International Journal of Fracture

, Volume 212, Issue 1, pp 89–103 | Cite as

What is the tensile strength of a ceramic to be used in numerical models for predicting crack initiation?

  • Dominique LeguillonEmail author
  • Eric Martin
  • Oldrich Sevecek
  • Raul Bermejo
Original Paper


Criteria for predicting initiation of cracks in brittle materials like ceramics are based on two parameters: the material fracture toughness and the tensile strength. Standardized experiments exist to estimate the former. However, the tensile strength is often taken from experiments (mainly uniaxial bending) on specimens with various geometries and surface finish, usually tested under ambient conditions at a given loading rate. The reported strength is commonly the Weibull characteristic strength, which scatters due to the critical defect size distribution on the tested specimen. In this work, we propose a definition of the “inherent” or “intrinsic” tensile strength to be used in numerical models, making a distinction between extrinsic defects due to manufacturing and intrinsic ones relying on the microstructure. Our approach is based on the Finite Fracture Mechanics theory and the Coupled Criterion applied to small surface flaws and its influence on the measured (extrinsic) strength. Numerical results are compared with experiments on alumina reported in the literature. In addition, a model for the Petch law (strength vs. grain size) in polycrystalline materials is proposed using the Coupled Criterion, which predicts an initial crack length of increasing numbers of grains as the grain size decreases.


Ceramics Crack initiation Finite fracture mechanics Coupled criterion Tensile strength 



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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Dominique Leguillon
    • 1
    Email author
  • Eric Martin
    • 2
  • Oldrich Sevecek
    • 3
  • Raul Bermejo
    • 4
    • 5
  1. 1.Institut Jean Le Rond d’AlembertSorbonne Université, Centre National de la Recherche ScientifiqueParisFrance
  2. 2.Laboratoire des Composites Thermo-Structuraux, CNRS UMR 5801Université de BordeauxPessacFrance
  3. 3.Institute of Solid Mechanics, Mechatronics and Biomechanics, Faculty of Mechanical EngineeringBrno University of TechnologyBrnoCzech Republic
  4. 4.Institut fuer Struktur- und FunktionskeramikMontanuniversitaet LeobenLeobenAustria
  5. 5.Department of Materials Science and EngineeringThe Pennsylvania State UniversityUniversity ParkUSA

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