Universal shapes formed by two interacting cracks

TL;DR

This paper explores the universal formation of 'en passant' crack patterns in elastic plates, revealing a consistent 2:1 aspect ratio and a square root shape governed by initial conditions and crack interactions.

Contribution

It introduces a simple geometric model explaining the universal crack shape and aspect ratio across diverse materials.

Findings

Cracks form a 2:1 aspect ratio lenticular fragment.

The shape follows a universal square root form.

The model links crack shape to initial offset and velocity.

Abstract

We investigate the origins of the widely-observed "en passant" crack pattern which forms through interactions between two approaching cracks. A rectangular elastic plate is notched on each long side and then subjected to quasistatic uniaxial strain from the short side. The two cracks propagate along approximately straight paths until they pass each other, after which they curve and release a lenticular fragment. We find that for materials with diverse mechanical properties, the shape of this fragment has an aspect ratio of 2:1, with the length scale set by the initial crack offset $s$ and the time scale set by the ratio of $s$ to the pulling velocity. The cracks have a universal square root shape which we understand using a simple geometric model of the crack-crack interaction.