IEC TR 62048:2011

IEC/TR 62048 ®
Edition 2.0 2011-05
TECHNICAL
REPORT
colour
inside
Optical fibres – Reliability – Power law theory

IEC/TR 62048:2011(E)
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IEC/TR 62048 ®
Edition 2.0 2011-05
TECHNICAL
REPORT
colour
inside
Optical fibres – Reliability – Power law theory

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
PRICE CODE
XB
ICS 33.180.10 ISBN 978-2-88912-481-7

– 2 – TR 62048  IEC:2011(E)
CONTENTS
FOREWORD . 5
1 Scope . 7
2 Symbols . 7
3 General approach . 7
4 Formula types . 10
5 Measuring parameters for fibre reliability . 11
5.1 General . 11
5.2 Length and equivalent length . 11
5.3 Reliability parameters . 12
5.3.1 Prooftesting . 12
5.3.2 Static fatigue . 12
5.3.3 Dynamic fatigue . 13
5.4 Parameters for the low-strength region . 13
5.4.1 Variable prooftest stress . 13
5.4.2 Dynamic fatigue . 14
5.5 Measured numerical values . 16
6 Examples of numerical calculations . 17
6.1 General . 17
6.2 Failure rate calculations . 17
6.2.1 FIT rate formulae . 17
6.2.2 Long lengths in tension . 18
6.2.3 Short lengths in uniform bending . 19
6.3 Lifetime calculations . 22
6.3.1 Lifetime formulae . 22
6.3.2 Long lengths in tension . 22
6.3.3 Short lengths in uniform bending . 23
6.3.4 Short lengths with uniform bending and tension . 25
7 Fibre weakening and failure . 27
7.1 Crack growth and weakening . 27
7.2 Crack fracture . 29
7.3 Features of the general results . 30
7.4 Stress and strain . 30
8 Fatigue testing . 31
8.1 Static fatigue . 31
8.2 Dynamic fatigue . 33
8.2.1 Fatigue to breakage . 33
8.2.2 Fatigue to a maximum stress . 34
8.3 Comparisons of static and dynamic fatigue . 35
8.3.1 Intercepts and parameters obtained . 35
8.3.2 Time duration . 35
8.3.3 Dynamic and inert strengths . 36
8.3.4 Plot non-linearities . 36
8.3.5 Environments . 37
9 Prooftesting . 37
9.1 General . 37
9.2 The prooftest cycle . 37

TR 62048  IEC:2011(E) – 3 –
9.3 Crack weakening during prooftesting . 38
9.4 Minimum strength after prooftesting . 39
9.4.1 Fast unloading . 39
9.4.2 Slow unloading . 40
9.4.3 Boundary condition . 41
9.5 Varying the prooftest stress . 41
10 Weibull probability . 41
10.1 General . 41
10.2 Strength statistics in uniform tension . 42
10.2.1 Unimodal probability distribution . 42
10.2.2 Bimodal probability distribution . 43
10.3 Strength statistics in other geometries . 44
10.3.1 Stress non-uniformity . 44
10.3.2 Uniform bending . 44
10.3.3 Two-point bending . 45
10.4 Weibull static fatigue before prooftesting . 45
10.5 Weibull dynamic fatigue before prooftesting . 47
10.6 Weibull after prooftesting . 49
10.7 Weibull static fatigue after prooftesting . 52
10.8 Weibull dynamic fatigue after prooftesting . 53
11 Reliability prediction . 54
11.1 Reliability under general stress and constant stress . 54
11.2 Lifetime and failure rate from fatigue testing . 55
11.3 Certain survivability after prooftesting . 56
11.4 Failures in time . 57
12 B-value: elimination from formulae, and measurements . 58
12.1 General . 58
12.2 Approximate Weibull distribution after prooftesting . 58
12.2.1 "Risky region" during prooftesting . 58
12.2.2 Other approximations . 59
12.3 Approximate lifetime and failure rate . 61
12.4 Estimation of the B-value . 62
12.4.1 Fatigue intercepts . 62
12.4.2 Dynamic failure stress . 62
12.4.3 Obtaining the strength . 62
12.4.4 Stress pulse measurement . 63
12.4.5 Flaw growth measurement . 63
13 References . 63

