Griffith-based analysis of crack initiation location in a Brazilian test

TL;DR

This study uses Griffith criterion and finite element analysis to determine the crack initiation location in Brazilian tests, revealing that current standards are often invalid for many rock-like materials and proposing a new validation protocol.

Contribution

It introduces a comprehensive analysis of crack nucleation in Brazilian tests using the Griffith criterion, expanding beyond the center stress assumption, and provides a practical MATLAB tool for validation.

Findings

The valid range of Brazilian test conditions is narrower than previously thought.

Current standards are often inappropriate for many rock-like materials.

A new protocol and MATLAB tool help validate test conditions for accurate tensile strength estimation.

Abstract

The Brazilian test has been extremely popular while prompting significant debate. The main source of controversy is rooted in its indirect nature; the material tensile strength is inferred upon assuming that cracking initiates at the centre of the sample. Here, we use the Griffith criterion and finite element analysis to map the conditions (jaws geometry and material properties) that result in the nucleation of a centre crack. Unlike previous studies, we do not restrict ourselves to evaluating the stress state at the disk centre; the failure envelope of the generalised Griffith criterion is used to establish the crack nucleation location. We find that the range of conditions where the Brazilian test is valid is much narrower than previously assumed, with current practices and standards being inappropriate for a wide range of rock-like materials. The results obtained are used to develop a protocol that experimentalists can follow to obtain a valid estimate of the material tensile strength. This is showcased with specific case studies and examples of valid and invalid tests from the literature. Furthermore, the uptake of this protocol is facilitated by providing a MATLAB App that determines the validity of the experiment for arbitrary test conditions.