A Proposed Weight Function Method for 3-D Embedded Cracks Subject to Arbitrary Stress Distribution

Abstract The current library of API 579-1/ASME FFS-1 2021 Fitness-for-Service (API 579-1) stress intensity factor solutions includes options for arbitrary stress distributions in the thickness direction applied to various semi-elliptical surface crack configurations. However, for elliptical embedded cracks, the listed solutions are limited to fourth order polynomial stress distributions, which can be a poor approximation in some applications. To address this limitation, a new approximate weight function method is proposed. The proposed method shares several theoretical and practical similarities with the API 579-1 Annex 9B approach used for surface cracks subject to arbitrary stress distributions and with the 2-D embedded crack weight function solutions from Altstadt [2024]. However, as shown in the provided derivation, the proposed weight function approach for elliptical embedded cracks also has some distinct differences. The proposed weight function is intended for plates and axially oriented elliptical embedded cracks in cylinders. Stress intensity factor solutions from the integration of the product of the weight functions and stress distributions were compared to linear elastic finite element results for representative geometries. As with any approximate weight function approach, the accuracy of the method is partially dependent on the number of weight function terms included. For typical fitness for service applications, reasonably accurate results are found when five or six coefficients are included in the respective weight functions; however, fewer terms can be successfully used for some embedded cracked scenarios. Discussion is provided on the limitations of applicability and opportunities for possible refinements. Future efforts will examine if the newly proposed method can be used for embedded circumferential cracks in cylinders, meridional cracks in spheres, and other cracked component configurations.