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JOM

, Volume 69, Issue 11, pp 2137–2149 | Cite as

Simulation and Modeling in High Entropy Alloys

  • I. Toda-Caraballo
  • J. S. Wróbel
  • D. Nguyen-Manh
  • P. Pérez
  • P. E. J. Rivera-Díaz-del-Castillo
Article

Abstract

High entropy alloys (HEAs) is a fascinating field of research, with an increasing number of new alloys discovered. This would hardly be conceivable without the aid of materials modeling and computational alloy design to investigate the immense compositional space. The simplicity of the microstructure achieved contrasts with the enormous complexity of its composition, which, in turn, increases the variety of property behavior observed. Simulation and modeling techniques are of paramount importance in the understanding of such material performance. There are numerous examples of how different models have explained the observed experimental results; yet, there are theories and approaches developed for conventional alloys, where the presence of one element is predominant, that need to be adapted or re-developed. In this paper, we review of the current state of the art of the modeling techniques applied to explain HEAs properties, identifying the potential new areas of research to improve the predictability of these techniques.

Notes

Acknowledgements

I.T.C. is grateful for financial support of the fellowship 2016-T2/IND-1693, from the Programme Atracción de talento investigador (Consejería de Educación, Juventud y Deporte, Comunidad de Madrid). J.S.W. acknowledges the financial support from the Foundation of Polish Science Grant HOMING (No. Homing/2016-1/12). The HOMING programme is co-financed by the European Union under the European Regional Development Fund. The simulations were partially carried out by J.S.W. with the support of the Interdisciplinary Centre for Mathematical and Computational Modelling (ICM), University of Warsaw, under Grant No. GA69-30. The work at CCFE has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014–2018 under Grant Agreement No. 633053 and funding from the RCUK Energy Programme [Grant No. EP/P012450/1]. The views and opinions expressed here do not necessarily reflect those of the European Commission. D.N.M. would like to acknowledge the support from Marconi-Fusion, the High Performance Computer at the CINECA headquarters in Bologna (Italy), for its provision of supercomputer resources. P.E.J.R.D.C.’s work was supported by Grant EP/L025213/1 from the UK Engineering and Physical Sciences Research Council (EPSRC). He is grateful to Prof. Claudio Paoloni for the provision of laboratory facilities at Lancaster University.

