New theory explaining Griffith strength results on nano-cracked glass fibres

The purpose of this paper is to propose a mechanism and theory that can explain the extraordinary increase in measured strength that Griffith observed for glass fibres containing nano-cracks. His 1921 theory (Griffith 1921 Phil. Trans. R. Soc. Lond. A 221, 163-198. (doi:10.1098/rsta.1921.0006)) predicted that the strength of a cracked sample should be independent of sample size, yet his results on stretched glass fibres gave strength increasing almost as the inverse of fibre diameter. He proposed a 'flaw statistics' argument in an attempt to explain these bizarre results, suggesting strength increased because large defects were less likely in the smaller volumes. But this 'flaw statistics' concept is unnecessary because the Griffith energy criterion of cracking must give a size effect, as demonstrated in many different crack-testing configurations. In general, the Griffith energy criterion for crack equilibrium predicts strength rising for smaller samples because such samples contain less volume energy to create new crack surface energy. The problem is that this 'size effect' idea has not until now been properly defined for the simple tension crack test. The new idea proposed is that many nano-cracks are likely to exist in an experimental glass sample, so these must also obey the thermodynamic analysis. A problem then arises because, as the main crack propagates, other cracks may close, but healing is not reversible in glass so thermodynamics does not apply completely to these secondary cracks. Crack healing is in the Griffith theory, which is perfectly reversible mathematically, though not explicitly stated. This article is part of the theme issue 'Nanocracks in nature and industry'.