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Original Article
Experimental study on flexural fatiguebehavior of glass fibers/epoxy hybridcomposites with statistical analysis
AI Selmy1, MA Abd El-baky1 and NA Azab2
Abstract
Flexural fatigue behaviors were investigated experimentally for unidirectional glass fiber (U)/random glass fiber (R)/epoxyhybrid composite laminates. Three different hybrid composites, i.e. [0.5R/U/U]S, [U/0.5R/U]S and [U/U/0.5R]S werefabricated using hand lay-up technique with 37% total fiber volume fraction (V fT), unidirectional glass fiber relativevolume fraction (V fU/V fT) ¼ 0.8 and of 5.5 0.2 mm thickness. Flexural fatigue tests were performed at zero mean
stress. A 20% reduction of the flexural stiffness was taken as a failure criterion. The effects of layer stacking sequenceson both initial stress–no. of cycles to failure relationships and the relative surface temperature increase of the mentionedcomposites were investigated. The specimen failure modes have been recorded and discussed. The S–N curves andfatigue safe workability areas for the fabricated hybrid composites have been constructed as design curves. Two-para-meter Weibull distribution function was used to obtain the scatter in the experimental results and to construct thereliability graphs for the fabricated hybrid composites.
Keywords
Hybrid composite laminates, fatigue strength, statistical analysis, hand lay-up
Introduction
In recent years, composite materials are used exten-
sively in many industrial applications such as aerospace
and other tactical applications, accurate prediction of
mechanical performance becomes increasingly import-
ant.1 In these applications, fatigue loads are usually
unavoidable. For this reason, recent designs do not spe-
cify the mechanical properties of advanced composite
materials without fatigue analysis.2
The heterogeneous and anisotropic nature of fiber-
reinforced composites leads to the formation of differ-
ent stress levels within the material so that the fracture
process includes various combinations of damage
modes such as matrix cracking, fiber breakage, delam-
ination, debonding and ply failure. Voids and defects
contained in composites act as sites for nucleation of
fatigue failure.3
The response to cyclic loading in composite mater-
ials will depend on the fiber arrangement and volume
fraction as well as on the matrix, fiber and interface
properties. When the matrix is a polymer, interfacial
debonding will generally occur near the end of a frac-
tured fiber, and a transverse matrix crack may also
propagate in this region. If the fibers are not degraded
by cyclic loading and the cyclic strains are insufficient
to generate fatigue effects in the matrix, then the com-
posite will show little or no reduction in strength during
the cyclic loading.4,5
Fatigue damage sequence in all materials is crack
initiation, crack propagation and crack separation. In
conventional metallic materials, much of the fatigue life
is spent before cracks appear; however, once a crack
forms, it propagates rapidly and the material fails.
1Mechanical Design and Production Engineering Department, Faculty of
Engineering, Zagazig University, Egypt2Mechanical Design and Production Engineering Department, Faculty of
Engineering, Ein-Shams University, Egypt
Corresponding author:
AI Selmy, Mechanical Design and Production Engineering Department,
Faculty of Engineering, Zagazig University, Egypt.
Email: [email protected]; [email protected]
Journal of Reinforced Plastics
and Composites
32(23) 1821–1834
! The Author(s) 2013
Reprints and permissions:
sagepub.co.uk/journalsPermissions.nav
DOI: 10.1177/0731684413496879
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In composite materials, cracks form after a few cycles
even at lower stress levels.6
A large variation usually exists in the fatigue-life
data results even at a certain stress level and under
carefully controlled test procedures. Nowadays, accur-
ate characterization of this variation is required so the
scatter in fatigue life has been a subject of statisticalanalysis by various researchers.7,8
In assessing the reliability of composite structures,
the Weibull distribution function has proved to be
useful and versatile means of describing composite
material properties data. This is because the probabil-
ity density function of the Weibull distribution has a
wide variety of shapes. For example, when the shape
parameter ¼ 3.2, Weibull cumulative distribution
function is equivalent to the normal distribution and
the Rayleigh distribution is a Weibull distribution
with ¼ 2.0.9
Hybrids consisting of mixed fiber materials can be
used when a single fiber material does not have all the
desired properties. Random glass fiber (R) compos-
ites are used extensively in high volume applications
due to low manufacturing cost, but their mechanical
properties are considerably poorer than those of uni-
directional glass fiber (U) composites. So, hybrid com-
posites consisting of mixed (R) and (U) fibers offer a
low manufacturing cost with better mechanical proper-
ties. Also, the design flexibility offered by these and
other composite configurations is obviously quite
attractive to designers and the potential now exists to
design not only the structure but also the structural
material itself.The main objectives of the present work are as
follows:
. constructing the S–N curves of the fabricated inter-
ply hybrid composite laminates and recording the
flexural stiffness degradation during the testing;
. measuring the relative mid-length surface tempera-
ture at each stress level during testing;
. investigating the effect of the layer stacking
sequences on S–N curves and
. finally, statistically analyzing the test result data
using Weibull distribution and constructing the reli-
ability curves used in practical design applications.