Figure 1 – Weibull dynamic fatigue plot near the prooftest stress level. 15
Figure 2 – Instantaneous FIT rates per fibre km versus time for applied stress/prooftest
stress percentages (bottom to top): 10 %, 15 %, 20 %, 25 %, 30 % . 18
Figure 3 – Averaged FIT rates per fibre km versus time for applied stress/prooftest
stress percentages (bottom to top): 10 %, 15 %, 20 %, 25 %, 30 % . 19
Figure 4 – Instantaneous FIT rates per bent fibre metre versus time . 20
Figure 5 – Averaged FIT rates per bent fibre metre versus time for bend diameters
(top to bottom): 10 mm, 20 mm, 30 mm, 40 mm, 50 mm . 21

– 4 – TR 62048  IEC:2011(E)
Figure 6 – 1-km lifetime versus failure probability for applied stress/prooftest stress
percentages (top to bottom): 10 %, 15 %, 20 %, 25 %, 30 % . 23
Figure 7 – Lifetimes per bent fibre metre versus failure probability for bend diameters
(bottom-right to top-left): 10 mm, 20 mm, 30 mm, 40 mm, 50 mm . 24
Figure 8 – Static fatigue: applied stress versus time for a particular applied stress . 32
Figure 9 – Static fatigue: schematic data of failure time versus applied stress . 32
Figure 10 – Dynamic fatigue: applied stress versus time for a particular applied stress rate . 33
Figure 11 – Dynamic fatigue: schematic data of failure time versus applied stress rate . 34
Figure 12 – Prooftesting: applied stress versus time . 38
Figure 13 – Static fatigue schematic Weibull plot . 47
Figure 14 – Dynamic fatigue schematic Weibull plot. 48

Table 1 – Symbols . 7
Table 2 – FIT rates of Figures 2 and 3 at various times . 19
Table 3 – FIT rates of Figures 4 and 5 at various times . 21
Table 4 – FIT rates of Table 3 neglecting stress versus strain non-linearity . 22
Table 5 – One kilometer lifetimes of Figure 6 for various failure probabilities . 24
Table 6 – One-meter lifetimes of Figure 7 for various failure probabilities . 25
Table 7 – Lifetimes of Table 6 neglecting stress versus strain non-linearity . 25
Table 8 – Bend plus 30 % of proof test tension for 30 years . 26

TR 62048  IEC:2011(E) – 5 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
OPTICAL FIBRES –
Reliability – Power law theory

FOREWORD
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The main task of IEC technical committees is to prepare International Standards. However, a
technical committee may propose the publication of a technical report when it has collected
data of a different kind from that which is normally published as an International Standard, for
example "state of the art".
IEC 62048, which is a technical report, has been prepared by subcommittee 86A: Fibres and
cables, of IEC technical committee 86: Fibre optics.
This second edition cancels and replaces the first edition published in 2002, and constitutes a
technical revision. The main changes with respect to the previous edition are listed below:
– correction to the FIT equation in addition to all call-outs and derivations;
– insertion of a new section explaining how to numerically calculate bends and tension;
– editorial corrections of inconsistencies.

– 6 – TR 62048  IEC:2011(E)
The text of this technical report is based on the following documents:
Enquiry draft Report on voting
86A/1357/DTR 86A/1375/RVC
Full information on the voting for the approval of this technical report can be found in the
report on voting indicated in the above table.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
The committee has decided that the contents of this publication will remain unchanged until
the stability date indicated on the IEC web site under "http://webstore.iec.ch" in the data
related to the specific publication. At this date, the publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
IMPORTANT – The “colour inside” logo on the cover page of this publication indicates
that it contains colours which are considered to be useful for the correct understanding
of its contents. Users should therefore print this publication using a colour printer.

