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In this paper I have studied the fiber bundle model with a fraction {\alpha}of infinitely strong fibers. Inclusion of such unbreakable fraction has beenproven to affect the failure process in early studies, especially around acritical value {\alpha}_c . The present work has a twofold purpose: (i) studyof failure abruptness, mainly the brittle to quasi-brittle transition point({\delta}_c ) with varying {\alpha} and (ii) variation of {\alpha}_c as wechange the disorder introduced in the model. The brittle to quasi-brittletransition is confirmed from the failure abruptness. On the other hand, the{\alpha}_c is obtained from the knowledge of failure abruptness and statisticsof avalanches. It is observed that {\delta}_c scales to lower values,suggesting more quasi-brittle like continuous failure even at low strength ofdisorder, when {\alpha} is increased. Also, the critical fraction {\alpha}_c,required to make the model deviate from the conventional results, increaseswith decreasing {\delta} values. The analytical expression for {\alpha}_c showsgood agreement with the numerical result. Finally, the findings in the paperare compared with previous results as well as with the real life application ofcomposite materials.

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