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

Abstract

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, J _Lρ, 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 K _t 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.