International Journal of Fracture

, Volume 44, Issue 2, pp 111–131 | Cite as

Determination of fracture energy, process zone longth and brittleness number from size effect, with application to rock and conerete

  • Z. P. Ba<zant
  • M. T. Kazemi
Article

Abstract

The dependence of the fracture energy and the effective process zone length on the specimen size as well as the craek extension from the notch is analyzed on the basis of Ba<zant's approximate size effect law. The fracture energy and the effective length of the fracture process zone is defined on the basis of the extrapolation to an infinite specimen size, for which the definitions are independent of the shape of the specimen or structure. Both of these material properties are expressed in terms of the size effect law parameters and the function describing the nondimensional energy release rate. Ba<zant's size effect law for the nominal stress σN at failure is reformulated in a manner in which the parameters are the fracture energy and the effective (elastically equivalent) process zone length. A method to determine these material properties from σN-data by linear and nonlinear regressions is shown. This method permits these properties to be evaluated solely on the basis of the measured maximum loads of specimens of various sizes and possibly also of different shapes. Variation of both the fracture energy and the effective process zone length as a function of the specimen size is determined. The theoretical results agree with previous fracture tests of rock as well as concrete and describe them adequately in relation to the inevitable random scatter of the tests.

Résumé

En se reposant sur la loi des effets dimensionnels approximatifs développée par Ba<zant, on étudie la liasion de dépendance entre la taille de l'éprouvette et l'énergie de rupture, la longueur de la zone de détérioration ainsiqque l'étendue de la fissure au départ d'une entaille.

On définit l'énergie de rupture et la longueur effective de la zone où se produit un processus de rupture en se hasant sur une extrapolation à une éprouvette de taille infinie, pour laquelle les définitions ne dépendent pas de la forme de l'éprouvette ou de la structure. Ces deux propriétés du matériau sont exprimées en fonction des parametres de la loi régissant l'effet dimensionnel et d'une relation exprimant de manière non dimensionnelle la vitesse de relaxation de l'énergie.

La loi de Bažant relative à la tension nominale à la rupture est reformulée de manière à ce que les paramètres en soient l'énergie de rupture et la longueur effective (ou son équivalent élastique) de la zone de déterioration.

On donne une méthode de détermination de ces propriétés du matériau à partir de données de, par régressions linéaire et non linéaire. Cette méthode permét d'évaluer ces propriétés sur la seule base du relevé des charges maximum agissant sur des éprouvettes de diverses tailles et, éventuellement, de formes différentes.

On détermine l'évolution de l'énergie de rupture et de la longeur effective de la zone de détérioration en fonction de la dimension de l'éprouvette. Les résultats théoriques sont en accord avec des essais entrepris précédemment sur des roches et sur du béton, et en rendent bien compte, en dépit de l'inévitable dispersion propre aux essais.

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Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • Z. P. Ba<zant
    • 1
  • M. T. Kazemi
    • 1
  1. 1.Center for Advanted Cement-Based MaterialsNorthwestern UniversityEvanstonUSA

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