 2
Characteristics of Epoxy Resin SR 1500/SD 2505
Young’s modulus
(GPa)
Tensile strength
(MPa)
Flexural strength
(MPa)
2.9-3.2 74-77 115-120
T a b l e 3
Characteristics of Kevlar and Glass Fibers
Reinforce
ment type
Surface
mass
(g/m2)
Density
(kg/m3)
Young’s
modulus
(GPa)
Shear
modulus
(GPa)
Poisson’s
ratio
Ultimate
strength
(MPa)
Elongation
at rupture
Glass 300 2540 74 30 0.25 2500 4.8
Kevlar 400 1450 130 12 0.40 2900 2.6
The laminates are prepared in vacuum by m oulding with the use o f the
so-called “technique o f the bag” to obtain 300 X 300 mm wafers. The plies are
lam inated and im pregnated at room tem perature, then m oulded under vacuum
(30 kPa) for 10 hours. The wafers were cut out with a diamond tip disk saw
according to standard ASTM D 790-8a.
68 ISSN 0556-171X. npoôëeubi npounocmu, 2003, N 2
Flexural Fatigue Behavior o f Cross-Ply Laminates
1.2. Tests.
1.2.1. Static Tests. The investigation o f specimens (Table 1) is carried out in
3-point bending (Fig. 1) using a universal hydraulic m onotonic testing machine
(INSTRON m odel 8516 o f capacity 100 kN) whose control and data acquisition
are perform ed by a computer. A t least five tests are carried out for each type o f
laminates w ith a test speed o f 2 mm/min.
• -
a b
Fig. 1. Experimental setup: (a) Instron 8516 servo-hydraulic testing machine; (b) specimen under
3-point bending test.
1.2.2. Fatigue Tests. Two types o f tests types were carried out on specimens
identical to those used in the previous static case with a sinusoidal waveform with
a frequency o f 10 Hz.
a) First test type.
These tests, carried out in displacement control, allow the determination o f
the influence o f the stacking sequence on fatigue resistance. To do so, we
considered the laminates GFL 2 (04/904), GFL 5 [(02/902)s]s, GFL 6 [(0/90)4]s and
GFL 7 [(02/902)2]s all o f w hich possess the same num ber o f plies at 0° and at 90°
(the ratio o f the layer thickness equals to 1). These laminates are piled up so that
the thickness o f the 90°-oriented layers is different. The loading level r (r =
= d m x/ d rup ), representing the ratio o f the m axim um displacement to the static
rupture displacement, is taken to have a constant value o f 60% o f that o f static
rupture displacement. Several loading ratios, R, which is the ratio o f the minimum
and m aximum displacements (R = d mî / d max = 0.1, 0.25, 0.4, 0.55, 0.7) are
considered.
b) Second test type.
These tests are carried out by considering two load types: (i) the first m ethod
consists o f carrying out displacement control tests. The average displacement
(d av) is m aintained constant at 40% o f the static rupture displacement (d rup ).
Several loading levels r are considered in order to plot Wu,hler’s curves for GFL 2
and HGKFL laminates, (ii) the second method is carried out in load control with a
constant load ratio R equal to 0. To plot the endurance diagrams, we considered
several loading levels ranging from 95% to 40% o f the static rupture load for
GFL 2 and KFL laminates.
ISSN 0556-171X. npoôëeMbi npounocmu, 2003, № 2 69
A. R. Bezazi, A. E l Mahi, J.-M. Berthelot, B. Bezzazi
2. R esults an d Discussion.
2.1. S ta tic Tests. Figure 2 represents load evolution as a function of
displacement for various tested laminates. The results are analyzed by grouping
each tim e a num ber o f lam inates. This makes it possible to reveal the effects o f
(i) stacking sequence, (ii) the thickness and the interior or exterior disposition of
the 0°- and 90°-oriented layers in the laminate, and (iii) finally, the type o f the
reinforcement on stiffness, load, and displacement at rupture o f the laminate.
Displacement (mm) Displacement (mm)
b
t
ndac
Displacement (mm) Displacement (mm)
Displacement (mm)
e
Fig. 2. Load evolution as a function of displacement in 3-point bending. The influence of stacking
sequences (a), effects of thickness of 90°-oriented layers (b), effects of thickness of 0°-oriented
layers (c), effects of disposition of 0°-oriented plies (d), and reinforcement type effects (e).
70 ISSN 0556-171X. npo6n.eubi npounocmu, 2003, N 2
Flexural Fatigue Behavior o f Cross-Ply Laminates
2.1.1. Influence o f Stacking Sequences. The num ber o f plies with the layers
oriented at 0° and at 90° is the same (the ratio o f the layer thickness equals to 1).