Experimental work
Specimen fabrication
Three kinds of interply hybrid composite laminates, i.e.
[U/U/0.5R]S, [U/0.5R/U]S and [0.5R/U/U]S of constant
(V fU/V fT) ¼ 0.8 have been fabricated using hand lay-up
technique in order to study the effect of ply stacking
sequence on the fatigue behavior. Each fabricated
hybrid composite consists of five plies with a total
thickness of 5.5 0.2 mm. The processing lay-ups of
the fabricated hybrid composite laminates are outlined
in Figure 1. The constituent materials are epoxy resin
(kemapoxy 150RGL) ¼ 1.07 0.02 g/cm3 as a matrix
and roving E-fiber glass L ¼ 2.4 g/m and random
E-fiber glass random distributed glass-mat with
¼ 900g/m2. The details about the fabrication tech-
nique are illustrated elsewhere.10,11 The total fiber
volume fraction (V fT) and the unidirectional relative
fiber volume fraction (V fU/V fT) were determined experi-
mentally by the matrix physical removing using ignition
test according to BS 3691.12 The average value of total
fiber volume fraction is 37%. The S–N relationships
were drawn using four different initial stress levels for
each hybrid composite type. For each initial stress level
five specimens were tested.
Test procedure
Constant deflection flexural fatigue tests were per-
formed using AVERY DENISON 7305 testing
machine13 shown in Figure 2(a). The machine specifi-
cations are 24 maximum oscillating angle and 1420
cycles per minute. Grips are provided for specimens’
fixation. Metallic packing shims are used to bring the
centerline of the specimen on the machine axis.
Figure 2(b) is the top view of the flexural fatigue testing
machine (AVERY-DENISON) indicating all the
Figure 1. Processing lay-ups of three unidirectional glass fiber (U)/random glass fiber (R)/epoxy hybrid composite laminates.
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required details whilst Figure 2(c) is a section view
rotated 90 shows the fixation of the test specimen
to the machine. The oscillating load is imposed at
free end of the specimen by a reciprocating spindle
driven by a connecting rod, crank and double eccen-
tric disc. The eccentric disc is adjustable to give bend-
ing angle range. The load is measured at the oppositeend of the specimen by a torsion dynamometer of a
moment of 30 Nm. The angle of twist is registered on
dial gauges in terms of divisions. A calibration curve
for the machine dynamometer is provided giving the
relationship between dial gauge reading in terms of
divisions and imposed torque on the dynamometer
as shown in Figure 2(d). Initial static loads can be
applied by rotating the dynamometer housing in its
bearings by a pair of adjusting screws. The revolution
counter fitted to the motor records the number of
cycles. When the specimen breaks the machine is
stopped automatically by cut-out switches. The details
of the machine adjustment and test procedure are
reported in the machine catalog. All fatigue tests in
the present work have zero mean stress, i.e. a cyclic
stress ratio Rs ¼ S min/S max¼ 1. The details of test
procedure are illustrated in ref.13
Residual stiffness degradation of flexural fatigue
test specimens
The reciprocating arm of the testing machine was used
to measure the residual stiffness ratio (EI )/(EI )0 as fol-
lows: the amplitude of the reciprocating arm ( y) has a
linear function with the applied bending moment on thetest specimen.
