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

Abstract In the present paper, the physical meaning of J V (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 J V , 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 J V , 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 J V parameter was used for the estimation of the static failure load of sharp V-notches specimens under mode I loading. Furthermore, the J V ρ 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 J V ρ method agrees with the classic peak stress approach.