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

Abstract

In this paper I have studied the fiber bundle model with a fraction α of infinitely strong fibers. Inclusion of such 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) study of failure abruptness, mainly the brittle to quasi-brittle transition point (δ_c ) with varying α and (ii) variation of α_c as we change the disorder introduced in the model. The brittle to quasi-brittle transition is confirmed from the failure abruptness. On the other hand, the α_c is obtained from the knowledge of failure abruptness and statistics of avalanches. It is observed that δ_c scales to lower values, suggesting more quasi-brittle like continuous failure even at low strength of disorder, when α is increased. Also, the critical fraction α_c, required to make the model deviate from the conventional results, increases with decreasing δ values. The analytical expression for α_c shows good agreement with the numerical result. Finally, the findings in the paper are compared with previous results as well as with the real life application of composite materials.