(a)
(c) (d)
(b)
Figure 2. Flexural fatigue testing machine (type AVERY-DENISON) (details and calibration).
Figure 3. The dimensions of fatigue test specimen.
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Test specimen deflection,
y ¼PL3
3EI ð1Þ
where EI is the flexural stiffness of test specimen; P is
the applied load on the test specimen and L is the can-tilever length of the test specimen. The initial bending
moment (at the start of the test) is (M 0).
M 0 ¼ a
0 ¼ P0L ¼
3 yðEI Þ0
L2 ð2Þ
and the bending moment after a certain number of
cycles is
M ¼ a ¼ PL ¼3 yðEI Þ
L2 ð3Þ
where a is the dial gauge reading after (N ) cycles and a0is the dial gauge reading at the start of the test, and
L and y have constant values. Therefore, the residual
stiffness ratio is given by
ðEI Þ
ðEI Þ0
¼ M
M 0
¼ a
a0
ð4Þ
The failure criterion of the flexural fatigue used in
the present study is defined as: the specimen fails when
the residual stiffness of the specimen (EI )/(EI )0 reaches
80% of its initial stiffness value.14 In the present work,
the elastic modulus degradation model proposed by Jenet al.15 was used to illustrate the relationship between
the stiffness reduction ratio, (EI )/(EI )0, and the number
of cycles (N ) as follows:
EI ð Þ=ðEI Þ0 ¼ Ai N ð ÞBi ð5Þ
where Ai and Bi are constants depending on the test
specimen material and are calculated from the fatigue
experimental data.
Temperature measurements of fatiguetest specimens
When a material is subjected to fatigue (repeated)
loads, mechanical energy is consumed inside the
material by transforming into other types of energy
such as heat and sound. As composites’ thermal con-
ductivity is low, a part of the loss energy is stored
inside the material as heat energy and the composite
temperature increases.14 This relative temperature
rise has been measured by a thermocouple during
testing.
Statistical analysis of fatigue-life data
The two-parameter Weibull distribution function is
used to statistically analyze fatigue-life data results. It
is characterized by a probability density function f (n)
and the associated cumulative distribution function
F (n) as follows:
f ðnÞ ¼
n
exp
n
ð6Þ
F ðnÞ ¼ 1 exp n
ð7Þ
where n is the random variable value (N ), is the shape
parameter at certain stress level S a and is the scale
parameter at certain stress level S a.
Analysis of fatigue-life data by the graphical method The reliability function, LR(n) is defined as
LRðnÞ ¼ 1 F ðnÞ. Substituting this value of F (n) in
equation (7) it is converted to
LRðnÞ ¼ exp n
ð8Þ
By taking the logarithm twice on both sides of equa-
tion (8), it becomes
In In 1
LRðnÞ ¼ InðnÞ InðÞ ð9Þ
From equation (9), it is clear that relationship
between ln[ln(1/LR)] and ln(n) is a linear one. The line
slope presents the shape parameter and the scale
parameter can be obtained from the second term of
equation (9).
In order to obtain a graph from equation (9), the
number of failure cycles (N ) of each stress level (S a)
are first arranged in ascending order, serial number is
given for each value (i ¼ 1 , 2 , 3 , . . . , n) and the reliability
function LR for each N at a given stress level S a is
calculated from median ranking method16shown in
equation (10):
LR ¼ 1 ði 0:3Þ
ðk þ 0:4Þ
ð10Þ
where i is the failure serial number and k is the total test
number of samples under consideration at a particular
stress level S a. The reliability function in the form of
ln[ln(1/LR)] for each N is plotted on a graph against
ln(N ). Then the shape parameter and the scale par-
ameter can be determined.
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Scatter analysis of fatigue-life data
Mean time to failure (MTTF), standard deviation (SD)
and coefficient of variation (CV) of two-parameter
Weibull distribution were calculated from the following
equations:8
MTTF ¼ 1 þ1
ð11Þ
SD ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ
2
2 1 þ
1
s ð12Þ
C :V : ¼SD
N o¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ 2
2 1 þ 1
1 þ 1
s
ð13Þ
where is gamma function.
