Use of J-integral to predict static failures in sharp V-notches and rounded U-notches

In the present paper, the physical meaning of JV (namely, the classic J-integral applied to either sharp V-notch) is discussed. Consider a Cartesian reference frame having the x-axis parallel to the notch bisector, each mode of JV, for a given circular path, is proportional to the correspondent mode of the classic J-integral of a virtual crack having length equal to the path radius and emanating from the tip of the V-notch. Analytical and numerical results have been performed for linear elastic materials. Additionally, in order to verify the formulations of JV, experimental result of embedded cracks of sharp V-notch was considered. Then, by introducing a characteristic path radius ρ*, assumed to be dependent only on the material properties, the JV parameter was used for the estimation of the static failure load of sharp V-notches specimens under mode I loading. Furthermore, the JVρ parameter (namely, the classic J-integral applied to U-rounded notches) was used to analyze the static failure of two new series of specimens with double U-notches made of brittle material (PMMA and PVC glass) subjected to tensile loading. This method allowed us to prove that when the ratio between the notch tip radius and ρ* is small the approach agrees with the classic J-integral, whereas when ρ* becomes small with respect to the notch tip radius, the JVρ method agrees with the classic peak stress approach