A J-integral-based approach to predict the fatigue strength of components weakened by sharp V-shaped notches

Abstract

In the present paper, Rice's J-integral is applied to sharp V-shaped notches subjected to mixed mode loading. The material is thought of as obeying a linear elastic or a power hardening law. J, which is no longer an invariant, as it was in the crack-case, is analytically given as a function of the relevant Mode I-II Notch Stress Intensity Factors (N-SIFs). As soon as a convenient choice of the integration path is made, J is demonstrated to be able to summarise the fatigue properties of steel and aluminium welded joints of different geometry. By imposing the coincidence between elastic and plastic J-integral values, both the degree of singularity and the plastic N-SIF value are evaluated on the basis of the relevant linear elastic values. When N-SIF's are unknown, a general method suitable for determining J is reported. Finally, a new operator, JL, has been defined for sharp V-shaped notches. It is an invariant in the ambit of validity of the asymptotic stress distributions and in the presence of Mode I loading. In the linear elastic case, JL coincides with Rice's J-integral when the notch opening angle is null (i.e. when the notch becomes a crack).