TR 62048  IEC:2011(E) – 7 –
OPTICAL FIBRES –
Reliability – Power law theory

1 Scope
This technical report provides guidelines and formulae to estimate the reliability of fibre under
a constant service stress. It is based on a power law for crack growth which is derived
empirically, but there are other laws which have a more physical basis (for example, the
exponential law). All these laws generally fit short-term experimental data well but lead to
different long-term predictions. The power law has been selected as the most reasonable
representation of fatigue behaviour by the experts of several standard-formulating bodies.
Reliability is expressed as an expected lifetime or as an expected failure rate. The results
cannot be used for specifications or for the comparison of the quality of different fibres. This
document develops the theory behind the experimental principles used in measuring the fibre
parameters needed in the reliability formulae. Much of the theory is taken from the referenced
literature and is presented here in a unified manner. The primary results are formulae for
lifetime or for failure rate, given in terms of the measurable parameters. Conversely, an
allowed maximum service stress or extreme value of another parameter may be calculated for
an acceptable lifetime or failure rate.
For readers interested only in the final results of this technical report – a summary of the
formulae used and numerical examples in the calculation of fibre reliability – Clauses 5 and 6
are sufficient and self-contained. Readers wanting a detailed background with algebraic
derivations will find this in Clauses 7 to 12. An attempt is made to unify the approach and the
notation to make it easier for the reader to follow the theory. Also, it should ensure that the
notation is consistent in all test procedures. Clause 13 has a limited set of mostly theoretical
references, but it is not necessary to read them to follow the analytical development in this
technical report.
NOTE Clauses 7 to 11 reference the B-value, and this is done for theoretical completeness only. There are as yet
no agreed methods for measuring B, so Clause 12 gives only a brief analytical outline of some proposed methods
and furthermore develops theoretical results for the special case in which β can be neglected.
2 Symbols
Table 1 provides a list of symbols found in this document. Each symbol is first defined in the
subclause or paragraph indicated in the final column of the table.
Table 1 – Symbols
Subclause or
Symbol Unit Name
paragraph
a Crack size (11.1) 7.1
A Flaw depth 7.1
µm
a
µm Radius of glass fibre 10.3
f
b dimensionless Bend designation 12.1.2
B GPa x s Crack strength preservation parameter or B-value 7.1
B GPa x s Transitional B-value at the slow-unloading/fast-unloading boundary 9.4
c dimensionless Non-linearity term for stress versus strain 7.4
C dimensionless Additive dimensionless prooftest term or C-value 10.6

