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A physically-based constitutive model for the prediction of yield strength in the precipitate-hardened high-entropy alloys

沉淀强化高熵合金屈服强度及本构模型研究

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Abstract

Precipitate-hardened high-entropy alloys (HEAs) exhibit great mechanical strength and exceptional ductility. However, the existing model fails to accurately predict the yield strength contributing from the solid solution strengthening and precipitate strengthening in the HEAs due to the neglect of the crucial roles including the complex chemical element, precipitate-size distribution, and the precipitate-spatial distribution. Moreover, a unified strength model for analyzing the yield strength in the HEAs is still lacking. A developed precipitate strengthening model considering the size distribution and spatial distribution is established and shows a higher accuracy compared to the existing model. The results show that the precipitate strengthening is the dominant contribution to the yield strength. It reveals that the effect of spatial distribution on precipitate strengthening is more pronounced than that of the precipitate-size distribution. This developed model provides a theoretical framework for determining the precipitate strengthening and the yield strength of HEA, and then subsequently guides the design of the high-strength HEAs.

摘要

沉淀强化高熵合金表现出优异的强度和延展性. 然而, 由于现有的模型忽略了高熵合金中复杂化学元素、析出相尺寸分布和空间分布在内的关键作用, 使之无法准确预测高熵合金中固溶强化和沉淀强化对屈服强度的贡献. 此外, 还缺乏统一的强度模型来分析高熵合金中的屈服强度. 本文建立了考虑尺寸分布和空间分布的沉淀强化模型, 与现有模型相比, 该模型具有更高的精度. 结果表明,沉淀强化在屈服强度中起主要贡献作用. 此外, 空间分布对沉淀强化的影响比析出相尺寸分布的影响更显著. 该模型为确定高熵合金的沉淀强化和屈服强度提供了理论框架, 并为设计高强度高熵合金提供指导.

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References

  1. E. P. George, D. Raabe, and R. O. Ritchie, High-entropy alloys, Nat. Rev. Mater. 4, 515 (2019).

    Article  Google Scholar 

  2. Y. Zhang, T. T. Zuo, Z. Tang, M. C. Gao, K. A. Dahmen, P. K. Liaw, and Z. P. Lu, Microstructures and properties of high-entropy alloys, Prog. Mater. Sci. 61, 1 (2014).

    Article  Google Scholar 

  3. J. Li, Y. Chen, Q. He, X. Xu, H. Wang, C. Jiang, B. Liu, Q. Fang, Y. Liu, Y. Yang, P. K. Liaw, and C. T. Liu, Heterogeneous lattice strain strengthening in severely distorted crystalline solids, Proc. Natl. Acad. Sci. USA 119, e2200607119 (2022).

    Article  Google Scholar 

  4. B. Cantor, I. T. H. Chang, P. Knight, and A. J. B. Vincent, Microstructural development in equiatomic multicomponent alloys, Mater. Sci. Eng.-A 375–377, 213 (2004).

    Article  Google Scholar 

  5. J. W. Yeh, S. K. Chen, S. J. Lin, J. Y. Gan, T. S. Chin, T. T. Shun, C. H. Tsau, and S. Y. Chang, Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes, Adv. Eng. Mater. 6, 299 (2004).

    Article  Google Scholar 

  6. C. Lee, F. Maresca, R. Feng, Y. Chou, T. Ungar, M. Widom, K. An, J. D. Poplawsky, Y. C. Chou, P. K. Liaw, and W. A. Curtin, Strength can be controlled by edge dislocations in refractory high-entropy alloys, Nat. Commun. 12, 5474 (2021).

    Article  Google Scholar 

  7. O. El-Atwani, N. Li, M. Li, A. Devaraj, J. K. S. Baldwin, M. M. Schneider, D. Sobieraj, J. S. Wróbel, D. Nguyen-Manh, S. A. Maloy, and E. Martinez, Outstanding radiation resistance of tungsten-based high-entropy alloys, Sci. Adv. 5, eaav2002 (2019).

