-
fn
, I
r E
chit
07;ine
and land transportation. Most of these materials aresubjected to
cycling loading during the service conditions.The mechanisms of
composite materials under cycling load-
As it is in inhomogeneous all materials, it can be seengreat
dierences in static strength and fatigue life testresults among the
samples in the same conditions in GFRPcomposites having anisotropy
structure as well. Statisticalevaluations are very important
because of the dierentdistribution of the test results in GFRP
samples. When
* Corresponding author. Tel.: +90 266 612 1194; fax: +90 266 612
1257.E-mail address: [email protected] (_I. Ay).
Available online at www.sciencedirect.com
Materials and Design 29 (20
Materials1. Introduction
In recent years, glass-ber reinforced polyester (GFRP)composite
materials have developed more rapidly than met-als in structural
applications. They are used alternativelyinstead of metallic
materials because of their low density,high strength and rigidity
[14]. The studies on reliability ofstructure depending on damage
tolerance are very importantfor todays composite researchers since
GFRP are used aspreferable structures in fan blades, wind turbine,
in air, sea
ing and their fracture behaviors are really complex
[14].Because, anisotropy structure ofGFRPmaterials forms threeaxial
local stresses in itself. Static and fatigue failures inmulti-layer
composites contain dierent damage combinations likematrix cracking,
bermatrix debonding, ply delaminationand ber fracture. The form of
each type failure is dierentdepending onmaterial properties, number
of layers and load-ing type [3,5]. Thus, knowing the fatigue
behavior under thecyclic loading is essential for using composite
materials safelyand in practical structural designs
[14].Abstract
The bending fatigue behaviors were investigated in glass
ber-reinforced polyester composite plates, made from woven-roving
withfour dierent weights, 800, 500, 300, and 200 g/m2, random
distributed glass-mat with two dierent weights 225, and 450 g/m2
and poly-ester resin. The plates which have ber volume ratio Vf @
44% and obtained by using resin transfer moulding (RTM) method were
cutdown in directions of [0/90] and [45]. Thus, eight dierent
ber-glass structures were obtained. These samples were tested in a
com-puter aided fatigue apparatus which have xed stress control and
fatigue stress ratio [R = 1]. Two-parameter Weibull distribution
func-tion was used to analysis statistically the fatigue life
results of composite samples. Weibull graphics were plotted for
each sample usingfatigue data. Then, SN curves were drawn for
dierent reliability levels (R = 0.99, R = 0.50, R = 0.368, R =
0.10) using these data.These SN curves were introduced for the
identication of the rst failure time as reliability and safety
limits for the benet of designers.The probabilities of survival
graphics were obtained for several stress and fatigue life levels.
Besides, it was occurred that RTM condi-tions like ber direction,
resin permeability and full inltration of bers are very important
when composites (GFRP) have been used foralong time under dynamic
loads by looking at test results in this study. 2007 Elsevier Ltd.
All rights reserved.
Keywords: Glass-ber reinforced polyester composite (GFRP);
Bending fatigue; Fatigue life; Weibull distribution; Mean life;
Survival life; ReliabilityanalysisStatistical analysis of
bendingdistribution in glass-ber rei
Raif Sakin a
a Edremit Technical Vocational School of Higheb Department of
Mechanical Engineering, Engineering and Ar
Received 19 January 20Available onl0261-3069/$ - see front
matter 2007 Elsevier Ltd. All rights
reserved.doi:10.1016/j.matdes.2007.05.005atigue life data using
Weibullforced polyester composites
_rfan Ay b,*
ducation, Balikesir University, Edremit, Turkey
ecture Faculty, Balikesir University, 10145 Balikesir,
Turkey
accepted 16 May 20072 June 2007
www.elsevier.com/locate/matdes
08) 11701181
&Design
-
great safety coecient was used in the past, this distribu-tion
in the results was relatively unimportant. With thedevelopment of
high performance aircraft, the changeabil-ity of mechanical
properties of GFRP composites hasgained great importance. Analyzing
the reliability of com-posite materials is an inevitable need
because of brittle frac-ture in structure and especially wide
scatter of fatigue data.Thus, for the safe application of composite
materials inindustry, their fatigue data as statistically must be
under-stood well. The statistical properties used, generally
dependon usual distribution in mean strength. But especially,
Wei-bull distribution has more reliable values than other
distri-butions in fatigue data evaluations from the point
ofvariables in life and strength parameters [3,6]. So, it hasbeen
proved in literature that Weibull distribution will be
obtained at Vf @ 44% approximately. It was observed that bubbles
wereconned and incomplete inltration occurred in some layers.
