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Explanation of size effect in concrete fracture using non-uniform energy distribution

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Abstract

A local fracture energy model originally proposed to explain the influence of fracture process zone (FPZ) on fracture energy of cementitious materials is further developed in this study. By assuming a bilinear distribution for the fracture energy distribution, the ligament-dependent fracture energyG f is obtained. The analytical expression ofG f contains two important prameters: the intrinsic size-independent fracture energyG F and a reference ligament sizea *l which determines the intersection of the two linear fracture energy functions. It is shown that the ligament-dependentG f approaches the size-independentG F asymptotically. As a result,G F can be determined from the ligament-dependentG f results. It is also found that while the reference ligament sizea *l is influenced by the specimen geometry, size and loading conditions, the derived fracture energyG F is virtually constant. The present local fracture energy distribution model is also discussed and compared with the original local fracture energy model.

Résumé

Cette étude présente un développement plus approfondi d'un modèle de l'énergie locale de rupture, originairement proposé pour expliquer l'effet de la taille de la zone d'endommagement sur l'énergie de rupture des matériaux à base de ciment. En supposant une distribution bilinéaire de l'énergie locale de rupture, on peut obtenir l'énergie de rupture Gf dépendante de la longueur du ligament. L'expression analytique de l'énergie de rupture GF contient deux paramètres importants: l'énergie de rupture GF, indépendante de la taille, et une valeur de référence de la longueur du ligament, a *l , qui détermine l'intersection de la distribution bilinéaire de l'énergie locale de rupture. On montre que l'énergie de rupture dépendante du ligament Gf tend asymptotiquement vers la valeur de l'énergie de rupture non-dépendante de la taille, GF. Ainsi, GF peut être déduite de l'énergie dépendante du ligament, Gf. On a aussi remarqué que l'énergie de rupture GF, ainsi déduite, demeure virtuellement constante bien que la logueur de référence du ligament, a *l , puisse être influencée par la géométrie et la taille de l'éprouvette et les conditions de sollicitations. Ce modèle de distribution d'énergie locale de rupture est discuté en détail dans cette contribution et est comparé avec le modèle original de l'énergie locale de rupture.

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Authors and Affiliations

  1. Department of Mechanical and Materials Engineering, University of Western Australia, 35 Stirling Highway, 6009, Crawley, WA, Australia

    K. Duan & X. -Z. Hu

  2. Institute for Building Materials, Suriss Federal Institute of Technology, CH-8093, Zürich, Switzerland

    F. H. Wittmann

Authors
  1. K. Duan
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  2. X. -Z. Hu
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  3. F. H. Wittmann
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Editorial Note Prof. Folker H. Wittmann is a RILEM Senior Member.

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Duan, K., Hu, X.Z. & Wittmann, F.H. Explanation of size effect in concrete fracture using non-uniform energy distribution. Mat. Struct. 35, 326–331 (2002). https://doi.org/10.1007/BF02483151

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