IntJ FatiguelO No
3 (1988) pp 171-177
The Strength-Life Equal Rank
Assumption and its application to
the fatigue life prediction of
composite materials
P. M. Barnard, R. J. Butler and P. T. Curtis
The authors have re-examined the Strength-Life Equal Rank Assumption (SLERA)
that is used in the fatigue life prediction of composite materials, and suggest that
this assumption may be valid for a wide range of fibre-reinforced epoxy laminates
subjected to tensile, compressive or shear fatigue Ioadings. The evidence presented
here suggests that there may be an exact correlation between the initial static strength
and fatigue life expectancy. A corollary is that scatter in the fatigue data is a consequence
of the variation in the static strengths of individual specimens. Using SLERA, an efficient
and usable life predictive technique has been developed for fibre-reinforced composite
materials.
Key words: fatigue; fatigue life prediction; composite materials; Strength-Life Equal
Rank Assumption (SLERA)
Introduction
S c a t t e r in f a t i g u e d a t a
The possibility of a correlation between the static strength
and fatigue life distributions for composite materials was
first suggested by Hahn and Kim, 1 though the Strength-Life
Equal Rank Assumption (SLERA) was named by Chou and
Croman. 2 The SLERA states that if a sample of components
could be tested for both static strength and fatigue life
expectancy, each individual member would occupy the same
rank in both the strength and life data sets. The SLERA
is normally expressed in a form that lends itself to usage
in the life prediction of composite materials, that is, for
a given sample, the statically strongest members would have
the longest fatigue life expectancy.
The SLERA, though potentially very powerful, has
not found wide support in the literature for two main reasons;
first, it cannot be proved; secondly, it is argued that SLERA
carmot be applied to notched specimens because their
s~rength increases during fatigue, see Fig. 1, and therefore
the life expectancy would also increase, which is contrary
to engineering intuition.
The evidence presented in the subsequent sections of
this paper will provide conclusive evidence for the validity
of the SLERA. The argument that notched specimens invalidate the SLERA is false, because SLERA makes no assumption about residual properties. The SLERA states that there
is a correlation between the static strength and the fatigue
life expectancy of a sample of nominally identical components. As the fatigue life progresses, the strength of each
component changes. For each component at a given cyclic
life there is still a correlation between residual strength and
residual life expectancy, but the correlation need not be the
same as the initial one.
The scatter in fatigue data has two components, a fatigue
component and a static one: 4 The fatigue component is
induced by variations in the propagation rates associated
with the fatigue failure mechanisms. The static component
is due to the variation in static strengths of the sample
members under test, and may be visualized by taking a
hypothetical SIN curve, Fig. 2. Take a set of specimens
with static strengths that range from 500 to 1000 MPa, with
a mean of 750 MPa, that are fatigue tested at 600 MPa.
Specimens that have a strength less than 600 MPa will fail
~ 600 ~"
[]
~
~
%
~_50o
300
-I
×(2)* - ~
a
I
I
I
I
I
~
~.
0
I
2
3
4
5
6
, I
7
Log cycles to foilure
Fig. 1 Variation of residual =rength with number of fatigue c y c l ~
for carbon f i b r e / e p o ~ ( 0 , ~ ) T ~ / 9 1 4
laminate: + is plain nonwoven; D is centre-notched n o n - w o v e n ; x is plain w o v e n and
0 is centre-notched w o v e n ~
0142-1123/88/030171-07 $3.00 © 1988 Butterworth & Co (Publishers) Ltd
Int J Fatigue July 1988
17/
Coupon strength
5oo M
I000" Ml=k:l
----_
v 60(3
%
Specimen strength (MPo) 500
750
I000
~
N ( cycles )
20%, and from Fig. 3 t h e life expectancy range would be
n3 to n4. It can b e seen that as the applied stress decreases
the fatigue scatter bands decrease, ie the shape-function,
which is a measure of the spread of a distribution, is
dependent upon the stress level.
The shape function is not only a function o f the stress
level, but is also a function of the slope of the S i N curve.