Incompleteinltrated plates were not tested and evaluated (see Fig.
2). Eight dierentmaterial combinations were obtained by cutting the
plates in the directionof [0/90] and [45] as shown in Table 2.
Fatigue test samples were pre-pared from these plates with
dimensions of 25 250 3.00 mm as shownin Fig. 3 [11]. By preparing
samples with the dimension of18 140 3.00 mm from the same plates
according to the ASTM 790-00three point bending tests were carried
out and obtained maximum bendingstrength (Table 4) [12].
Especially in the formation of SN curves, (Figs. 7 and 10) the
maxi-mum bending strength values were considered as one cycle
strength value[11,13,14].
3. Fatigue tests
Fatigue samples (shown in Fig. 3) were tested in the fati-gue
apparatus specially designed and improved by us (seeFig. 4) [11].
Test conditions were as follows:
Motor: 0.5 HP 1390 rpmMain shaft: 30 rpm (0.5 Hz)Test frequency:
2 HzTemperature: roomControl: stress (load)Loading ratio: R =
1Maximal number of cycle: 1 million
The experimental conditions of the rotating fatigue tests
R. Sakin, _I. Ay / Materials and Duseful in the evaluation of
fatigue data reliability in com-posite structures [3,610].
The aim of this study is to investigate the failure of fanblades
and wind turbines made by composite materialsinstead of aluminum
which is caused by bending fatigueforces. And then, the test
results for these composites underreversal stress (bending) are to
analysis as statistical byusing Weibull distribution. Consequently,
any engineercan use these SN curves at the various reliability
levelsfor their practical applications.
2. Experimental procedure
2.1. Materials and test specimens
General purposive and unsaturated polyester resin, glass-mat
andwoven-roving as shown in Table 1 were used for this study. In
order toobtain GFRP sample by RTM method; heated mold system was
con-structed [11].
The mold was sprayed with a mold release agent to facilitate the
laterremoval of the molding. Then one layer of glass-mat and one
layer woven-roving put into the mold as shown in Fig. 1a and b. The
properties of poly-ester resin other additive materials were
prepared in accordance withRTM as shown in Table 1. Then, the
prepared mixture was injected intothe mold under pressure between
0.51 bar. At about 40 C, 12 h later, themold was opened and a plate
with dimension of 310 600 3.00 mm wasremoved out of the mold. In
the study, the volume of glass-ber was
Table 1Composition of GFRP plates
Matrix Orthophthalic polyester resina (Neoxil CE92N8)Monomer
Styreneb (15% of matrix volume)Catalyst Cobalt naphthenateb (0.2%
of matrix volume)Hardener Methyl ethyl ketone peroxideb (MEKP)
(0.7% of matrix
volume)Reinforcement Woven-rovinga,c
Density: 2.5 g/cm3
Weight per unit area: 800, 500, 300, and 200 g/m2
Fiber direction: [0/90] and [45]
Glass-mata,c
Density: 2.5 g/cm3
Weight per unit area: 225 and 450 g/m2
Fiber direction: Random
a (CamElyaf A.S., Turkey).
b (Poliya A.S., Turkey).c (Fibroteks A.S., Turkey).Fig. 1. (a)
Schematic picture of glass-ber used and (b) arrangement
ofglass-ber.