The plies are piled up so that the thickness o f the layers oriented at 90° is different
between GFL 2 (04/904)s, GFL 7 [(02/902)2]*, GFL 5 [(02/902)s]s and GFL 6
[(0/90)4]s. It is clear from Fig. 2a that the GFL 2 laminate is more rigid than the
three others, while its load and displacement at rupture are the lowest. This can be
attributed to the cracks initiated on GFL 2, thus occupying a very large surface
proportional to the thickness o f the 90°-oriented layer (8 adjacent plies). Similar
behavior was obtained for other materials GFL 5, GFL 6, and GFL 7.
2.1.2. Effects o f 9 0 °-Oriented Layer Thickness. To demonstrate the effect of
the thickness o f layers oriented at 90° and externally disposed in the laminate, we
considered GFL 8 (902/06)s, GFL 1 (904/04)s, and GFL 3 (906/02)s. Figure 2b
shows that laminate GFL 8, with the smallest layer thickness oriented at 90° (2
plies), is the m ost rigid one, whose rupture load is the highest; followed by GFL 1
(4 plies) and then by GFL 3 (6 plies). In terms o f displacement, the least rigid
laminate GFL 3 has the largest displacement at rupture followed by GFL 1 and
then GFL 8.
2.1.3. Effects o f0 °-Oriented Layer Thickness. The laminates studied are GFL 9
(02/906)s, GFL 2 (04/904)s, and GFL 4 (06/902)s. They all possess the same num ber
o f plies, w ith different thickness o f layers oriented at 0° and externally disposed in
the lam inate. A n increase in the thickness o f 0°-oriented layers leads to an
increase in both stiffness and load at rupture in bending and to a reduction in the
displacement at rupture o f the laminate as illustrated in Fig. 2c, which shows that
the m aterial o f the largest 0°-oriented layer thickness (6 plies), GFL 4, is the most
rigid with the weakest displacement at rupture, followed by GFL 2 (4 plies) and
then GFL 9 (2 plies).
2.1.4. Influence o f the 0 °-Oriented Layer Disposition. The laminates are
gathered by couples: GFL 9 (02/906)s and GFL 3 (906/02)s, GFL 1 (904/04)s and
GFL 2 (04/904)s, and GFL 4 (06/902)s and GFL 8 (902/06)s. Each couple has the
same num ber o f plies oriented at 0° and 90°, the difference lies in the layer
disposition in the laminate (externally or internally oriented at 0°). Figure 2d
shows that, for the above three couples, the laminates w ith the layers externally
oriented at 0° are the m ost rigid but have the weakest displacements at rupture. As
an example, we consider a couple o f laminates GFL 9 and GFL 3, for which we
note that (i) the laminate GFL 9 having the layers externally oriented at 0° is much
more rigid than GFL 3, (ii) the load at rupture o f the laminate GFL 9 is four times
larger than that o f GFL 3 while its displacement at rupture is three times less
important.
2.1.5. Influence o f the Reinforcement Type. In order to study the effect o f the
type o f reinforcement on the stiffness and load and displacement at rupture, we
considered the following laminates: (i) glass fiber GFL 2 (04G/904G)s; (ii) Kevlar
fiber KFL (02K/902K)s, and (iii) hybrid glass and Kevlar fiber HGKFL
(02G/0K/902G/90K)s. The results obtained for these three laminates are shown in
Fig. 2e. It is clear that the KFL laminate is the m ost rigid followed by GFL 2 and
then HGKFL. It should also be noted that the presence o f Kevlar fibers leads to a
nonlinear behavior o f the laminate, w hich is m uch more pronounced in the Kevlar
laminate KFL.
ISSN 0556-171X. npoôëeMbi npounocmu, 2003, N 2 71
A. R. Bezazi, A. E l Mahi, J.-M. Berthelot, B. Bezzazi
2.2. O bservation of R u p tu re Topographies. Optical and scanning electronic
microscopes (SEM) have been used to observe the fracture topographies o f the
broken specimens after static tests; the obtained m icrographs are illustrated in
Fig. 3. This observation shows the presence o f three types o f damage, which lead to
the total rupture o f the laminate: (i) delamination between the layers oriented at 90°
and those oriented at 0°, (ii) transverse cracking in the layers oriented at 90° and
(iii) finally, rupture o f fibers. Analysis o f ruptures o f various glass laminates, GFL 1
to GFL 9, in static tests allows us to classify them into two categories according to
the disposition o f the layers externally or internally oriented at 0° in the laminate:
___ ._____ .... _ _ „ - _ i r .
-4_
v ' ' ^ .
h
Fig. 3. Micrographs of different types of damage: optical (a, c, e-h) and SEM (b, d). (a, b)
delamination and transverse crack; (c) delamination and rupture of compressed face; (d) transverse
crack; (e) transverse crack in the tensile face; f) delamination, transverse crack, and rupture of
compressed face; (g) laminate KFL; (h) hybrid laminate HGKFL.
