Exactly solvable model for a velocity jump observed in crack propagation in viscoelastic solids

TL;DR

This paper presents an exactly solvable model that explains the physical origin of the velocity jump in crack propagation within viscoelastic solids, revealing a dynamic glass transition near the crack tip.

Contribution

It introduces a novel solvable model incorporating linear viscoelasticity and a cutoff length, elucidating the velocity jump phenomenon in crack propagation.

Findings

Velocity jump arises from a dynamic glass transition near the crack tip.

The model quantifies slow and fast crack propagation regimes.

Provides insights for developing tougher polymer materials.

Abstract

Needs to impart appropriate elasticity and high toughness to viscoelastic polymer materials are ubiquitous in industries such as concerning automobiles and medical devices. One of the major problems to overcome for toughening is catastrophic failure linked to a velocity jump, i.e., a sharp transition in the velocity of crack propagation occurred in a narrow range of the applied load. However, its physical origin has remained an enigma despite previous studies over 35 years. Here, we propose an exactly solvable model that exhibits the velocity jump incorporating linear viscoelasticity with a cutoff length for a continuum description. With the exact solution, we elucidate the physical origin of the velocity jump: it emerges from a dynamic glass transition in the vicinity of the propagating crack tip. We further quantify the velocity jump together with slow- and fast-velocity regimes of crack propagation, which would stimulate the development of tough polymer materials.