esign 29 (2008) 11701181 1171were stress controlled exural
loading with a 30 rpm rotat-ing speed. The maximum stress was
applied on specimen
-
nd DInfiltration at the corners is so weak. (White zones)
1172 R. Sakin, _I. Ay / Materials atwice during one revolution
(horizontal positions of a spec-imen), it might be logical to count
two cycles for one revo-lution. Thus, the frequency of the rotating
fatigue tests inthis study was considered as 2 Hz [13]. The samples
havebeen aected by lift and drag forces during the rotationin this
fatigue test. Because of lower rotating speed, theeects of these
forces were negligible. For loading the cal-culated weight to the
specimens, steel disks, which had var-ious dimensions and
thicknesses (i.e. various weights), wereused. Bending stresses have
been only caused by theweights have been accepted as eective
[11,13]. During
Fig. 2. Inltration ratio
Table 2GFRP sample groups and their structures (Vf @ 44%)
Group Fiber direction Woven-roving
800 g/m2 500 g/m2
A [45] 3a B [45] 4C [45] D [45] E [0/90] 3 F [0/90] 4G [0/90] H
[0/90] a Indicates number of layers in the sample.
Fig. 3. (a) Fatigue sample dimensions aInfiltration (medium)
Infiltration (well)
esign 29 (2008) 11701181the test, when the sample is horizontal
position (0and180), maximum stress is occurred. The absolute
valuesof these stresses are equal to each other (rmax =
rmin).During the rotation at 0 while the upper bers are sub-jected
to tension, the lower ber are subjected to compres-sion. When the
sample position is 180, upper bers aresubjected to compression and
the lower bers are subjectedto tension. Thus, this stage was
tension-compression fullyreversed. In this situation fatigue stress
ratio is R = 1.
The pictures of samples broken result of the fatigue testare
shown in Fig. 5. Fiber-free bearings shows starting
in some laminates.
Glass-mat
300 g/m2 200 g/m2 225 g/m2 450 g/m2
4 4 15 4 2 7 8 4 4 15 4 2 7 8
nd (b) sample connection position.
-
nd DR. Sakin, _I. Ay / Materials apoint of the fatigue crack
(Fig. 5b). This can also be consid-ered as the weakest part of the
sample. As the fatigue crackhas occurred in the weakest part,
matrix (polyester) andber (glass-ber) separate from each other and
the crackgrows until the ber breaks down. The weakest part
inbermatrix interface is ber-free bearings and dry bers(not
inltrated) [15]. These samples have been not testedin this study.
This condition is one of the most importantpoints that should be
taken into account. Transversematrix- ber separation generally
starts at the upper bers.The rigidity and exibility of the upper
and lower bersdecrease at the highest levels of the cycling bending
process(tension-compression). Thus, the value of elasticity
modulewill reduce by passage of time under cycling loading [16].On
the other hand, the separation between longitudinalber and matrix
is similar to the separation in the trans-verse matrix cracks
[16].
Fig. 4. (a) Front view and (b) left-side view. Schematic view of
mesign 29 (2008) 11701181 11734. Statical analysis of fatigue life
data
4.1. Theory of Weibull distribution
Weibull distribution is being used to model extreme val-ues such
as failure times and fatigue life. Two popular formsof this
distribution are two- and three-parameter Weibulldistributions. The
probability density function (PDF) oftwo-parameter distribution has
been indicated in the fol-lowing Eq. (1). This PDF Equation is the
most known def-inition of two-parameter Weibull distribution
[2,3,17,18]
f x ba
xa
b1e
xa b aP 0; bP 0 1
where a and b is the scale, shape parameter. The advanta-ges of
two-parameter Weibull distribution are as follows[3]:
ulti-specimen and xed stress bending fatigue test apparatus.
-
tes
nd D It can be explainwith a simple function and applied easily.
It is used frequently in the evaluation of fatigue life
ofcomposites.
Its usage is easy having present graphics and simple cal-
Fig. 5. (a) The pictures of the samples broken as a result of
the fatiguezoom: 40X). Pictures of GFRP samples.
1174 R. Sakin, _I. Ay / Materials aculation methods. It gives
some physical rules concerning failure when theslope of theWeibull
probability plots taken into account.
If PDF Equation is integrated, cumulative density func-tion
(CDF) in Eq. (2) is obtained. Eq. (3) derives from Eq.(2).
