Fractal and topological characterization of branching patterns on the fracture surface of cross-linked dimethacrylate resins

1573-4803

Springer Online Journal Archives 1860-2000

Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics

Abstract The branching patterns formed as a result of crack growth in dimethacrylate resins below their glass transition temperatures looked similar to fractal trees. The skeletons of the patterns were analysed numerically for their topological and geometrical properties. The number of branches, N i , mean branch lengths, N i , and branch angles of a particular order, defined according to the Strahler and inverted Weibel schemes, followed exponential scaling behaviour: N i ∼ (R b )−i and L i ∼ (R l ) i . Using the relationship for the fractal dimension D=In R B /In R L , a value of D=1.4 was obtained for the fracture pattern. Fractal behaviour was also examined by the box-counting method which indicated a power-law dependence of the mass on the box size with fractal dimension exponent D=1.4 in the case of the fracture pattern. However, the mass-shell method for both the fracture pattern and the fractal trees gave an exponential increase of mass with distance from the origin, rather than the power-law behaviour expected for fractals. This was attributed to the fact that branches of different sizes were distributed in restricted regions of space closer to the periphery, rather than uniformly over the whole pattern.

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