IEC TR 62048:2014

IEC TR 62048 ®
Edition 3.0 2014-01
TECHNICAL
REPORT
colour
inside
Optical fibres –
Reliability – Power law theory

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IEC TR 62048 ®
Edition 3.0 2014-01
TECHNICAL
REPORT
colour
inside
Optical fibres –
Reliability – Power law theory

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
PRICE CODE
XB
ICS 33.180.10 ISBN 978-2-8322-1369-8

– 2 – TR 62048 © IEC:2014(E)
CONTENTS
FOREWORD . 5
INTRODUCTION . 7
1 Scope . 8
2 Normative references . 8
3 Symbols . 8
4 General approach . 10
5 Formula types . 10
6 Measuring parameters for fibre reliability . 11
6.1 Overview . 11
6.2 Length and equivalent length . 11
6.3 Reliability parameters . 12
6.3.1 Overview . 12
6.3.2 Proof-testing . 12
6.3.3 Static fatigue . 12
6.3.4 Dynamic fatigue . 13
6.4 Parameters for the low-strength region . 13
6.4.1 Overview . 13
6.4.2 Variable proof test stress . 13
6.4.3 Dynamic fatigue . 14
6.5 Measured numerical values. 17
7 Examples of numerical calculations . 17
7.1 Overview . 17
7.2 Failure rate calculations . 18
7.2.1 FIT rate formulae . 18
7.2.2 Long lengths in tension . 18
7.2.3 Short lengths in uniform bending . 20
7.3 Lifetime calculations . 22
7.3.1 Lifetime formulae . 22
7.3.2 Long lengths in tension . 22
7.3.3 Short lengths in uniform bending . 23
7.3.4 Short lengths with uniform bending and tension . 25
8 Fibre weakening and failure . 26
8.1 Crack growth and weakening . 26
8.2 Crack fracture . 28
8.3 Features of the general results . 29
8.4 Stress and strain . 30
9 Fatigue testing . 30
9.1 Overview . 30
9.2 Static fatigue . 30
9.3 Dynamic fatigue . 32
9.3.1 Overview . 32
9.3.2 Fatigue to breakage . 32
9.3.3 Fatigue to a maximum stress . 34
9.4 Comparisons of static and dynamic fatigue . 34
9.4.1 Intercepts and parameters obtained . 34
9.4.2 Time duration . 34

TR 62048 © IEC:2014(E) – 3 –
9.4.3 Dynamic and inert strengths . 35
9.4.4 Plot non-linearities . 36
9.4.5 Environments. 36
10 Proof-testing . 37
10.1 Overview . 37
10.2 The proof test cycle . 37
10.3 Crack weakening during proof-testing . 38
10.4 Minimum strength after proof-testing . 39
10.4.1 Overview . 39
10.4.2 Fast unloading . 39
10.4.3 Slow unloading . 40
10.4.4 Boundary condition . 41
10.5 Varying the proof test stress . 41
11 Statistical description of strength by Weibull probability models . 41
11.1 Overview . 41
11.2 Strength statistics in uniform tension . 41
11.2.1 Unimodal probability distribution . 41
11.2.2 Bimodal probability distribution . 43
11.3 Strength statistics in other geometries . 43
11.3.1 Stress non-uniformity . 43
11.3.2 Uniform bending . 44
11.3.3 Two-point bending . 45
11.4 Weibull analysis for static fatigue before proof-testing . 45
11.5 Weibull analysis for dynamic fatigue before proof-testing . 47
11.6 Weibull distribution after proof-testing . 49
11.7 Weibull analysis for static fatigue after proof-testing . 51
11.8 Weibull analysis for dynamic fatigue after proof-testing . 53
12 Reliability prediction . 54
12.1 Reliability under general stress and constant stress . 54
12.2 Lifetime and failure rate from fatigue testing . 55
12.3 Certain survivability after proof-testing . 56
12.4 Failures in time . 57
13 B-value: elimination from formulae, and measurements . 58
13.1 Overview . 58
13.2 Approximate Weibull distribution after proof-testing . 58
13.2.1 Overview . 58
13.2.2 "Risky region" during proof-testing . 58
13.2.3 Other approximations . 59
13.3 Approximate lifetime and failure rate . 61
13.4 Estimation of the B-value . 62
13.4.1 Overview . 62
13.4.2 Fatigue intercepts . 62
13.4.3 Dynamic fatigue failure stress . 62
13.4.4 Obtaining the strength . 62
13.4.5 Stress pulse measurement . 63
13.4.6 Flaw growth measurement . 63