– 8 – TR 62048  IEC:2011(E)
Subclause or
Symbol Unit Name
paragraph
C dimensionless Average additive dimensionless prooftest term or C-value 12.1.1
a
C dimensionless Transitional value of C at the slow-unloading/fast-unloading 10.6
boundary
D Mm Fibre-axe separation in two-point bending 10.3.3
E GPa Young's modulus 7.4
E
GPa Zero-stress Young's modulus 7.4
f(h) dimensionless Cumulative number of failures as a function of the number of hours 11.4
h
F dimensionless Fibre failure probability 11.1
F dimensionless Fibre failure probability during prooftesting 12.1.2
p
h dimensionless proportionality constant 10.1.1
i dimensionless Rank order, sorted by increasing failure stress 5.3.2
I Strength integral over the sample surface (assuming interior flaws 10.2.1
are negligible)
1/2
Stress intensity factor 7.1
GPa x µm
K (t)
I
1/2
Critical stress intensity factor 7.1
GPa x µm
K (t)
Ic
L km Fibre effective length under uniform stress, or equivalent tensile 10.2.1
length
L
km Fibre length in uniform bend 10.3.2
b
L
km Mean survival length, or survival length, during prooftesting 10.6
p
L
km Gauge length, reference length 10.2.1
m "Inert" Weibull parameter or m-value
dimensionless 10.2.1
m dimensionless m-value under dynamic fatigue 10.5
d
m dimensionless m-value under static fatigue 10.4
s
n dimensionless Stress corrosion susceptibility parameter or n-value 10.2
N dimensionless Total number of specimens tested 5.3.2
–1
N km Mean breakrate per unit length during prooftesting 10.6
p
–1
km Flaws per unit length not exceeding inert strength S 10.2.1
N(S)
P
dimensionless Fibre survival probability 10.2.1
P dimensionless Fibre survival probability of each strip 6.2.4
i
P dimensionless Fibre survival probability after prooftesting 10.6
p
R m Fibre bend radius 10.3.2
S GPa Strength 10.1.1
S GPa Minimum initial strength 10.5
min
GPa "Inert" strength of a crack 7.1
S(t)
S
GPa Strength after prooftesting 9.3
p
S GPa Minimum strength after prooftesting 9.4
pmin
S GPa Strength after unloading 9.2
u
S GPa Minimum strength after unloading 9.3
u
min
S GPa Weibull gauge strength 10.2.1
t s Variable of time 7.1
s Critical survival time 9.3.2
ˆ
t
t
s Time to failure under dynamic fatigue, or prooftesting dwelltime 8.2.1, 9.2
d
TR 62048  IEC:2011(E) – 9 –
Subclause or
Symbol Unit Name
paragraph
t s Lifetime (time to failure) under constant stress or static fatigue 7.2, 8.1
f
testing
t s Lifetime after prooftesting 10.8
fp
t s Minimum lifetime for certain survival after prooftesting 10.8
fp
min
t (1) dimensionless Intercept on a static fatigue plot 8.1
f
t ms Prooftest loadtime 9.2
l
t ms Effective prooftime 9.3
p
t ms Prooftest unloadtime 9.2
u
t years Service time in years 6.1
y
t0 dimensionless Static Weibull time-scaling parameter 10.4
V µm/s Crack growth velocity 7.1
V Critical crack growth velocity 7.1
C µm/s
w dimensionless Weibull cumulative probability ordinate scale 5.3.2
i
wout
dimensionless Median Weibull cumulative probability ordinate scale 5.3.2
i
x
dimensionless Factor relating bend length to equivalent tensile length 10.3.2
Y
dimensionless Crack geometry shape parameter 7.1
z
dimensionless Length factor 11.1
α dimensionless Ratio of prooftest unload parameters to crack parameters 9.4
n (n-2)/m
β GPa -s-km Weibull β-value 10.4, 10.5
n (n-2)/m
β GPa -s-km Weibull β-value for each failure stress 5.3.2
i
ε dimensionless Strain corresponding to a particular stress 7.4
-1 -1
λi km -yr. Breaks/length-time (instantaneous failure rate) 11.1
-1 -1
λa km -yr. Averaged failure rate 11.2
σ(t) GPa Stress applied to a crack 7.1
σ GPa Applied stress under static fatigue testing and lifetime 8.1, 11.2
a
GPa/s Applied stress rate under dynamic fatigue testing 8.2.1

σ
a
GPa Maximum bend stress 6.3.4
σ
b
σf GPa Failure stress under dynamic fatigue testing, without prooftesting 8.2.1
σfp GPa Failure stress after prooftesting 10.8
σfp GPa Minimum failure stress after prooftesting 10.8
min
σf(1) dimensionless Intercept on a dynamic fatigue plot 8.2.1
σp GPa Prooftest stress 9.2
σ GPa (Non-failing) maximum stress 5.3.2
max
GPa Applied stress during unloading 9.2
σ
u
GPa/s Positive unloading stress rate 9.2

σ
u
σ0 GPa Dynamic Weibull stress-scaling parameter 10.5

3 General approach
First, the equivalence of the growth of an individual crack and its associated weakening is
shown. This is related to applied stress or strain as an arbitrary function of time. Applied
stress can be taken to fracture, from which the lifetime of the crack is calculated. Next, the
destructive tests of static and dynamic fatigue are reviewed, along with their relationship to

