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Size effect and boundary conditions in the brazilian test: theoretical analysis

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Abstract

Splitting strength determined in the Brazilian test is assumed to be a property independent of size and uniquely related to the intrinsic material strength. However, as was experimentally demonstrated by various authors, the splitting strength depends on the specimen size. In this paper, the size effect in the Brazilian test is analyzed theoretically using a nonlinear fracture model based on cohesive crack concepts and the results obtained are compared with the classical strength limit approach. Two important variables are studied: the load-bearing strip and the geometry of the specimen. From the numerical results a closed form expression is proposed, dependent on the width of the bearing strip and on geometry. The results confirm that splitting strength decreases with the specimen size, tending towards an asymptotic solution for large size specimens. Within the size range analyzed (0.1 m to 2.5 m diameter for typical concrete) the splitting strength can vary by up to 25% in cylindrical specimens and by up to 35% in prismatic square section specimens, although this size effect is strongly dependent on the load-bearing strip. For widths of bearing strip smaller than 4% of the specimen diameter, the effect of the specimen size is negligible and the splitting strength approaches the tensile strength for any practical specimen size.

Résumé

La résistance mécanique en traction indirecte déterminé à partir de l'essai brésilien est censée être une propriété indépendante de la taille des éprouvettes et devrait dépende seulement de la rśsistance mécanique intrinsèque du matériau. Cependant, comme l'ont montré expérimentalement plusieurs auteurs, la résistance mécanique dépend de la taille des éprouvettes.

Dans cet article, une analyse théorique de l'effet de taille dans l'essai de compression diamétrale, a été développée en employant un modèle de rupture non-linéaire basé sur les concepts de la théorie de la fissure cohésive. Les résultats obtenus ont été confronté à ceux qui proviennent de l'approche de la théorie de la contrainte limite. Deux variables importantes ont été étudiées: la forme des appuis et la géométrie des éprouvettes.

Une expression analytique fermée dépendante de la largeur des appuis et de la géométrie a été trouvée. Les résultats confirment que la résistance mécanique décroît avec la taille des éprouvettes, tendant toujours vers une solution asymptotique pour des éprouvettes de grande taille. Dans le domaine des tailles analysées (0,1 à 2,5 m de diamètre pour un béton conrant), la résistance peut varier jusqu'à 25% dans des éprouvettes cylindriques et jusqu'à 35% dans le cas des éprouvettes prismatiques de section carrée, bien que cet effet soit aussi très dépendant de la largeur des appuis. Pour des largeurs d'appuis inférieures à 4%, du diamètre, l'effet de taille devient négligeable et le résultat s'approche de la résistance mécanique pour toutes dimensions d'éprouvettes.

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Authors and Affiliations

  1. Departmento de Construcciones, Facultad de Ingeniería, Universidad Nacional de La Plata, La Plata, Argentina

    C. Rocco

  2. Departamento de Ciencia de Materiales, Escuela de Ingeeieros de Caminos, Universidad Politécnica de Madrid, Ciudad Universitaria, 28040, Madrid, Spain

    G. V. Guinea,  J. Planas (RILEM Senior Members) &  M. Elices

Authors
  1. C. Rocco
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  2. G. V. Guinea
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  3. J. Planas
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  4. M. Elices
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Additional information

Both participate in the work of RILEM Technical Committee QFS (Size effect and scaling of quasibrittle fracture). Prof. Elices also participates in RILEM TC 147-FMB (Fracture mechanics applications to anchorage and bond) and 148-SSC (Test methods for the strain softening response of concrete). Prof. G. Guinea is the 1994 Robert l'Hermite medallist. The first part of this paper (experimental analysis) has been published in Materials no 217.

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Rocco, C., Guinea, G.V., Planas, J. et al. Size effect and boundary conditions in the brazilian test: theoretical analysis. Mat. Struct. 32, 437–444 (1999). https://doi.org/10.1007/BF02482715

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  • DOI: https://doi.org/10.1007/BF02482715

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