Fundamental solutions for dilute distributions of inclusions embedded in microcracked solids

K. X. Hu, A. Chandra*, Y. Huang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Dilute distributions of inclusions such as second-phase particles, foreign grains, or other inhomogeneities exist in a variety of materials. In the neighborhood of an inclusion, there is always a possibility of crack initiation due to stress concentration. The problem of a solid containing an inclusion surrounded by multiple cracks is investigated in this paper. The present analysis provides fundamental solutions for crack tip behavior and damage evaluation for a solid containing cracks and dilute distributions of inclusions. A distribution of dislocations approach is pursued to model crack-crack and crack-inclusion interactions accurately and efficiently. Both transformation loading from the inclusion and remote loading on the matrix are considered, and the effects of crack-crack and crack-inclusion interactions are investigated in detail. The numerical results for radial crack systems reveal that crack-inclusion interactions produce stress retardation for the harder inclusions only if the matrix is subject to remote loading. Unlike the remote loading on the matrix, transformation loading on the inclusion produces stress amplification for hard inclusions. The opposite holds for softer or weaker inclusions. It is also observed that crack-crack interactions can produce either retardation or amplification of stress intensity factors, but retardation prevails as the number of radial cracks increases. The competition between crack-crack and crack-inclusion interactions for amplification or retardation is also examined.

Original languageEnglish (US)
Pages (from-to)281-294
Number of pages14
JournalMechanics of Materials
Issue number3
StatePublished - Sep 1993

ASJC Scopus subject areas

  • Materials Science(all)
  • Instrumentation
  • Mechanics of Materials


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