References

  1. 1.
    I. Toda-Caraballo, E.I. Galindo-Nava, and P.E.J. Rivera-Díaz-Del-Castillo, J. Alloys Compd. 566, 217 (2013).CrossRefGoogle Scholar
  2. 2.
    D.B. Miracle and O.N. Senkov, Acta Mater. 122, 448 (2017).CrossRefGoogle Scholar
  3. 3.
    J.S. Wróbel, D. Nguyen-Manh, M.Y. Lavrentiev, M. Muzyk, and S.L. Dudarev, Phys. Rev. B 91, 024108 (2015).CrossRefGoogle Scholar
  4. 4.
    Z. Leong, J.S. Wróbel, S.L. Dudarev, R. Goodall, I. Todd, and D. Nguyen-Manh, Sci. Rep.-UK 7, 39803 (2017).CrossRefGoogle Scholar
  5. 5.
    Y. Zhang, T.T. Zuo, Z. Tang, M.C. Gao, K.A. Dahmen, P.K. Liaw, and Z.P. Lu, Prog. Mater. Sci. 61, 1 (2014).CrossRefGoogle Scholar
  6. 6.
    M. Widom, W.P. Huhn, S. Maiti, and W. Steurer, Metall. Mater. Trans. A 45, 196 (2014).CrossRefGoogle Scholar
  7. 7.
    M.C. Troparevsky, J.R. Morris, P.R.C. Kent, A.R. Lupini, and G.M. Stocks, Phys. Rev. X 5, 011041 (2015).Google Scholar
  8. 8.
    R. Raghavan, K.C. Hari, Kumar, and B.S. Murty, J. Alloys Compd. 544, 152 (2012)CrossRefGoogle Scholar
  9. 9.
    F. Zhang, C. Zhang, S.L. Chen, J. Zhu, W.S. Cao, and U.R. Kattner, Calphad 45, 1 (2014).CrossRefGoogle Scholar
  10. 10.
    O.N. Senkov, J.D. Miller, D.B. Miracle, and C. Woodward, Calphad 50, 32 (2015).CrossRefGoogle Scholar
  11. 11.
    I. Toda-Caraballo, J.S. Wróbel, S.L. Dudarev, D. Nguyen-Manh, and P.E.J. Rivera-D-az-Del-Castillo, Acta Mater. 97, 156 (2015).CrossRefGoogle Scholar
  12. 12.
    Z. Wang, W. Qiu, Y. Yang, and C.T. Liu, Intermetallics 64, 63 (2015).CrossRefGoogle Scholar
  13. 13.
    Y.F. Ye, C.T. Liu, and Y. Yang, Acta Mater. 94, 152 (2015).CrossRefGoogle Scholar
  14. 14.
    Y. Deng, C.C. Tasan, K.G. Pradeep, H. Springer, A. Kostka, and D. Raabe, Acta Mater. 94, 124 (2015).CrossRefGoogle Scholar
  15. 15.
    I. Toda-Caraballo and P.E.J. Rivera-Díaz-Del-Castillo, Acta Mater. 85, 14 (2015).CrossRefGoogle Scholar
  16. 16.
    I. Toda-Caraballo, Scripta Mater. 127, 113 (2017).CrossRefGoogle Scholar
  17. 17.
    Z. Wu, H. Bei, G.M. Pharr, and E.P. George, Acta Mater. 81, 428 (2014).CrossRefGoogle Scholar
  18. 18.
    Y. Zhang, Y.J. Zhou, J.P. Lin, G.L. Chen, and P.K. Liaw, Adv. Eng. Mater. 10, 534 (2008).CrossRefGoogle Scholar
  19. 19.
    M.G. Poletti and L. Battezzati, Acta Mater. 75, 297 (2014).CrossRefGoogle Scholar
  20. 20.
    S. Guo and C.T. Liu, Prog. Nat. Sci. 21, 433 (2011).CrossRefGoogle Scholar
  21. 21.
    S. Guo, C. Ng, J. Lu, and C.T. Liu, J. Appl. Phys. 109, 103505 (2011).CrossRefGoogle Scholar
  22. 22.
    Y. Zhang, Z.P. Lu, S.G. Ma, P.K. Liaw, Z. Tang, Y.Q. Cheng, and M.C. Gao, MRS Commun. 4, 57 (2014).CrossRefGoogle Scholar
  23. 23.
    I. Toda-Caraballo and P.E.J. Rivera-Díaz-Del-Castillo, Intermetallics 71, 76 (2016).CrossRefGoogle Scholar
  24. 24.
    F. Tancret, I. Toda-Caraballo, E. Menou, and P.E.J. Rivera Díaz-Del-Castillo, Mater. Des. 115, 486 (2017).CrossRefGoogle Scholar
  25. 25.
    L. Asensio Dominguez, R. Goodall, I. Todd, Mater. Sci. Tech.-UK 31, 1201 (2015)Google Scholar
  26. 26.
    M.C. Gao, B. Zhang, S.M. Guo, J.W. Qiao, and J.A. Hawk, Metall. Mater. Trans. A 47, 3322 (2016).CrossRefGoogle Scholar
