Material independent crack arrest statistics

TL;DR

This paper models crack propagation in heterogeneous brittle materials, revealing universal critical behavior and deriving statistical distributions for crack arrest, with applications to indentation cracks in alumina.

Contribution

It introduces a universal framework for crack arrest statistics in heterogeneous materials, linking phase transition theory to crack propagation and arrest phenomena.

Findings

Crack propagation exhibits universal critical exponents independent of local medium properties.

Derived an analytical expression for the distribution of crack radii at arrest.

Experimental data on alumina indentation cracks agree with the theoretical predictions.

Abstract

The propagation of (planar) cracks in a heterogeneous brittle material characterized by a random field of toughness is considered, taking into account explicitly the effect of the crack front roughness on the local stress intensity factor. In the so-called strong-pinning regime, the onset of crack propagation appears to map onto a second-order phase transition characterized by universal critical exponents which are independent of the local characteristics of the medium. Propagation over large distances can be described by using a simple one-dimensional description, with a correlation length and an effective macroscopic toughness distribution that scale in a non-trivial fashion with the crack front length. As an application of the above concepts, the arrest of indentation cracks is addressed, and the analytical expression for the statistical distribution of the crack radius at arrest is derived. The analysis of indentation crack radii on alumina is shown to obey the predicted algebraic expression for the radius distribution and its dependence on the indentation load.