Data from: Three-dimensional surface parameters and multi-fractal spectrum of corroded steel

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.

为研究腐蚀钢材表面的多重分形行为，本研究采用魏尔斯特拉斯-曼德博罗特（Weierstrass-Mandelbrot）方法，以高整体精度构建了一系列Q235钢腐蚀表面的分形表面。通过计算腐蚀钢分形表面的多重分形谱，探究W-M型腐蚀表面的多重分形特性。基于腐蚀钢材表面多重分形谱的形状特征，本研究采用最小二乘法对腐蚀表面的多重分形谱进行二次拟合，并对拟合函数开展定量分析，以此简化腐蚀表面多重分形特性的计算流程。结果表明，二次曲线拟合法可很好地拟合腐蚀表面的多重分形谱，且能准确预测其演化规律与发展趋势。本研究成果可应用于钢材腐蚀表面形成机理的相关研究，同时为钢材腐蚀损伤本构模型的构建提供了全新的研究思路。