Volume 52 Issue 3
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Wu X R, Xu W. Weight function theory and applications for crack analysis: A review and outlook. Advances in Mechanics, 2022, 52(3): 415-507 doi: 10.6052/1000-0992-21-060
Citation: Wu X R, Xu W. Weight function theory and applications for crack analysis: A review and outlook. Advances in Mechanics, 2022, 52(3): 415-507 doi: 10.6052/1000-0992-21-060

Weight function theory and applications for crack analysis: A review and outlook

doi: 10.6052/1000-0992-21-060
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  • Corresponding author: xrwu621@163.com
  • Received Date: 2021-11-29
  • Accepted Date: 2022-02-09
  • Available Online: 2022-03-07
  • Publish Date: 2022-09-25
  • Fracture mechanics is the theoretical foundation for fatigue and fracture analyses of engineering materials and structures, damage tolerance design, and structural integrity assessment. Being the single characterizing parameter of the linear elastic crack tip singular stress/strain field and the crack deriving force, the stress intensity factor (SIF) plays a vital role in fracture mechanics analysis. The weight function method (WFM) is a powerful method for the determination of SIFs for cracks under complex load conditions, with remarkable computational efficiency and reliable solution accuracy, and is easy to use. Combined with the authors’ teamwork on WFM research in the past several decades, this article presents a comprehensive review of the historical developments of various WFMs over the past 50 years and also a brief outlook. The main topics include: a brief introduction of three types of analytical weight function approaches for 2D crack problems and accuracy verification based on Green’s functions; the slice synthesis weight function method and the point weight function method for 3D crack problems; various practical applications of WFMs, including determination of the key fracture mechanics parameters of SIFs and crack opening displacements under complex loadings, cohesive/bridging model analyses, WFM for multiple collinear cracks and residual strength prediction of panels containing multiple site damage, engineering weight function approaches to complex crack configurations, and inverse application of WFM for the determination of stress distributions in un-cracked bodies.

     

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