The Breakdown of Linear Elastic Fracture Mechanics near the Tip of a Rapid Crack

TL;DR

This study investigates the limitations of linear elastic fracture mechanics (LEFM) near crack tips in brittle elastomers, revealing deviations from LEFM predictions at high crack velocities through high-resolution experimental measurements.

Contribution

The paper provides high-resolution experimental data showing the breakdown of LEFM near crack tips in dynamic fractures of brittle elastomers, highlighting non-uniqueness of stress intensity and strain singularities.

Findings

Stress intensity factor appears non-unique near the crack tip

Crack tip deviates from parabolic shape predicted by LEFM

Strains ahead of the crack tip are more singular than LEFM predicts

Abstract

We present high resolution measurements of the displacement and strain fields near the tip of a dynamic (Mode I) crack. The experiments are performed on polyacrylamide gels, brittle elastomers whose fracture dynamics mirror those of typical brittle amorphous materials. Over a wide range of propagation velocities ($0.2-0.8c_s$), we compare linear elastic fracture mechanics (LEFM) to the measured near-tip fields. We find that, sufficiently near the tip, the measured stress intensity factor appears to be non-unique, the crack tip significantly deviates from its predicted parabolic form, and the strains ahead of the tip are more singular than the $r^{-1/2}$ divergence predicted by LEFM. These results show how LEFM breaks down as the crack tip is approached.