ABSTRACT
Damage, strain localization, and fracture are not always interpretable in the frame work of continuum mechanics. In particular, the scale effect on nominal tensile strength has not found satisfactory explanations. The reason for this has to be sought in the fact that the micromechanical damage phenomena, and thus the inherent disorder of the material, have been disregarded. Fractal geometry and renormalization group theory can provide today a rational and consistent expla nation, harmonizing and enriching the empirical approach of Weibull and the phenomenological assumption of Griffith. Material ligaments at peak stress can be considered as multifractals, of dimension 1.5 at small scales, and dimension 2 at large scales. This means that, at large scales, the disorder is not visible, the size of the heterogeneities being limited. A transition from extreme disorder (slope — 1/2) to extreme order (zero slope) may therefore be evidenced in the bilogarithmic strength versus size diagram. A Multifractal Scaling Law (MFSL) is proposed with a concavity opposite to that of the Bazant's Size Effect Law (SEL). The size effects on some significant experimental tests reported in the literature are inter preted by the MFSL very consistently.
