Strength distribution of dental restorative ceramics: Finite weakest link model with zero threshold

Jia Liang Le, Zdeněk P. Bažant*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


Ensuring a small enough failure probability is important for the design and selection of restorative dental ceramics. For this purpose, the two-parameter Weibull distribution, which is based on the weakest link model with infinitely many links, is usually adopted to model the strength distribution of dental ceramics. This distribution has been thoroughly validated for perfectly brittle materials. However, dental ceramics are generally quasibrittle because the inhomogeneity size is not negligible compared to the size of the ceramic part. For such materials, the experimental histograms of many quasibrittle materials have been shown to exhibit strong deviations from the two-parameter Weibull distribution. As a remedy, the three-parameter Weibull distribution, which has a nonzero threshold, has been proposed. However, the improvement of the fits of histograms of quasibrittle materials has been only partial. Instead of making the threshold non-zero, the correct remedy is to consider the weakest link model to have a finite number of links, each of them representing one finite-size representative volume element of material. This model has recently been justified on the basis of the probability of random jumps of atomic lattice cracks over the activation energy barriers on the free energy potential of the lattice. It is shown that, in similarity to other quasibrittle materials, this new model allows excellent fits of the experimental strength histograms of various types of dental ceramics.

Original languageEnglish (US)
Pages (from-to)641-648
Number of pages8
JournalDental Materials
Issue number5
StatePublished - May 2009


  • Crack propagation
  • Dental ceramics
  • Failure
  • Fracture
  • Probabilistic modeling
  • Safety
  • Scaling
  • Size effect
  • Statistics
  • Strength

ASJC Scopus subject areas

  • Materials Science(all)
  • Dentistry(all)
  • Mechanics of Materials

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