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Application of fractal theory to study morphology of manganese sulfide inclusion in resulfurized free-cutting steels

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Abstract

The morphology and distribution of manganese sulfide (MnS) inclusions have a significant influence on the comprehensive performance, which is an important research field for resulfurized steels. Based on the experiments of non-aqueous electrolyte and scanning electron microscope observation, the fractal theory was employed to study the three-dimensional morphologies of MnS inclusions. The results showed that the edge fractal dimension of MnS inclusions was between 1.59 and 1.88. In addition, similar morphology of MnS inclusions had a close fractal dimension. The MnS edge fractal dimension is highly positively correlated with the morphological parameters. The multifractal spectrums of MnS inclusions on two-dimensional plane of as-cast and as-rolled resulfurized free-cutting steels were calculated. The large-size MnS inclusions belong to large probability subset, while the small-size MnS inclusions belong to small probability subset. The multifractal spectrum can truly and effectively reflect the difference and non-uniformity of distribution of MnS inclusions on 2D plane. On the premise of similar content of MnS, with the refinement of MnS inclusions, the multifractal spectrum width and the multifractal spectrum symmetry parameter were decreased. The multifractal spectrum provides a new method for studying the second phase in materials.

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Acknowledgements

The authors gratefully express their appreciation to National Key Research and Development Program of China (Grant No. 2018YFB0704400) and National Natural Science Foundation of China (Grant Nos. 51874195 and 52074179) for supporting this work. One of the authors, Xiang-yu Xu, gratefully acknowledges support from the Youth Program of National Natural Science Foundation of China (Grant No. 52104335) and Shanghai “Super Postdoctoral” Incentive Plan (Grant No. 2020194).

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Authors and Affiliations

  1. Center for Advanced Solidification Technology (CAST); State Key Laboratory of Advanced Special Steel, School of Materials Science and Engineering, Shanghai University, Shanghai, 200444, China

    Xiang-yu Xu, Zhi-qi Zeng, Qian-ren Tian, Chen-wei Cao, Ping Shen & Jian-xun Fu

  2. Baosight Software Co., Ltd., Information Service Headquarters, Shanghai, 201203, China

    Zhi-qi Zeng

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  1. Xiang-yu Xu
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  2. Zhi-qi Zeng
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Correspondence to Jian-xun Fu.

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Xu, Xy., Zeng, Zq., Tian, Qr. et al. Application of fractal theory to study morphology of manganese sulfide inclusion in resulfurized free-cutting steels. J. Iron Steel Res. Int. 30, 137–149 (2023). https://doi.org/10.1007/s42243-022-00826-z

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  • DOI: https://doi.org/10.1007/s42243-022-00826-z

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