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Lug is one of the most important lap joints in many engineering structures, especially airframes. Through‐thickness and part‐through cracks emanating from pin‐loaded lug hole are frequently encountered due to stress concentration. Stress intensity factors for various crack geometries are the prerequisite for damage tolerance design of attachment lug. In this paper, analytical 2D weight functions for through‐thickness crack in lug are derived considering the contact condition between the pin and lug. With the derived 2D weight function, a highly efficient 3D slice synthesis weight function method (SSWFM) is then developed to determine 3D SIFs of hole‐edge corner/surface crack in straight and tapered lugs under various pin loadings. The resulting 3D SIFs are verified by comparisons with the numerical FEM/Franc3D solutions and literature data. The SSWFM is about 1800 times faster than the numerical FEM/Franc3D and therefore will significantly enhance damage tolerance analysis capability for attachment lugs. Highlights: Accurate and wide‐range weight functions of pin‐loaded cracked lug are derived considering the contact constraint.A 3D weight function method for corner and surface cracks of lug is established.It is accurate and much faster than FEM for SIF calculation. [ABSTRACT FROM AUTHOR]

The stress intensity factor (SIF) is the foundation of fracture mechanics analysis. Accurate determination of SIFs is at the very heart of damage tolerance design and fatigue crack growth life prediction. The weight function method (WFM) is a powerful method for SIF‐determination involving complex load conditions. This article presents a review of the historical development over the past five decades and the current state‐of‐the‐art in three‐dimensional (3D) WFMs. The discussions are focused on the slice synthesis weight function method (SSWFM) and the point weight function method (PWFM). The powerfulness of the 3D WFMs is shown by a variety of examples with complex part‐through crack configurations under uni‐ and bi‐variant loadings. Solution accuracy is verified by comparisons of SIFs with various numerical methods. Use of the substitute geometry concept to expand the capability of 3D WFMs for solving real‐world engineering 3D crack problems is demonstrated. Some remaining challenges are briefly discussed. Highlights: This article presents a review of the historical development and the current state‐of‐the‐art in 3D WFMs.The 3D WFMs is powerful for complex part‐through crack configurations.The WFMs can solve real‐world 3D crack problems with substitute geometry concept.Some remaining challenges are briefly discussed. [ABSTRACT FROM AUTHOR]