– 10 – TR 62048  IEC:2011(E)
each other. These tests measure parameters useful in the theory. This also shows the
difference between "inert" strength and "dynamic" strength.
The above single-crack theory is then extended to a statistical distribution of many cracks.
This is done in terms of a survival (or failure) Weibull probability distribution in strength. It can
allow for several deployment geometries in testing and service. The inert distribution and the
distributions obtained by static or dynamic fatigue testing are derived for before and after
prooftesting. The latter is sometimes done with approximations that may not require knowing
the B-value explicitly. Finally, the various parameters measured by the above testing are
related to formulae for fibre reliability, that is, lifetime and failure rate.
Some of the main assumptions in the development are as indicated below.
– The relationship between the stress intensity factor, applied stress and flaw size is given
by Equation (29); while at fracture, the relationship between the critical stress intensity
factor, strength, and flaw depth is given by Equation (30).
– The crack growth velocity is related to the stress intensity factor by Equation (32).
– The Weibull distribution of stress (before any prooftesting) is unimodal according to
Equations (85) and (86), or bimodal according to Equation (91). The (m, S ) pair
appropriate to the desired survival probability level and length must be used. Deployment
lengths will differ upon the application such as fibre on reels, in cable, splice trays, or
within a connector or other component. Because of the low failure probabilities desired,
however, the low-strength extrinsic mode must usually be used.
– The values of the fatigue parameters, both static and dynamic, depend upon the fibre
environment, fibre ageing, and fibre preconditioning prior to testing. In theory, they are
taken to be independent of time, so that some engineering judgement is needed to decide
the practical values to be used in the calculations. This also implies that the corresponding
static and dynamic parameters equal each other (for the same environment and time
duration).
– Zero-stress ageing is not accounted for. Since the above parameters are independent of
time, the strength decreases due only to stress fatigue following the power law according
to 7.1.
4 Formula types
The formulae utilise parameters obtained from fatigue testing-to-failure, and from prooftesting
with potential random failures. In the service condition of interest, a fibre of effective length L
(dependent upon deployment geometry) is subjected to a constant applied service stress that
does not change with time. (This stress is tensile, including bending stress. Torsional or
compressive stresses are not covered.) The lifetime as a function of failure probability or
failure rate as a function of time are given.
The formulae assume a Weibull distribution with parameters that vary among fibre types and
perhaps among fibres of the same type. Moreover, they change with environment and applied
stress levels. The Weibull distribution may have several nominally linear terms depending
upon several levels of flaw strength. It is important that the Weibull parameters for the term of
interest be used in the formulae. These are obtained from fatigue measurements. Generally,
the low-strength region near the prooftest stress and below is of interest, and measurements
must be on long fibre gauge lengths and with many samples, so that the total fibre length
tested is large. Parameters measured for a small number of short samples, characterizing the
high-strength region, will differ from the preceding ones. They must not be used in the
formulae to extrapolate to lower-strength lower-probability regions.
Within the above power-law assumptions, the equations of Clauses 7 to 11 are algebraically
"exact". However, in some applications, certain terms may be negligible, and more
approximate and simpler algebraic equations are given in Clause 12. This has the advantage
that the B-value, for which there is yet no standard test method and which has been reported
to span several orders of magnitude, is not required.

TR 62048  IEC:2011(E) – 11 –
Even with these formulae, there is no assured way of accurately predicting fibre reliability.
Some fibres may break before the most conservative of predictions, while others may last
longer than the most pessimistic of predictions. After fibre manufacture, fatigue or damage
may occur due to cabling, installation, or operation; this usually cannot be accounted for in
the theory. A start on estimating these effects could be made by measuring the parameters of
fibres after each of these stages, but this is not commonly done.
For convenience in assisting the reader to find the derivations of equations, if desired, the
formulae summarized in Clauses 5 and 6 include the indication in brackets of the equations
listed in Clauses 7 to 12. However, it is not necessary to refer to the derivations to be able to
follow Clauses 5 and 6.
5 Measuring parameters for fibre reliability
5.1 General
This clause outlines how the parameters in the reliability (lifetime and failure rate) equations
are obtained in the approximation of the small B-value. Prooftest parameters are obtained
from testing the full length of fibre to be deployed. By contrast, both static and dynamic
fatigue procedures use many short-length test samples. These are used to obtain "linear"
Weibull plots of the cumulative failure probability F scaled as ln-ln (where P = 1 – F is the
P
survival probability) versus the ln of a suitable variable (failure time or failure stress). For
situations in which the plot may be fitted to two or more straight line parts, that part closest to
the anticipated service stress should be used in obtaining the needed parameters.
5.2 Length and equivalent length
The testing and service geometries may differ from each other. The symbol L is the gauge
length in static or dynamic fatigue testing, whereas L is the in-service length subjected to
constant applied service stress. The gauge length equals the actual length only for the case
of longitudinal tension. Other geometries require equivalent lengths.
For uniform bending (for example, mandrel wrap), the in-service bend length L is replaced by
b
an approximate equivalent in-service tensile length L given by Equation (97).
L
b
L≈ 0,4
(1)
x
The same relationship holds between the gauge bend length L and the equivalent gauge
b0
length L . In this equation there is the factor Equation (98).
mn m n
d
x= = m n= (2)
s
n− 2 n+ 1
using inert, static fatigue, and dynamic fatigue parameters, respectively, as obtained below.
For two-point bending, the equivalent length depends upon the applied stress in a complex
way. Computation of the equivalent in-service length for an arbitrary applied service stress is
difficult. The equivalent gauge length is approximately 10 µm to 30 μm, depending upon the
failure stress.
– 12 – TR 62048  IEC:2011(E)
5.3 Reliability parameters
5.3.1 General
This subclause outlines methods that are commonly used to derive reliability parameters.
5.3.2 Prooftesting
n
• Obtain the composite prooftest parameter σ t , where σ is the actual prooftest stress
p p
p
during dwell, and n is the stress-corrosion susceptibility parameter (or n-value). The
effective prooftime is given by Equation (64).
t + t
l u
t = t + (3)
p d
n+ 1
obtained from the loadtime t , the dwelltime t , and the unloadtime t .
l d u
• (Optional) If from prooftesting the mean number of breaks N per length or the mean
p
survival length L during prooftesting is known, calculate Equations (172) and (173).
p
n−2
n
σ t
p p
n
m
β= =σ t L
p p p
(4)
n−2
m
N
p
m
m
d
where = m = (5)
s
n− 2 n+ 1
If this is not possible, obtain β as a fit parameter in 5.2.2, 5.2.3, or 5.3.
5.3.3 Static fatigue
• Obtain the static Weibull plot of scaled probability versus the natural log of failure times t
f
for any particular constant applied stress σ (Equation (174)).
a
m m
1 L
 s s
n n n
ln = (t σ + tσ ) −(tσ )
f a p p p p
 
