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

® Registered trademark of the International Electrotechnical Commission

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– 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

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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

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– 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

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TR 62048  IEC:2011(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
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8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
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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 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.

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– 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.

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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
2
B GPa x s Crack strength preservation parameter or B-value 7.1
2
B GPa x s Transitional B-value at the slow-unloading/fast-unloading boundary 9.4
0
c dimensionless Non-linearity term for stress versus strain 7.4
C dimensionless Additive dimensionless prooftest term or C-value 10.6

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– 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
0
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
0
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
0
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
0
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

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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

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– 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 distri
...