Snapback instability at crack ligament tearing and its implication for fracture micromechanics

Zdeněk P. Bažant*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


The microcracking in the fracture process zone ahead of a major crack is assumed to consist, in the initial stage, of a two-dimensional array of small circular(penny-shaped) cracks and, in the terminal stage, of a two-dimensional array of small circular ligaments, all located on the main crack plane. Both cases are solved in three-dimensions according to linear elastic fracture mechanics. The solution is approximate but asymptotically exact both for very small circular cracks and very small circular ligaments. The spacing of the cracks as well as the ligaments is governed by the spacing of the large aggregate pieces. The curve of the transverse displacement v due to cracks versus the remote applied normal stress is calculated and is found to exhibit snapback instability at which a negative slope changes to a positive slope and v reaches its maximum possible value. Since several other influencing physical mechanisms were neglected in the analysis, it still remains to be verified whether the snapback instability does actually occur in the concrete fracture process. The asymptotic behavior at ligament tearing is further analyzed, based on St.-Venant's principle, for arbitrary general three- and two-dimensional situations and it is shown that when the ligament transmits a force (mode I, II or III), its final tearing is always characterized by snapback instability, which determines maximum possible displacement due to crack. When, however, the ligaments transmit only a moment (bending or torsional), there is no snapback instability.

Original languageEnglish (US)
Pages (from-to)951-967
Number of pages17
JournalCement and Concrete Research
Issue number6
StatePublished - Nov 1987

ASJC Scopus subject areas

  • Building and Construction
  • Materials Science(all)

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