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.