A Recipe for Composite Materials: An Approach through Fiber Bundle Model

TL;DR

This paper investigates the fracture process of composite materials using a fiber bundle model, analyzing how the distribution of fiber strengths and the number of components influence the likelihood of abrupt failure.

Contribution

It introduces an analytical and numerical study of the critical threshold distribution width in fiber bundle models with multiple components, revealing its inverse relation to the number of fibers.

Findings

Critical width of threshold distribution decreases with more fibers.

Abrupt failure tendency reduces as the number of components increases.

Phase diagram shows decreased abrupt fracture risk with larger composites.

Abstract

Strengthening of materials and preventing abrupt fracture are really challenging jobs in the field of engineering and material science. Such problems can be resolved by using composite materials. In this work, we have studied the fracture process of a composite material in light of fiber bundle model with different elastic constants as well as different random threshold breaking strength of fibers. The critical width of the threshold distribution ($\delta_c$), for which abrupt failure occurs, is studied both analytically and numerically with increasing number of components $(k)$ in the composite and it is shown that $\delta_c$ is inversely related to $k$. Corresponding phase diagram for the model suggests decrease in the tendency of abrupt fracture as number of components in the composite increase.