T-stress, mixed-mode stress intensity factors, and crack initiation angles in functionally graded materials: A unified approach using the interaction integral method

Jeong Ho Kim, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review

Abstract

For linear elastic functionally graded materials (FGMs), the fracture parameters describing the crack tip fields include not only stress intensity factors (SIFs) but also T-stress (nonsingular stress). These two fracture parameters are important for determining the crack initiation angle under mixed-mode loading conditions in brittle FGMs (e.g. ceramic/ceramic such as TiC/SiC). In this paper, the mixed-mode SIFs and T-stress are evaluated by means of the interaction integral, in the form of an equivalent domain integral, in combination with the finite element method. In order to predict the crack initiation angle in brittle FGMs, this paper makes use of a fracture criterion which incorporates the T-stress effect. This type of criterion involves the mixed-mode SIFs, the T-stress, and a physical length scale rc (representative of the fracture process zone size). Various types of material gradations are considered such as continuum models (e.g. exponentially graded material) and micromechanics models (e.g. self-consistent model). Several examples are given to show the accuracy and efficiency of the interaction integral scheme for evaluating mixed-mode SIFs, T-stress, and crack initiation angle. The techniques developed provide a basic framework for quasi-static crack propagation in FGMs.

Original languageEnglish (US)
Pages (from-to)1463-1494
Number of pages32
JournalComputer Methods in Applied Mechanics and Engineering
Volume192
Issue number11-12
DOIs
StatePublished - Mar 14 2003

Keywords

  • Finite element method
  • Functionally graded material
  • Interaction integral
  • Stress intensity factor
  • T-stress

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

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