– 4 – TR 62048 © IEC:2014(E)
Annex A (informative) Statistical strength degradation map. 64
Bibliography . 65

Figure 1 – Weibull dynamic fatigue plot near the proof test stress level . 16
Figure 2 – Instantaneous FIT rates of 1 km fibre versus time for applied stress/proof
test stress percentages (bottom to top): 10 %, 15 %, 20 %, 25 %, 30 % . 19
Figure 3 – Averaged FIT rates of 1 km fibre versus time for applied stress/proof test
stress percentages (bottom to top): 10 %, 15 %, 20 %, 25 %, 30 % . 19
Figure 4 – Instantaneous FIT rates of bent fibre with 1 m effective length versus time . 21
Figure 5 – Averaged FIT rates of bent fibre with 1 m effective length versus time for
bend diameters (top to bottom): 10 mm, 20 mm, 30 mm, 40 mm, 50 mm . 21
Figure 6 – 1 km lifetime versus failure probability for applied stress/proof test stress
percentages (top to bottom): 10 %, 15 %, 20 %, 25 %, 30 % . 23
Figure 7 – Lifetimes of bent fibre with 1 m effective length 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 . 31
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 . 32
Figure 11 – Dynamic fatigue – Schematic data of failure time versus applied stress rate . 34
Figure 12 – Proof-testing – Applied stress versus time . 38
Figure 13 – Static fatigue schematic Weibull plot . 47
Figure 14 – Dynamic fatigue schematic Weibull plot . 48
Figure A.1 – Schematic diagram of the statistical strength degradation map . 64

Table 1 – Symbols . 8
Table 2 –FIT rates of 1 km fibre in Figures 2 and 3 at various times. 20
Table 3 – FIT rates of 1 metre effective length bent fibre in Figures 4 and 5 at
various times . 22
Table 4 – FIT rates of Table 3 neglecting stress versus strain non-linearity. 22
Table 5 – 1 km lifetimes in years of Figure 6 for various failure probabilities . 23
Table 6 – Lifetimes of bent fibre with 1 metre effective length in years of Figure 7
for various failure probabilities . 24
Table 7 – Lifetimes in years of Table 6 neglecting stress versus strain non-linearity . 245
Table 8 – Calculated results in case of bend plus 30 % of proof test tension for 30
years . 26

TR 62048 © IEC:2014(E) – 5 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
OPTICAL FIBRES –
Reliability – Power law theory

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote
international co-operation on all questions concerning standardization in the electrical and electronic fields. To
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2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international
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5) IEC itself does not provide any attestation of conformity. Independent certification bodies provide conformity
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6) All users should ensure that they have the latest edition of this publication.
7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and
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other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and
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8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of
patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
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/TR 62048, which is a technical report, has been prepared by subcommittee 86A: Fibres
and cables, of IEC technical committee 86: Fibre optics.
This third edition cancels and replaces the second edition published in 2011, and constitutes
a technical revision.
The main changes with respect to the previous edition are listed below:
– correction to the unit of failure rates in Table 1;

– 6 – TR 62048 © IEC:2014(E)
– correction to the FIT equation for instantaneous failure rate [19] in addition to all call-outs
and derivations;
– insertion of a new note about fibre length dependency of failure rates;
– addition of informative Annex A and relevant reference;
– editorial corrections of inconsistencies.
The text of this technical report is based on the following documents:
Enquiry draft Report on voting
86A/1537/DTR 86A/1554/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.
A bilingual version of this publication may be issued at a later date.

