Arrested Cracks in Nonlinear Lattice Models of Brittle Fracture

TL;DR

This paper extends lattice models of brittle fracture to nonlinear force laws, revealing that arrested cracks are highly sensitive to local conditions and exist within a very narrow displacement range, with potential experimental implications.

Contribution

It introduces a generalized nonlinear lattice model for brittle fracture and analyzes the conditions for arrested cracks, highlighting their sensitivity and narrow existence range.

Findings

Arrested cracks exist in a very small displacement range.

Small local changes near the crack tip greatly affect crack arrest.

Results may have implications for interpreting recent fracture experiments.

Abstract

We generalize lattice models of brittle fracture to arbitrary nonlinear force laws and study the existence of arrested semi-infinite cracks. Unlike what is seen in the discontinuous case studied to date, the range in driving displacement for which these arrested cracks exist is very small. Also, our results indicate that small changes in the vicinity of the crack tip can have an extremely large effect on arrested cracks. Finally, we briefly discuss the possible relevance of our findings to recent experiments.