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Simple Approach to Model the Strength of Solid-Solution High Entropy Alloys in Co-Cr-Fe-Mn-Ni System

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Strength of Materials Aims and scope

A simple fitting approach is introduced for modeling the strength (hardness) of quaternary and quinary face-centered cubic (fcc) solid solution high entropy alloys (HEAs) in the Co-Cr-Fe-Mn-Ni system. The strength of solid solution HEAs could be modeled by a polynomial equation where experimental data are used to find the polynomial coefficients. It is observed that the proposed polynomial could model the strength of solid solution HEAs very well. Effects of constituent elements on the hardness of quinary Co-Cr-Fe-Mn-Ni alloys are investigated; the results indicate that alloys’ strength decreases with the Fe content. The softening effect of Fe is explained by considering its impact on reducing the shear modulus of alloys. Furthermore, the effects of parameters enthalpy of mixing and valence electron concentration on the strength of HEAs are investigated. The results show that the enthalpy of mixing has a noticeable impact on the hardness of quinary Co-Cr-Fe-Mn-Ni alloys, and the strength increases with decreasing the enthalpy of mixing. Furthermore, the results show that quinary Co-Cr-Fe-Mn-Ni alloys’ hardness increases with the parameter valence electron concentration.

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References

  1. E. P. George, D. Raabe, and R. O. Ritchie, “High-entropy alloys,” Nature Reviews Materials, 4, 515-534 (2019).

    Article  CAS  Google Scholar 

  2. D. B. Miracle, “High entropy alloys as a bold step forward in alloy development,” Nature Communications, 10, 1805 (2019).

    Article  CAS  Google Scholar 

  3. D. B. Miracle and O. N. Senkov, “A critical review of high entropy alloys and related concepts,” Acta Materialia, 122, 448-511 (2017).

    Article  CAS  Google Scholar 

  4. Y. F. Ye, Q. Wang, J. Lu, et al., “High-entropy alloy: challenges and prospects,” Materials Today, 19 (6), 349-362 (2016).

    Article  CAS  Google Scholar 

  5. C. Zhang, F. Zhang, S. Chen, and W. Cao, “Computational thermodynamics aided high-entropy alloy design,” JOM, 64, 839-845 (2012).

    Article  CAS  Google Scholar 

  6. C. Jiang and B.P. Uberuaga, “Efficient Ab initio modeling of random multicomponent alloys,” Physical Review Letters, 116, 105501(2016).

  7. Y. Lederer, C. Toher, K.S. Vecchio, and S. Curtarolo, “The search for high entropy alloys: a high throughput ab-initio approach,” Acta Materialia, 159, 364-383 (2018).

    Article  CAS  Google Scholar 

  8. O. N. Senkov, J. D. Miller, D. B. Miracle, and C. Woodward, “Accelerated exploration of multiprincipal element alloys with solid solution phases,” Nature Communications, 6, 6529 (2015).

    Article  CAS  Google Scholar 

  9. C. Varvenne, A. Luque, and W. A. Curtin, “Theory of strengthening in fcc high entropy alloys,” Acta Materialia, 118, 164-176 (2016).

    Article  CAS  Google Scholar 

  10. F. Thiel, D. Utt, A. Kauffmann, et al., “Breakdown of Varvenne scaling in (AuNiPdPt)1−xCux high-entropy alloys,” Scripta Materialia, 18, 15-18 (2020).

    Article  Google Scholar 

  11. G. Bracq, M. Laurent-Brocq, C. Varvenne, et al., “Combining experiments and modelling to explore the solid solution strengthening of high and medium entropy alloys,” Acta Materialia, 177, 266-279 (2019).

    Article  CAS  Google Scholar 

  12. M. L. Brocq, L. Perrière, R. Pirès, F. Prima, P. Vermaut, Y. Champion, “From diluted solid solutions to high entropy alloys: on the evolution of properties with composition of multi-components alloys,” Materials Science and Engineering A, 696, 228-235 (2017).

    Article  Google Scholar 

  13. D. R. Askeland, P. P. Fulay, and W. J. Wright, The Science and Engineering of Materials, Cengage Learning, Stamford, CT (2011), p. 266.

  14. B. C. Peters and A. Hendrickson, “The strength of tantalum columbium alloy single crystals”, Acta Metallurgica, 14 (9), 1121-1122 (1966).