F fx 1 e xa b
21 F fx e xa
b
3F sx 1 F fx 4Rx 1 Px 5In the above equations;
x variable (usually life). Failure cycles in this study(Nf),
b shape parameter or Weibull slope,a characteristic life or
scale parameter,Ff(x) probability of failure (Px),Fs(x) probability
of survival or reliability (Rx).
If the natural logarithm of both sides of the Eq. (3) istaken,
the following Eq. (6) can be written.
ln ln1
1 F fx
b lnx b lna 6When the Eq. (6) is rearranged as linear equation,
Y = ln(ln(1/(1 Ff (x)))), X = ln (x), m = b and c = b (ln(a))is
written. Hence, a linear regression model in the formof Eq. (7) is
obtained
ts and (b) front view of cracked zone as a result of fatigue
(Group: E,
esign 29 (2008) 11701181Y mX c 7a ec=b 8In Eq. (2), when x =
a,
F fx 1 e1b
F fx 1 0:368F fx Px 0:632 63:2% is obtained:According to Eq. (8)
characteristic life (a) is the time or
the number of cycles at which 63.2% of the population isexpected
to fail. The life of critical parts (roller bearing,blade etc.)
designed for fatigue is indicated as P10, P1,P0.1 for lower failure
probabilities [19]. In this study, asshown in Fig. 10, SN plots
were drawn for the values ofP1, P50, P63.2, P90 (or R99, R50,
R36.8, R10) and this studyalso guides the designers. NPx or NRx are
values of life indi-cating X% failure probability and can be
calculated fromEq. (9). The median life values (50% life) can be
calculatedEq. (10) or can be read from the graphics in Fig. 11. In
thisstudy, survival graphics drawn for each stress value ofGFRP
samples is given in Fig. 11.
NPx NRx a lnRx1=b 9NP50 NR50 a ln21=b 10Mean life (mean time to
failure = MTTF = N0), stan-dard deviation (SD) and coecient of
variation (CV) of
-
two-parameter Weibull distribution were calculated fromthe
following Equations [3,18,20,21]
MTTF N 0 a C1 1=b 11SD a
C1 2=b C21 1=b
q12
CV SDN 0
a
C1 2=b C21 1=b
qa C1 1=b 13
where (C) is gamma function.
4.2. Application of Weibull distribution
The drawing of Weibull line for X and Y, the parameterof Weibull
distribution and reliability analysis processescan be carried out
by software such as Microsoft Exceland SPSS [17,22]. Microsoft
Excel has been used in thisstudy. The following processes were
carried out to drawWeibull lines and obtain parameters.
1. The number of failure cycle corresponding to eachstress was
located successively.
2. Serial number was given for each value(i = 1,2,3, . . .
,n).
3. Each value for failure probability was used in Ber-nards
Median Rank formula given in Eq. (14).
MR i 0:3n 0:4 14
where i is failure serial number and n is total testnumber of
samples [2224].
4. ln(ln(1/(1 MR))) values were calculated for eachcycle value
(Y-axis).
5. ln(cycle) values were calculated for each cycle
value(X-axis).
6. Only the data given for group-A samples as examplein Table 3
was transferred to Microsoft Excel. Forregression analysis, the
Analysis ToolPak Add-Inwas loaded into Microsoft Excel [11,22].
7. The graphics of ln(cycle) and ln(ln(1/(1 MR))) val-ues were
drawn as shown in Fig. 6.
8. Y = mX + c linear equation given in the Eq. (7) wasobtained
in the most reasonable form from thisgraphics.
Table 3Summarized Weibull values of GFRP samples for Group-A
[11]
Stress amplitude, Sa (MPa) Cycle Rank Med. Rnk. MR In(cycle)
(X-axis) ln(ln(1/(1 MR))) (Y-axis) a b360 1 0.129630 5.886104
1.974459736 2 0.314815 6.601230 0.972686
106.728 922 3 0.500000 6.826545 0.366513 947 2.2041010 4
0.685185 6.917706 0.1447671016 5 0.870370 6.923629 0.714455
. . . . . . . .
