Statistics of branched fracture surfaces

Abstract

A statistical analysis of fracture surfaces of the polycrystalline intermetallic compound ${\mathrm{Ni}}_{3}$Al is reported. Although these surfaces contain secondary branches, a roughness exponent \ensuremath{\zeta} can be defined, and is found close to 0.8. The number of branches is shown to have nontrivial fluctuations, which exhibit a power-law increase with an exponent strongly dependent upon the dynamics of crack branching during crack propagation. Moreover, the probability distributions of both heights and averaged heights are shown to slowly decrease, i.e., like power laws, for high enough altitudes. Dynamical effects could be responsible for these ``anomalous'' statistics.