Strength of Optical fibers – Weibull Statistics

Have you ever searched the formula to calculate the strength of optical fibers? Many of our readers have asked to write a post about the strength of optical fibers. Therefor we requested our expert content contributors to provide a blogpost for strength of optical fibers. Here you can read that post;

Optical fibers have very high linear strength, which is attributed to the pure nature of the material used to manufacture optical fiber i.e. silica. Silica glass optical fibers on the contrary are highly brittle also. This nature of brittleness of silica glass induces many micro-cracks on the surface of the glass portion of optical fiber.

These micro-cracks grow when the optical fibers goes to make cables through coloring process, Loose tube making process/Ribbon process, Stranding and subsequent armoring and sheathing process. The subsequent processes induce strain on optical fibers and the strain causes the micro-cracks to grow.

The rate of micro-crack growth is an important parameter to determine the lifetime of optical fiber when they are held under strain like those happening in optical fiber cables laid in ducts/buried or aerially. The bending induced by the cabling process will result in the growth of micro-cracks.

So, it is important to understand and identify the nature of micro-crack population and the crack growth before being able to predict the fiber performance. Weibull statistics do look into those micro-cracks by describing crack or flaw distributions using Weibull statistics.

For brittle materials we make use of Weibull statistics to analyze the nature. The basic formula used by Weibull statistics to describe a failure mode is given below:

Weibull formula for strength of optical fiber
Weibull formula for Strength of Optical fiber

Where,
Fp is the Failure probability for individual fiber sample
L is the length of optical fiber
m is the flaw population constant describing distribution range of flaw population
a is the breaking stress and
ao is the Characteristic stress describing relative value of flaw population

A weibull plot is a plot of log In 1/1-Fp against log a. A random set of breaking stresses will produce a straight line with a gradient of m.

Low strength breaks are attributable to flaws induced while manufacturing the optical fibers including proof testing. These flaws are called as extrinsic flaws. The intrinsic flaws are the tighter distribution of high strength breaks are attributable to silica bonding.

In order to fully characterize the strength performance of optical fibers, it is required to determine the m values and associated constants for all flaw populations. The effect of gauge length while comparing two weibull plots is also important. There is greater chance of finding low strength flaws in each length for longer lengths. The fiber breaks during service of an optical fiber in the cable has its route in the above mentioned point. If shorter lengths are used then a greater number of tests shall be conducted to get information on the same number of larger cracks.

In order to determine the behavior of intrinsic flaws short gauge lengths are used some times. Small number of tests can be used to characterize the population as intrinsic flaws are part of a uniform distribution. This information is useful in investigating the effects of a parameter known to influence all flaw populations in the same way.

We have referred the technical note issued by Optical Fibers, UK in preparing this post.

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