72 ISSN 0556-171X. npoôëeuu npouHocmu, 2003, № 2
Flexural Fatigue Behavior o f Cross-Ply Laminates
- layers externally oriented at 0 ° in the laminate: the specimens are little
damaged by transverse cracking, whereas rupture is mainly due to delamination
between the layers oriented at 0° and those at 90°. Beyond that, two cases o f final
rupture o f the laminates are observed: (i) the externally oriented layers at 0° (Fig. 3a
and 3b) rem ain without considerable damage in the laminates GFL 9 (02/906)s,
GFL 2 (04/904)s, and GFL 4 (06/902)s; these laminates o f type (0n/90m)s consist o f
three layers, in which the one oriented at 90° has the largest thickness that favors
delamination; and (ii) the externally oriented layers at 0° (Fig. 3f) o f the
compressed face break in the case o f laminates GFL 5 [(02/902)s]s, GFL 6
[(0/90)4]s, and GFL 7 [(02/902)2]s. This can be explained by the fact that the
thickness o f the layers oriented at 90° is small since they are separated by layers
oriented at 0°. In these two cases, brittle fracture o f the laminates is observed as
confirmed by the evolution o f the load as a function o f the displacement given in
Fig. 2.
- layers externally oriented at 90 ° in the laminate: their damage (Fig. 3 c and
3d) is mainly due to transverse cracking leading to rupture o f fibers o f the
compressed face in the laminates GFL 8 (902/06)s, GFL 1 (904/04)s, and GFL 3
(906/02)s. These laminates o f type (90n/0m)s do not exhibit brittle fracture.
The presence o f K evlar fibers in the laminate changes the order o f the
occurrence o f damage mechanisms as well as the rupture modes. For the Kevlar
fiber laminate KFL (02K/902K)s shown in Fig. 3g, one initially observes
delamination between the lower layer (strained) oriented at 0° and the layer
oriented at 90°, followed by transverse cracking that propagates in the layer
oriented at 90° to reach the higher layer oriented at 0°. This crack leads to
delamination o f the above layer causing its rupture. For the hybrid glass-Kevlar
fiber laminate HGKFL (02G/0K/902G/90K)s shown in Fig. 3h, brittle fracture was
noted. This rupture is the result o f delamination and transverse cracking in the
Kevlar fiber layer oriented at 90°, while a glass fiber layer oriented at 90° seems
not to be affected. This behavior can be explained by a poor Kevlar fiber-matrix
epoxy adherence [27].
2.3. F atigue Tests.
2.3.1. Influence o f Stacking Sequences on Fatigue Behavior, During these
tests, we recorded the evolution o f the m aximum load F as a function o f the
num ber o f cycles N. The obtained results for various loading ratios R are shown
in Figs. 4 and 5. The m axim um load F is norm alized by that obtained in the first
cycle F0 . The description and analysis o f such results (Fig. 4) show that the loss
o f load, F / F 0, extending until the rupture o f the specimen, can be divided into
three stages:
Stage I: corresponds to a sharp decrease, from the first cycles, in the ratio
F / F 0 due to the cracking multiplication o f the resin.
Stage II: shows a very slow decrease in the form o f a shelf corresponding to
almost the total fatigue life o f the specimen due to a stable crack propagation.
Stage III: a very short stage wherein we observe again a sudden growth o f
damage until the total rupture o f the specimen.
This behavior is in good agreement w ith the works o f Talreja [11] and Muc
[34] who distinguished three phases in the development o f fatigue damage: in the
first phase the matrix cracking, in the second the delamination or interfacial
ISSN 0556-171X. npodrnMbi npounocmu, 2003, N2 2 73
A. R. Bezazi, A. E l Mahi, J.-M. Berthelot, B. Bezzazi
debonding, and finally, the fiber breakage. It should be noted that the first stage is
associated with less than 2 0 % o f the fatigue life but with about 80% o f the
damage ratio (F /F 0 ).
Figure 5 represents the development o f the damage ratio F /F 0 as a function
o f the num ber o f cycles for different stacking sequences o f lam inates GFL 5,
GFL 6 , GFL 7, and GFL 2 for various loading ratios R. Analysis o f the results
shows that under cyclic loading, the fatigue life depends on the loading ratio R
and the stacking sequence.
Number of cycles N
Fig. 4. A typical curve of rigidity evolution as a function of the number of cycles, N .
Number of cycles N Number of cycles N
c d
Fig. 5. Evolution of the rigidity loss, F/F0, as a function of the number of cycles, N : (a) laminate
GFL 2; (b) laminate GFL 5; (c) laminate GFL 6; (d) laminate GFL 7.
