WCA MAY 2015

Failure probability of 1km of optical fibre

0.069 GPa proof tested fibre 20 per cent long-term load

0.069 GPa proof tested fibre 40 per cent long-term load

1.38 GPa proof tested fibre 20 per cent long-term load

1.0ppm per km

1,600 years

0.0 years 0.0 years

530 years* 5.3 years*

1.0ppm per 100km

16 years

* The failure rate varies greatly, with the change in proof-test going from 0.69 GPa to 1.38 GPa ❍ ❍ Table 1 : Comparison of failure probabilities (1ppm lifetime)

The intrinsic strength and n values are typically specified by end users to ensure long-term reliability of the cable. Unfortunately, the extrinsic portion, shown as region II, plays an important role in characterising the long-term reliability of an optical cable. This region contains flaws closer to the proof-test level that are spaced at a frequency which may be several kilometres apart. Over time, these can become fibre breaks if the cable is left in tension. Understanding this region requires information that can only be gathered by measuring many kilometres of fibre. Higher proof test levels will eliminate some of the larger flaws in the fibre. However, the exact impact to optical fibre reliability in a deployed cable is hard to determine without more information on the overall flaw distribution in the fibre. One way to illustrate this would be to proof-test an optical cable at a level just shy of the intrinsic strength of the fibre, or about 3.8 GPa (550 kpsi). If a 1,000m fibre sample generated from that experiment were left at a constant stress of 110 kpsi, the fibre would likely break in less than a day, or well in advance of the 40-year expected life time. This example is an extreme case, but highlights the importance of understanding the complex equations that govern reliability. 4 Guidance from IEC technical report on reliability One of the currently accepted reliability models has been published by the IEC [4] . One of the equations found in that report is used to predict fibre lifetime – the lifetime equation for optical fibre after proof testing. This can be shown as the following expression:

The traditional rule of thumb that has been used to derive 20 per cent of the proof stress as a long-term maximum allowable load assumes these two variables are independent, which is not consistent with Figure 1 . Hundreds of kilometres of fibre must be tested to fully understand the relationship between the failure rate and the applied stress. Table 1 gives the results comparing three scenarios. The first is 0.69 GPa proof-tested fibre with a long-term load of 20 per cent of the proof-test load. Generating the data we used following values substituted into Equation 1 : n d =20 m d = 2.5 t p = 0.05 seconds N p = 1 break every 250km The table shows that an optical fibre meeting the conservative criteria above would exhibit reasonable mechanical performance for the 0.69 GPa at 20 per cent of the proof test level. The second case shows that the same fibre was maintained at 40 per cent of the proof test level. In this case, the 1ppm failure rate would be reached in less than a year. The third case is 1.38 GPa proof-tested fibre with a long-term load of 20 per cent of the proof test level. For this set of conditions, 1ppm failure probability is met in less than six years. Note that data in Table 1 is representative of fibre in a non-aggressive environment. Terms such as zero stress ageing, macro bends, abrasion and other factors can greatly reduce the fibre lifetime. 5 Discussion Fibre lifetime is the sum of the intrinsic and extrinsic failure probability. This paper focuses on long lengths of fibre under axial load in a regime where failure is dominated by extrinsic failures. The results shown in Table 1 highlight the error in the common requirement for optical cables, which holds that the long-term load on the optical fibres is simply 20 per cent of the proof-test level. If the fibre break rate was the same for the 0.69 GPa and 1.38 GPa proof tested fibre, then both fibres would have the same 1ppm life-time. We know this is not the case from the data of Figure 1 . When this knowledge is included in the analysis, the results change dramatically. Typically, long-term reliability expectation for optical cables is that the fibre failure probability should be less than 1ppm in 30 years.

Where: t f is time to failure (lifetime) t p is proof test time σ p is proof test stress σ a is applied stress F is failure probability N p

is the proof test break rate L is the length under tension m d is the Weibull m parameter from dynamic fatigue n is the stress corrosion parameter The expression is complex, but we can make a few observations. Figure 1 shows that the greater the applied stress, the greater the failure probability. Thus, the failure probability term in the equation, F, is directly related to the applied stress term, σ a .

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Wire & Cable ASIA – May/June 2015