Fracture Toughness and Maximum Stress in a Disordered Lattice System

TL;DR

This study investigates how disorder in a lattice system affects fracture toughness and maximum stress, revealing that disorder can enhance energy absorption and fracture resistance.

Contribution

It introduces a disordered lattice model with mixed spring types and demonstrates that disorder can increase fracture toughness and maximum stress compared to uniform systems.

Findings

Maximum stress is higher in disordered systems.

Fracture energy is larger in some disordered configurations.

Disorder leads to more tortuous fracture surfaces.

Abstract

Fracture in a disordered lattice system is studied. In our system, particles are initially arranged on the triangular lattice and each nearest-neighbor pair is connected with a randomly chosen soft or hard Hookean spring. Every spring has the common threshold of stress at which it is cut. We make an initial crack and expand the system perpendicularly to the crack. We find that the maximum stress in the stress-strain curve is larger than those in the systems with soft or hard springs only (uniform systems). Energy required to advance fracture is also larger in some disordered systems, which indicates that the fracture toughness improves. The increase of the energy is caused by the following two factors. One is that the soft spring is able to hold larger energy than the hard one. The other is that the number of cut springs increases as the fracture surface becomes tortuous in disordered systems.