# Brittle to quasibrittle transition in a compound fiber bundle

## TL;DR

This paper investigates the transition from brittle to quasibrittle failure in a fiber bundle model with bimodal strength distribution, identifying critical parameters that govern the transition.

## Contribution

It introduces a fiber bundle model with a bimodal strength distribution and analytically determines the critical width for brittle to quasibrittle transition.

## Key findings

- Identified the critical width $d_c(s,p)$ for the transition.
- Confirmed the transition through numerical simulations.
- Provided insights into how distribution parameters affect failure behavior.

## Abstract

The brittle to quasibrittle transition has been studied for a compound of two different kinds of fibrous materials, having distinct difference in their breaking strengths under the framework of the fiber bundle model. A random fiber bundle model has been devised with a bimodal distribution of the breaking strengths of the individual fibers. The bimodal distribution is assumed to be consisting of two symmetrically placed rectangular probability distributions of strengths $p$ and $1 - p$, each of width $d$, and separated by a gap $2s$. Different properties of the transition have been studied varying these three parameters and using the well known equal load sharing dynamics. Our study exhibits a brittle to quasibrittle transition at the critical width $d_c(s,p) = p(1/2 - s)/(1 + p)$ confirmed by our numerical results.