m (6)
s
P (t )
 β
p f
Determine parameters m and β from the characteristics of the plot.
s
• Obtain the best-fit straight line to the log of failure times versus the log of applied stresses
(Equation (48)).
logt (σ )≈ logt (1)− n logσ
(7)
f a f a
Measure the static stress-corrosion susceptibility parameter as the negative slope –n of this
line. The term t (1) is the "intercept" of this line on the ordinate axis, that is, the value of
f
failure time where the applied stress is unity. (This value will depend on the units used, and
may require a straight-line extrapolation beyond the data points. It does not have the
dimension of time.)
TR 62048  IEC:2011(E) – 13 –
5.3.4 Dynamic fatigue
describes how to measure both short-length and long-length strength
IEC 60793-1-31
distributions of optical fibres.
• Obtain the dynamic Weibull plot of scaled probability versus natural log of failure stresses

σ
σ for any particular constant applied stress rate (Equation (175)).
a
f
m
 
d
n+1
m
  n+1 
d
σ
1  f  L
n n
 
n+1
ln = +σ t −(σ t )
 
p p p p (8)
 m
 
P (σ ) (n+ 1)σ d
p f a
 
 
n+1
β
 
 
Determine parameters m and β from the characteristics of the plot.
d
• Obtain the best-fit straight line to the log of failure stresses versus the log of applied
stress rates (Equation (53)).