For a fixed sample at a freed stress level, the scatter bands
are larger for a shallow SIN curve than for a steep one,
which is particularly important for nonlinear SIN curves.
For example at the 600 MPa stress level, see Fig. 3, as the
SIN curve gets steeper, so the life expectancy range changes
f r o m n a "-~ tt2 tO n 5 - - ~ n 6.
Estimation of the static c o m p o n e n t of
f a t i g u e scatter
Fig. 2 HypotheticalS/Ncurve
on loading, .that is they are effectively tested at 100% of
their strength. Progressively stronger specimens are-effectively tested at lower percentages of their ultimate strength,
thus specimens with a strength of 1000 MPa are tested at
60% of their strength, and consequendy have longer fatigue
life expectancies than weaker specimens. The SLERA will
only apply if the fatigue component of the fatigue scatter
is negligible, or else is some function of the static component.
The SLERA states that the stronger the specimen, the
longer the life expectancy. As a result an exact correlation
exists between strength and life expectancy. In addition the
SLERA~ implies that the life expectancy is a function of
the appli-~d load, therefore the lower the applied stress-the
longer the fatigue life. This effectively defines the SIgN
(stress-life) curve, therefore the SLER_A and the SIN curve
are essentially the same.
If the applied stress is plotted as a function of specimen
strength, the SIN curve may be envisaged as the applied
stress-life expectancy relationship. Then .at a f~xed applied
stress~ each specimen in a sample will be tested at different
percentages of its static strength, and its fatigue life expectancy can be estimated from the X/N curve. For example,
let the range of strengths in th~ sample be 800-1000 MPa
and the applied stress level be 600 MPa; the applied stress
as a function of specimen strength thus ranges from 75 to
65%. From Fig. 3 this would result in a corresponding
life expectancy range of n 1 to nz.
If the applied stress level had been 200 MPa, the applied
stress as a function of specimen strength would be 25 to
The technique
The SLERA states that there is a correlation between the
static distribution f(6) and the life distribution fin), where.
f ( ) is the probability density function of stress or life. The
cumulative functions P(o) and P(n) are similarly correlated.
Most authors (eg References 1 and 2) have assumed a direct
correlation between the cumulative functions, ie P(cr) =
P(n). In the present study such a correlation has not been
assumed, and it is suggested that f(o) = g[f(n)] and P(o)
= b[P(n)], whereg and b are some function of the bracketed
terms. The present authors suggest that the functional relationship between the probability density functions is the gIN
curve, where S is the applied stress and N is the mean
cycles to failure. If the applied stress is expressed as a percentage of the individual specimen strength, and a generalized
SIN curve is used, the correlation is given by
IOOS _ a (log (n) + c)b + d
where a, b, c and d are constants, S is the applied stress,
o is the specimen strength and n is the specimen life. (Note
ff e or d = 0 and b = 1 this reduces to a log-linear relationship).
Since this relationship is for an individual specimen,
any quantile of the static distribution may be used to obtain
the corresponding life quantile, and the relationship may
be rewritten as
100S _ a(log (np) + c) b + d
%
I00
where p denotes the percentile (/e p = 1,2,...99). It should
be noted thatp/100 = P(xp), where x = ~ or n.
If it is assumed that the fatigue distribution is a twoparameter We]bull distribution then
P(n,)
~
(1)
=1-expE - ',"'/(n'Y~'l
50
-~
m
25
0
n I /75
n6
nz
n3
r/4
Cycles
Fig. 3 Dependency of fatigue scatter upon the applied stress level
and slope of the SIN curve
172
where I]~is the shape parameter and ~1~is the scale parameter.
For the present, it is assumed that the SIN constants a,
b, c and d are known, and that the static distribution is
also known. Then for any stress level, by choosing any
two values of ~0, the corresponding n~0values can be found
by using Equation (1), and consequently the values of lie
and ~le Let the subscripts y and z denote the first and second
n~ values, then
P(n~,) = 1 - exp
[ -
\ fir/
d
Int J Eatigue July 1988
and P(n~) = 1
- exp[ -
ooo ..