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 document using a
colour printer.
___________
Numbers in square brackets refer to the Bibliography.

TR 62048 © IEC:2014(E) – 7 –
INTRODUCTION
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
technical report 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 6 and 7
– are sufficient and self-contained. Readers wanting a detailed background with algebraic
derivations will find this in Clauses 8 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. The Bibliography 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. Annex A introduces a statistical strength degradation
(SSD) map which gives intuitive understanding of the physical meaning of the formulae
appearing in Clauses 10 and 11.
NOTE Clauses 8 to 12 reference the B-value, and this is done for theoretical completeness only. There are as yet
no agreed methods for measuring B, so the Bibliography gives only a brief analytical outline of some proposed
methods and furthermore develops theoretical results for the special case in which B can be neglected.

– 8 – TR 62048 © IEC:2014(E)
OPTICAL FIBRES –
Reliability – Power law theory

1 Scope
This technical report is a guideline that gives formulae to estimate the reliability of fibre under
a constant service stress based on a power law for crack growth.
NOTE Power law 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 a most reasonable representation of fatigue behaviour by the
experts of several standard-formulating bodies.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and
are indispensable for its application. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any
amendments) applies.
IEC 60793-1-30, Optical fibres – Part 1-30: Measurement methods and test procedures –
Fibre proof test
IEC 60793-1-31, Optical fibres – Part 1-31: Measurement methods and test procedures –
Tensile strength
3 Symbols
Table 1 provides a list of symbols found in this report. Each symbol appears in the
subclause(s) indicated in the final column of the table.
Table 1 – Symbols
Symbol Unit Name Subclause
a Flaw depth 8.1
µm
a Radius of glass fibre 11.3
µm
f
B GPa ×s Crack strength preservation parameter or B-value 8.1
B GPa ×s Transitional B-value at the slow-unloading/fast-unloading 10.4
boundary
c Dimensionless Non-linearity term for stress versus strain 8.4
C Dimensionless Additive dimensionless proof test term or C-value 11.6
C Dimensionless Transitional value of C at the slow-unloading/fast-unloading 11.6
boundary
D Mm Fibre-axes separation in two-point bending 11.3.3
E
Gpa Zero-strain Young's modulus 8.4
F Dimensionless Fibre failure probability 12.1
1/2
GPa×µm Stress intensity factor 8.1
K (t)
I
1/2
K GPa×µm Critical stress intensity factor 8.1
Ic
TR 62048 © IEC:2014(E) – 9 –
Symbol Unit Name Subclause
L km Fibre effective length under uniform stress, or equivalent 11.2.1
tensile length
L km Fibre length in uniform bend 11.3.2
b
L km Mean survival length, or survival length, during proof-testing 11.6
p
L km Gauge length, reference length 11.2.1
m Dimensionless "Inert" Weibull parameter or m-value 11.2.1
m Dimensionless m-value under dynamic fatigue 11.5
d
m m-value under static fatigue
Dimensionless 11.4
s
n Dimensionless Stress corrosion susceptibility parameter or n-value 6.3, 8.1
–1
N km Mean break rate per unit length during proof-testing 11.6
p
–1
km Flaws per unit length not exceeding inert strength S 11.2.1
N(S)
P Dimensionless Fibre survival probability 11.2.1
P Dimensionless Fibre survival probability after proof-testing 11.6
p
R M Fibre bend radius 11.3.2
GPa "Inert" strength of a crack 8.1
S(t)
S GPa Strength after proof-testing 10.3
p
S
GPa Minimum strength after proof-testing 10.4
pmin
S GPa Weibull gauge strength 11.2.1
t s Variable of time 8.1
t s Time to failure under dynamic fatigue 8.3.2
d
Dwell time of proof test 6.3.2, 6.4.2,
10.2, 10.3
t s Lifetime (time to failure) under constant stress or static fatigue 8.2, 9.2
f
testing
t s Lifetime after proof-testing 11.8
fp
t s Minimum lifetime for certain survival after proof-testing 11.8
fp
min
t (1)
Dimensionless Intercept on a static fatigue plot 9.2
f
t ms Loading time of proof test 10.2
l
t ms Effective proof test time 10.3
p
t ms Unloading time of proof test 10.2
u
t Dimensionless Static Weibull time-scaling parameter 11.4
V Crack growth velocity 8.1
µm/s
V Critical crack growth velocity 8.1
C µm/s
x Dimensionless Factor relating bend length to equivalent tensile length 11.3.2
Y Dimensionless Crack geometry shape parameter 8.1
α Dimensionless Ratio of unloading parameters of proof test to crack 10.4
parameters
n (n-2)/m
β GPa ×s×km Weibull β-value 11.4, 11.5
ε Dimensionless Strain corresponding to a particular stress 8.4
–1
λ s Instantaneous failure rate 12.1
i
–1
λ s Averaged failure rate 12.2
a
σ(t) GPa Stress applied to a crack 8.1
σ
a GPa Applied stress under static fatigue testing and service time 9.2, 12.2
GPa/s Applied stress rate under dynamic fatigue testing 8.3.2

