Three-dimensional fractures of different fractal dimensions have been const
ructed with successive random addition algorithm, the applicability of vari
ous dimension determination methods at nanometer scale has been studied. As
to the metallic fractures, owing to the limited number of slit islands in
a slit plane or limited datum number at nanometer scale, it is difficult to
use the area-perimeter method or power spectrum method to determine the fr
actal dimension. Simulation indicates that box-counting method can be used
to determine the fractal dimension at nanometer scale. The dimensions of fr
actures of valve steel 5Cr21Mn9Ni4N have been determined with STM. Results
confirmed that fractal dimension varies with direction at nanometer scale.
Our study revealed that, as to theoretical profiles, the dependence of frac
tal dimension with direction is simply owing to the limited data set number
, i.e, the effect of boundaries. However, the dependence of fractal dimensi
on with direction at nanometer scale in real metallic fractures is correlat
ed to the intrinsic characteristics of the materials in addition to the eff
ect of boundaries. The relationship of fractal dimensions with the mechanic
al properties of materials at macrometer scale also exists at nanometer sca
le.