Velocity Fluctuations in Dynamical Fracture: the Role of Microcracks

TL;DR

This paper investigates how interactions between macro and micro cracks in stressed materials cause significant velocity fluctuations, providing a theoretical model that aligns with experimental observations.

Contribution

It introduces a simplified dynamical model of crack interactions that explains velocity fluctuations in fast-moving cracks.

Findings

Crack interactions lead to large velocity fluctuations.

The model qualitatively matches experimental velocity fluctuation data.

A simplified ODE-based approach effectively captures crack dynamics.

Abstract

We address the velocity fluctuations of fastly moving cracks in stressed materials. One possible mechanism for such fluctuations is the interaction of the main crack with micro cracks (irrespective whether these are existing material defects or they form during the crack evolution). We analyze carefully the dynamics (in 2 space dimensions) of one macro and one micro crack, and demonstrate that their interaction results in a {\em large} and {\em rapid} velocity fluctuation, in qualitative correspondence with typical velocity fluctuations observed in experiments. In developing the theory of the dynamical interaction we invoke an approximation that affords a reduction in mathematical complexity to a simple set of ordinary differential equations for the positions of the cracks tips; we propose that this kind of approximation has a range of usefulness that exceeds the present context.