    Article  CAS  Google Scholar 

  15. J. R. Stephens and W. R. Witzke, “Alloy hardening and softening in binary molybdenum alloys as related to electron concentration,” Journal of the Less Common Metals, 29, 371-388 (1972).

    Article  CAS  Google Scholar 

  16. W. Fang, R. Chang, X. Zhang, et al., “Effects of cobalt on the structure and mechanical behavior of non-equal molar CoxFe50−xCr25Ni25 high entropy alloys,” Materials Science and Engineering A, 723, 221-228 (2018).

    Article  CAS  Google Scholar 

  17. K. G. Pradeep, C. C. Tasan, M. J. Yao, et al., “Non-equiatomic high entropy alloys: approach towards rapid alloy screening and property-oriented design,” Materials Science and Engineering A, 648, 183-192 (2015).

    Article  CAS  Google Scholar 

  18. M. P. Agustianingrum, I. Ondicho, D. E. Jodi, et al., “Theoretical evaluation of solid solution interaction in Fex(CoCrMnNi)100–x medium- and high-entropy alloys,” Materials Science & Engineering A, 759, 633-639 (2019).

    Article  CAS  Google Scholar 

  19. Y. Zhou, X. Jin, X. Y. Du, et al., “Comparison of the structure and properties of equiatomic and non-equiatomic multicomponent alloys,” Materials Science and Technology, 34 (8), 988-991 (2018).

    Article  CAS  Google Scholar 

  20. M. Tian, C. Wu, Y. Liu, H. Peng, et al., “Phase stability and microhardness of CoCrFeMnxNi2–x high entropy alloys,” Journal of Alloys and Compounds, 811, 152025 (2019).

  21. M. Laurent-Brocq, L. Perrière, R. Pirès, et al., “Combining tensile tests and nanoindentation to explore the strengthening of high and medium entropy alloys,” Materialia, 7, 100404 (2019).

  22. F. Gil Coury, P. Wilson, K. D. Clarke, et al., “High-throughput solid solution strengthening characterization in high entropy alloys,” Acta Materialia, 167, 1-11 (2019).

    Article  Google Scholar 

  23. K. Jin, Y. F. Gao, and H. Bei, “Intrinsic properties and strengthening mechanism of monocrystalline Ni containing ternary concentrated solid solutions,” Materials Science & Engineering A, 695, 74-79 (2017).

    Article  CAS  Google Scholar 

  24. Z. Wu, H. Bei, G. M. Pharr, and E. P. George, “Temperature dependence of the mechanical properties of equiatomic solid solution alloys with face-centered cubic crystal structures,” Acta Materialia, 81, 428-441 (2014).

    Article  CAS  Google Scholar 

  25. Y. Y. Zhao and T. G. Nieh, “Correlation between lattice distortion and friction stress in Ni-based equiatomic alloys,” Intermetallics, 86, 45-50 (2017).

    Article  CAS  Google Scholar 

  26. X. Liu, Z. Pei, and M. Eisenbach, “Dislocation core structures and Peierls stresses of the high-entropy alloy NiCoFeCrMn and its subsystemssubsystems,” Materials and Design, 180, 107955 (2019).

  27. S. S. Sohn, A. K. Silva, Y. Ikeda, et al. “Ultrastrong medium-entropy single-phase alloys designed via severe lattice distortion,” Advanced Materials, 31 (8), 1807142 (2019).

    Article  Google Scholar 

  28. L. Zhang, Y. Xiang, J. Han, and D. J. Srolovitz, “The effect of randomness on the strength of high-entropy alloys,” Acta Materialia, 166, 424-434 (2019).

    Article  CAS  Google Scholar 

  29. R. Chen, G. Qin, H. Zheng, et al. “Composition design of high entropy alloys using the valence electron concentration to balance strength and ductility,” Acta Materialia, 144, 129-137 (2018).

    Article  CAS  Google Scholar 

  30. F. G. Coury, K. D. Clarke, C. S. Kiminami, et al., “High throughput discovery and design of strong multicomponent metallic solid solutions,” Scientific Reports, 8, 8600 (2018).

    Article  Google Scholar 

  31. H. S. Oh, S. J. Kim, K. Odbadrakh, et al., “Engineering atomic-level complexity in high-entropy and complex concentrated alloys,” Nature Communications, 10, 2090 (2019).