74 ISSN 0556-171X. Проблемы прочности, 2003, N 2
Flexural Fatigue Behavior o f Cross-Ply Laminates
The average displacement determines the damage mechanisms activated at
the beginning o f cycling, while the amplitude determines the propagation velocity
o f the multiplication o f these mechanisms. For the same m aximum displacement,
one notes for all laminates that: (i) for small R, corresponding to a large
amplitude (weak average displacement), the initial damage is small with a
considerably high growth rate leading to a very short fatigue life; the total rupture
is quickly reached after only a few thousands o f cycles; (ii) for large R,
corresponding to a small amplitude (high average displacement), a lot o f damage
mechanisms are activated w ith a slow propagation, the fatigue life is very long
and rupture is only partial even when the num ber o f cycles is larger than 106.
To put into evidence the effects o f stacking sequences on the fatigue
resistance o f the cross-ply laminates, we further compared (Fig. 6 ) the
development o f the load as a function o f the num ber o f cycles for three loading
ratios (R = 0.1, 0.4, and 0.7). The results obtained show that the laminates having
plies oriented at 90° bounded by those oriented at 0° have good resistance to
fatigue in three-point bending.
In order to determine the performances o f the materials in fatigue, various
damage criteria ( N s, N 3 , N 5 , N i0, and N r ) are considered in the literature
from the curves giving the evolution o f the load as a function o f the num ber o f
cycles. The m ost severe criterion is that characterizing the material by the value
N s , which corresponds to the num ber o f cycles at the end o f the linear domain.
The criteria N 3, N 5, and N 10 correspond to falls o f 3%, 5%, and 10% o f the
load (or displacement) in relation to the initial load (or displacement),
respectively. The criterion N R corresponds to the num ber o f cycles at the final
rupture o f the specimen. Finally, the performances in fatigue can be characterized
by the num ber o f cycles necessary to have rupture o f the m aterial when this
num ber o f cycles is reached. In our study, we have chosen the criterion N 10,
which is the m ost frequently used one in the literature [7, 9, 15, 20]. Moreover,
beyond 10%, a lot o f mechanisms are involved and their description becomes
more difficult, for example, for higher damage rates, the effect o f local heating in
the specimen cannot be neglected [9].
In Table 4, we summarize the obtained values o f the fatigue life, using the
criterion N 10, as functions o f the ratio R for various laminates (GFL 5, GFL 6 ,
GFL 7, and GFL 2) studied.
T a b l e 4
Fatigue Life, N 10, as a Function of the Load Ratio, R, for Various Stacking Sequences
Laminates Ratio R
0.1 0.25 0.4 0.55 0.7
GFL 2 (04/904)s 1.5 • 103 0.65 • 104 3.60 • 104 1.02 • 105 1.12 • 106
GFL 5 [(02/902)s]s 2.5-103 0.45 • 104 2.15 •104 4.00 • 105 1.40-106
GFL 7 [(02/902)2]s 1.5 • 103 1.80 • 104 7.30 • 104 1.67 • 105 1.27 •106
GFL 6 [(0/90)4]s 5.0 •103 1.30 • 104 4.80 • 104 0.82 • 105 0.95 • 106
ISSN 0556-171X. npoôëeMbi npounocmu, 2003, № 2 75
A. R. Bezazi, A. E l Mahi, J.-M. Berthelot, B. Bezzazi
Number of cycles N
a
Number of cycles N
b
0.6
0.5
1
'■ N >
!< 0.75
................ G FI. 5
------------ G FI. 6
------------ G FL 7
G FL 8
10 100 1000 100(H) |00(NN) 1000000 IF. 107
Number of cycles N
c
Fig. 6. Evolution of the rigidity loss, F/F0, as a function of the number of cycles, N , at different
loading ratios, R: (a) R = 0.1; (b) R = 0.4; (c) R = 0.7.
2.2.2. Endurance Tests. The evolution o f stiffness is one o f the m ost widely
used methods to follow the development o f damage by fatigue o f composites. In
the case o f fatigue in bending w ith im posed displacement, a clear-cut rupture o f a
specimen is not generally observed. Therefore, the definition o f the fatigue life
rests on conventional criteria defined for a given rate o f stiffness loss (N 10 or
76 ISSN 0556-171X. npoôëeubi npounocmu, 2003, N 2
Flexural Fatigue Behavior o f Cross-Ply Laminates
N 5). The fatigue life can be shown in a diagram o f endurance giving the
maximum level o f the displacement or load as a function o f the fatigue life (N 10
or N 5).