logσ
a

logσ (σ )≈ logσ (1)+
(9)
f a f
n+ 1
Measure the dynamic stress-corrosion susceptibility parameter from the slope of this
n+ 1
line.
The term σ (1) is the "intercept" of this line on the ordinate axis, that is, the value of failure
f
stress where the applied stress rate is unity. (This value will depend on the units used, and
may require a straight-line extrapolation beyond the data points. It does not have the
dimension of stress.)
5.4 Parameters for the low-strength region
5.4.1 General
This subclause describes the way to measure the strength distribution at sufficiently low
probability to represent the distribution of failure strengths near the prooftest stress level for
the second mode of the Weibull distribution (shown as the extrinsic region in Figure 14).
Normally, the fibre population has been prooftested once according to Clause 9.
NOTE These implementations are used only for characterization and not for specification.
5.4.2 Variable prooftest stress
This method (briefly mentioned in 9.5) subjects a full length of fibre to a certain prooftest
stress, another length to a higher prooftest stress, and so on for several increasing levels of
prooftest stress. The mean survival length L (or number of breaks N per unit length) is
p p
counted for each length and stress level. This resembles a static fatigue test in which the
failure stress (the prooftest stress σ ) varies. However, the failure time does not exceed the
p
fixed prooftime t . The n-values are obtained by the fatigue measurements of 5.3.
p
First, consider the case in which there is no initial prooftest at manufacture. From
Equations (171) and (173) one has
___________
IEC 60793-1-31:2001, Optical fibres – Part 1-31: Measurement methods and test procedures – Tensile
strength.
– 14 – TR 62048  IEC:2011(E)
ln L + m (n ln σ + ln t – ln β) = 0 (10)
p s p p
so a logarithmic plot of mean survival length versus prooftest stress should be close to a
straight line. The slope is –nm , while the stress and length “intercepts” are (lnβ− lnt ) and
s p
n
m (ln t – ln β), respectively.
s p
In Reference [11] , fibres with a 400 µm jacket and initial lengths of 10 km to 15 km were
used, with five proofstrains of 0,8 % to 3,5 %. There was no other initial prooftest.
−m
s
Equation (10) is equivalent to Equations (18) to (20) of Reference [11] with C=β . With a
duration time t of 1 s, it was found that nm = 2,07, so that with n = 20, one has m = 0,1035.
d s s
nm m
m
s s
s
Also, m ln t + ln C = –2,09, so that β = 8,085 GPa x s x km.
s p
More common is the case in which there is an initial prooftest at manufacture. If the second
prooftest stress is significantly above the first, then Equation (10) can still be used.
In Reference [12], the prooftest stress level at manufacture was not stated. A minimum
sample length of 10 km or 20 km was used, and each sample was subjected to a different one
of five prooftest stress levels between 1 GPa and 4 GPa. The prooftest speed was reduced to
minimize breakage during the start-up acceleration period, so the duration time t was
d
normalized to 1 s using n = 23. The failure probabilities F per meter were calculated for each
stress and plotted to fit the straight line of the form
 1 
ln = M lnσ + ln K
 
p
(11)
1− F
 
With another “ln” on the left (apparently missing), this is equivalent to Equation (101) for static
fatigue (ignoring the initial prooftesting) if
m
s
 t 
d
M≡ nm and K≡  (12)
s
 
β
 
From this it was determined that M = 1,69, so we find m = 0,0735, and K = 0,000418, so that
s
nm m
m
s s s
GPa x s x km.
β = 2,392
5.4.3 Dynamic fatigue
This is a form of dynamic testing with censoring, as mentioned in 8.2.2, and with more details
on the apparatus given in Reference [5].
A specimen is a single gauge length L of fibre. (A recommended gauge length L is longer
0 0
than 1 m; for example, 10 m to 20 m.) A sample is a group of specimens from a given
population of fibres.
Each specimen is loaded to a failure stress σ , or, with censoring, to a (non-failing) maximum
f
stress σ (for example, 2,4 GPa, about 3,2 % strain from Equation (44)). The recommended
max

strain rate σ is fast (for example, greater than 200 %min, about 2,6 GPa/s, from
a
Equation (43)). The sample size should be large enough to provide an adequate
representation of the second Weibull mode (for example, so that 1 km of the total specimens
fail).
___________
Numbers in square brackets refer to the Bibliography.

TR 62048  IEC:2011(E) – 15 –
The following data are recorded
– the total number of specimens tested: N, whether or not failure occurred;
– the failure stress values of those specimens that failed: σ in GPa. Here i is the rank
fi
order, sorted by increasing failure stress.

– the stress rate (converted from strain rate): σ in GPa/s.
a
– the gauge length of the specimens: L in km.
A Weibull plot in the form of Figure 1 may also be presented (without the curve fits). The
points are measurements from about 0,8 GPa to 2,4 GPa, for an acrylate-coated fused silica
fibre with a cladding diameter of 125 μm.
Calculation of Weibull parameters
Here the data of the measurement is analysed. According to Equation (86), the Weibull
cumulative probability ordinate scale is of the form
 1 
 
ln ln ,
 
 
1− F
 
 
where F = 1 – P is the cumulative failure probability.
Hence compute
 
 i 
w = ln− ln
...