Nano-samples give higher brittle strength by the Griffith energy principle

Abstract

The purpose of this paper is to show that brittle test samples give a huge size effect that can take several different forms depending on the sample geometry, crack position and mode of force application. Sometimes crack equilibrium force depends on sample dimension d or d 1/2 and sometimes the force is independent of area, for example in peel or lap joint cracking. This big size effect arises from the potential energy term in the conservation theory, not considered by Griffith but dominating certain cracks. These examples illustrate the fact that strength of a brittle material containing a crack is an unsatisfactory concept because the cracks absorb surface energy driven by volume energy terms or by potential energy terms or a mixture of the two, leading to a disconnection between applied cracking force and sample cross-section area. The flaw statistics argument mentioned by Griffith is unnecessary, though strength can be affected in certain circumstances by the presence of random flaws. An unusually large size effect is shown experimentally for thermal shock of ceramic tubes, in which the cracking force increases as the cube of diameter goes down. This thermal shock resistance of fine tubes has proved important for application of ceramic fuel cells but cannot be explained by fracture mechanics theory at present. The conclusion is that experimental results show the Griffith energy criterion for cracking is correct whereas the Galilean stress criterion fails. The concept ‘strength of brittle materials’ is therefore untenable for most crack testing geometries. This article is part of the theme issue 'Nanocracks in nature and industry'.