(\ ~n r' Y) r l ]
Therefore
I-logO- P(.0) l
,
=
'°gbo
1
. . . . .
m))J
~aoo~-~.~
~
and
1
~l~ = ( _ log[1 - P(ny)])tmf = ( - log[1 - P(n3]) amf
The values of ~ and ~le are for the static component
of the fatigue scatter. Thus from a known SIN curve, the
amount of scatter as a direct result of the variations in static
strength can be calculated using these ~f and llf values.
The probability of surviving n: cycles is the combined
probability of having a strength greater than the applied
load plus the probability of having a life expectancy of greater
than n:. Assuming that the static distribution is also a twoparameter Weibull distribution, the probability of failure at
or before n: is given by
P(n,)
=I
-
exp[
- (nP~ ~f -
\nd
,
102
103
,
104
105
106
107
108
N (cycles)
Fig. 5 Experimental data and the 1 and 99 percentile curves for
the static component of fatigue scatter for a 58% fibre volume fraction
[(0,90 + 45)a], carbon/epoxy laminate under compressive loading
25
('Y'l
\~] J
(3)
where ~, and ~l, are the shape and scale parameters of the
static distribution and the values for fl~ and ~]e have been
calculated as above. The life percentiles are therefore given
by
(.s~,]~l~
~, ~ ~{-logO - ~ , ~ - ~ ] ~
i'1
¢ X
×
X
XX
X
~ z(
_~
15
IO
Experimental verification
The 1 and 99 percentile curves of the static component of
fatigue scatter have been determined for a number of unidirectional, crossply and quasi-isotropic 'E'-glass and XAS carbon-fibre-reinforced epoxy laminates subjected to constant
amplitude tension-tension, compression-compression and
shear-shear fadgue loading. A representative sample of these
curves are given in Figs 4 to 6. A full description of material
and experimental details and test results for tension and compression loadings may be found in Reference 4, and for
the shear in Reference 5. For all the laminates tested, there
is a good correlation between the experimental fatigue dam
and the I and 99 percentile scatter bands estimated from
the static data and the XIN curve as described above.
10z
~o~
=04
io5
~o6
=ov
~o8
N (cycles)
Fig. 6 Experimental data and the 1 and 99 percentile curves for
the static component of fatigue scatter for a 58% fibre volume fraction
(0), carbon/epoxy laminate under shear loading
It would appear that for fibre-reinforced epoxy
laminates, the scatter in the fatigue data may be a direct
consequence of variations in the static strength, ie there is
no fatigue component. If there were a fatigue component,
the experimental fatigue scatter bands should be greater than
those for the static component alone. These findings strongly
support the validity of the SLERA for the materials under
investigation.
I000
900
800
~,,,~
Fatigue life prediction using the SLERA
x~ XX ~
Case1 : $ / N c u r v e is known (lea, b, cand d
are known)
~ 700
~ 600
~ 50C
400
3o0
I
103
104
I
I
105
106
107
N (cycles)
Fig. 4 Experimental data and the 1 and 99 percentile curves for
the static component of fatigue scatter for a 57% fibre volume fraction
(0ha 'E'-glass/epoxy laminate under tensile loading
Int J F a t i g u e J u l y 1988
Assume that the SIN fatigue curve has been developed previously together with the static strength distribution, for a
batch of a certain material. If static tests on a new batch
of the same material reveal a different strength to that measured on the initial batch, the fatigue life expectancy of the
new batch may be determined as follows. It will be assumed
that the static distribution of the new batch has been characterized by the static tests, ie ]3, and ~1, are known, therefore
% and P(%) can be calculated. From Equation 1 if % =
vh then
IOOS
qs
= a (log 01r) + c) + d
173
Therefore
/fF100s
n, :
@1- c)
(4)
Case 2:
From Equation (2)
• [log0 ~r = tOgLlog(1
predicted 1 and 99 percentile curves, are shown in Fig. 7.
It can be seen that the prediction shows a good correlation
with the experimental data.
