Original Article

International Journal of Fracture

, Volume 141, Issue 1, pp 269-286

First online:

Fractal dimension of metallic fracture surface

  • Piotr KotowskiAffiliated withInstitute of Materials Science and Applied Mechanics, Wrocław University of Technology Email author 

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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 enable minimization 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 method has 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 to the 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 dimension was changing inversely proportional to da/dN. Obtained results confirm that fractal dimension do not depend on the investigated material.


Method Fractal dimension Fracture surface Metal