A review of three‐dimensional weight function methods for the analysis of various surface/corner crack problems.

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]