Role of surface waves on the relation between crack speed and the work of fracture

TL;DR

This paper investigates how surface wave emission influences crack propagation, revealing that phonon emission reduces fracture work delivery and creates forbidden crack speed ranges, with implications for fracture mechanics models.

Contribution

It introduces a new finite element model for large-scale 3D elasticity and fracture simulations, analyzing surface phonon effects on crack speed and energy release.

Findings

Surface phonon emission reduces fracture work delivery.

Forbidden crack speed ranges are identified due to surface wave effects.

A new finite element model enables large-scale 3D fracture simulations.

Abstract

We show that the delivery of fracture work to the tip of an advancing planar crack is strongly reduced by surface phonon emission, leading to forbidden ranges of crack speed. The emission can be interpreted through dispersion of the group velocity, and Rayleigh and Love branches contribute as well as other high frequency branches of the surface wave dispersion relations. We also show that the energy release rate which enters the Griffith criterion for the crack advance can be described as the product of the continuum solution with a function that only depends on the lattice geometry and describes the lattice influence on the phonon emission. Simulations are performed using a new finite element model for simulating elasticity and fractures. The model, built to allow fast and very large three-dimensional simulations, is applied to the simplified case of two dimensional samples.