Multifractal nature of concrete fracture surfaces and size effects on nominal fracture energy

Experimental evidence of the fractality of fracture surfaces has been widely recognized in the case of concrete, ceramics and other disordered materials. An investigationpost mortem on concrete fracture surfaces of specimens broken in direct tension has been carried out, yielding non-integer (fractal) dimensions of profiles, which are then related to the ‘renormalized fracture energy’ of the material. No unique value for the fractal dimension can be defined: the assumption of multifractality for the damaged, material microstructure produces a dimensional increment of the dissipation space with respect to the number 2, and represents the basis for the so-called multifractal scaling law. A transition from extreme Brownian disorder (slope 1/2) to extreme order (zero slope) may be evidenced in the bilogarithmic diagram: the nominal fracture energyGF increases with specimen size by following a nonlinear trend. Two extreme scaling regimes can be identified, namely the fractal (disordered) regime, corresponding to the smallest sizes, and the homogeneous (ordered) regime, corresponding to the largest sizes, for which an asymptotic constant value ofGF is reached.ResumeOn a largement établi la preuve expérimentale du caractère fractal des surfaces de rupture dans le cas du béton, des céramiques et d'autres matériaux ‘désordonnés’. Une étudepost mortem menée sur des surfaces de rupture d'échantillons cassés par traction directe révèle des dimensions non intégrales (fractales) des profils dont on a établi la relation avec l'énergie de rupture ‘renormalisée’ du matériau. Il n'est pas possible d'établir une valeur unique de la dimension fractale: en présumant la multifractalité de la microstructure du matériau endommagé, on obtient une augmentation dimensionnelle par rapport au numéro 2 et on établit la base de la loi dite d'échelle multifractale. Dans le diagramme à deux logarithmes on peut voir, une transition du désordre de Brown extrême (inclinaison 1/2) à l'ordre extrême (inclinaison zéro); l'énergie de fracture nominaleGF augmente avec les dimensions de l'échantillon suivant une tendance non linéaire. On peut voir deux régimes extrêmes d'échelle, c'est-à-dire le régime fractal désordonné) . qui correspond aux dimensions minimales, et le régime homogène (ordonné), qui correspond aux dimensions maximales pour lesquelles on atteint une valeur constante asymptotique deGF.

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