Self-Similarity and Fractality in Microcrack Coalescence and Solid Rupture

Fractal concepts are used to study the complex shapes of fracture surfaces, as well as damage phenomena presenting statistical characteristics. While at the beginning of the loading process the microcracks can be considered as two-dimensional surfaces, as the load is increased the microcracks grow, coalesce and form an invasive fractal set with a dimension larger than two. When the evolving dimension assumes the notable value of 2.5, the microcrack set may be considered as extremely disordered, and percolation of the cracks is very likely, in particular for sufficiently large specimens. Percolation favours catastrophic and brittle behaviours and produces fracture surfaces of a Brownian character, where the local dimension is again 2.5. An additional assumption is that of considering material resisting sections at peak stress as lacunar fractals of a local dimension equal to 1.5. The above-mentioned fractalities produce the well-known scale dependence of fracture energy and tensile strength, respectively.