  27. 27.
    R. Feng, M.C. Gao, C. Lee, M. Mathes, T. Zuo, S. Chen, J.A. Hawk, Y. Zhang, and P.K. Liaw, Entropy 18, 333 (2016).CrossRefGoogle Scholar
  28. 28.
    A.B. Melnick and V.K. Soolshenko, J. Alloys Compd. 694, 223 (2017).CrossRefGoogle Scholar
  29. 29.
    H.W. Yao, J.W. Qiao, J.A. Hawk, H.F. Zhou, M.W. Chen, and M.C. Gao, J. Alloys Compd. 696, 1139 (2017).CrossRefGoogle Scholar
  30. 30.
    D. Ma, M. Yao, K.G. Pradeep, C.C. Tasan, H. Springer, and D. Raabe, Acta Mater. 98, 288 (2015).CrossRefGoogle Scholar
  31. 31.
    M.C. Gao, J.W. Yeh, P.K. Liaw, and Y. Zhang, editors, High-Entropy Alloys: Fundamentals and Applications, 1st ed. (Springer, Cham, 2016).Google Scholar
  32. 32.
    O.N. Senkov, G.B. Wilks, D.B. Miracle, C.P. Chuang, and P.K. Liaw, Intermetallics 18, 1758 (2010).CrossRefGoogle Scholar
  33. 33.
    X. Yang and Y. Zhang, Mater. Chem. Phys. 132, 233 (2012).CrossRefGoogle Scholar
  34. 34.
    Y. Dong, Y. Lu, J. Kong, J. Zhang, and T. Li, J. Alloys Compd. 573, 96 (2013).CrossRefGoogle Scholar
  35. 35.
    A. Kumar and M. Gupta, Metals 6, 199 (2016).CrossRefGoogle Scholar
  36. 36.
    Y. Dong, Y. Lu, L. Jiang, T. Wang, and T. Li, Intermetallics 52, 105 (2014).CrossRefGoogle Scholar
  37. 37.
    A.K. Singh, N. Kumar, A. Dwivedi, and A. Subramaniam, Intermetallics 53, 112 (2014).CrossRefGoogle Scholar
  38. 38.
    I. Toda-Caraballo and P.E.J. Rivera-Díaz del Castillo, JOM 67, 108 (2015).CrossRefGoogle Scholar
  39. 39.
    H.K.D.H. Bhadeshia, Stat. Ana. Data Min. 1, 296 (2009).MathSciNetCrossRefGoogle Scholar
  40. 40.
    M.C. Gao and D.E. Alman, Entropy 15, 4504 (2013).CrossRefGoogle Scholar
  41. 41.
    D.B. Miracle, J.D. Miller, O.N. Senkov, C. Woodward, M.D. Uchic, and J. Tiley, Entropy 16, 494 (2014).CrossRefGoogle Scholar
  42. 42.
    B. Zhang, M.C. Gao, Y. Zhang, S. Yang, and S.M. Guo, Mater. Scie. Tech.-UK 31, 1207 (2015).Google Scholar
  43. 43.
    T. Gómez-Acebo, B. Navarcorena, and F. Castro, J. Phase Equilib. Diff. 25, 237 (2004).CrossRefGoogle Scholar
  44. 44.
    C. Guéneau, N. Dupin, B. Sundman, C. Martial, J.C. Dumasean, S. Gossé, S. Chataine, F.D. Bruycker, D. Manara, and R.J.M. Konings, J. Nucl. Mater. 419, 145 (2011).CrossRefGoogle Scholar
  45. 45.
    R. Mathieu, N. Dupin, J.-C. Crivello, K. Yaqoob, A. Breidi, J.-M. Fiorani, N. David, and J.-M. Joubert, Calphad 43, 18 (2013).CrossRefGoogle Scholar
  46. 46.
    C. Zhang, F. Zhang, S. Chen, and W. Cao, JOM 64, 839 (2012).CrossRefGoogle Scholar
  47. 47.
    F. He, A. Wang, Y. Li, Q. Wu, J. Li, J. Wang, and C.T. Liu, Sci. Rep. 6, 34628 (2016).CrossRefGoogle Scholar
  48. 48.
    N.G. Jones, R. Izzo, P.M. Mignanelli, K.A. Christofidou, and H.J. Stone, Intermetallics 71, 43 (2016).CrossRefGoogle Scholar
  49. 49.
    E.I. Galindo-Nava, P.E.J. Rivera-Díaz-del Castillo, Acta Mater. 128, 120 (2017)CrossRefGoogle Scholar
  50. 50.
    G. B. Olson and M. Cohen, Metall. Trans. A 7, 1897 (1976).Google Scholar
  51. 51.
    R. Li, S. Lu, D. Kim, S. Schnecker, J. Zhao, S.K. Kwon, and L. Vitos, J. Phy. Condens. Matter 28, 395001 (2016).CrossRefGoogle Scholar
  52. 52.
