Abstract
Within the framework of Bažant’s theory, the size effect on the ultimate fracture properties of notched structures is studied from an energy based asymptotic analysis in which the resistance curve behavior is considered through an analytic expression. The scaling on the relative crack length at peak load as well as the size effect on the corresponding resistance to crack growth are investigated. It is shown that, for intermediate structure sizes, the relative crack length at peak load decreases with respect to the structure size while the resistance grows. These scalings lead to a size effect on nominal strength which is in agreement with Bažant’s Size Effect Law (SEL) for small and large structures sizes, but for intermediate sizes, an additional asymptotic regime occurs instead of a simple crossover regime as expected in SEL. The slope and the extent in size of the additional asymptotic regime depend only on the exponent characterizing the curvature of the R-curve. The comparison between the resulting size effect and Bažant’s SEL shows that SEL provides an approximate size effect which is in agreement with the expected asymptotic behaviors, with the exception of the extreme cases corresponding to very strong and slight R-curve’s curvatures. On this basis, the safety design of large structures is discussed.
Similar content being viewed by others
References
Bažant ZP (1984) Size effect in blunt fracture: concrete, rock, metal. J Eng Mech 110: 518–535
Bažant ZP (1997a) Scaling of structural failure. Appl Mech Rev 50(10):593–627, and references therein
Bažant ZP (1997b) Scaling of quasibrittle fracture: asymptotic analysis. Int J Fract 83: 19–40
Bažant ZP (2000) Size effect. Int J Solid Struct 37:69–80, and references therein
Bažant ZP (2004) Scaling theory for quasibrittle structural failure. Proc Natl Acad Sci 14: 13400–13407
Bažant ZP, Cedolin L (1991) Stability of structures: elastic, inelastic, fracture and damage theories. Oxford University Press, New York, USA
Bažant ZP, Li Z (1996) Zero-brittleness size-effect method for one-size fracture test of concrete. J Eng Mech 122(5): 458–468
Dasgupta R, Hay JC, Ortiz-Longo CR, White KW, Vipulanandan C (1998) Experimental study of the microstructural influence of the strain-softening behavior of cement mortar. Cem Concr Res 28(10): 1429–1444
Ebrahimi ME, Chevalier J, Fantozzi G (2003) R-curve evaluation and bridging stress determination in alumina by compliance analysis. J Eur Ceram Soc 23: 943–949
Morel S (2007) R-curve and size effect in quasibrittle fracture: Case of notched structures. Int J Solid Struct 44: 4272–4290
Morel S, Mourot G, Schmittbuhl J (2003) Influence of the specimen geometry on. R-curve behavior and roughnening of fracture surfaces. Int J Fract 121: 23–42
Morel S, Dourado N, Valentin G, Morais J (2005) Wood: a quasibrittle material. R-curve behavior and peak load evaluation. Int J Fract 131: 385–400
Tran DK, Kobayashi AS, White KW (2001) Crack growth in aluminium at high temperature. Eng Fract Mech 68: 149–161
Weibull W (1939) Phenomenon of rupture in solids. Proc R Swed Inst Eng Res (Ingeniors Vetenskaps Akademien) 153: 1–55
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Morel, S. Size effect in quasibrittle fracture: derivation of the energetic Size Effect Law from equivalent LEFM and asymptotic analysis. Int J Fract 154, 15–26 (2008). https://doi.org/10.1007/s10704-008-9291-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10704-008-9291-6