    Article  Google Scholar 

  8. Q. Pan, L. Zhang, R. Feng, Q. Lu, K. An, A. C. Chuang, J. D. Poplawsky, P. K. Liaw, and L. Lu, Gradient cell-structured high-entropy alloy with exceptional strength and ductility, Science 374, 984 (2021).

    Article  Google Scholar 

  9. Y. Zhao, J. M. Park, J. Jang, and U. Ramamurty, Bimodality of incipient plastic strength in face-centered cubic high-entropy alloys, Acta Mater. 202, 124 (2021).

    Article  Google Scholar 

  10. B. Gludovatz, A. Hohenwarter, D. Catoor, E. H. Chang, E. P. George, and R. O. Ritchie, A fracture-resistant high-entropy alloy for cryogenic applications, Science 345, 1153 (2014).

    Article  Google Scholar 

  11. Y. Wang, J. Wang, M. Lei, and Y. Yao, A crystal plasticity coupled damage constitutive model of high entropy alloys at high temperature, Acta Mech. Sin. 38, 122116 (2022).

    Article  MathSciNet  Google Scholar 

  12. H. Chen, X. Zhang, C. Liu, W. Xiong, M. Tan, and L. H. Dai, Theoretical analysis for self-sharpening penetration of tungsten high-entropy alloy into steel target with elevated impact velocities, Acta Mech. Sin. 37, 970 (2021).

    Article  Google Scholar 

  13. J. Y. He, H. Wang, Y. Wu, X. J. Liu, H. H. Mao, T. G. Nieh, and Z. P. Lu, Precipitation behavior and its effects on tensile properties of FeCoNiCr high-entropy alloys, Intermetallics 79, 41 (2016).

    Article  Google Scholar 

  14. J. Y. He, H. Wang, H. L. Huang, X. D. Xu, M. W. Chen, Y. Wu, X. J. Liu, T. G. Nieh, K. An, and Z. P. Lu, A precipitation-hardened high-entropy alloy with outstanding tensile properties, Acta Mater. 102, 187 (2016).

    Article  Google Scholar 

  15. L. Guo, J. Gu, X. Gong, S. Ni, and M. Song, CALPHAD aided design of high entropy alloy to achieve high strength via precipitate strengthening, Sci. China Mater. 63, 288 (2020).

    Article  Google Scholar 

  16. Y. L. Zhao, Y. R. Li, G. M. Yeli, J. H. Luan, S. F. Liu, W. T. Lin, D. Chen, X. J. Liu, J. J. Kai, C. T. Liu, and T. Yang, Anomalous precipitate-size-dependent ductility in multicomponent high-entropy alloys with dense nanoscale precipitates, Acta Mater. 223, 117480 (2022).

    Article  Google Scholar 

  17. X. Wu, B. Wang, C. Rehm, H. He, M. Naeem, S. Lan, Z. Wu, and X. L. Wang, Ultra-small-angle neutron scattering study on temperature-dependent precipitate evolution in CoCrFeNiMo0.3 high entropy alloy, Acta Mater. 222, 117446 (2022).

    Article  Google Scholar 

  18. S. H. Shim, H. Pouraliakbar, B. J. Lee, Y. K. Kim, M. S. Rizi, and S. I. Hong, Strengthening and deformation behavior of as-cast CoCrCu1.5 MnNi high entropy alloy with micro-/nanoscale precipitation, Mater. Sci. Eng.-A 853, 143729 (2022).

    Article  Google Scholar 

  19. S. Y. Li, W. P. Wu, and M. X. Chen, An anisotropic micromechanics model for predicting the rafting direction in Ni-based single crystal superalloys, Acta Mech. Sin. 32, 135 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  20. D. N. Seidman, E. A. Marquis, and D. C. Dunand, Precipitation strengthening at ambient and elevated temperatures of heat-treatable Al(Sc) alloys, Acta Mater. 50, 4021 (2002).