In this part o f our investigation, endurance tests are carried out in load
control in the case o f laminates GFL 2 (04/904)5 and KFL (02K/902K)s and in
displacement control in the case o f laminates GFL 2 and HGKFL
(02G/0k/902G/90k)s w ith a 10 Hz frequency sinusoidal wave. The endurance curves
are plotted for the load or displacement m aximum as a function o f the fatigue life
N 10 and N 5 .
Figure 7 represents W ohler’s curve for laminates GFL 2 and HGKFL. These
results show the evolution o f the m aximum load norm alized to the static rupture
load as a function o f the fatigue life N 10. In Fig. 8 , we present Wu,hler’s curve
for laminates GFL 2 and KFL, representing the evolution o f the m aximum
displacement norm alized to the static rupture displacement as a function o f the
fatigue life N 10 .
1 10 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1E +07
Number of cycles N
Fig. 7. S — N curves for laminates GFL 2 and HGKFL in displacement control using N i0 criterion.
Number of cycles N
Fig. 8. S — N curves of laminates GFL 2 and KFL in load control using N i0 criterion.
Analysis o f the obtained results shows the influence o f reinforcement type
on the fatigue life o f laminates. Indeed, the Wohler curve o f hybrid glass-K evlar
fiber (HGKFL) laminates lies below that o f the glass-fiber laminate GFL 2 in
displacement control (Fig. 7), whereas S - N curves for Kevlar-fiber laminates
ISSN 0556-171X. npoôëeMbi npounocmu, 2003, N 2 77
A. R. Bezazi, A. E l Mahi, J.-M. Berthelot, B. Bezzazi
(KFL) ones lie above those o f the GFL 2 laminates (Fig. 8) in load control. The
presence o f Kevlar fibers in the laminate makes it more sensitive to fatigue in the
case o f 3-point bending and this can be explained by the poor fiber-matrix
adherence [27].
Figure 9 represents endurance diagrams for the criteria o f fatigue life N 10
and N 5 . The variation o f the loading level r as a function o f the num ber of
cycles N can be described by a simple equation:
r = 1 - K log N , (1)
w here K is the slope o f the straight line o f the fitted experim ental data. This
constant corresponds to the rate o f decrease in the m axim um load or the
adm issible m axim um displacem ent expressed in % decrease per cycle. This
form o f representation allows us to show the influence o f the reinforcem ent type
and the criterion o f fatigue life on the rate o f independent deterioration o f the
control type. Indeed, the value o f K is low er in the case o f K FL and H G K FL
lam inates than that o f GFL 2 laminate. The rate o f deterioration increases w ith a
decrease in the fatigue life criterion. W e also notice that the evolution o f the
load or displacem ent loss w ith both m ethods o f control and in both cases o f
fatigue life crosses the axis at about r = 1 that corresponds to the loading level
equal to that o f the static rupture.
r= 1046 9 -0 .0621 Inl}(i )
r= 10597 - 0.06 57 lniN.)
♦ N10 GFL2
4 N c, G FL 2
100 1000 10000 100000 E-t-06 £ 1-07
Number of cycles N
r=lX6S -0.0562 Infl JD) # N ]Q KFL
r= LD23S -O.OE33 ln(W:) *H 5 KFL
]00 3000 30000 100000 3E+06 3E+07
Number of cycles N
Fig. 9. S — N curves for both modes of control using N 5 and Ni0 criteria: (a) displacement control
for GFL 2 laminate; (b) displacement control for hybrid HGKFL laminate; (c) load control for
GFL 2 laminate; (d) load control for hybrid HGKFL laminate.
78 ISSN 0556-171X. npo6neMbi npouHocmu, 2003, № 2
Flexural Fatigue Behavior o f Cross-Ply Laminates
It should be noted that endurance tests are characterized by dispersion o f
fatigue life values depending on the reinforcement type in the laminate. Indeed,
the tests on the Kevlar fiber laminate are characterized by an appreciable
dispersion o f fatigue life values as compared to other laminates. Generally, this
dispersion m ay be attributed to the heterogeneous nature o f the laminates.
Moreover, specimens do not always have the same characteristics: volume
fraction, defect distribution, strength at static rupture, etc. Fatigue rupture
depends on random processes whose combination results in dispersion o f the
fatigue life values between the specimens subjected to the same loading level r .
Furthermore, it is worth noting that both dispersion and rupture criteria have the
same trend.
Conclusions. This investigation deals with an experimental approach
involving the m echanical behavior o f different Kevlar- and glass-fiber cross-ply
laminates w ith epoxy resin in three-point bending under static and fatigue
loading. Static study showed the influence o f the stacking sequence, the thickness
effect o f the layers oriented at 0° and 90°, their internal or external disposition in
the laminate, and the reinforcement type on the values o f the load and
displacement at rupture o f the laminates.
