Abstract :
In this study, a complete method of
determination of the fractal dimension for fracture
surfaces of ferrous alloys has been proposed.
This dimension is determined for the vertical profile
obtained by the profile technique cross-section.
The image of the profile, seen through the microscope
coupled with a camera, is recorded in a computer,
where numerical processing is performed.
For calculation of the same fractal dimension, the
fd3 program has been used, which is available
through the Internet. The essential element of the
method is optimisation concerning microscopic
magnification (scale of a length), resolution of the
recorded image and selection of the grey level
threshold at binarization. The tests for the stability
of discretization, which enableminimization of the
error of the measurement, have also been carried
out. These tests consist in checking the difference
in fractal dimensions for the same profile obtained
in two different methods of contouring as well as
the difference between capacitive, informative and
correlative dimensions. In both cases, too big difference
suggests that the determined dimension
is not reliable. This method allows determination
of the fractal dimension with an absolute accuracy
of 0.05 in non-dimensional units. The methodhas been employed in many studies. In this paper
the following tests have been presented: a “fractal
map” of the fracture surface was made, an influence
of the mechanical notch radius in a compact
specimen on the fractal dimension of the fracture
surface, an influence of the distortion rate on the
fractal dimension, an effect of fatigue crack propagation
rate on the fractal dimension and influence
of the stress-intensity factor on the fractal dimension
of the fracture surface. The following materials
were examined: Armco iron, P355N steel and
41Cr4 steel in different states after the heat treatment.
The measurements have been made for the
specimens of the compact type. There was considered
an influence of location of the place of
measurement on the fractal dimension being determined.
The dimension was determined on the
profiles lying longwise and crosswise the crack
propagation direction. It has been found that the
fractal dimension of the fracture surface does not
depend on a place of measurement. This suggests,
among other things, that a distinction between the
places, which were created under conditions of the
plane stress, and the places, which were created
under conditions of the plane strain state, cannot
be made with the help of the fractal dimension.
When testing an influence of the radius of the
mechanical tip notch on the fractal dimension of
a fracture surface, this dimension was determined
in the places located at different distances from
the tip of the mechanical notch. With respect tothe radii up to 1.0 mm, no significant differences
in fractal dimensions have been found. The fractal
dimensions of the fracture surface for all examined
materials were practically the same and they
ranged from 2.02 to 2.10. However in some ranges
of da/dN rate the dimensionwas changing inversely
proportional to da/dN. Obtained results confirm
that fractal dimension do not depend on the investigated
material.
