Scaling of quasibrittle fracture: Asymptotic analysis

Zdeněk P. Bažant*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

201 Scopus citations


Fracture of quasibrittle materials such as concrete, rock, ice, tough ceramics and various fibrous or particulate composites, exhibits complex size effects. An asymptotic theory of scaling governing these size effects is presented, while its extension to fractal cracks is left to a companion paper [1] which follows. The energy release from the structure is assumed to depend on its size D, on the crack length, and on the material length cf governing the fracture process zone size. Based on the condition of energy balance during fracture propagation and the condition of stability limit under load control, the large-size and small-size asymptotic expansions of the size effect on the nominal strength of structure containing large cracks or notches are derived. It is shown that the form of the approximate size effect law previously deduced [2] by other arguments can be obtained from these expansions by asymptotic matching. This law represents a smooth transition from the case of no size effect, corresponding to plasticity, to the power law size effect of linear elastic fracture mechanics. The analysis is further extended to deduce the asymptotic expansion of the size effect for crack initiation in the boundary layer from a smooth surface of structure. Finally, a universal size effect law which approximately describes both failures at large cracks (or notches) and failures at crack initiation from a smooth surface is derived by matching the aforementioned three asymptotic expansions.

Original languageEnglish (US)
Pages (from-to)19-40
Number of pages22
JournalInternational Journal of Fracture
Issue number1
StatePublished - 1997


  • Asymptotic methods
  • Crack initiation
  • Energy release
  • Load capacity
  • Nonlinear fracture mechanics
  • Quasibrittle fracture
  • Scaling
  • Size effect
  • Stable load growth
  • Structural strength

ASJC Scopus subject areas

  • Computational Mechanics
  • Modeling and Simulation
  • Mechanics of Materials


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