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Energy scaling, size effects and ductile-brittle transitions in fracture

The strain energy release rate at a growing crack which preserves geometrical similarity is proportional to the crack length. If this in turn scales with some dimensional imposed by the test, the apparent critical stress for fracture will be a function of that dimension; this explains numerous such size effects reported in the literature. Such effects may be associated with any field of inhomogeneous tensile stress. For cracks developed in plastic-elastic stress fields the strain energy release rate is a function of the linear dimension of the plastic zone, and a ductile-brittle transition occurs when the critical zone size for crack instability is equal to some specimen or test dimension. This consideration is used to compare the behaviour of a wide range of materials in two tests, notched bar and indentation.