Stability in a fiber bundle model: Existence of strong links and the effect of disorder.

Abstract

The present paper deals with a fiber bundle model which consists of a fraction α of infinitely strong fibers. The inclusion of such an unbreakable fraction has been proven to affect the failure process in early studies, especially around a critical value α_{c}. The present work has a twofold purpose: (i) a study of failure abruptness, mainly the brittle to quasibrittle transition point with varying α and (ii) variation of α_{c} as we change the strength of disorder introduced in the model. The brittle to quasibrittle transition is confirmed from the failure abruptness. On the other hand, the α_{c} is obtained from the knowledge of failure abruptness as well as the statistics of avalanches. It is observed that the brittle to quasibrittle transition point scales to lower values, suggesting more quasi-brittle-like continuous failure when α is increased. At the same time, the bundle becomes stronger as there are larger numbers of strong links to support the external stress. High α in a highly disordered bundle leads to an ideal situation where the bundle strength, as well as the predictability in failure process is very high. Also, the critical fraction α_{c}, required to make the model deviate from the conventional results, increases with decreasing strength of disorder. The analytical expression for α_{c} shows good agreement with the numerical results. Finally, the findings in the paper are compared with previous results and real-life applications of composite materials.