. . . . . . . .
. . . . . . . .11111
1
R. Sakin, _I. Ay / Materials and Design 29 (2008) 11701181
1175960,633 1 0.129630979,766 2 0.314815
50.257 1,088,925 3 0.5000001,108,771 4 0.6851851,170,104 5
0.870370
Y=
1.92
1x-
16.14
3
Y=
2.20
4X-
15.10
3
Y=
9.00
8X-
91.31
8
-2.3
-2.0
-1.8
-1.5
-1.3
-1.0
-0.8
-0.5
-0.3
0.0
0.3
0.5
0.8
1.0
5 6 7 8 9 10ln(N )
ln(ln
(1/(1-
Med
ian R
ank)
))f
Fig. 6. Weibull lines for GFR3.775348 1.9744593.795069
0.9726863.900702 0.366513 1,103,609 11.8003.918763 0.1447673.972603
0.714455
Y=
4.40
4X-
49.18
Y=
2.09
2X-
26.25
5Y
=5.
981X
-80
.71
5
Y=
11.80
0X-
164.
189
1 12 13 14 15
106.728 MPa
85.336 MPa
76.264 MPa
68.895 MPa
61.954 MPa
55.751 MPa
50.257 MPaP samples in Group-A.
-
Table 4According to test results, Weibull parameters for each
stress amplitude [11]
Stress amplitude,Sa (MPa)
Characteristic life,(a) (cycle)
Shapeparameter (b)
Weibull meanlife (cycle)
Group: A203.120 1 1.000 1106.728 947 2.204 83985.336 4472 1.921
396776.268 25,270 9.008 23,93068.895 70,756 4.404 64,49061.954
282,538 2.092 250,24955.751 725,345 5.981 672,80150.257 1103 609
11.800 1,056,907
Group: B258.288 1 1.000 1116.764 917 5.112 84393.788 8204 4.015
743884.403 60,613 6.229 56,34876.105 186,720 2.730 166,11168.653
468,909 4.552 428,20161.550 779,735 5.091 716,67857.922 1,253,868
4.313 1,141,429
Group: C278.313 1 1.000 1128.039 1422 3.597 1281103.769 8184
2.533 726493.235 21,058 3.766 19,02284.152 64,604 3.797
58,38675.485 162,344 4.628 148,39268.028 351,042 2.773
312,47463.378 915,776 10.639 873,46661.221 1,262,614 9.156
1,196,578
Group: D265.468 1 1.000 1111.502 1182 1.719 105397.072 4125
1.678 368487.219 17,128 2.825 15,25778.800 44,060 3.066
39,38370.792 192,165 1.830 170,75963.757 459,053 2.674
408,09657.411 807,018 22.523 787,84853.070 1,556,050 4.324
1,416,720
Group: E353.540 1 1.000 1163.271 1233 1.864 1095129.452 5971
3.988 5412106.908 49,840 4.088 45,23196.166 269,491 2.308
238,75591.170 617,135 10.157 587,49788.734 887,796 6.363
826,28186.640 1,109,131 14.472 1,069,82284.250 1,532,755 4.910
1,405,857
Group: F375.200 1 1.000 1151.934 3195 2.532 2836123.852 9534
2.047 8446111.613 39,695 2.388 35,185100.138 216,224 4.479
197,26690.322 349,306 6.519 325,52781.316 670,939 5.040
616,31873.201 1,053,763 10.309 1,003,780
145.837 2011 1.388 1835
1176 R. Sakin, _I. Ay / Materials and D9. b and c values were
obtained by linear regressionapplication (least squares method). m
= b parameterwas obtained directly from the slope of the line.