    Article  Google Scholar 

  21. J. F. Nie, and B. C. Muddle, Characterisation of strengthening precipitate phases in a Mg−Y−Nd alloy, Acta Mater. 48, 1691 (2000).

    Article  Google Scholar 

  22. M. P. Petkov, J. Hu, E. Tarleton, and A. C. F. Cocks, Comparison of self-consistent and crystal plasticity FE approaches for modelling the high-temperature deformation of 316H austenitic stainless steel, Int. J. Solids Struct. 171, 54 (2019).

    Article  Google Scholar 

  23. S. Peng, Y. Wei, and H. Gao, Nanoscale precipitates as sustainable dislocation sources for enhanced ductility and high strength, Proc. Natl. Acad. Sci. USA 117, 5204 (2020).

    Article  Google Scholar 

  24. E. Nembach, Particle Strengthening of Metals and Alloys (Wiley, New York, 1997).

    Google Scholar 

  25. M. F. Ashby, Physics of Strength and Plasticity (MIT Press, Cambridge, 1969).

    Google Scholar 

  26. T. Gladman, The Physical Metallurgy of Microalloyed Steels (CRC Press, Boca Raton, 1996).

    Google Scholar 

  27. H. Wen, T. D. Topping, D. Isheim, D. N. Seidman, and E. J. Lavernia, Strengthening mechanisms in a high-strength bulk nanostructured Cu−Zn−Al alloy processed via cryomilling and spark plasma sintering, Acta Mater. 61, 2769 (2013).

    Article  Google Scholar 

  28. K. Ma, H. Wen, T. Hu, T. D. Topping, D. Isheim, D. N. Seidman, E. J. Lavernia, and J. M. Schoenung, Mechanical behavior and strengthening mechanisms in ultrafine grain precipitation-strengthened aluminum alloy, Acta Mater. 62, 141 (2014).

    Article  Google Scholar 

  29. C. Booth-Morrison, D. C. Dunand, and D. N. Seidman, Coarsening resistance at 400 °C of precipitation-strengthened Al−Zr−Sc−Er alloys, Acta Mater. 59, 7029 (2011).

    Article  Google Scholar 

  30. X. Liu, P. Liu, W. Zhang, Q. Hu, Q. Chen, N. Gao, Z. Tu, Z. Fan, and G. Liu, Microstructure and mechanical properties of face-centered-cubic-based Cr-free equiatomic high-entropy alloys, Adv. Eng. Mater. 23, 2000848 (2021).

    Article  Google Scholar 

  31. Y. Mu, L. He, S. Deng, Y. Jia, Y. Jia, G. Wang, Q. Zhai, P. K. Liaw, and C. T. Liu, A high-entropy alloy with dislocation-precipitate skeleton for ultrastrength and ductility, Acta Mater. 232, 117975 (2022).

    Article  Google Scholar 

  32. V. Nandal, R. Sarvesha, S. S. Singh, E. W. Huang, Y. J. Chang, A. C. Yeh, S. Neelakantan, and J. Jain, Influence of pre-deformation on the precipitation characteristics of aged non-equiatomic Co1.5CrFeNi1.5 high entropy alloys with Ti and Al additions, J. Alloys Compd. 855, 157521 (2021).

    Article  Google Scholar 

  33. L. Li, Q. Fang, J. Li, B. Liu, Y. Liu, and P. K. Liaw, Lattice-distortion dependent yield strength in high entropy alloys, Mater. Sci. Eng.-A 784, 139323 (2020).

    Article  Google Scholar 

  34. E. O. Hall, The deformation and ageing of mild steel: III discussion of results, Proc. Phys. Soc. B 64, 747 (1951).

    Article  Google Scholar 

  35. W. H. Liu, Y. Wu, J. Y. He, T. G. Nieh, and Z. P. Lu, Grain growth and the Hall-Petch relationship in a high-entropy FeCrNiCoMn alloy, Scripta Mater. 68, 526 (2013).