Analysis o f the observed fracture topographies o f specimens broken in static
investigations via optical and SEM techniques made it possible to classify rupture
as a function o f the internal or external disposition o f the layers oriented at 0° in
the laminate:
For glass-fiber laminates o f type (0n/90m)s, brittle fracture has been observed.
The specimens are little damaged by transverse cracking w ith the rupture o f the
laminate caused by delamination w ith and without rupture o f the compressed
face. However, for KFL and HKGFL, non-brittle rupture was obtained mainly
because o f the presence o f K evlar fibers.
For the laminates o f type (90n/0m), damage is m ainly due to transverse
cracking in the 90° externally oriented layers leading to rupture o f the fibers o f the
compressed face. This type o f damage, inducing non-brittle rupture, is observed
in the laminates.
The influence o f the stacking sequence on the fatigue behavior has been
studied by considering four types o f laminates for several loading ratios R in
displacement control. The loading level r has been considered constant and equal
to 60% o f the displacement at rupture. Analysis o f these results shows that (i) the
behavior and the fatigue life depends on the ratio R and (ii) the laminates whose
plies are oriented at 90° and separated by those at 0° resist better to fatigue.
Indeed, the fatigue life N increases with R .
Wu,hler’s curves are obtained by using the fatigue life criteria N 5 and N 10
in load control for lam inates GFL 2 and KFL, and in displacement control for
laminates GFL 2 and HKGFL. It is noticed that in the case o f load control,
damage o f the laminates is m ore pronounced than that in displacement control.
Glass fiber laminates GFL 2 resist better to fatigue than HKGFL laminates in
displacement control, whereas they seem to be less resistant to fatigue than the
KFL laminates in load control. The presence o f the Kevlar fiber in the laminate
makes it m ore sensitive to fatigue in three-point bending that can be attributed to
the poor fiber-m atrix adherence [27].
ISSN 0556-171X. npoôëeMbi npounocmu, 2003, N 2 79
A. R. Bezazi, A. E l Mahi, J.-M. Berthelot, B. Bezzazi
Rupture in fatigue depends on a series o f random processes leading to
dispersed results due to the heterogeneous nature o f the laminates and
manufacturing. Despite dispersions, which is more pronounced in load control,
particularly for the K evlar fiber laminate KFL, the analysis o f these results shows
clearly the influence o f the reinforcement type on the fatigue life o f the laminates
studied.
The evolution o f the loading level r as a function o f the logarithm o f the
fatigue life N is described by the same relationship r = 1 — K log N , thus
showing the influence o f the reinforcement type and the fatigue life criterion on
the rate o f degradation.
Acknowledgements. I would like to thank Professors A. Dogmane, B. Bencer,
and A. Haddad.
Р е з ю м е
У рамках експериментального підходу описано механічну поведінку різних
ламінатів із матрицею з епоксидної смоли, що перехресноармовані кевларо-
вими волокнами і скловолокнами, в умовах статичного і циклічного три-
точкового згину. При статичних випробуваннях розглядаються послідов
ність укладення шарів і волокон, товщини орієнтованих під кутом 90° шарів
і вплив типу армування на механічну поведінку ламінатів у процесі наванта
ження, а також на реалізацію різних режимів пошкодження, що призводить
до руйнування. Дослідження при циклічному навантаженні складається з
двох етапів. На першому етапі розглядається вплив послідовності укладення
шарів і волокон на поведінку і довговічність чотирьох типів армованих
скловолокнами ламінатів, на другому етапі - вплив типу армування на
циклічну міцність і опір ламінатів при циклічному навантаженні. Випробу
вання на втому виконано у м ’якому режимі навантаження для армованих
скловолокнами і гібридними волокнами (кевлар + скло) ламінатів. На основі
критеріїв зниження жорсткості на 5 і 10% в координатах напруження -
число циклів до руйнування побудовано криві утоми. Аналіз отриманих
результатів дозволяє оцінити вплив послідовності укладення шарів і типу
армування на поведінку перехресноармованих ламінатів при циклічному
навантаженні. Наявність кевларових волокон у ламінатах запезчує їх нелі
нійну поведінку при статичних випробуваннях і низьку циклічну міцність при
випробуваннях на втому в умовах триточкового згину.
1. C. K. H. Dharan, “Fatigue failure in graphite fibers and glass fibers-polymer
com posites,” J. Mater. Sci., 10, 1665-1670 (1975).
2. J. Awerbuch and H. T. Hahn, “Fatigue o f filamentary composite m aterials,”
in: A STM STP 636 (1977), pp. 248-266.
