A boundary layer framework considering material gradation effects

Do Jun Shim, Glaucio H. Paulino, Robert H. Dodds

Research output: Contribution to journalArticlepeer-review


This paper describes the development and application of a novel modified boundary layer (MBL) model for graded nonhomogeneous materials, e.g. functionally graded materials (FGMs). The proposed model is based on a middle-crack tension, M(T), specimen with traction boundary conditions applied to the top and lateral edges of the model. Finite element analyses are performed using WARP3D, a fracture mechanics research finite element code, which incorporates elements with graded elastic and plastic properties. Elastic crack-tip fields obtained from the proposed MBL model show excellent agreement with those obtained from full models of the cracked component for homogeneous and graded nonhomogeneous materials. The K-T dominance of FGMs is investigated by comparing the actual stress fields with the asymptotic stress fields (the Williams' solution). The examples investigated in the present study consider a crack parallel to the material gradient. Results of the present study provide insight into the K-T dominance of FGMs and also show the range of applicability of the proposed MBL model. The MBL model is applied to analyze the elastic-plastic crack-tip response of a Ti/TiB FGM SE(T) specimen. The numerical results demonstrate that the proposed MBL model captures the effect of T-stress on plastic zone size and shape, constraint effects, etc. for such configurations.

Original languageEnglish (US)
Pages (from-to)593-615
Number of pages23
JournalEngineering Fracture Mechanics
Issue number5
StatePublished - Mar 2006
Externally publishedYes


  • 3-D finite element analysis
  • Functionally graded material (FGM)
  • Graded element
  • K-T dominance
  • Modified boundary layer model

ASJC Scopus subject areas

  • General Materials Science
  • Mechanics of Materials
  • Mechanical Engineering


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