    S. Huang, W. Li, S. Lu, F. Tian, J. Shen, E. Holmstrm, and L. Vitos, Scripta Mater. 108, 44 (2015).CrossRefGoogle Scholar
  53. 53.
    A. van de Walle and G. Ceder, Rev. Mod. Phys. 74, 11 (2002).CrossRefGoogle Scholar
  54. 54.
    M.S. Lucas, D. Belyea, C. Bauser, N. Bryant, E. Michel, Z. Turgut, S.O. Leontsev, J. Howarth, S.L. Semiatin, M.E. McHenry, and C.W. Miller, J. Appl. Phys. 113, 17A923 (2013).CrossRefGoogle Scholar
  55. 55.
    M.Y. Lavrentiev, D. Nguyen-Manh, and S.L. Dudarev, Phys. Rev. B 81, 184202 (2010).CrossRefGoogle Scholar
  56. 56.
    M. Calvo-Dahlborg, J. Cornide, J. Tobola, D. Nguyen-Manh, J.S. Wróbel, J. Juraszek, S. Jouen, and U Dahlborg, J. Phys. D Appl. Phys. 50, 185002 (2017).CrossRefGoogle Scholar
  57. 57.
    J. Connolly and A. Williams, Phys. Rev. B 27, 5169 (1983).CrossRefGoogle Scholar
  58. 58.
    M.E.J. Newman and G.T. Barkema, Monte Carlo methods in statistical physics. Springer, Berlin (1999).MATHGoogle Scholar
  59. 59.
    A. Fernández-Caballero, J.S. Wróbel, P.M. Mummery, and D. Nguyen-Manh, J. Phase Equilibria Diffus. 38, 391 (2017).CrossRefGoogle Scholar
  60. 60.
    M.Y. Lavrentiev, J.S. Wróbel, D. Nguyen-Manh, and S.L. Dudarev, Phys. Chem. Chem. Phys. 16, 16049 (2014).CrossRefGoogle Scholar
  61. 61.
    E.J. Pickering, R. Murioz-Mureno, H.J. Stone, and N.G. Jones, Scripta Mater. 113, 106 (2016).CrossRefGoogle Scholar
  62. 62.
    M. W. Finnis, Interatomic Forces in Condensed Matter. Oxford University Press, Oxford (2003)CrossRefGoogle Scholar
  63. 63.
    M. Aoki, D. Nguyen-Manh, V. Vitek, and D.G. Pettifor, Prog. Mat. Sci. 52, 154 (2007).CrossRefGoogle Scholar
  64. 64.
    D. Nguyen-Manh, V. Vitek, and A.P. Horsfield, Prog. Mater. Sci. 52, 255 (2007).CrossRefGoogle Scholar
  65. 65.
    M. Mrovec, D. Nguyen-Manh, C. Elsasser, and P. Gumbsch, Phys. Rev. Lett. 106, 246402 (2011).CrossRefGoogle Scholar
  66. 66.
    M.W. Finnis and J.E. Sinclair, Philos. Mag. A 50, 45 (1984).CrossRefGoogle Scholar
  67. 67.
    M.S. Daw and M.I. Baskes, Phys. Rev. B 29, 6443 (1984).CrossRefGoogle Scholar
  68. 68.
    M.I. Baskes, Phys. Rev. B 46, 2727 (1992).CrossRefGoogle Scholar
  69. 69.
    S.L. Dudarev and P.M. Derlet, J. Phys: Condens. Matter 17, 7097 (2005).Google Scholar
  70. 70.
    F. Gransberg, K. Nordlund, M.W. Ullah, K. Jin, C. Lu, H. Bei, L.M. Wang, F. Djurabekova, W.J. Weber, and Y. Zhang, Phys. Rev. Lett. 116, 135504 (2016).CrossRefGoogle Scholar
  71. 71.
    W.M. Choi, Y. Kim, D. Seol, and B.J. Lee, Comput. Mater. Sci. 130, 121 (2017).CrossRefGoogle Scholar
  72. 72.
    Z. Tang, M.C. Gao, H. Diao, T. Yang, J. Liu, T. Zuo, Y. Zhang, Z. Lu, Y. Cheng, Y. Zhang, K.A. Dahmen, P.K. Liaw, and T. Egami, JOM 65, 1848 (2013).CrossRefGoogle Scholar
  73. 73.
    M.S. Anzorena, A.A. Bertolo, L. Gagetti, A.J. Kreiner, H.O. Mosca, G. Bozzolo, and M.F. del Grosso, Mater. Des. 111, 382 (2016).CrossRefGoogle Scholar
  74. 74.
    N.D. Stepanov, N.Y. Yurchenko, D.V. Skibin, M.A. Tikhonovsky, and G.A. Salishchev, J. Alloys Compd. 652, 266 (2015).CrossRefGoogle Scholar
  75. 75.
    J. Wang, Y. Liu, B. Liu, Y. Wang, Y. Cao, T. Li, and R. Zhou, Mater. Sci. Eng. A 689, 233 (2017).CrossRefGoogle Scholar
