Disorder induced brittle to quasi-brittle transition in fiber bundles

TL;DR

This paper studies how disorder in fiber stiffness causes a transition from brittle to quasi-brittle failure in fiber bundles, revealing critical behavior and phase transition characteristics.

Contribution

It introduces a disorder-induced transition in fiber bundle failure, analyzing the critical exponents and phase diagram through simulations.

Findings

Disorder lowers the strength of fiber mixtures compared to individual components.

A brittle to quasi-brittle transition occurs with power-law distributed stiffness.

Critical exponents and phase diagram of the transition are determined.

Abstract

We investigate the fracture process of a bundle of fibers with random Young modulus and a constant breaking strength. For two component systems we show that the strength of the mixture is always lower than the strength of the individual components. For continuously distributed Young modulus the tail of the distribution proved to play a decisive role since fibers break in the decreasing order of their stiffness. Using power law distributed stiffness values we demonstrate that the system exhibits a disorder induced brittle to quasi-brittle transition which occurs analogously to continuous phase transitions. Based on computer simulations we determine the critical exponents of the transition and construct the phase diagram of the system.