10. a parameter was obtained from the Eq. (8)11. The mean
fatigue life corresponding to each stress
was calculated from Eq. (11), and the variation coef-cients were
calculated from Eq. (13). The dierencebetween mean fatigue life and
the variation coe-
117.274 9379 3.211 8402105.754 41,617 25.650 40,74195.132 77,664
4.330 70,71685.619 175,290 3.669 158,11776.938 384,464 4.135
349,14169.377 785,661 9.065 744,23664.270 1,595,150 6.289
1,483,682Table 4 (continued)
Stress amplitude,Sa (MPa)
Characteristic life,(a) (cycle)
Shapeparameter (b)
Weibull meanlife (cycle)
Group: G348.198 1 1.000 1147.771 1354 1.351 1241119.308 16,786
3.177 15,029107.214 51,365 2.322 45,51096.241 139,934 2.227
123,93586.771 254,726 8.218 240,19877.882 481,137 7.360
451,23573.941 1,244,927 4.278 1,132,769
Group: H311.504 1 1.000 1
esign 29 (2008) 11701181cients were given in Fig. 9.12. The
above processes were carried out in order for all
samples group and Weibull graphics and parameterswere obtained a
and b parameters obtained areshown in Table 4.
The results of the processes carried out above have
beensummarized in Table 3. Example Weibull graphics for eachstress
value has been given in Fig. 6 [11].
5. Results and discussion
5.1. The SN curves
106 cycles which is corresponding to fatigue strength hasbeen
taken into account as a failure criterion in the evalua-tion of
fatigue tests [11,13,25]. The SN curves obtained foreight dierent
average fatigue life of GFRP samples havebeen shown in Fig. 7.
Power Function has been used inEq. (15) for the evaluation of
fatigue test data [2,3,6,11,26].
Sa a N fb 15In this equation;
Sa stress amplitude (fatigue strength),
-
Nf number of cycle (fatigue life),a and b are constants (Its
given for each material group in
Fig. 7).
Fig. 7. SN curves for ei
Table 5The stress (fatigue strength) values and decrease rate in
106 cycles
R. Sakin, _I. Ay / Materials and Design 29 (2008) 11701181
1177Group Stress amplitude, Sa (MPa) Decrease rate (%)
E 84.210 37.7A 52.435F 77.022 21.7B 60.333
G 74.167 17.2C 61.400H 69.544 20.0D 55.644
Fig. 8. The relationship of stress amplitude,The eects on
fatigue strength are obtained from SNcurves for each GFRP group.
They are ber direction,weight per unit area, maximum stress values
correspondingto 106 cycles and decrease rate in maximum stress
ampli-tude values of bers having same weight per unit areabut in
dierent directions. These eects have been shownin Table 5 and Fig.
8.
We can make the following comment for the directionsof [0/90],
[45] in woven-roving composites which have800, 500, 300 and 200
g/m2 weight per unit area and havingthe same volume (Vf @ 44%) from
Table 5 and Fig. 8.
The change in fatigue strength corresponding to 106
ght dierent samples.cycles depends on ber direction and weight
per unit areacan be seen in Table 5 and Fig. 8. The strength in the
direc-tion of [0/90] is higher. On the other hand, the strength
weight per unit area and ber direction.
-
100
e L
on
nd Dhas decreased suddenly because of existing of the
shearstresses formed in weak interfaces on planes at [45]and bers
at the direction of [45] have had to carry overload nearly 1.9
times more than that of the bers at thedirection of [0/90]. Thus,
anisotropy property betweenthe samples of groups E&A is
dominant reduced fatiguestrength at the rate of 37.7%. Because of
high resin perme-ability of composite having groups E&A
woven-roving,inltrations is better but the weak matrix
cross-section isbigger than that of composite having groups
F&B, G&Cand H&D [11,27].
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1000 10000
Mean Fatigu
Coe
ffici
ent o
f Var
iatio
n, C
.V.
Fig. 9. Eect of mean fatigue life
1178 R. Sakin, _I. Ay / Materials a5.2. Scatter in the fatigue
life results
CV values for fatigue life of GFRP samples have calcu-lated by
using Eq. (13). Coecient of variation (CV)graphics which is
calculated by Eq. (11) corresponding tomean life (MTTF) has been
shown in Fig. 9. Accordingto these results, scatter in the fatigue
life values has the wid-est between 103104 and 105106. The rst
widest scatterwas observed at the life range 103104 cycles for
GFRPsamples because of the larger defects in structure at
highstress level at the beginning of test. But later, the
secondwidest scatter was observed at the life range 105106
cycles.Because, the small defects in structure reach a critical
valueat the dierent stress level. This trend for dierent
samplegroup is extremely important for the application anddesign of
GFRP structure [3].