A correlation coefficient R2 is calculated to deter-
mine the correlation between the experimental and
the fitted results for the fabricated hybrid polymeric
composite laminates.
Reliability analysis of fatigue-life test results
The term reliability is used for the probability of func-
tional performance of a part under current service con-
dition and in definite time period.17 Reliability means
that ‘a material can be used without failure’. This is
known as the probability of survival.18
Rearranging equation (8), the following relation can
be obtained:
n ¼ In1In In 1
LR
n oþ InðÞ
24
35 ð14Þ
Equation (14) is used to calculate the fatigue lives
(N ) at a given stress level (S a) corresponding to different
reliabilities (LR). LR – N curves were drawn for different
reliability levels (LR ¼ 0.01, 0.10, 0.20 , . . . , 0.90 and
0.99) using the fatigue data. These LR – N curves were
introduced for the identification of the first failure time
as reliability and safety limits for the benefit of mech-
anical designers.
Results and discussion
Relationship between residual stiffness and number
of cycles in fatigue test
The variation of the experimental data and fitted values
of the residual stiffness ratio (EI )/(EI )0 of the
three hybrid composite specimens versus the number of
cycles are shown in Figure 4. Each item of Figure 4(a)
to (c) has three curves representing relation between
(EI )/(EI )0 and (N ). The curves in each item represent
the average degradation of five samples under different
initial stress levels (S a). The curves in Figure 4 show a
reasonable agreement between the fitted values of resi-
dual stiffness ratios (EI )/(EI )0 and the experimental
ones. Using equation (5), the power function constantsAi and Bi were estimated for each hybrid composite
laminate type from the experimental data except those
of the endurance limit values where no residual stiffness
degradation has been traced due to its long duration
time of the endurance test. It is clear from Figure 4 that
as the initial stress increases the stiffness ratio (EI )/(EI )0degradation rate increases.
Temperature measurements of fatigue
test specimens
For different initial stress levels (S a) the surface tem-
perature increases until it reaches approximately a con-
stant value at different fatigue cycles. After that the
temperature remains constant as shown in Figure 5
until failure occurs. This constant value of temperature
depends on S a. The same result was found by Dally and
Broutman.18 From Figure 6, it is noted that as S aincreases, the surface temperature increases. This
result may be attributed to increasing applied alternat-
ing stress, which increases the corresponding internal
strain deformation that is partially converted into
heat and leads to increase in sample surface tempera-
ture. The lines connected to data points in Figures 5
and 6 are merely for suggesting data trend.
S–N curves of fatigue test specimens
Figure 7 represents the S–N curves of [U/U/0.5R]S,[U/0.5R/U]S and [0.5R/U/U]S hybrid composite speci-
mens, respectively. The ordinate denotes the initial
applied stress and 80% of the initial applied stress
(the failure criterion) while the abscissa denotes the
fatigue life (number of cycles to failure, N ) for
four hybrid composite types. The experimental data
results were curve fitted by the power function
[S a
¼ Ai (N )Bi ]. In Figure 7, filled circles and open circles
are from the same set of data, the former are plotted at
initial stress while the latter are plotted at 80% of the
initial stress.
The values of Ai and Bi were calculated from the
experimental data using least-squares curve fitting.
These two constants depend on the material type.
Based on 20% reduction of initial flexural stiffness
taken as a failure criterion in this study, the safe fati-
gue-life areas shown in Figure 7 represent the fatigue
safe workability for the fabricated hybrid composite
laminates.
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Figure 8 shows S–N curves for the hybrid and non-
hybrid composites. The non-hybrid composite lamin-
ates, i.e. [U]5 and [R]5 are the parent materials tested
elsewhere.13 The S–N curves for [U]5 and [R]5 compos-
ite laminates are shown in Figure 8. It is clear from this
figure that correlation coefficients (R2) values are very
close to 1.0. That means the obtained experimental
results have scatter values approximately in the
order of 5%.
