Fracture Roughness Scaling: a case study on planar cracks

TL;DR

This study investigates the roughness of planar fracture fronts, revealing two distinct regimes with different scaling behaviors separated by a crossover length, and relates these to fracture mechanics models.

Contribution

It identifies and characterizes two roughness regimes in fracture fronts and links the crossover scale to fracture toughness and stress intensity fluctuations.

Findings

Below crossover, roughness exponent is 0.60, consistent with coalescence model.

Above crossover, roughness exponent is 0.35, consistent with fluctuating line model.

Crossover length scale relates to fluctuations in fracture toughness.

Abstract

Using a multi-resolution technique, we analyze large in-plane fracture fronts moving slowly between two sintered Plexiglas plates. We find that the roughness of the front exhibits two distinct regimes separated by a crossover length scale $\delta^*$. Below $\delta^*$, we observe a multi-affine regime and the measured roughness exponent $\zeta_{\parallel}^{-} = 0.60\pm 0.05$ is in agreement with the coalescence model. Above $\delta^*$, the fronts are mono-affine, characterized by a roughness exponent $\zeta_{\parallel}^{+} = 0.35\pm0.05$, consistent with the fluctuating line model. We relate the crossover length scale to fluctuations in fracture toughness and the stress intensity factor.