5.3. Reliability analysis of fatigue results and bounds for
the
SN curves
The term Reliability is used for the probability of func-tional
performance of a part under current service condi-tion and in
denite time period. This also is known as theprobability of
survival [3,28]. The probability of survivalgraphics corresponding
to each stress values of GFRPsamples has been shown in Fig. 11.
These graphics havebeen drawn by using Eqs. (3) and (4). The
probability50% survival of samples from these diagrams is
inter-sected by drawing horizontal line from Y-axis, hence
theprobability can be found in which cycle value it has.For example
as shown in the diagram in Fig. 11, whilethe stress is 50.257 MPa
and failure cycles are 1069858for group-A samples, these values are
86.640 MPa and1081394 cycles for group-E samples corresponding
to
000 1000000 10000000
ife (Cycles), No
A
B
CD
E
F
GH
the coecient of variation, CV.
esign 29 (2008) 1170118150% Reliability.The bending fatigue test
results of GFRP materials
have been scattered in a great scale because of theiranisotropy
structures and semi-brittle behaviours. Safelife = Reliability is
an important parameter for design inthis type of structure.
Reliability means that a materialcan be used without failure. The
denition of reliabilityin engineering has been shown in Figs. 10
and 11. Fig. 10shows SN curves belong to several reliability levels
ofGFRP samples. As SN curves belong to average valuesfor each
sample in Fig. 7 and the curves having 50% reli-ability in Fig. 10
are closer to each other, the SN curveobtained from the average
fatigue data in scatteredposition can be accepted as 50%
reliability of survival aswell. The SN curves have been given
belonging to fourdierent safe levels (R = 0.99, R = 0.50, R =
0.368,R = 0.10) in order, in Fig. 10. These SN curves
providepossibility of prediction reliability fatigue life needed
todesigner.
6. Conclusions
In this study, the following results have beenobtained.
-
nd DR. Sakin, _I. Ay / Materials a(1) It has been observed that
the lowest fatigue strengthis in group-A, the highest fatigue
strength is ingroup-E.
Fig. 10. The SN curves for dierent reesign 29 (2008) 11701181
1179(2) The SN curves depending on mean life values for allgroups
of GFRP composites have been presented inorder practicing engineers
could nd them useful.
liable levels (ABCDEFGH).
-
nd D70%
80%
90%
100%ur
viva
l106.73 MPa85.34 MPa76.27 MPa68.90 MPa61.95 MPa55.75 MPa50.25
MPa
1180 R. Sakin, _I. Ay / Materials a(3) The most interesting
result is the fatigue strength dif-ference (37.7%) between the
samples having the sameber weight in group E&A. Generally, this
suddenstrength reduction resulting from the change of berdirection,
in GFRP samples is a very important pointthat should be taken into
account in designs [11].
0%
10%
20%
30%
40%
50%
60%
100 1000 10000 100000 1000000 10000000
100 1000 10000 100000 1000000 10000000
100 1000 10000 100000 1000000 10000000
100 1000 10000 100000 1000000 10000000
Prob
abili
ty o
f S
0%10%20%
30%40%50%60%70%80%90%
100%
Fatigue Life (Cycles), Ln(Nf)
Fatigue Life (Cycles), Ln(Nf)
Prob
abili
ty o
f Sur
viv
al
116.764 MPa93.788 MPa84.403 MPa76.105 MPa68.653 MPa61.550
MPa57.922 MPa
0%10%20%30%40%50%60%70%80%90%
100%
Fatigue Life (Cycles), Ln(Nf)
Prob
abili
ty o
f Sur
viva
l
128.039 MPa103.769 MPa93.235 MPa84.152 MPa75.485 MPa68.028
MPa63.378 MPa61.221 MPa
0%10%20%30%40%50%60%70%80%90%
100%
Fatigue Life (Cycles), Ln(Nf)
Prob
abili
ty o
f Sur
viva
l
111.502 MPa97.072 MPa87.219 MPa78.800 MPa70.792 MPa63.757
MPa57.411 MPa53.070 MPa
Fig. 11. Probability of survival g70%
80%90%
100%
rviv
al
163.271 MPa129.452 MPa106.908 MPa96.166 MPa91.170 MPa88.734
MPa86.640 MPa84.250 MPa
esign 29 (2008) 11701181(4) As group E&A specimens have more
resin permeabil-ity, fatigue data distribution of these samples
haveless scattering because of full inltration duringRTM. The group
H&D specimens having less resinpermeability and incomplete
inltration have thewidest scatter in life values under the high
stress.
