From fuzziness to robustness - A multi-filament fiber model

Whiskers or fibers can contribute to the strength of bonding layers of electronic and opto-electronic packaging. A model of polymeric bonding layer containing fibers is studied. The reliability of filaments, such as carbon whiskers or nano-tubes, under tensile stress, is characterized by a strength probability distribution with high variance, leading to reliability fuzziness. One of quality engineering's goals is to minimize such fuzziness. Splitting the whisker into numerous smaller whiskers reaches this goal. The intact state becomes multi-state instead of single-state, where complete failure happens when all small whiskers fail. Such multi-state introduces fuzziness into the reliability state of the fiber. We show the increase in internal failure fuzziness reduces the overall reliability fuzziness. Analytical and simulation results demonstrate two special modes of loading: static loading, in which whiskers collapse sequentially under one load, and dynamic loading by repetitive shocks (load pulses) that cause aging of the fiber. The conclusion is that division into smaller whiskers may weaken the fiber but reduce the reliability fuzziness.