Comparison of fractal analyses methods and fractal dimension for pre-treated stainless steel surfaces and the correlation to adhesive joint strength

Abstract.

The fractal dimensions of six differently mechanically pre-treated stainless steel samples were investigated using five fractal algorithms. The surfaces were analyzed using a profiler, atomic force microscopy (AFM), scanning electron microscopy (SEM) and light microscopy (LM), and thereafter adhesively bonded and tested in single-overlap joints to test their tensile strength. All samples showed different fractal behavior, depending on the microscopic methods and fractal algorithms. However, the overall relation between fractal dimension and tensile strength is qualitatively the same, except for the SEM images. This verifies that tensile strength is correlated to fractal dimension, although only within the length-scale of the profiler and the light microscope (≈0.5–100 μm). The AFM method was excluded in this comparison, since the limitation in the z-direction for the AFM scanner made it difficult to scan the rougher parts of the blasted samples. The magnitude of the surfaces is a parameter not often considered in fractal analysis. It is shown that the magnitude, for the Fourier method, is correlated to the arithmetic average difference, R_a, but only weakly to the fractal dimension. Hence, traditional parameters, such as R_a, tell us very little about the spatial distribution of the elevation data.