Size-Effect Testing of Cohesive Fracture Parameters and Nonuniqueness of Work-of-Fracture Method

Zdeněk P. Bažant*, Qiang Yu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

50 Scopus citations


The cohesive crack model has been widely accepted as the best compromise for the analysis of fracture of concrete and other quasibrittle materials. The softening stress-separation law of this model is now believed to be best described as a bilinear curve characterized by four parameters: the initial and total fracture energies Gf and GF, the tensile strength ft', and the knee-point ordinate σ1. The classical work-of-fracture test of a notched beam of one size can deliver a clear result only for GF. Here it is shown computationally that the same complete load-deflection curve can be closely approximated with stress-separation curves in which the ft' values differ by 77% and Gf values by 68%. It follows that the work-of-fracture test alone cannot provide an unambiguous basis for quasibrittle fracture analysis. It is found, however, that if this test is supplemented by size-effect testing, all four cohesive crack model parameters can be precisely identified and the fracture analysis of structures becomes unambiguous. It is shown computationally that size-effect tests do not suffice for determining GF and ft', which indicates that they provide a sufficient basis for computing neither the postpeak softening of fracturing structures nor the peak loads of a very large structure. However, if the size-effect tests are supplemented by one complete softening load-deflection curve of a notched specimen, an unambiguous calculation of peak loads and postpeak response of structures becomes possible. To this end, the notched specimen tests must be conducted in a certain size range, whose optimum is here established by extending a previous analysis. Combination of the work-of-fracture and size-effect testing could be avoided only if the ratios GF/Gf and σ1/ft' were known a priori, but unfortunately their estimates are far too uncertain.

Original languageEnglish (US)
Pages (from-to)580-588
Number of pages9
JournalJournal of Engineering Mechanics
Issue number8
StatePublished - Aug 3 2011


  • Cracking
  • Parameters
  • Size effect

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering


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