The influence of layer stacking sequences on S–N
relationship of hybrid composite laminate specimens
was illustrated in Figure 9. It is clear from Figure 9
that the layer stacking sequence has a great effect on
the fatigue-life values.
Flexural fatigue strength at the endurance limit of
[0.5R/U/U]S, when the R-fiber is at the surface of the
composite and the U-fiber is located at the middle is
about half that of hybrid composite with the opposite
Figure 4. Experimental and fitted data of (EI)/(EI)0 vs. N for hybrid composites.
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arrangement, [U/U/0.5R]S. This behavior can be attrib-
uted to better load resistance of the stiffer U-fiber at
exterior layers, where maximum flexural stress occurs at
the outer layers. From comparing the flexural and shear
strengths of those hybrid composites, it was noticed
that those for [0.5R/U/U]S are 279MPa and 30.6MPa
while the corresponding values for [U/U/0.5R]S are
783 MPa and 37.3 MPa.10 Finally, it is noticed that
the fatigue endurance limit of hybrid systems is influ-
enced by the material type combinations in addition to
their arrangement across the thickness.
Failure modes
Unlike metals fatigue damage in fiber-reinforced com-
posites occurs at multiple locations in the form of fiber
breakage, delamination, debonding and matrix crack-
ing. Depending on the stress level, fiber length, fiber
orientation, constituent properties and lamination con-
figuration, some of these failure modes may appear
either individually or in combination quite early in
the life cycle of a composite. The damage grows in
size or intensity in a progressive manner until the
final rupture takes place.19
The flexural fatigue failure modes of unidirectional
glass fiber (U)/random glass fiber (R)/epoxy hybrid
composite specimens which are used in the current
study were visually investigated. For all the specimens,
the damage was visible on both surfaces of the speci-
men at the same location, and had the same gen-
eral appearance, indicating that uniform length
Figure 5. Mid-length surface temperature measurement for hybrid composites.
Figure 6. Effect of Sa on relative surface temperature rise for
the hybrid composites.
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delaminations have been formed across the width of the
specimen.
The [U/U/0.5R]S and [U/0.5R/U]S hybrid composite specimens’
failure modes. For [U/U/0.5R]S and [U/0.5R/U]S hybrid
composite specimens when loaded at high stress levels,
a complete failure occurs as a transverse wide crack
near the fixed end rapidly propagated along the speci-
men width as cycles increase as shown in Figure 10(a).
Delamination occurred at the outer surfaces edges
Figure 7. S–N curves for hybrid composite laminates.
Figure 8. S–N curves of unidirectional glass fiber/random glass fiber/epoxy hybrid and non-hybrid13 composite laminates.
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parallel to specimen axis. The same signs of failure have
been noticed for medium and low stress levels as
shown in Figure 10(b) and (c). Note that the width of
the fracture zone becomes lesser than that in Figure
10(a). The white-colored region of damage is perhaps
due to fretting of the matrix as a result of friction
between fibers and matrix. Debonding between fibersand matrix is found at the surface edges.
The [0.5R/U/U]S hybrid composite specimens’ failure
modes. When the [0.5R/U/U]S hybrid composite speci-
men loaded at high stress level (S a ¼ 67.49 MPa), com-
plete failure occurred as a transverse crack propagated
from one side to the other across the specimen width at
the specimen mid-span as cycles increased as shown in
Figure 11(a). When the specimens loaded at stress levels
Figure 11. The [0.5R/U/U]S hybrid composite failure modes.
Figure 10. The [U/U/0.5R]S and [U/0.5R/U]S hybrid composites common failure modes.
Figure 12. Microscopic evidence of flexural fatigue damage.Figure 9. The effect of stacking sequence on mean endurance
limit.
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(S a ¼ 57.66 and 46.66 MPa), complete fracture occurs
at the specimen mid-span as shown in Figure 11(b)
and (c). No delamination occurred at the outer surface
edges parallel to the specimen axis.
In general it is noticed that for the three hybrid com-
posites, no signs of failure were observed at the four
different endurance stress levels. The microscopic inves-
tigation of the damage zone is illustrated in Figure 12.