σ
a
– 10 – TR 62048 © IEC:2014(E)
Symbol Unit Name Subclause
σ GPa Failure stress under dynamic fatigue testing, without proof- 8.3.2
f
testing
σ GPa Failure stress after proof-testing 11.8
fp
σ GPa Minimum failure stress after proof-testing 11.8
fpmin
σ(1) Dimensionless Intercept on a dynamic fatigue plot 8.3.2
f
σ GPa Proof test stress 10.2
p
σ GPa Dynamic Weibull stress-scaling parameter 11.5
4 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
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
proof-testing. 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 proof-testing) 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 shall 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 fatigue 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 8.1.
5 Formula types
The formulae utilize parameters obtained from fatigue testing-to-failure, and from proof-testing
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

TR 62048 © IEC:2014(E) – 11 –
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 proof test stress and below is of interest, and measurements
shall 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 shall not be used in the
formulae to extrapolate to lower-strength lower-probability regions.
Within the above power law assumptions, the equations in Clauses 8 to 12 are algebraically
"exact". However, in some applications, certain terms may be negligible, and more
approximate and simpler algebraic equations are given in Clause 13. This has the advantage
in 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.
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 6 and 7 include the indication in brackets of the equations
listed in Clauses 8 to 13. However, it is not necessary to refer to the derivations to be able to
follow Clauses 6 and 7.
6 Measuring parameters for fibre reliability
6.1 Overview
This clause outlines how the parameters in the reliability (lifetime and failure rate) equations
are obtained in the approximation of the small B-value. Proof test 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.
6.2 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).

– 12 – TR 62048 © IEC:2014(E)
L
b
L≈ 0,4
x
(1)
The same relationship holds between the gauge bend length L and the equivalent gauge
b0
length L . In this equation there is the factor of Equation (98), i.e.
mn m n
d
x= = m n=
s
n− 2 n+ 1
(2)
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.
6.3 Reliability parameters
6.3.1 Overview
This subclause outlines methods that are commonly used to derive reliability parameters.
6.3.2 Proof-testing
n
– Obtain the composite proof test parameter σ t , where σ is the actual proof test stress
p p p
during dwell, and n is the stress-corrosion susceptibility parameter (or n-value). The
effective proof test time is given by Equation (64), i.e.
t + t
l u
t = t +
p d
n+ 1
(3)
obtained from the loading time t , the dwell time t , and the unloading time t .
l d u
– (Optional) If from proof-testing the mean number of breaks N per length or the mean
p
survival length L during proof-testing is known, calculate Equations (172) and (173), i.e.
p
n−2
n
σ t
p p
n
m
β= =σ t L
p p p
n−2
m
N
p
(4)
m
m
d
where = m = (5)
s
n− 2 n+ 1
If this is not possible, obtain β as a fitting parameter in 6.3.3, 6.3.4, or 6.4.
6.3.3 Static fatigue
– Obtain the static Weibull plot of scaled probability versus the natural logarithm of failure
times t for any particular constant applied stress σ [Equation (174)]
f a
m m
1 L
 s s
n n n
ln = (t σ + tσ ) −(tσ )
f a p p p p
 
m
s
P (t )
 
β
p f
(6)
– Determine parameters ms and β from the characteristics of the plot.

