Fiber bundle model of thermally activated creep failure

TL;DR

This paper introduces a fiber bundle model for thermally activated creep failure, deriving lifetime distributions and scaling laws that align with simulations and previous theories, enhancing understanding of thermal breakdown in materials.

Contribution

It develops a new equal load sharing fiber bundle model using transition state theory, providing analytical and simulation results for lifetime distributions under thermal activation.

Findings

Lifetime distribution matches simulations for uniform thresholds.

Asymptotic scaling agrees with Gaussian noise models at low temperature.

Avalanche size distribution aligns with earlier quasistatic loading theories.

Abstract

An equal load sharing fiber bundle model for thermally activated breakdown is developed using transition state theory to describe the rate of elementary failures. The lifetime distribution, average, variance and their asymptotic limits for uniform fiber failure thresholds are derived and found to be in excellent agreement with simulations. The asymptotic scaling with regards to the number of fibers matches analytical approximations in the low temperature limit derived by Roux and co-workers for a model of thermal breakdown by stationary Gaussian noise. For the case of randomly distributed fiber failure strengths, the lifetime distribution is derived as a multidimensional integral with no closed form solution. Simulations with different fiber strength distributions indicate that, in the limit of large fiber numbers, the statistics of bundle lifetimes shows a similar asymptotic scaling for distributed and for uniform thresholds. Fiber breakage by thermal activation occurs in avalanches triggered by individual thermally activated failure events, and the asymptotic avalanche size distribution obtained from the simulations matches earlier theoretical results derived for quasistatic loading.