A new path independent integral applied to notched components under mode I loadings

In the present work, the J-integral is applied to rounded V-shaped notches subjected to mode I loading. The material is thought of as obeying a purely linear elastic law. Both numerical and analytical solutions are presented, after careful study of the principal stress along the notch-free edge. When the notch depth-to-radius ratio tends toward infinity, this stress assumes a cosine-type form. Indeed, some analogies with respect to sharp V-shaped notches are highlighted. If an appropriate integration path is chosen, an operator, JL(rho), is defined, which is invariant with respect to the integration radius and coincides with that pertaining to a sharp V-shaped notch of the same depth. This operator allows estimation of stress concentration factor Kt for V-shaped notches under mode I loading on the basis of the relevant Notch Stress Intensity Factors (N-SIF). A sound agreement is achieved, in particularly in U-notch cases, since the notch depth-to-radius ratio is taken into account as well as the real notch profile.