TR 62048 © IEC:2014(E) – 13 –
– Obtain the best-fit straight line to the logarithm of failure times versus the logarithm of
applied stresses (see Equation (48))
lgt (σ )≈ lgt (1)− nlgσ
f a f a
(7)
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.)
6.3.4 Dynamic fatigue
IEC 60793-1-31 describes how to measure both short-length and long-length strength
distributions of optical fibres.
– Obtain the dynamic Weibull plot of scaled probability versus the natural logarithm of failure

stresses σ for any particular constant applied stress rate (see Equation (175))
σ
f a
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
 m
 
P (σ ) (n+ 1)σ d
p f  a 
 
n+1
β
 
 
(8)
Determine parameters m and β from the characteristics of the plot.
d
– Obtain the best-fit straight line to the logarithm of failure stresses versus the logarithm of
applied stress rates, as given in Equation (53):

lgσ
a
lgσ (σ )≈ lgσ (1)+
f a f
n+1
(9)
Measure the dynamic stress-corrosion susceptibility parameter from the slope of this
n+ 1
line.
(1) is the "intercept" of this line on the ordinate axis, that is, the value of failure
The term σ
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.)
6.4 Parameters for the low-strength region
6.4.1 Overview
This subclause describes the way to measure the strength distribution at sufficiently low
probability to represent the distribution of failure strengths near the proof test stress level for
the second mode of the Weibull distribution (shown as the extrinsic region in Figure 14).
Normally, the fibre population has been proof-tested once according to Clause 10.
NOTE These implementations are used only for characterization and not for specification.
6.4.2 Variable proof test stress
This method (briefly mentioned in 10.5) subjects a full length of fibre to a certain proof test
stress, another length to a higher proof test stress, and so on for several increasing levels of

– 14 – TR 62048 © IEC:2014(E)
proof test 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 proof test stress σ ) varies. However, the failure time does not exceed the
p
fixed proof test time t . The n-values are obtained by the fatigue measurements of 6.3.
p
First, consider the case in which there is no initial proof test at manufacture. From
Equations (171) and (173) one has
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 proof test stress should be close to a
(lnβ− lnt )
straight line. The slope is –nm , while the stress and length “intercepts” are and
p
s
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 proof test strains of 0,8 % to 3,5 %. There was no other initial proof test.
−m
s
Equation (10) is equivalent to Equations (18) to (20) of Reference [11] with C=β . With a
dwell 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
m nm m
s s s
Also, m ln t + ln C = –2,09, so that β = 8,085 GPa ⋅ s ⋅km.
s p
More common is the case in which there is an initial proof test at manufacture. If the second
proof test stress is significantly above the first, then Equation (10) can still be used.
In Reference [12], the proof test 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 proof test stress levels between 1 GPa and 4 GPa. The proof test speed was reduced
to minimize breakage during the start-up acceleration period, so the dwell 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
1− F
 
(11)
With another “ln” on the left (apparently missing), this is equivalent to Equation (101) for static
fatigue (ignoring the initial proof-testing) 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
m nm m
s s s
β = 2,392 GPa ⋅ s ⋅km.
6.4.3 Dynamic fatigue
6.4.3.1 Overview
This is a form of dynamic fatigue testing with censoring, as mentioned in 9.3.3, and with more
details on the apparatus given in Reference [5].

TR 62048 © IEC:2014(E) – 15 –
6.4.3.2 Data acquisition of dynamic fatigue
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

st
...