Scatter analysis in fatigue-life data of fatigue test
results
Figure 13 shows the graphical analysis of fatigue-life
data for [U/U/0.5R]S, [U/0.5R/U]S, and [0.5R/U/U]S
hybrid composite laminate specimens, respectively.
Also, Figure 13 indicates both the corresponding fitting
related equations and the correlation coefficients (R2)
for the different hybrid composites at different stress
levels (S a). A good linear relationship between ln
(ln(1/LR)) and ln (N ) was observed indicating that the
experimental data can be well described with the
Weibull distribution equation.
The values of shape parameter and the scale par-
ameter of Weibull distribution function have been
calculated from the above-mentioned related equations
and their values are listed in Tables 1 to 3. MTTF, SD
and CV of two-parameter Weibull distribution were
calculated and are recorded in the above-mentioned
Figure 13. Graphical analysis of fatigue-life data for hybrid composite laminates.
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Figure 14. MTTF vs. CV for hybrid composite specimens.
MTTF: mean time to failure; CV: coefficient of variation.
Table 2. Statistical analysis of fatigue-life data for [U/0.5R/U]S hybrid composite.
Test no.
Sa (initial stress)
97.70 (MPa) 83.51 (MPa) 66.44 (MPa) 52.47 (MPa)
1 6.00E + 03 1.20E + 04 1.60E + 05 7.25E + 06
2 6.00E + 03 1.30E + 04 2.63E + 05 7.66E + 06
3 7.00E + 03 1.40E + 04 3.01E + 05 8.30E + 06
4 9.00E + 03 1.70E + 04 3.83E + 05 8.80E + 06
5 1.15E + 04 2.20E + 04 3.78E + 05 1.00E + 07
3.331 3.946 2.806 7.992
8.867E + 03 1.726E + 04 3.378E + 05 8.874E + 06
Mean life 7.958E + 03 1.563E + 04 3.008E + 05 8.357E + 06
Standard deviation 2.631E + 03 4.435E + 03 1.161E + 05 1.240E + 06
Coefficient of variation 0.331 0.284 0.386 0.148
Table 1. Statistical analysis of fatigue-life data for [U/U/0.5R]S hybrid composite.
Test no.
Sa (initial stress)
126.36 (MPa) 106.89 (MPa) 84.54 (MPa) 61.68 MPa))
1 6.50E + 03 1.31E + 04 5.40E + 05 8.00E + 06
2 7.00E + 03 1.75E + 04 5.72E + 05 8.66E + 06
3 7.50E + 03 1.85E + 04 6.40E + 05 9.20E + 06
4 8.00E + 03 2.55E + 04 7.72E + 05 9.80E + 06
5 1.05E + 04 3.80E + 04 9.61E + 05 1.00E + 07
5.109 2.435 4.115 11.238 8.571E + 03 2.570E + 04 7.671E + 05 9.511E + 06
Mean life 7.879E + 03 2.279E + 04 6.964E + 05 9.091E + 06
Standard deviation 1.773E + 03 9.982E + 03 1.904E + 05 9.796E + 05
Coefficient of variation 0.225 0.438 0.273 0.108
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tables. Table 1 shows that the maximum scatter in fati-
gue-life data for [U/U/0.5R]s hybrid composite is found
at stress level S a ¼ 106.89 MPa. It is noticed from Table
2 that the widest dispersions in fatigue-life data for
[U/0.5R/U]S hybrid composite were observed at
S a ¼ 97.70 MPa and 66.44 MPa.
According to results shown in Table 3, the widest
scatter in fatigue-life data for [0.5R/U/U]S hybrid
Figure 15. Reliability graphs for three hybrid composites under different stress levels.
Table 3. Statistical analysis of fatigue-life data for [0.5R/U/U]S hybrid composite.
Test no.
