FRACTAL AND TOPOLOGICAL CHARACTERIZATION OF BRANCHING PATTERNS ON THEFRACTURE SURFACE OF CROSS-LINKED DIMETHACRYLATE RESINS

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.