100 1000 10000 100000 1000000 10000000
100 1000 10000 100000 1000000 10000000
0%
10%20%
30%40%
50%
60%
100 1000 10000 100000 1000000 10000000Fatigue Life (Cycles),
Ln(Nf)
Prob
abili
ty o
f Su
0%
10%
20%30%
40%
50%
60%
70%
80%
90%
100%
100 1000 10000 100000 1000000 10000000Fatigue Life (Cycles),
Ln(Nf)
Prob
abili
ty o
f Sur
viva
l
151.934 MPa123.852 MPa111.613 MPa100.138 MPa90.322 MPa81.316
MPa73.201 MPa
0%10%20%30%40%50%60%70%
80%90%
100%
Fatigue Life (Cycles), Ln(Nf)
Prob
abili
ty o
f Sur
viva
l
147.771 MPa119.308 MPa107.214 MPa96.241 MPa86.771 MPa77.882
MPa73.941 MPa
0%
10%20%
30%40%
50%60%70%
80%90%
100%
Fatigue Life (Cycles), Ln(Nf)
Prob
abili
ty o
f Sur
viva
l
145.837 MPa117.274 MPa105.754 MPa95.132 MPa85.619 MPa76.938
MPa69.377 MPa64.270 MPa
raphs for GFRP specimens.
-
Also, they showed sudden fracture behaviors. Thiscriteria is
extremely important in high stress andlow cycle processes.
(5) The scatter value in all sample groups has been
[8] Lin SH, Ma CCM, Tai NH. Long ber reinforced polyamide
andpolycarbonate composites. II: Fatigue behavior and
morphologicalproperty. J Vinyl Addit Technol 2004;2(1):806.
R. Sakin, _I. Ay / Materials and Design 29 (2008) 11701181
1181decreased in about 106 cycles taken as a failure crite-rion and
the scatter values have been closer to eachother. This result is
useful for designers because ofthe accuracy and exact repeatability
of the test inabout 106 cycles.
(6) Safe design life for brittle structured composites hasgreat
importance. SN curves for reliability levels asR = 0.99, R = 0.50,
R = 0.368, and R = 0.10 havebeen drawn and presented for designers.
These dia-grams can be considered as reliability or safety limitsin
identication of the rst failure time of a compo-nent under any
stress amplitude. Especially, the usageof SN curves (R = 0.99)
should be advised in thedesign of air-craft which have to have
higher safetyand reliability.
(7) Fatigue life distribution diagrams have been obtainedby
using two-parameter Weibull distribution functionfor GFRP
composites. The reliability percentage (%)can be found easily
corresponding to any life (cycle)or stress amplitude from these
diagrams.
Acknowledgements
The study has been partly granted by Unit of ScienticResearch
Projects in Balkesir University. Besides, theauthors thank
Fibroteks Woven Co. and Glass-Fiber Co.(Sisecam) for their material
and workmanship support.
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Statistical analysis of bending fatigue life data using Weibull
distribution in glass-fiber reinforced polyester
compositesIntroductionExperimental procedureMaterials and test
specimens
Fatigue testsStatical analysis of fatigue life dataTheory of
Weibull distributionApplication of Weibull distribution
Results and discussionThe S-N curvesScatter in the fatigue life
resultsReliability analysis of fatigue results and bounds for the
S-N curves
ConclusionsAcknowledgementsReferences