Experimental Determination of the Fractal Dimension of Microcrack Patterns and Fracture Surfaces

  • B. Chiaia
Part of the International Centre for Mechanical Sciences book series (CISM, volume 378)


Three different investigations on the scaling properties of damage in concrete are described. In the case of uniaxial tensile tests, a laser profilometer was adopted to scan the post-mortem fracture surfaces. In a second investigation, splitting tests were carried out and optical microscopy was used to detect the stress-induced crack patterns. In the third investigation (compression tests), a fusible alloy was injected inside the cracked specimen under load and, afterwards, scanning electron microscopy (SEM) was applied. The fundamental concepts of fractal geometry are introduced, and the methods developed to extract the fractal dimension are described. The application of these algorithms to the experimental damage patterns shows that self-affine scaling is often provided by disordered materials, and that piecewise fractality (geometrical multifractality) comes into play due to the interaction of internal and external scale lengths. The formation and evolution of a cloud of interacting microcracks in the damage process zone (a network with fractal dimension even larger than 2.5) can be related to the characteristic softening mechanical behaviour. The catastrophic jump to the final fracture surface (with local dimension comprised between 2.0 and 2.5) identifies the rupture transition. It is shown that also the damage networks induced by compression may present a fractal dimension larger than 2.5 in the bulk, but the local dimension of each microfracture never exceeds 2.5.


Fracture Surface Fractal Dimension Linear Elastic Fracture Mechanics Hurst Exponent Fracture Profile 
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© Springer-Verlag Wien 1997

Authors and Affiliations

  • B. Chiaia
    • 1
  1. 1.Polytechnic of TurinTurinItaly

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