Estimating Terminal Velocity of Rough Cracks in the Framework of Discrete Fractal Fracture Mechanics

TL;DR

This paper investigates the terminal velocity of rough, fractal cracks by analyzing stress singularities, roughness limits, and energy balance, revealing that crack speed approaches a material-dependent fraction of Rayleigh wave speed.

Contribution

It introduces a novel approach to predict the terminal velocity of fractal cracks using asymptotic energy balance and fractal geometry analysis.

Findings

Crack roughness reaches an upper bound during propagation.

Terminal crack velocity is a material-dependent fraction of Rayleigh speed.

The study provides a theoretical framework for dynamic fractal crack propagation.

Abstract

In this paper we first obtain the order of stress singularity for a dynamically propagating self-affine fractal crack. We then show that there is always an upper bound to roughness, i.e. a propagating fractal crack reaches a terminal roughness. We then study the phenomenon of reaching a terminal velocity. Assuming that propagation of a fractal crack is discrete, we predict its terminal velocity using an asymptotic energy balance argument. In particular, we show that the limiting crack speed is a material-dependent fraction of the corresponding Rayleigh wave speed.