Zv. Djordjevic et al., FRACTAL AND TOPOLOGICAL CHARACTERIZATION OF BRANCHING PATTERNS ON THEFRACTURE SURFACE OF CROSS-LINKED DIMETHACRYLATE RESINS, Journal of Materials Science, 30(11), 1995, pp. 2968-2980
The branching patterns formed as a result of crack growth in dimethacr
ylate resins below their glass transition temperatures looked similar
to fractal trees. The skeletons of the patterns were analysed numerica
lly for their topological and geometrical properties. The number of br
anches, N-i, mean branch lengths, L(i), and branch angles of a particu
lar order, defined according to the Strahler and inverted Weibel schem
es, followed exponential scaling behaviour: N-i similar to (R(B))(-i)
and L(i) similar to (R(L))(i). Using the relationship for the fractal
dimension D = ln R(B)/ln R(L), a value of D = 1.4 was obtained for the
fracture pattern. Fractal behaviour was also examined by the box-coun
ting 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 fr
acture pattern. However, the mass-shell method for both the fracture p
attern and the fractal trees gave an exponential increase of mass with
distance from the origin, rather than the power-law behaviour expecte
d for fractals. This was attributed to the fact that branches of diffe
rent sizes were distributed in restricted regions of space closer to t
he periphery, rather than uniformly over the whole pattern.