Tearing of thin sheets: Cracks interacting through an elastic ridge

TL;DR

This paper investigates how two cracks in a thin brittle sheet interact during tearing, revealing power-law behaviors influenced by elastic and fracture energies, with experimental validation and new regimes identified.

Contribution

It introduces a detailed analysis of crack interactions through elastic ridges, identifying two distinct power-law regimes and their underlying mechanics.

Findings

Cracks attract each other following a power law with exponent 8/11.

A second regime with exponent 9/8 appears at small crack tip distances.

Experimental results closely match the theoretical power-law predictions.

Abstract

We study the interaction between two cracks propagating quasistatically during the tearing of a thin brittle sheet. We show that the cracks attract each other following a path described by a power law resulting from the competition between elastic and fracture energies. The power law exponent (8/11) is in close agreement with experiments. We also show that a second (asymptotic) regime, with an exponent of 9/8, emerges for small distances between the two crack tips due to the finite transverse curvature of the elastic ridge joining them.