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 {\alpha} 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 {\alpha}_c . The present work has a twofold purpose: (i) study of failure abruptness, mainly the brittle to quasi-brittle transition point ({\delta}_c ) with varying {\alpha} and (ii) variation of {\alpha}_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 {\alpha}_c is obtained from the knowledge of failure abruptness and statistics of avalanches. It is observed that {\delta}_c scales to lower values, suggesting more quasi-brittle like continuous failure even at low strength of disorder, when {\alpha} is increased. Also, the critical fraction {\alpha}_c, required to make the model deviate from the conventional results, increases with decreasing {\delta} values. The analytical expression for {\alpha}_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.