BSI PD IEC/TR 62048:2011
$198.66
Optical fibres. Reliability. Power law theory
| Published By | Publication Date | Number of Pages |
| BSI | 2011 | 70 |
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.
PDF Catalog
| PDF Pages | PDF Title |
|---|---|
| 4 | CONTENTS |
| 7 | FOREWORD |
| 9 | 1 Scope 2 Symbols Tables Table 1 – Symbols |
| 11 | 3 General approach |
| 12 | 4 Formula types |
| 13 | 5 Measuring parameters for fibre reliability 5.1 General 5.2 Length and equivalent length |
| 14 | 5.3 Reliability parameters |
| 15 | 5.4 Parameters for the low-strength region |
| 17 | Figures Figure 1 – Weibull dynamic fatigue plot near the prooftest stress level |
| 18 | 5.5 Measured numerical values |
| 19 | 6 Examples of numerical calculations 6.1 General 6.2 Failure rate calculations |
| 20 | Figure 2 – Instantaneous FIT rates per fibre km versus time for applied stress/prooftest stress percentages (bottom to top): 10 %, 15 %, 20 %, 25 %, 30 % |
| 21 | Figure 3 – Averaged FIT rates per fibre km versus time for applied stress/prooftest stress percentages (bottom to top): 10 %, 15 %, 20 %, 25 %, 30 % Table 2 – FIT rates of Figures 2 and 3 at various times |
| 22 | Figure 4 – Instantaneous FIT rates per bent fibre metre versus time(top to bottom): 10 mm, 20 mm, 30 mm, 40 mm, 50 mm |
| 23 | 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 Table 3 – FIT rates of Figures 4 and 5 at various times |
| 24 | 6.3 Lifetime calculations Table 4 – FIT rates of Table 3 neglecting stress versus strain non-linearity |
| 25 | Figure 6 – 1-km lifetime versus failure probability for applied stress/prooftest stress percentages (top to bottom): 10 %, 15 %, 20 %, 25 %, 30 % |
| 26 | 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 Table 5 – One kilometer lifetimes of Figure 6 for various failure probabilities |
| 27 | Table 6 – One-meter lifetimes of Figure 7 for various failure probabilities Table 7 – Lifetimes of Table 6 neglecting stress versus strain non-linearity |
| 28 | Table 8 – Bend plus 30 % of proof test tension for 30 years |
| 29 | 7 Fibre weakening and failure 7.1 General 7.2 Crack growth and weakening |
| 31 | 7.3 Crack fracture |
| 32 | 7.4 Features of the general results 7.5 Stress and strain |
| 33 | 8 Fatigue testing 8.1 General 8.2 Static fatigue |
| 34 | Figure 8 – Static fatigue: applied stress versus time for a particular applied stress Figure 9 – Static fatigue: schematic data of failure time versus applied stress |
| 35 | 8.3 Dynamic fatigue Figure 10 – Dynamic fatigue: applied stress versus time for a particular applied stress rate |
| 36 | Figure 11 – Dynamic fatigue: schematic data of failure time versus applied stress rate |
| 37 | 8.4 Comparisons of static and dynamic fatigue |
| 39 | 9 Prooftesting 9.1 General 9.2 The prooftest cycle |
| 40 | 9.3 Crack weakening during prooftesting Figure 12 – Prooftesting: applied stress versus time |
| 41 | 9.4 Minimum strength after prooftesting |
| 43 | 9.5 Varying the prooftest stress 10 Weibull probability 10.1 General |
| 44 | 10.2 Strength statistics in uniform tension |
| 46 | 10.3 Strength statistics in other geometries |
| 47 | 10.4 Weibull static fatigue before prooftesting |
| 49 | 10.5 Weibull dynamic fatigue before prooftesting Figure 13 – Static fatigue schematic Weibull plot |
| 50 | Figure 14 – Dynamic fatigue schematic Weibull plot |
| 51 | 10.6 Weibull after prooftesting |
| 54 | 10.7 Weibull static fatigue after prooftesting |
| 55 | 10.8 Weibull dynamic fatigue after prooftesting |
| 56 | 11 Reliability prediction 11.1 Reliability under general stress and constant stress |
| 57 | 11.2 Lifetime and failure rate from fatigue testing |
| 58 | 11.3 Certain survivability after prooftesting |
| 59 | 11.4 Failures in time |
| 60 | 12 B-value: elimination from formulae, and measurements 12.1 General 12.2 Approximate Weibull distribution after prooftesting |
| 63 | 12.3 Approximate lifetime and failure rate |
| 64 | 12.4 Estimation of the B-value |
| 66 | Bibliography |