  76. 76.
    L. Patriarca, A. Ojha, H. Sehitoglu, and Y.I. Chumlyakov, Scripta Mater. 112, 54 (2016).CrossRefGoogle Scholar
  77. 77.
    Q. Yao, S.-L. Shang, Y.-J. Hu, Y. Wang, Y. Wang, Y.-H. Zhu, and Z.-K. Liu, Intermetallics 78, 1 (2016).CrossRefGoogle Scholar
  78. 78.
    Q. Yao, S.-L. Shang, K. Wang, F. Liu, Y. Wang, Q. Wang, T. Lu, and Z.-K. Liu, J. Mater. Res. 32, 2100 (2017).CrossRefGoogle Scholar
  79. 79.
    P. Pérez, Corros. Sci. 49, 1172 (2007).CrossRefGoogle Scholar
  80. 80.
    P. Pérez, G. Salmi, A. Muñoz, and M.A. Monge, Scripta Mater. 60, 1008 (2009).CrossRefGoogle Scholar
  81. 81.
    P. Pérez, V.A.C. Haanappel, and M.F. Stroosnijder, Oxid. Met. 53, 481 (2000).CrossRefGoogle Scholar
  82. 82.
    P. Pérez, V.A.C. Haanappel, and M.F. Stroosnijder. Mater. Sci. Eng. A, 284, 126, (2000).CrossRefGoogle Scholar
  83. 83.
    J.J. Van de Broek and J.L. Meijering, Acta Metall. 16, 375 (1968).Google Scholar
  84. 84.
    S. Wang, Y. Wu, F. Gesmundo, and Y. Niu, Oxid. Met. 65, 299 (2006).Google Scholar
  85. 85.
    X.J. Zhang, S.Y. Wang, F. Gesmundo, and Y. Niu, Oxid. Met. 69, 151 (2008).Google Scholar
  86. 86.
    P. Pérez, J.L. González-Carrasco, and P. Adeva, Oxid. Met. 48, 143 (1997).CrossRefGoogle Scholar
  87. 87.
    D.L. Douglass, Corros. Sci. 8, 665 (1968).CrossRefGoogle Scholar
  88. 88.
    P. Pérez and P. Adeva, Oxid. Met. 65, 15 (2006).CrossRefGoogle Scholar
  89. 89.
    H. Lai, Y. Cao, P. Viklund, F. Karlsson, L.-G. Johansson, and K. Stiller, Oxid. Met. 80, 505 (2013).CrossRefGoogle Scholar
  90. 90.
    W. Kai, W.L. Jang, R.T. Huang, C.C. Lee, H.H. Hsieh, and C.F. Du, Oxid. Met. 63, 169 (2005).CrossRefGoogle Scholar
  91. 91.
    W. Kai, C.C. Li, F.P. Cheng, K.P. Chu, R.T. Huang, L.W. Tsay, and J.J. Kai, Corros. Sci. 121, 116 (2017).CrossRefGoogle Scholar
  92. 92.
    T.K. Tsao, A.C. Yeh, C.M. Kuo, and H. Murakami, Entropy 18, 62 (2016).CrossRefGoogle Scholar
  93. 93.
    M.B. Karpetz, E.S. Makarenko, A.N. Mislibchenko, N.A. Krapibka, B.F. Gorban, S.J. Makarenko, Metallofiz. Noveishie Tekhnol 36, 829 (2014) (in Russian).CrossRefGoogle Scholar
  94. 94.
    T.M. Butler, J.P. Alfano, R.L. Martens, and M.L. Weaver, JOM 67, 246 (2015).CrossRefGoogle Scholar
  95. 95.
    J. Dabrowa, G. Cieślak, M. Stygar, K. Mroczka, K. Berent, T. Kulik, and M. Danielewski, Intermetallics 84, 52 (2017).CrossRefGoogle Scholar
  96. 96.
    H. Prasad, S. Singh, and B.B. Panigrahi, J. Alloys Compd. 692, 720 (2017).CrossRefGoogle Scholar
  97. 97.
    S.T. Chen, W.Y. Tang, Y.F. Kuo, S.Y. Chen, C.H. Tsau, T.T. Shun, and J.W. Yeh, Mater. Sci. Eng. A 527, 5818 (2010).CrossRefGoogle Scholar
  98. 98.
    H.M. Daoud, A.M. Manzoni, R. Völkl, N. Wanderka, and U. Glatzel, Adv. Eng. Mater. 17, 1134 (2015).CrossRefGoogle Scholar
  99. 99.
    T.M. Butler and M.L. Weaver, J. Alloys Compd. 674, 229 (2016).CrossRefGoogle Scholar
  100. 100.
    Y.X. Liu, C.Q Cheng, J.L. Shang, R. Wang, P. Li, and J. Zhao, Trans. Nonferrous Met. Soc. China 25, 1341 (2015).CrossRefGoogle Scholar
  101. 101.
