Scaling of quasi-brittle fracture and the fractal question

Zdenĕk P. Bažant*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


The paper represents an extended text of a lecture presenting a review of recent results on scaling of failure in structures made of quasibrittle materials, characterized by a large fracture process zone, and examining the question of possible role of the fractal nature of crack surfaces in the scaling. The problem of scaling is approached through dimensional analysis, the laws of thermodynamics and asymptotic matching. Large-size and small-size asymptotic expansions of the size effect on the nominal strength of structures are given, for specimens with large notches (or traction-free cracks) as well as zero notches, and simple size effect formulas matching the required asymptotic properties are reported. The asymptotic analysis is carried out, in general, for fractal cracks, and the practically important case of nonfractal crack propagation is acquired as a special case. Regarding the fractal nature of crack surfaces in quasibrittle materials, the conclusion is that it cannot play a signification role in fracture propagation and the observed size effect. The reason why Weibull statistical theory of random material strength does not explain the size effect in quasibrittle failures is explained. Finally, some recent applications to fracture simulation by particle models (discrete element method) and to the determination of size effect and fracture characteristics of carbon-epoxy composite laminates are briefly reviewed.

Original languageEnglish (US)
Pages (from-to)361-367
Number of pages7
JournalJournal of Engineering Materials and Technology, Transactions of the ASME
Issue number4
StatePublished - Oct 1995

ASJC Scopus subject areas

  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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