Abstract
To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel.
Highlights
A rough surface with self-similarity and scale invariance always has a fractal geometrical property[1,2]
When a fractal dimension (D) was known, the corresponding fractal surface can be obtained by employing the W-M fractal function, and the function is expressed as follows: Zðx; yÞ 1⁄4 X 1 CnlÀð3ÀDÞn sin1⁄2lnðx cos Bn þ y sin BnÞ þ An
It can be found that the fractal surfaces with D value of 2.2, 2.3, 2.5, and 2.8 had more than 90% accuracy for simulating the corroded surfaces exposed for 0.5, 1, 2 and 4 years, respectively
Summary
A rough surface with self-similarity and scale invariance always has a fractal geometrical property[1,2]. Many studies have been conducted on the morphology characteristics of rough surfaces on the basis of fractal geometry theory. In actual projects, the morphology of rough surface often presents variability, i.e., anisotropic and local characteristics in spatial distribution[14,15], which makes the fractal geometry theory difficulty to be applied in practical engineering. The surface of corroded steel becomes gradually roughening from the very beginning of a plane. Due to a large number of bumps or potholes (pits) and planar regions (without pits) on corroded surface of steel, the rough surface attacked by the corrosive pitting presents larger discreteness and concave convex feature. The existing research results show that the surface attack by corrosive
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