3. H. T. Hahn and L. Lorenzo, “Fatigue failure mechanisms in composite
laminates. Advances in fracture research,” in: Proc. 6th Inter. Conf. on
Fracture (New Delhi, India, 4 -10 Dec.) (1984), pp. 549-568.
4. J. F. Mandell, “Fatigue behavior o f fiber resin composites, developments in
reinforced plastics,” in: G. Pritchard (Ed.), Applied Science Publishers,
London, N ew York (1982), pp. 67-107.
80 ISSN 0556-171X. Проблеми прочности, 2003, № 2
Flexural Fatigue Behavior o f Cross-Ply Laminates
5. R. Talreja, “Fatigue o f composite materials: damage m echanisms and
fatigue-life diagram s,” Proc. Roy. Soc. London, A(378), 461-415 (1981).
6. H. C. Kim and L. J. Ebert, “Fatigue life limiting parameters in fiber glass
com posites,” J. Mater. Sci., 14, 2616-2624 (1919).
1. A. Djebbar, F. Sidoroff, et L. Vincent, “Etude du couplage traction-
cisaillement dans le cas de sollicitations en flexion de matériaux composites
verre/époxyde,” Journée Nationale des Composites (JNC), 1 Nov., 81-90
(1990).
8. M. D ody, Modélisation des Caractéristiques Mécaniques et Études
Expérimentales de l'Endommagement d'un Composite, Ph. D. Thesis,
Université de Franche-Comté, Besançon, France (1985).
9. L. Fiore, Contribution à l'Étude du Comportement en Fatigue de Matériaux
Composites à Renfort Verre Unidirectionnel, Ph. D. Thesis, Ecole Centrale
de Lyon, France (1988).
10. J.-M. Berthelot, P. Leblond, A. El Mahi, and J.-F. Le Corre, “Transverse
cracking o f cross-ply laminates. Part 1. Analysis,” J. Compos., 27A, 989
1001 (1996).
11. R. Talreja, Fatigue o f Composite Materials, Lancaster Technol. Publishing,
(1990).
12. J.-M. Berthelot, “Analysis o f the transverse cracking o f cross-ply laminates:
a generalized approach,” J. Compos. Mater., 31, 1180-1805 (1991).
13. A. D ’amore, G. Caprino, R. Stupak, J. Zhou, and L. Nicolais, “Effect of
stress ratio on the flexural fatigue behavior of continuous stand mat
reinforced plastics,” J. Sci. Eng. Compos. Mater., 5 (1), 1-8 (1996).
14. J. Li, B. Zhou, and T. He, “Residual properties of an infection-molded poly
(phenylene enther ketone)/carbon composite during flexural fatigue,” J.
Compos. Sci. Technol., 57, 669-616 (1991).
15. M. Salvia, L. Fiore, P. Fournier, and L. Vincent, “Flexural fatigue behavior
o f UDGFRP - experimental approach,” Int. J. Fatigue, 19 (3), 253-262
(1991).
16. A. Salaün, Etude de l'Endommagement en Flexion 3 Points et en Flambage
de Composites Carbone/Époxy 1D et 2D à Plis Croisés, Ph. D. Thesis,
Université de Caen, France (1998).
11. A. Salaün and M. G om ia, “ S tatic fa tigue and cyclic b eh av io r o f
unidirectional carbon/epoxy,” J. Compos. Ann. Chim. Sci. Mater., 23, 19-22
(1998).
18. G. C aprino and G. G iorleo, “Fatigue lifetim e o f glass fiber/epoxy
com posites,” J. Compos., 30A, 299-304 (1999).
19. L. V. Griffin, J. C. Gibeling, R. B. Martin, V. A. Gibson, and S. M. Stover,
“The effects of testing methods on the flexural fatigue life of human cortical
bone,” J. Biomech, 30, 105-109 (1999).
20. S. Tamboura, H. Sidhom, et H. P. Lieurade, “M atériau composite à fibers de
carbone et m atrice époxyde: étude du m écanisme d ’endommagement,”
Matériau et Techniques, Nos. 3-4, 15-20 (1996).
ISSN 0556-171X. npoôëeMbi npounocmu, 2003, N 2 81
A. R. Bezazi, A. E l Mahi, J.-M. Berthelot, B. Bezzazi
21. M. G. Stout, D. A. Koss, C. Liu, and J. Idasetima, “Damage development in
carbon/epoxy laminates under quasi-static and dynamic loading,” Compos.
Sci. Technol., 59, 2339-2350 (1999).
22. N. J. Lee, K. E. Fu, and J. N. Yang, “Prediction o f fatigue damage and life
for composite laminates under service loading spectra,” Compos. Sci.
Technol., 56, 635-648 (1996).
