Scaling exponents for fracture surfaces in homogenous glass and glassy ceramics

TL;DR

This study examines the scaling behavior of fracture surfaces in silica glass and glassy ceramics, revealing different roughness exponents and scaling regimes linked to the process zone size, with a LEFM-based model explaining the ceramics' exponents.

Contribution

It provides the first detailed comparison of fracture surface scaling in homogeneous glass and glassy ceramics, introducing a model that reproduces observed exponents in ceramics.

Findings

Family-Viseck scaling observed in both materials

Roughness exponent of ~0.75 in glass, ~0.4 in ceramics

Model based on LEFM reproduces ceramic exponents

Abstract

We investigate the scaling properties of post-mortem fracture surfaces in silica glass and glassy ceramics. In both cases, the 2D height-height correlation function is found to obey Family-Viseck scaling properties, but with two sets of critical exponents, in particular a roughness exponent $\zeta\simeq 0.75$ in homogeneous glass and $\zeta\simeq 0.4$ in glassy ceramics. The ranges of length-scales over which these two scalings are observed are shown to be below and above the size of process zone respectively. A model derived from Linear Elastic Fracture Mechanics (LEFM) in the quasistatic approximation succeeds to reproduce the scaling exponents observed in glassy ceramics. The critical exponents observed in homogeneous glass are conjectured to reflect damage screening occurring for length-scales below the size of the process zone.