$/N curve u n k n o w n
This is often the case for a new material or component
for which no previous data are available. The question often
asked is what safe fatigue Life expectancy can we expect
for this material/component before any service experience
is available? To answer this question the
and
the distributional form of the life expectancy need to be
known.
The main object of Life prediction is to extrapolate data
generated in laboratory environments to service environments. Without any further information, the safest way to
do this is to assume either a linear or log-linear extrapolation.
Therefore, if the
curve is assumed to be log-Linear,
k b = 1 and d = 0, conservative estimates of the life
expectancy will be made. If we assume that the SLERA
applies, and that the fatigue distribution is a two-parameter
Weibull distribution, it follows from Equations (3) and (4),
as shown in the previous example, that
l
P(n,))J l°g (n~)
SIN curve
but
l
[log0 - P(nz))]= A
°gL og(1
where _/t is a constant. Therefore
A
~f
~
SIN
A
m
log(n - log(n,,
From Equation (1)
Hz xpF '['°°s d)}lID- c]
S = mlog ('qr) + c and S
=
Pf
Fatigue testing at two stress levels thus allows the constants
and A to be evaluated, and consequently vlf
and ~3f values at all stress levels allowing the generation
of
(probability-stress-life) curves. By using Equation
(1) the static distribution parameters vh and 13s can also be
estimated.
m, ¢
Therefore
I r=
.4
-
A
(IOOS {)'/o_ (IOOS ~)'/~
(5)
\
It can be seen that the only unknowns in Equations (4)
and (5) are rlf and ~f. Therefore, the rlf and ~f values as
a function of S can be determined.
Example of process
Fatigue data on a [(0,90, 4- 45)2], laminate of Ciba Giegy's
XAS/914 have been generated by Chung. 6 Subsequent work
by the present authors indicated that the static strength of
a supposedly identical laminate was 25% greater than that
of Chung's. This increase was attributed to increases in fibre
strengths that occurred during the time that elapsed between
the two sets of work. 7 Using Chung's data and the static
distribution o f the new material, the fatigue distribution of
the new material could be estimated. The constants for the
relationship from Chung's work were a --4.75694541, b = 1, c = -27.0209935 and d -- 0. This
is a log-linear
curve given by
P-S-N
Example of process
Nineteen specimens manufactured from a material, which
was later identified as the ICI APC2 material (carbon-fibrereinforced poly ether ether ketone), were supplied by one
of the authors (PTC). The object was to identify the full
tensile static and fatigue distributions of this material, including the 1 and 99 percentiles, from the nineteen specimens.
One of the specimens was statically tested to give art
indication of the mean tensile strength, so that appropriate
fatigue stress levels could be chosen. Two samples of 8
specimens were fatigue tested at 60% and 40% of the strength
of the statically tested specimen. The final two specimens
70(
o ChungIs]
x Presentwork
~ x
SIN
×
SIN
~
100S
%
-
128.537391 - 4.75694541 log(np)
For the new material ~ls = 700.89 and ~, = 34.33,
and the corresponding 1 and 99 percentiles are ~l = 613
and o99 = 732.78. From Equation (4)
x
x x ~
g_
~ 50C
~
o
. . . . . ~ × × ×7 ~
qf = exp( 27.0209935 - 0.02999330
from Equation (5)
1093.07291
~f-
S
The ~lf and ~f values as a function of S can therefore
be calculated, as can the corresponding n~ values from
Equation (3). The Chung and new data, including the
174
. . . . .
$0(
I0 ~
I
104
I
105
I
106
%~ ~
107
~
I0 8
N (cycles)
Fig. 7 Chung's s and the pre~nt authors" experimental data for a
~ % fibre volume fraction [0,~, • 45)=], carbon/epo~ laminate
under tensile loading and the 1 and 99 percentile c u ~ for the
static component of fatigue sca~er for the authors" material predict~
from Chung's data
Int J F a t i g u e J u l y 1 9 8 8
were used to verify the prediction. A fuU description o f
material and experimental details and test results may be
found in Reference 4.
