Effects of roll pattern and reduction ratio on optical characteristics of A1008 cold–rolled steel specimens: analytical approach and experimental correlations

Cold rollings of A1008 steel specimens are carried out in this study to analyze the influences of roll’s surface pattern and specimen’s reduction ratio on surface morphologies, optical properties, and mechanical properties of rolled samples. A 3D fractal formula, along with dedicated algorithms developed, is applied to solve the periodic (characteristics) lengths and fractal dimensions for roll and rolled surfaces along and perpendicular to the rolling directions. The correlation for every fractal parameter between roll and the rolled specimen is developed to be a function of roll’s surface pattern and reduction ratio first. The light tracking simulations were then carried out for rolled samples only. Rockwell hardness and tensile tests were conducted to evaluate the specimen’s hardness and Young’s modulus. A roll having a higher fractal dimension, or a longer periodic length, can result in a higher fractal dimension and a longer periodic length of the rolled specimen, respectively. A larger reduction ratio also results in the rolled surface with higher fractal dimensions and longer periodic lengths. Increasing the fractal dimensions of a rolled specimen can elevate the maximum illuminance and, conversely, lower the minimum illuminance, while an increase in periodic lengths can increase the minimum illuminance and decrease the maximum illuminance. A decrease in the fractal dimensions and/or increase in the periodic lengths of rolled surfaces in the two directions can raise the illuminance uniformity. For the specimens prepared with the same roll pattern, an increase in reduction ratio can bring an increment in illuminance uniformity and hardness of rolled samples. This study provides an efficient way to determine the roll pattern and reduction ratio that satisfies the specific demands in optical properties.