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Analytical Applications of the J-Integral

It has recently been shown by experiment that a quantity known as the J-Integral may be a useful fracture criterion in the inelastic range. The mathematical definition of the J-Integral is first used here, in combination with some simplifying assumptions, to derive the known relationship between the conventional elastic stress concentration factor of a sharp notch and the elastic stress intensity factor for a crack of the same shape. The same assumptions, together with a generalization of Neuber's equation for the inelastic stress and strain concentration factors for a sharp notch, are then used to derive a relationship between the J-Integral and the parameter K I c d of the Equivalent Energy Method. The purpose of this derivation is to identify a set of assumptions which, in combination, lead to an explicit relationship between the two parameters. A graphical procedure for estimating upper and lower bounds on the full restraint value of the fracture toughness is also discussed.