Modeling failure of high performance fibers: on the prediction of long-term time-to-failure

Our objective is to predict the time-to-failure distribution of fibers at loads for which mean time-to-failure is comparable or longer than the fibers' economic lifetime. We describe load induced time-to-failure of high performance fiber in terms of a classical probabilistic failure model developed by Coleman. Mimicking a series of time-to-failure measurements, using Monte Carlo simulations, we will show how to capture model parameters and their variability using the least squares method and maximum likelihood estimation. It is relatively easy to obtain an accurate prediction for the maximum allowable fiber load such that time-to-failure exceeds a predefined minimum time-to-failure with high probability. However, obtaining a reliable lower prediction limit for time-to-failure at a given, low fiber load is very difficult and requires an unfeasible extensive program of time-to-failure measurements.