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

TL;DR

This study investigates how the presence of unbreakable fibers influences the failure behavior and transition points in the fiber bundle model, revealing that increasing the fraction of strong fibers promotes more continuous, quasi-brittle failure modes.

Contribution

The paper introduces an analytical and numerical analysis of the fiber bundle model with strong fibers, elucidating how their fraction affects failure abruptness and critical thresholds under varying disorder.

Findings

Failure abruptness confirms brittle to quasi-brittle transition.

Critical strong fiber fraction increases as disorder decreases.

Analytical expression for critical fraction matches numerical results.

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.