The tensile strength of the single specimen was 2054
MPa. The two fatigue stress levels were therefore 1232.4
and 821.6 MPa. The resulting fatigue data were rl~0) =
11 390, ~f(60) = 0.25, ~lf(~0) = 6061 510 and ~f(~0) = 0.67.
To evaluate the constant A , the ~f value at the lowe~ stress
was chosen. This was because it is advisable to use data
that have been generated at stress levels below the influence
of the static distribution.
80
70
~ 6O
.1:::
so
N
.~
i1~
4o
.~
~ ~0
20
I0
A = 821.6 x 0.67 = 550.472
i03
Therefore
550.472
S-
(6)
I
I
I
I
I
I04
i05
]06
i07
i08
,I
I09
gf
Fig. 9 Predicted Weibull scale parameter vs applied stress for a 60%
fibre volume fraction (0)1= carbon/PEEK laminate under tensile
loading
Also
S = m l o g 01f) + c
~
75
1232.4 = m l o g (11 390) + c
and
- 25
'l
821.6 = m l o g (6061 510) + c
x
x
Therefore
4o
m = - 6 5 . 4 4 5 5 a n d c = 1843.6931
~ 5o
Thus
(7)
~ ~o
The values o f ~e and ]If as a function o f applied stress are
shown in Figs 8 and 9. The resulting P - S - N curves and
experimental data are shown in Fig. 10. In this case, the
P - S - N curves do not include the conditional probability
that the strength is greater than the applied stress.
I0
S = - 6 5 . 4 4 5 5 l o g 0if) + 1843.6931
Estimation of static distribution
From Figs 10 and 11 it can be seen that the Weibull mean
SIN curve is nonlinear at such low values of the slope function, and is not representative of the fatigue population.
It is suggested that the median S/N curve should be used
as the strength-life correlation, and will be used in this
section. The procedure is outlined as follows:
I
I0 3
~0 2
I
~0 4
I
{O 5
I
tO 6
I
~0 7
10 8
N (cycles)
Fig, 10 Experimental data and predicted P - S - N curves for a 60%
fibre volume fraction (0)1= carbon/PEEK laminate under tensile
loading
IO0
90
70
Estimate the median SIN curve from the life parameters
estimated from Equations (6) and (7). Since the median
•
o~ 60
-~
E 50
90
~
8O
~0
~
70
2O
"~ 60
I0
f
0
"~ ,50
Asymptotic approach of mean to = 43%
I
I
I
I
I
I
I
I
I
I
I
I
I
2
3
4
5
6
7
8
9
I0
~1
I?-
P
Fig. 11 Mean and median of the Weibull distribution as a function
of percentage of the population vs shape parameter
~ 4o
.g
~
Median
Mean
$0
20
1C
I
0.2
I
I
0.6
I
I
1.0
I
I
1.4
~
1.8
2.2
I~f
Fig. 8 Predicted Weibull shape parameter vs applied stress for a
6 ~ fibre volume fraction (0)1= carbon/PEEK laminate under tensile
loading
Int J Fatigue July 1988
SIN curve is logslinear, only two stress levels are
required. At 1500 MPa, 13f = 0.367 and rlf = 191.
Therefore nso = 70. A t 500 MPa, I~f = 1.101 and
vie = 825 485 225. Therefore nso = 591 748 000.
1500 = mlog (70) + c
500 = mlog (591 748 000) + c
175
2.25
900'
-
002.00 -
. . . . . . -~,o~,~ • •
~ ~t~ ~ ~ , , ~
800
90-
i
I .75 -
~
o~ 1.S0- "~70
,
tO
•
~
•
22pts
II °~
e e ~~1
~
•
700
80-
o~
= ~.
<'
600
I~
._.E
~:}
&
•
~
.
m
1.25 -
~=
I t~.
I
2 p t s ~
QI
2
~ 5oo
~ 5o
71~'l"T •
224 2 2 p t ~ , , ~
"
40O
1.00 -
° t - - ' ° %~.
