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Integrating machine learning and CALPHAD method for exploring low-modulus near-β-Ti alloys

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Abstract

Traditional theoretical and empirical calculation methods can guide the design of β- and metastable β-alloys for bio-titanium. However, it is still difficult to obtain novel near-β-Ti alloys with low modulus. This study developed a method that combines machine learning with calculation of phase diagrams (CALPHAD) to facilitate the design of near-β-Ti alloys. An elastic modulus database of Ti–Nb–Zr–Mo–Ta–Sn system was constructed first, and then three features (the electron to atom ratio, mean absolute deviation of atom mass, and mean electronegativity) were selected as the key factors of modulus by performing a three-step feature selection. With these features, a highly accurate model was built for predicting the modulus of near-β-Ti alloys. To further ensure the accuracy of modulus prediction, machine learning with the elastic constants calculated was leveraged by CALPHAD database. The root mean square error of the well-trained model can be as low as 6.75 GPa. Guided by the prediction of machine learning and CALPHAD, three novel near-β-Ti alloys with elastic modulus below 50 GPa were successfully designed in this study. The best candidate alloy (Ti–26Nb–4Zr–4Sn–1Mo–Ta) exhibits an ultra-low modulus (36.6 GPa) after cold rolling with a thickness reduction of 20%. Our method can greatly save time and resources in the development of novel Ti alloys, and experimental verifications have demonstrated the reliability of this method.

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摘要

传统的理论和计算方法可以指导用于生物医疗的β和亚稳态β钛合金设计. 然而, 这些方法仍然难以获得具有低模量的新型近β钛合金. 本研究开发了一种将机器学习与相图计算 (CALPHAD) 相结合的方法, 以促进近 β钛合金的设计. 我们首先构建了Ti–Nb–Zr–Mo–Ta–Sn体系的弹性模量数据库, 然后通过执行三步特征选择方法, 选出了三个特征 (电子原子比, 原子质量平均绝对误差和平均电负性) 作为模量的关键因素. 利用这些特征, 我们建立了一个高精度模型来预测近β钛合金的模量. 为了进一步确保模量预测的准确性, 我们利用机器学习和 CALPHAD 数据库计算的弹性常数. 模型经训练后的模型均方根误差可低至 6.75 GPa. 在机器学习和 CALPHAD的指导下, 我们成功设计了三种弹性模量低于 50 GPa 的新型近 β钛合金. 最佳候选合金 (Ti–26Nb–4Zr–4Sn–1Mo–Ta) 在冷轧至厚度减少20%后表现出超低模量 (36.6 GPa). 我们的方法可以大大节省开发新型钛合金的时间和资源, 后续的实验验证了该方法的可靠性.

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Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (No. 52071339), the Natural Science Foundation of Hunan Province, China (No. 2020JJ4739) and Guangxi Key Laboratory of Information Materials (Guilin University of Electronic Technology), China (No. 201009-K).

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  1. Hao Zou and Yue-Yan Tian have contributed equally to this work.

Authors and Affiliations

  1. State Key Laboratory of Powder Metallurgy, Central South University, Changsha, 410083, China

    Li-Bin Liu

  2. School of Computer Science and Engineering, Central South University, Changsha, 410083, China

    Hao Zou, Ming-Ming Lu & Jian-Xin Wang

  3. School of Materials Science and Engineering, Central South University, Changsha, 410083, China

    Yue-Yan Tian, Li-Gang Zhang, Ren-Hao Xue, Zi-Xuan Deng & Li-Bin Liu

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  1. Hao Zou
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Zou, H., Tian, YY., Zhang, LG. et al. Integrating machine learning and CALPHAD method for exploring low-modulus near-β-Ti alloys. Rare Met. 43, 309–323 (2024). https://doi.org/10.1007/s12598-023-02333-w

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