    G.R. Holcomb, J. Tylczak, and C. Carney, JOM 67, 2326 (2015).CrossRefGoogle Scholar
  102. 102.
    Y.J. Chang and A.C. Yeh, J. Alloys Compd. 653, 379 (2015).CrossRefGoogle Scholar
  103. 103.
    W. Kai, C.C. Li, F.P. Cheng, K.P. Chu, R.T. Huang, L.W. Tsay, and J.J. Kai, Corros. Sci. 108, 209 (2016).CrossRefGoogle Scholar
  104. 104.
    C. Huang, Y. Zhang, J. Shen, and R. Vilar, Surf. Coat. Technol. 206, 1389 (2011).CrossRefGoogle Scholar
  105. 105.
    T.M. Butler and M.L. Weaver, Metals 6, 222 (2016).CrossRefGoogle Scholar
  106. 106.
    B. Gorr, F. Müller, M. Azim, H.J. Christ, T. Müller, H. Chen, A. Kauffmann, and M. Heilmaier, Oxid. Met. (2017). doi: 10.1007/s11085-016-9696-y.Google Scholar
  107. 107.
    B. Gorr, F. Mueller, H.J. Christ, T. Mueller, H. Chen, A. Kauffmann, and M. Heilmaier, J. Alloys Compd. 688, 468 (2016).CrossRefGoogle Scholar
  108. 108.
    O.N. Senkov, S.V. Senkova, D.M. Dimiduk, C. Woodward, and D.B. Miracle, J. Mater. Sci. 47, 6522 (2012).CrossRefGoogle Scholar
  109. 109.
    C.M. Liu, H.M. Wang, S.Q. Zhan, H.B. Tang, and A.L. Zhang, J. Alloys Compd. 583, 162 (2014).CrossRefGoogle Scholar
  110. 110.
    B. Gorr, M. Azim, H.J. Christ, T Mueller, D. Schliephake, and M. Heilmaier, J. Alloys Compd 624, 270 (2015).CrossRefGoogle Scholar
  111. 111.
    P. Kofstad, High Temperature Corrosion. (Elsevier Applied Science, London/New York 1988).Google Scholar
  112. 112.
    C. Wagner, J. Electrochem. Soc. 99, 369 (1952).CrossRefGoogle Scholar
  113. 113.
    F. Gesmundo, F. Viani, Y. Niu, and D.L. Douglass, Oxid. Met. 40, 373 (1993).CrossRefGoogle Scholar
  114. 114.
    F. Gesmundo, F. Viani, Y. Niu, and D.L. Douglass, Oxid. Met. 42, 239 (1994).CrossRefGoogle Scholar
  115. 115.
    F. Gesmundo, F. Viani, and Y. Niu, Oxid. Met. 45, 51 (1996).CrossRefGoogle Scholar
  116. 116.
    P. Saltykov, O. Fabrichnaya, J. Golczewski, and F. Aldinger, J. Alloys Compd. 381, 99 (2004).CrossRefGoogle Scholar
  117. 117.
    V.K. Tolpygo and D.R. Clarke, Acta Mater. 46, 5167 (1998).CrossRefGoogle Scholar
  118. 118.
    L.H. Rettberg, B. Laux, M.Y. He, D. Hovis, A.H. Heuer, T.M. Pollock, Metall. Mater. Trans. 47A, 1132 (2016)CrossRefGoogle Scholar
  119. 119.
    Y. Suo and S. Shen, Acta Mech. 226, 3375 (2015).MathSciNetCrossRefGoogle Scholar
  120. 120.
    N.K. Das, T. Shoji, and Y. Takeda, Corros. Sci. 226, 3375 (2010).Google Scholar

Copyright information

© European Union 2017

Authors and Affiliations

  • I. Toda-Caraballo
    • 1
  • J. S. Wróbel
    • 2
  • D. Nguyen-Manh
    • 3
  • P. Pérez
    • 4
  • P. E. J. Rivera-Díaz-del-Castillo
    • 5
  1. 1.Materalia Group/Physical Metallurgy DepartmentNational Centre for Metallurgical Research (CENIM-CSIC)MadridSpain
  2. 2.Faculty of Materials Science and EngineeringWarsaw University of TechnologyWarszawaPoland
  3. 3.Culham Centre for Fusion EnergyUnited Kingdom Atomic Energy AuthorityAbingdonUnited Kingdom
  4. 4.Manoeq Group/Physical Metallurgy Dept.National Centre for Metallurgical Research (CENIM-CSIC)MadridSpain
  5. 5.Department of EngineeringUniveristy of LancasterLancasterUnited Kingdom

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