Material-independent crack arrest statistics: application to indentation experiments

Abstract

An extensive experimental study of indentation and crack arrest statistics is presented for four different brittle materials (alumina, silicon carbide, silicon nitride, glass). Evidence is given that the crack length statistics is described by a universal (i.e., material independent) distribution. The latter directly derives from results obtained when modeling crack propagation as a depinning phenomenon. Crack arrest (or effective toughness) statistics appears to be fully characterized by two parameters, namely, an asymptotic crack length (or macroscopic toughness) value and a power law size-dependent width. The experimental knowledge of the crack arrest statistics at one given scale thus gives access to its knowledge at all scales.

Self-consistent scheme for toughness homogenization

“…An extension of this theory to three dimensional cracks that allow for an experimental interpretation of 3D crack roughness from such a planar pinning problem has been recently proposed (Bonamy et al 2006.) Last, still on the experimental side, let us mention that the analysis of crack arrest statistics of indentation cracks has been proposed based on the above presented depinning critical features (Charles et al 2004(Charles et al , 2006.…”

A critical evaluation of indentation crack lengths in air

“…The data measured here spanned more than 20 materials and consisted in most cases of more than 100 cracks/material over a large indentation load domain. The data from the selected publications by others spanned 10 materials and were typically concentrated over a smaller load domain but with a greater number of observations/load; extreme examples were the probabilistic studies of Charles et al, in which several hundred observations were collected for few indentation loads. In all, over 3500 indentation cracks in air from over 30 materials were analyzed here.…”

“…Reported data were manually digitized and converted to the common format of Equation 5. In some cases the data were reported as T air or a related quantity, 19,21,24,25 in some cases the data were reported as the reduced crack length l(P), 15 and in some cases the data were reported as the probability Pr(c air ) 22,23 (see above sections for notation).…”

Failure of heterogeneous materials: A dynamic phase transition?

“…These results were used [180] to predict the statistics of crack arrest lengths in various brittle materials for various indentation forces, and shown to describe the data fairly well (Fig. 51(b)).…”