23. J. A. M. Ferreira, J. D. M. Costa, P. N. B. Reis, and M. O. W. Richardson,
“Analysis o f fatigue and damage in glass-fiber reinforced polypropylene
composite m aterials,” Compos. Sci. Technol., 59, 1461-1467 (1999).
24. A. El Mahi, A. R. Bezazi, and J.-M. Berthelot, “The fatigue behavior and
damage development in cross-ply laminates in flexural tests,” in: Proc. Tenth
European Conf. on Composite Materials (ECCM-10), Bruge, Belgium (3-5
June, 2002).
25. A. R. Bezazi, A. El Mahi, J. -M. Berthelot, and B. Bezzazi, “Influence of
reinforcement in cross-ply laminates in flexural testing,” in: Proc. Conf. New
Trends in Fatigue and Fracture, Metz, France (8 -9 April, 2002).
26. A. R. Bezazi, A. El Mahi, J.-M. Berthelot, et B. Bezzazi, “Analyse de
l ’endommagement des stratifiés en flexion 3-points. Influence de la séquence
d ’em pilement,” in: Proc. XVème Congrès Francais de M écanique, Nancy,
France (3-7 Septembre, 2001).
27. J.-M. Berthelot, Composite Materials. Mechanical Behavior and Structural
Analysis, Springer, N ew Y ork (1999).
28. R. H. Ericksen, “Room tem perature creep o f Kevlar 49/epoxy composites,”
Compos., 6 (1976).
29. M. R. Piggott and B. Harris, “Compression strength of carbon, glass, and
Kevlar 49 fiber reinforced polyester resins,” J. Mater. Sci., 15, 2523-2538
(1980).
30. B. Harris, J. Adam, et H. Reiter, “Composites hybrides carbone-Kevlar et
carbone-verre, comportement en fatigue,” Journée Nationale des Composites
(JNC), 6, 649-660 (1988).
31. S. M. Bleay and L. Humbertone, “Mechanical and electrical assessment of
hybrid composites containing hollow glass reinforcement,” Compos. Sci.
Technol, 59, 1321-1329 (1999).
32. A.-K. Akbar, L. Glyn, Y. Lin, and M. Y iu-W ing, “On the fracture
mechanical behavior of fiber reinforced metal laminates (FRMLs),” in:
Comp. Meth. Appl. Mech. Eng., 185, 173-190 (2000).
33. Y. Shan and K. Liao, “Environmental fatigue of unidirectional glass-carbon
fiber reinforced hybrid composite,” Compos., Part B, 32, 355-363 (2001).
34. A. Muc, “Design o f composite structures under cyclic loads,” Comp. Struct.,
76, 211-218 (2000).
35. A. Laksimi, A. Benyahia, M. L. Benzeggagh, and X. L. Gong, “Initiation
and bifurcation mechanisms of cracks in multi-directional laminates,”
Compos. Sci. Technol., 60, 597-604 (2000).
82 ISSN 0556-171X. npoôëeMbi npounocmu, 2003, № 2
Flexural Fatigue Behavior o f Cross-Ply Laminates
36. R. O lsson, J. C. Thesken, F. B randt, N. Jonsson, and S. N ilsson,
“Investigations o f delamination criticality and the transferability o f growth
criteria” Compos. Struct., 36, 221-247 (1996).
37. K.-L. Choy, P. S. Rogers, D. Churchman, and M. T. Pirzada, “The
m echanical behavior o f glass-ceramic matrix composites,” Mater. Sci. Eng.,
A278, 187-194 (2000).
38. H. Plumtree and G. X. Cheng, “Fatigue param eter for off-axis unidirectional
fiber reinforced com posites,” Int. J. Fatigue, 21, 844-856 (1999).
39. L. Andre, L. Kenneth, et al. “Prediction o f stress-rupture life o f glass/epoxy
lam inates,” Int. J. Fatigue, 22, 467-480 (2000).
40. J.-M. Berthelot, and J.-F. Le Corre, “M odeling the transverse cracking in
cross-ply laminates: application to fatigue,” J. Compos., 30B, 569-577
(1999).
41. J.-M. Berthelot and J.-F. Le Corre, “Statistical analysis o f the progression of
transverse cracking and delamination in cross-ply laminates,” Compos. Sci.
Technol, 60, 2659-2669 (2000).
42. J.-M. Berthelot and J.-F. Le Corre, “A m odel for transverse cracking and
delamination in cross-ply lam inates,” Compos. Sci. Technol., 60, 1055-1066
(2000).
43. J.-M. Berthelot, A. El Mahi, and J. F. Le Corre, “Development o f transverse
cracking in cross-ply laminates during fatigue tests,” Compos. Sci. Technol.
(2001), to appear.
Received 21. 10. 2002
ISSN 0556-171X. Проблемы прочности, 2003, № 2 83
|