An explicit weight function which allows determination of the stress intensity factor for a semi-elliptical surface crack under arbitrary loading is proposed. It was derived by the approximate solution valid for an embedded elliptical crack in infinite body, and a suitable corrective function to account for the free surface effect was obtained on the basis of several accurate stress intensity factor solutions found in literature. By this weight function and a simple numerical quadrature, the SIF at any point of the crack front can be calculated for any loading condition. The method requires negligible time for model preparation and elaboration and little computing resources. It was tested for many crack shapes and loading conditions, and an accuracy of a few percent in the stress intensity factor evaluation was observed. This suggests using the proposed weight function in many practical problems, typical for pressure vessel technology, in which several fracture mechanics analyses are required.

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