    Article  Google Scholar 

  32. Q. J. Li, H. Sheng, and E. Ma, “Strengthening in multi-principal element alloys with local-chemical-order roughened dislocation pathways,” Nature Communications, 10, 3563 (2019).

    Article  Google Scholar 

  33. C. Niu, C. R. LaRosa, J. Miao, et al., “Magnetically-driven phase transformation strengthening in high entropy alloys,” Nature Communications, 9, 1363 (2018).

    Article  Google Scholar 

  34. Y. Zeng, X. Cai, and M. Koslowski, “Effects of the stacking fault energy fluctuations on the strengthening of alloys,” Acta Materialia, 164, 1-11 (2019).

    Article  CAS  Google Scholar 

  35. M. C. Gao, J. W. Yeh, P. K. Liaw, and Y. Zhang, High-Entropy Alloys: Fundamentals and Applications, Springer Publishing Co., New York, NY (2016).

  36. A. Takeuchi and A. Inoue, “Classification of bulk metallic glasses by atomic size difference, heat of mixing and period of constituent elements and its application to characterization of the main alloying element,” Materials Transactions, 46 (12), 2817-2829 (2005).

    Article  CAS  Google Scholar 

  37. S. S. Sohn, A. K. Silva, Y. Ikeda, et al., “Ultrastrong medium-entropy single-phase alloys designed via severe lattice distortion,” Advanced Materials, 31 (8), 1807142 (2019).

    Article  Google Scholar 

  38. A. R. Miedema, P. F. de Châtel, and F. R.de Boer, “Cohesion in alloys - fundamentals of a semi-empirical model,” Physica B+C, 100 (1), 1-28 (1980).

  39. L. Zhang, Y. Xiang, J. Han, and D. J. Srolovitz, “The effect of randomness on the strength of high-entropy alloys,” Acta Materialia, 2019, 166, 424-434.

    Article  CAS  Google Scholar 

  40. P. Singh, A. V. Smirnov, and D. D. Johnson, “Atomic short-range order and incipient long-range order in high entropy alloys”, Physical Review B, 91, 224204 (2015).

  41. A. Tamm, A. Aabloo, M. Klintenberg, et al., “Atomic-scale properties of Ni-based FCC ternary, and quaternary alloys,” Acta Materiali, 99, 307-312 (2015).

  42. A. Sharma, P. Singh, D. D. Johnson, et al. “Atomistic clustering-ordering and high-strain deformation of an Al0.1CrCoFeNi high-entropy alloy”, Scientific Reports, 6, 31028 (2016).

    Article  CAS  Google Scholar 

  43. Y. Ma, Q. Wang, C. Li, L. et al.,“Chemical short-range orders and the induced structural transition in high-entropy alloys,” Scripta Materialia, 144, 64-68 (2018).

  44. F. Pettinari-Sturmel, M. Jouiad, H. O. K. Kirchner, et al., “Local disordering and reordering phenomena induced by mobile dislocations in short-range-ordered solid solutions,” Philosophical Magazine A, 82, 3045-3054 (2022).

    Article  Google Scholar 

  45. F. Pettinari, M. Prem, G. Krexner, et al., “Local order in industrial and model γ phases of superalloys,” Acta Materialia, 13 (1), 2549-2556 (2001).

    Article  Google Scholar 

  46. J. R. Stephens and W. R. Witzke, “The role of electron concentration in softening and hardening of ternary molybdenum alloys,” Journal of the Less Common Metals, 41 (2), 265-282 (1975).

    Article  CAS  Google Scholar 

  47. Y. Hiraoka, T. Ogusu, and N. Yoshizawa, “Decrease of yield strength in molybdenum by adding small amounts of Group VIII elements,” Journal of Alloys and Compounds, 381 (1-2), 192-196 (2004).

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  1. Metallurgy Group, Niroo Research Institute (NRI), Tehran, Iran

    A. Shafiei

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Correspondence to A. Shafiei.

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Translated from Problemy Mitsnosti, No. 4, p. 106, July – August, 2022.

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Shafiei, A. Simple Approach to Model the Strength of Solid-Solution High Entropy Alloys in Co-Cr-Fe-Mn-Ni System. Strength Mater 54, 705–716 (2022). https://doi.org/10.1007/s11223-022-00448-6

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