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

46 Scopus citations

Abstract

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
Volume137
Issue number8
DOIs
StatePublished - Aug 3 2011

Keywords

  • Cracking
  • Parameters
  • Size effect

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering

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