Size effect in quasibrittle fracture: derivation of the energetic Size Effect Law from equivalent LEFM and asymptotic analysis

• Published in: International journal of fracture Vol. 154; no. 1-2; pp. 15 - 26
• Main Author: Morel, Stéphane
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Dordrecht Springer Netherlands 01.11.2008; Springer; Springer Nature B.V; Springer Verlag
• Subjects: Asymptotic properties; Automotive Engineering; Characterization and Evaluation of Materials; Chemical and Process Engineering; Chemistry and Materials Science; Civil Engineering; Classical Mechanics; Crack propagation; Crossovers; Curvature; Engineering Sciences; Exact sciences and technology; Food engineering; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Life Sciences; Materials Science; Mechanical Engineering; Original Paper; Peak load; Physics; Securities markets; Size effects; Solid mechanics; Structural and continuum mechanics; Quasibrittle fracture; R-curve; Size effect; R-curve’s curvature; Asymptotic behaviors; Plateau resistance; Crack length at peak load; R-curve's curvature; Energy analysis; Size effect .Asymptotic behaviors; Brittle fracture; Notch; Modeling; Crack propagation resistance; Crack length; Property structure relationship; Asymptotic approximation; Safety; Curvature; LINEAR ELASTIC FRACTURE; LEFM; PLATEAU RESISTANCE; FRACTURE QUASI-FRAGILE; SIZE EFFECT; FRACTURE PROCESS ZONE; CRACK LENGTH AT PEAK LOAD; THÉORIE DE BAZANT; FPZ; ASYMPTOTIC BEHAVIORS; R-CURVE; COURBE-R; COURBE DE RÉSISTANCE; R-CURVE’S CURVATURE; QUASIBRITTLE FRACTURE
• ISSN: 0376-9429; 1573-2673
• DOI: 10.1007/s10704-008-9291-6

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.