    Article  Google Scholar 

  36. N. N. Vinh, Study on dislocation cell structure, dislocation density-fatigue property relationship of a structural steel, J. Sci. Tech. Civ. Eng. 16, 29 (2022).

    Google Scholar 

  37. J. E. Bailey, and P. B. Hirsch, The dislocation distribution, flow stress, and stored energy in cold-worked polycrystalline silver, Philos. Mag. 5, 485 (1960).

    Article  Google Scholar 

  38. S. Ren, L. Li, Q. Fang, and J. Li, Modeling and analysis of yielding and strain hardening in metastable high-entropy alloys, Physica Status Solidi (b) 258, 2100247 (2021).

    Article  Google Scholar 

  39. J. Peng, L. Li, F. Li, B. Liu, S. Zherebtsov, Q. Fang, J. Li, N. Stepanov, Y. Liu, F. Liu, and P. K. Liaw, The predicted rate-dependent deformation behaviour and multistage strain hardening in a model heterostructured body-centered cubic high entropy alloy, Int. J. Plast. 145, 103073 (2021).

    Article  Google Scholar 

  40. J. Y. He, C. Zhu, D. Q. Zhou, W. H. Liu, T. G. Nieh, and Z. P. Lu, Steady state flow of the FeCoNiCrMn high entropy alloy at elevated temperatures, Intermetallics 55, 9 (2014).

    Article  Google Scholar 

  41. T. M. Pollock, and A. S. Argon, Creep resistance of CMSX-3 nickel base superalloy single crystals, Acta Metall. Mater. 40, 1 (1992).

    Article  Google Scholar 

  42. C. Xu, W. J. Dai, Y. Chen, Z. X. Qi, G. Zheng, Y. D. Cao, J. P. Zhang, C. C. Bu, and G. Chen, Control of dislocation density maximizing precipitation strengthening effect, J. Mater. Sci. Tech. 127, 133 (2022).

    Article  Google Scholar 

  43. Q. Fang, W. Lu, Y. Chen, H. Feng, P. K. Liaw, and J. Li, Hierarchical multiscale crystal plasticity framework for plasticity and strain hardening of multi-principal element alloys, J. Mech. Phys. Solids 169, 105067 (2022).

    Article  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 12172123), the Natural Science Foundation of Hunan Province (Grant Nos. 2022JJ20001 and 2021JJ40032), the Science and Technology Innovation Program of Hunan Province (Grant No. 2022RC1200), and the Natural Science Foundation of Changsha City (Grant No. kq2202139), the National Science Foundation (Grant Nos. DMR-1611180 and 1809640), and the US Army Research Office (Grant Nos. W911NF-13-1-0438 and W911NF-19-2-0049).

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Authors and Affiliations

  1. College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, China

    Siwei Ren  (任思危), Jia Li  (李甲), Hui Feng  (冯慧) & Qihong Fang  (方棋洪)

  2. Department of Materials Science and Engineering, The University of Tennessee, Knoxville, TN, 37996, USA

    Peter K. Liaw

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  1. Siwei Ren  (任思危)
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  2. Jia Li  (李甲)
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  5. Qihong Fang  (方棋洪)
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Correspondence to Hui Feng  (冯慧).

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Author contributions

Siwei Ren established the theoretical model and data collection and wrote the first draft of the manuscript. Jia Li, Hui Feng, Peter K. Liaw, and Qihong Fang provided the idea and reviewed, revised, and edited the manuscript. Siwei Ren, Jia Li, and Hui Feng revised and edited the final version.

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Ren, S., Li, J., Feng, H. et al. A physically-based constitutive model for the prediction of yield strength in the precipitate-hardened high-entropy alloys. Acta Mech. Sin. 39, 122393 (2023). https://doi.org/10.1007/s10409-022-22393-x

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