~s
40
0.75 -
I
~00
30.-
102
I
103
I
104
I
105
/V (cycles)
I
106
I
io 7
io 8
Fig. 12 Experimental data for a 45% fibre volume fraction (0)~= "E'-glass/epoxy laminate under tensile loading
.
-
Thus
m = -62.6955 and c = 1766.362
The median SIN curve is therefore given by
S = 1766.362 - 62.6955 log (n)
*
•
•
Calculate the 1 and 99 life percentiles at any stress level.
Let S = 1027 MPa, then ~ - 0.536 and ~lf = 265 756.
Therefore n~ = 49 and n99 = 4 538 900.
F r o m the median curve calculate the stress level, applied
to an average specimen, that would result in these lives:
S~1 = 1766.362 - 62.6955 log (49) = 1522.36 MPa
S~9 = 1766.362 - 62.6955 log (4 538 900) = 805.35 MPa
Calculate the percentage ratio o f S, to the single static
strength:
%S~ = 1522.36 x 100/2054 = 74.17%
%S~ 9 = 805.35 x 100/2054 = 39.21%
•
Using the cumulative distribution, the strength distributional parameters can be estimated, and are listed below
with some experimental data in brackets. The experimental
data were provided at a subsequent date by one o f the authors
(PTC).
p, = 9.63 (14.17)
vl~ = 2234.01 (2049.07)
p. = 2124.32 (1975.48)
~ = 259.70 (169.49)
c.v. = 12.23% (8.58)
estimated statistics are estithe experimental statistics
size o f 20. It can be seen
between the estimated and
Some limitations of the SLERA
The main limitation of the S L E R A is that it cannot predict
a change in fatigue failure mode as a function o f the stress
level. Dhar,an9 suggested that for 'E'-glass/epoxy under
tensile loadiag the dominant failure mechanism is a function
o f applied strain. Bamard et all° found that such a change
in failure mechanism may lead to a discontinuity in the SIN
curve, see Fig. 12. The S L E R A appears to be valid above
and below this discontinuity though the correlation between
strerigth and life is different, s Unless a change in failure
mode increases the slope o f the SIN curve the S L E R A will
provide conservative estimates, see Fig. 13.
A specimen tested at a fatigue stress level of 74.17%
of its strength would thus have a life expectancy of
49 cycles, and at 39.21% an expectancy o f 4 538 900.
The corresponding strength percentiles may be calculated from the applied stress level:
~t = 1027 x 100/74.17 = 1384.66 M P a
~9~ = 1027 x 100/39.21 = 2619.23 MPa
176
It should be noted that the
mates of the population, while
were calculated using a sample
that there is a good correlation
experimental values.
IOOC
90C
80~
~
~
2
~ 70C
n°
2pts
22p~s
I 1 ~ °'"
*~
~,
~
~
"'~...
~ ~OC
~
~
~
~
~
"-.
~, ~o~
××x
"~pts~
V~-~
~ ~~
~
~ " ~ #s
x ~x
~
x.~...x=~
~
~...~..~.
.~=
2p~
... ~
40¢
~...
x
~.2
~
Ors
, ,
x~,~x
30C
?-pts
20C
t
]02
10`3
I
I
I
IO4
105
N (cycles)
106
I
107
i08
Fig. 13 1 and 99 percentile curves for the static component of fatigue
scatter for the data in Fig. 12 predicted from the data in Fig. 4
Int J F a t i g u e J u l y 1 9 8 8
The SLERA cannot predict the residual strength,
though some researchers have attempted to do so, eg Chou
and Croman. 2 Chou and Croman assumed that the locus
of the residual strength quantile was equal to the combined
relevant static and fatigue quantiles, ie
n,/
=(57'\n4
\nO \7 j
where R is the residual strength and b is an experimentally
derived parameter that indicates the rate of degradation with
respect to fatigue cracks. Chou and Croman found that for
values of 13 greater than 1 the degradation is weak, and
for values less than 1 the degradation is strong. The present
authors have found that if a value of b = 1 is used in
conjunction with the rl~ and ~f values, as calculated above,
then for all the laminates investigated the residual strength
predictions have a good correlation with experimental data.
