R-curve modeling of rate and size effects in quasibrittle fracture

Zdeněk P. Bažant*, Milan Jirásek

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

55 Scopus citations


The equivalent linear elastic fracture model based on an R-curve (a curve characterizing the variation of the critical energy release rate with the crack propagation length) is generalized to describe both the rate effect and size effect observed in concrete, rock or other quasibrittle materials. It is assumed that the crack propagation velocity depends on the ratio of the stress intensity factor to its critical value based on the R-curve and that this dependence has the form of a power function with an exponent much larger than 1. The shape of the R-curve is determined as the envelope of the fracture equilibrium curves corresponding to the maximum load values for geometrically similar specimens of different sizes. The creep in the bulk of a concrete specimen must be taken into account, which is done by replacing the elastic constants in the linear elastic fracture mechanics (LEFM) formulas with a linear viscoelastic operator in time (for rocks, which do not creep, this is omitted). The experimental observation that the brittleness of concrete increases as the loading rate decreases (i.e. the response shifts in the size effect plot closer to LEFM) can be approximately described by assuming that stress relaxation causes the effective process zone lenght in the R-curve expression to decrease with a decreasing loading rate. Another power function is used to describe this. Good fits of test data for which the times to peak range from 1 sec to 250000 sec are demonstrated. Furthermore, the theory also describes the recently conducted relaxation tests, as well as the recently observed response to a sudden change of loading rate (both increase and decrease), and particularly the fact that a sufficient rate increase in the post-peak range can produce a load-displacement response of positive slope leading to a second peak.

Original languageEnglish (US)
Pages (from-to)355-373
Number of pages19
JournalInternational Journal of Fracture
Issue number4
StatePublished - Aug 1 1993

ASJC Scopus subject areas

  • Computational Mechanics
  • Modeling and Simulation
  • Mechanics of Materials

Fingerprint Dive into the research topics of 'R-curve modeling of rate and size effects in quasibrittle fracture'. Together they form a unique fingerprint.

Cite this