International Journal of Fracture

, Volume 154, Issue 1–2, pp 3–14 | Cite as

Size effect and quasi-brittle fracture: the role of FPZ

  • Xiaozhi Hu
  • Kai Duan
Original Paper


Fracture process zone (FPZ), or the crack-tip damage zone created by crack-bridging and micro-cracking activities, in a specimen of a concrete-like material is comparable to the crack size and un-cracked ligament, so fracture is typically quasi-brittle. Increasing or decreasing the specimen size, quasi-brittle fracture transition occurs towards the toughness-controlled or strength-controlled fracture, which is known as size effect (SE). In this study it is shown that the “size-dependent” quasi-brittle fracture transition is actually due to the interaction of FPZ with the nearest structure boundary rather than the size variation, and the widely-accepted SE for geometrically-similar specimens of different sizes is only a special case of quasi-brittle fracture controlled by the FPZ/boundary interaction. Relevant SE relations are critically reviewed and explained by emphasizing the key SE mechanism, FPZ/boundary interaction.


Fracture process zone (FPZ) Size effect (SE) Boundary effect (BE) Tensile strength Fracture toughness Scaling 


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  1. ASTM (1990) E399-90, Standard test method for plane-strain fracture toughness testing of high strength metallic materials. Amer Soc Testing Mater, PhiladelphiaGoogle Scholar
  2. Bazant ZP (1984) Size effect on blunt fracture: concrete, rock, metal. J Eng Mech 110: 518–535CrossRefGoogle Scholar
  3. Bazant ZP, Kazemi MT (1990) Determination of fracture energy, process zone length and brittleness number from size effect, with application to rock and concrete. Int J Fract 44(2): 111–131. doi: 10.1007/BF00047063 CrossRefGoogle Scholar
  4. Duan K, Hu XZ (2004a) Specimen boundary induced size effect on quasi-brittle fracture. Strength Fract Complex 2(2): 47–68Google Scholar
  5. Duan K, Hu XZ (2004b) Asymptotic analysis of boundary-effect on strength of concrete, In: Li VC, Leung CKY, Willam KJ, Billington SL (eds) Fracture mechanics of concrete structures. In: Proceedings of FraMCoS-5, April 12–16, 2004, Vail, Colorado, USA, Ia-FraMCoS, vol 1, pp 197–204Google Scholar
  6. Duan K, Hu XZ (2006) A simple method for evaluating flaw distributions responsible for size effects in the strength of small-scale silicon specimens. Key Eng Mater 312: 77–82CrossRefGoogle Scholar
  7. Duan K, Hu XZ, Wittmann FH (2006) Asymptotic analysis of boundary effects on fracture properties of quasi-brittle materials. Mech Mater 38: 128–141. doi: 10.1016/j.mechmat.2005.05.016 CrossRefGoogle Scholar
  8. Guinea GV, Elices M, Planas J (2000) Assessment of tensile strength through size effect curves. Eng Fract Mech 65: 189–207. doi: 10.1016/S0013-7944(99)00115-0 CrossRefGoogle Scholar
  9. Hillerborg A, Modeer M, Petersson PE (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement Concr Res 6: 773–782. doi: 10.1016/0008-8846(76)90007-7 CrossRefGoogle Scholar
  10. Hu XZ (1998) Size effects in toughness induced by crack close to free edge. In: Mihashi H, Rokugo K (eds) Fracture mechanics of concrete structures. Proceedings of FraMCoS-3, Japan. AEDIFICATIO Publishers, Freiburg, Germany, 1998, pp 2011–2020Google Scholar
  11. Hu XZ (2002) An asymptotic approach to size effect on fracture toughness and fracture energy of composites. Eng Fract Mech 69: 555–564. doi: 10.1016/S0013-7944(01)00102-3 CrossRefGoogle Scholar
  12. Hu XZ, Duan K (2005) Size effect on fracture of MEMS materials. J Mater Sci Tech 21(Suppl 1): 47–50Google Scholar
  13. Hu XZ, Duan K (2007) Size effect: influence of proximity of fracture process zone to specimen boundary. Eng Fract Mech 74: 1093–1100. doi: 10.1016/j.engfracmech.2006.12.009 CrossRefGoogle Scholar
  14. Hu XZ, Cotterell B, Mai YW (1985) A statistical theory of fracture in a two-phase brittle material. Proc R Soc Lond A 401: 251–265ADSMathSciNetGoogle Scholar
  15. Hu XZ, Mai YW, Cotterell B (1988) A statistical theory of time-dependent fracture for brittle materials. Philos Mag 58: 299–324ADSGoogle Scholar
  16. Karihaloo BL, Abdalla HM, Xiao QZ (2003) Size effect in concrete beams. Eng Fract Mech 70: 979–993. doi: 10.1016/S0013-7944(02)00161-3 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.School of Mechanical EngineeringUniversity of Western AustraliaPerthAustralia
  2. 2.PELM & Department of Infrastructures, Faculty of Science, Engineering & HealthCQ-UniversityGladstoneAustralia

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