Experimental Study on Flexural Fatigue Behavior of Glass Fibersepoxy Hybrid Composites With...

7/21/2019 Experimental Study on Flexural Fatigue Behavior of Glass Fibersepoxy Hybrid Composites With Statistical Analysis

http://slidepdf.com/reader/full/experimental-study-on-flexural-fatigue-behavior-of-glass-fibersepoxy-hybrid 1/14

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

jrp.sagepub.com

at East Carolina University on April 19, 2015 jrp.sagepub.comDownloaded from

http://jrp.sagepub.com/






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.

1822 Journal of Reinforced Plastics and Composites 32(23)








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.

Selmy et al. 1823








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.









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.

Selmy et al. 1825








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.









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.

Selmy et al. 1827








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.









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.

Selmy et al. 1829








(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.









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



Selmy et al. 1831








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











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.

References

1. Raman B and Rakesh C. Fatigue-life distributions and

failure probability for glass-fiber reinforced polymeric

composites. Compos Sci Technol 2009; 69: 1381–1387.

2. Abd Allah MH, Abdin EM, Selmy AI, et al. Short com-

munication: effect of mean stress on fatigue behaviour of

GFRP pultruded rod composites. Composites Part A 1997;

28A: 87–91.

3. Couillard RAA and Schwartz P. Bending fatigue of carbon

fiber reinforced epoxy composite strands. Compos Sci

Technol 1997; 57: 229–235.

4. Van PW and Degrieck J. A new coupled approach of resi-

dual stiffness and strength for fatigue of fiber-reinforced.

Int J Fatigue 2002; 24: 747–762.

5. Shan Y and Liao K. Environmental fatigue behavior and

life prediction of unidirectional glass–carbon epoxy hybrid

composites. Int J Fatigue 2002; 24: 847–859.

6. Tanimoto T and Amijima S. Progressive nature of fatigue

damage of glass fiber reinforced plastics. J Compos Mater

1975; 9: 380–390.

7. Lee J, Harris B, Almond DP, et al. Fibre composite

fatigue life determination. Composites Part A 1997; 28:

5–15.

Selmy et al. 1833








8. Philippidis TP and Vassilopoulos AP. Fatigue design

allowable for GRP laminates based on stiffness degrad-

ation measurements. Compos Sci Technol 2000; 60:

2819–2828.

9. Abdallah MH, Abdin EM, Selmy AI, et al. Reliability

analysis of GFRP pultruded composite rods. Int J

QualReliab Manage 1996; 13: 88–98.

10. Selmy AI, Elsesi AR, Azab NA, et al. In-plane shearproperties of unidirectional glass fiber (U)/random glass

fiber (R)/epoxy hybrid and non-hybrid composites.

Composites: Part B 2012; 43: 431–438.

11. Selmy AI, Elsesi AR, Azab NA, et al. Monotonic proper-

ties of unidirectional glass fiber (U)/random glass fiber

(R)/epoxy hybrid composites. Mater Des 2011; 32:

743–749.

12. BS 3691. E-glass fiber roving for reinforcement of poly-

ester and epoxy resin system. British Standard, 1990.

13. Selmy AI, Azab NA and Abd El-baky MA. Flexural

fatigue characteristics of two different types of glass

fiber/epoxy polymeric composite laminates with

statistical analysis. Composites Part B: Engineering

2013; 45: 518–527.

14. JIS K7119. Testing method of flexural fatigue of rigid

plastics by plane bending. Japanese Industrial Standard,

1972.

15. Jen MR, Hsu JM and Hwang DG. Fatigue Degradation

in Centrally Notched Quasi-Isotropic Laminates.

J Compos Mater 1990; 27: 823–837.16. Kennedy JB and Neville AM. Basic statistical methods for

engineers and scientists. New York: Dun-Donnelley

Publishers, 1986, p. 613.

17. Raif S and Irfan A. Statistical analysis of bending fatigue

life data using Weibull distribution in glass-fiber rein-

forced polyester composites. Mater Des 2008; 29:

1170–1181.

18. Dally JW and Broutman LJ. Frequency effects on the

fatigue of glass reinforced plastics. J Compos Mater

1967; 1: 424–443.

19. Mallick PK. Fiber-reinforced composites, 2nd ed.

New York: Marcel Dekker, 1993.


Experimental Study on Flexural Fatigue Behavior of Glass Fibersepoxy Hybrid Composites With...

Documents

Transcript of Experimental Study on Flexural Fatigue Behavior of Glass Fibersepoxy Hybrid Composites With...