Relationships between J-integral and the strain energy evaluated in a finite volume surrounding the tip of sharp and blunt V-notches

The concept of “elementary” volume and “micro structural support length” was introduced many years ago by Neuber. Neuber formulated the idea that, also in the presence of a sharp notch, a generic material is sensitive to a fictitious root radius whose value is only simply correlated to the ‘micro-structural support length’ and to the multiaxiality of the stress state. On the other hand, Rice’s J-integral is a commonly used elastic and elastic-plastic fracture parameter for the description of the local fields in the neighbourhood of stress concentrations and for the study of crack initiation and propagation. In order to be applied to un-cracked geometries, J-integral needs a path definition. A particular control area, which embraces the tip of sharp and blunt notches, is defined here, and over that area the mean value of the strain energy E(e) and J-integral are determined under Mode I loading. The semi-moon-like area Ω adapts itself as a function of the notch geometry leaving unchanged its depth Rc measured on the notch bisector line. The variability of the E(e)/J ratio versus Rc is analysed considering sharp V-notches as well as blunt notches with a semicircular root and an opening angle ranging from 0° to 135°. The analyses demonstrated that a linear law permits a link between the two parameters in the case of sharp V-notches and blunt V-notches with a large opening angle. By decreasing the angle, the linear law is valid only as a first approximation, due to the increasing influence of two elliptic integrals in the analytical formulation of J. Some elastic-plastic analyses limited to V-notches with a large opening angle confirm those findings.