Full details of the shear residual strength predictions can
be found in Reference 5, and the tensile and compressive
residual strength predictions can be found in Reference 4.
If the laminate is. notched the residual strengths predicted
using the model of Chou and Croman will be conservative.
Therefore the authors recommend that if residual strength
predictions are required a value of b = 1 should be used.
Therefore
"
=
-
1¢0 J
S-N
2)
The SLERA appears to be valid for a wide range of
fibre-reinforced plastic laminates, provided there is no
change in failure mode with fatigue life.
The SLERA is a definition of the SIN curve, therefore
the correlation between the strength and life is the SIN
Curve.
3)
4)
5)
Scatter in fatigue data is primarily due to static strength
variations, though additional scatter may occur in the
region of a failure mode change.
The scatter is a function of the applied stress, thus
the lower the stress the lower the scatter; and is an
inverse function of the slope of the S/N curve, thus
the greater the slope the lower the scatter.
A technique for predicting the static, fatigue and residual strength distributions from a small sample size
has been suggested. This small sample size may allow
testing of components without the prior requirement
of laboratory specimen and scale model testing. This
technique: can be easily computerized so that from input
data comprising one static result and perhaps two sets
of eight: fatigue results, the output data would be the
static digtribution parameters, P-S-N curves and P(R)-
Int J Fatigue July 1 9 8 8
of residual
strength-stress-life)
Acknowledgements
The authors would like to thank the technical staff at the
Cranfield Institute of Technology, and in particular Messrs
M. Crook, S. Gowans, M. Jones and M. Williams, for the
excellent technical services provided. This work has been
carried out with the support of the Procurement Executive
of the UK Ministry of Defence.
References
1.
2.
3.
4.
Hahn, H. "r. and Kim, R. Y. 'Proof testing of composite
materials' J Comp Mater9 (1975) pp 297-311
Chou, P. C. and Croman, R. 'Residual strength in fatigue
based on the Strength Life Equal Rank Assumption" ibid 12
(1978) pp 177-194
Curtis, P. T. and Moore, B. B. "A comparison of the fatigue
performance of woven and non-woven CFRP laminate' RAETR 85059 (1985)
Barnard, P. M. and Young, J. B. 'Cumulative fatigue and
life prediction of fibre composites: Final report" Report on
RAE Famborough Contract No. 11494/2028-0134 XR/MAT
(1983)
5.
Barnard, P. M. and Young, J. B. 'Shear fatigue life
prediction of fibre composites: Final report' Report on RAE
Farnborough Contract No. 11494/2028-0138 XR/MA T ( 1987 )
6.
Chung, K. M. "Cumulative fatigue and life prediction of
carbon fibre reinforced laminates" MSc thesis (Cranfield
Institute of Technology, England, 1982)
7.
Anon. Private communication (Ciba-Geigy Plastics and
Additives Company, Duxford, England)
8.
Barnard, P. M , "Cumulative fatigue and life prediction of
unidirectiona!ly reinforced 'E'-Glass/Epoxy laminates' PhD
thesis (Cranfield Institute of Technology, England, 1986)
9.
Dharan, C. K. 'Fatigue failure mechanisms in a unidirectionally reinforced composite material' Fatigue of Composite
Materials, ASTM STP 569 (American Society for Testing and
Materials, 1975)
10.
Barnard, P. M., Butler, R. J. and Curtis, P. T. 'Fatigue
scatter of unidirectional 'E'-Glass/Epoxy a fact or fiction?" in
Composite Structure 3, I. H. Marshall (ed) (Elsevier Applied
Science Publishers, 1985)
Conclusions
1)
(probability
curves.
Authors
i
Dr Barnard was formerly with the Cranfield Institute of
Technology and is now with the New Products Division
of Ruston Gas Turbines Ltd, Lincoln, UK. Mr Butler is
with Analysis & Design Consultants Ltd, Newport Pagnell,
UK and Dr Curtis is with the Materials & Structures Department of the Royal Aircraft Estabfishment, Famborough, UK.
177