Sa (initial stress)
67.49 (MPa) 57.66 (MPa) 46.66 (MPa) 33.50 (MPa)
1 5.00E + 03 1.00E + 04 3.30E + 05 7.50E + 06
2 6.00E + 03 1.20E + 04 3.50E + 05 7.80E + 063 7.00E + 03 1.30E + 04 4.28E + 05 8.20E + 06
4 9.00E + 03 1.45E + 04 4.49E + 05 9.50E + 06
5 1.20E + 04 1.70E + 04 5.60E + 05 1.00E + 07
2.926 5.164 4.691 7.767
8.778E + 03 1.441E + 04 4.614E + 05 9.110E + 06
Mean life 7.830E + 03 1.325E + 04 4.221E + 05 8.566E + 06
Standard deviation 2.912E + 03 2.955E + 03 1.024E + 05 1.315E + 06
Coefficient of variation 0.372 0.223 0.243 0.154
1832 Journal of Reinforced Plastics and Composites 32(23)
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composite specimens was observed at the test begin-
ning, i.e. at the life range from 103 to 104 cycles. This
result may be due to damage that occurs inside the test
specimens when the motor runs and the specimens are
suddenly loaded.
MTTF and CV values for fatigue life of four unidir-
ectional glass fiber/random glass fiber/epoxy hybridcomposite laminates are calculated from equations
(11) and (13). Figure 14 shows the effect of MTTF on
the CV. According to the results in this figure, the dis-
persion in fatigue-life values has the widest between 104
and 107 cycles. This trend for different hybrid compos-
ites is very important for the design, application and
development of hybrid composite structures. The lines
connected to data points in Figure 14 are merely for
suggesting data trend.
Reliability analysis of fatigue-life test results
The reliability graphs corresponding to each stress
value of unidirectional glass fiber/random glass fiber/
epoxy hybrid composite samples are shown in
Figure 15. These graphs are drawn by using equation
(14). The reliability 50% of samples from these dia-
grams is intersected by drawing horizontal line from
the Y -axis, hence the corresponding number of cycles
can be obtained. Figure 15 provides possibility of pre-
diction reliability of fatigue life needed to the mechan-
ical designers for the three hybrid composites. 103 104
105 106 107
Conclusions
Based on the experimental results the following conclu-
sions are drawn:
1. The S–N curves for the fabricated hybrid composites
have been constructed as design curves. The layer
stacking sequence has a great effect on flexural fati-
gue endurance limit of the fabricated hybrid com-
posites. Flexural fatigue endurance limit of [0.5R/
U/U]S, when the R-fiber is at the surface of the com-
posite and the U-fiber is located at the middle, is
about half that of hybrid composite with the oppos-
ite arrangement, [U/U/0.5R]S. Based on 20% reduc-
tion of initial flexural stiffness taken as a failure
criterion, the safe fatigue-life areas representing the
fatigue safe workability for the hybrid composite
laminates have been determined.
2. The initial applied stress (S a) has a significant effect
on the surface temperature relative increase of test
specimens for all the fabricated hybrid composites. It
is noted that as S a increases, the surface temperature
increases. For the hybrid composite laminates inves-
tigated in the present study, two modes of failure are
observed either in the specimen mid-span or near the
fixed end depending on the layer stacking sequences,
which establish different damage mechanisms. The
complete fracture of the hybrid composites was
observed at all stress levels except for fatigue endur-
ance limit where no stiffness degradation occurs.
3. Using Weibull distribution, reliability– N relation-ships at different stress levels have been established
for the studied hybrid composites, incorporating
reliability (probability of survival) into S–N relation-
ships. These relationships can be used by the design
engineers to obtain the fatigue life of the manufac-
tured hybrid composites for the desired level of reli-
ability. The reliability values can be found easily
corresponding to any fatigue life (N ) or stress amp-
litude from these diagrams. These diagrams can be
considered as reliability or safety limits in identifica-
tion of the first failure time of a component under
any stress amplitude. The usage of reliability
LR ¼ 0.99 should be advised in the design of aircraft
to have higher safety and reliability. The CVs
have their minimum values at the endurance limit
(107 cycles).
Funding
This research received no specific grant from any
funding agency in the public, commercial, or not-for-profit
sectors.
Conflict of interest
None declared.
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