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Atomistic simulations of grain boundary energies in austenitic steel

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Abstract

The energies of 388 grain boundaries with a range of misorientations and grain boundary plane orientations have been calculated using the meta-atom embedded atom method potential recently developed to simulate an austenitic twinning-induced plasticity (TWIP) steel. A comparison between the simulated grain boundary energies and the measured grain boundary population in an austenitic TWIP steel revealed that at fixed misorientations, there is a strong inverse correlation between the energy and the population. In addition, the Bulatov–Reed–Kumar five-parameter grain boundary energy function for face-centered cubic metals was used to produce a larger, more nearly continuous set of grain boundary energies. Interestingly, these interpolated grain boundary energies were consistent with the simulated energies and also inversely correlated with the measured grain boundary populations in an austenitic TWIP steel.

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References

  1. Bouaziz O, Allain S, Scott CP et al (2011) High manganese austenitic twinning induced plasticity steels: a review of the microstructure properties relationships. Curr Opin Solid State Mater Sci 15:141–168. https://doi.org/10.1016/j.cossms.2011.04.002

    Article  Google Scholar 

  2. Beladi H, Timokhina IB, Estrin Y et al (2011) Orientation dependence of twinning and strain hardening behaviour of a high manganese twinning induced plasticity steel with polycrystalline structure. Acta Mater 59:7787–7799. https://doi.org/10.1016/j.actamat.2011.08.031

    Article  Google Scholar 

  3. Barr CM, Vetterick GA, Unocic KA et al (2014) Anisotropic radiation-induced segregation in 316L austenitic stainless steel with grain boundary character. Acta Mater 67:145–155. https://doi.org/10.1016/j.actamat.2013.11.060

    Article  Google Scholar 

  4. Gutierrez-Urrutia I, Zaefferer S, Raabe D (2010) The effect of grain size and grain orientation on deformation twinning in a Fe–22wt.% Mn–0.6wt.% C TWIP steel. Mater Sci Eng A 527:3552–3560. https://doi.org/10.1016/j.msea.2010.02.041

    Article  Google Scholar 

  5. Michiuchi M, Kokawa H, Wang ZJ et al (2006) Twin-induced grain boundary engineering for 316 austenitic stainless steel. Acta Mater 54:5179–5184. https://doi.org/10.1016/j.actamat.2006.06.030

    Article  Google Scholar 

  6. Shimada M, Kokawa H, Wang ZJ et al (2002) Optimization of grain boundary character distribution for intergranular corrosion resistant 304 stainless steel by twin-induced grain boundary engineering. Acta Mater 50:2331–2341. https://doi.org/10.1016/S1359-6454(02)00064-2

    Article  Google Scholar 

  7. Barr CM, Thomas S, Hart JL et al (2018) Tracking the evolution of intergranular corrosion through twin-related domains in grain boundary networks. NPJ Mater Degrad 2:14. https://doi.org/10.1038/s41529-018-0032-7

    Article  Google Scholar 

  8. Sakaguchi N, Endo M, Watanabe S et al (2013) Radiation-induced segregation and corrosion behavior on Σ3 coincidence site lattice and random grain boundaries in proton-irradiated type-316L austenitic stainless steel. J Nucl Mater 434:65–71. https://doi.org/10.1016/j.jnucmat.2012.11.036

    Article  Google Scholar 

  9. Bouaziz O, Allain S, Scott C (2008) Effect of grain and twin boundaries on the hardening mechanisms of twinning-induced plasticity steels. Scr Mater 58:484–487. https://doi.org/10.1016/j.scriptamat.2007.10.050

    Article  Google Scholar 

  10. Steinmetz DR, Jäpel T, Wietbrock B et al (2013) Revealing the strain-hardening behavior of twinning-induced plasticity steels: theory, simulations, experiments. Acta Mater 61:494–510. https://doi.org/10.1016/j.actamat.2012.09.064

    Article  Google Scholar 

  11. Rohrer GS (2011) Grain boundary energy anisotropy: a review. J Mater Sci 46:5881–5895. https://doi.org/10.1007/s10853-011-5677-3

    Article  Google Scholar 

  12. Beladi H, Nuhfer NT, Rohrer GS (2014) The five-parameter grain boundary character and energy distributions of a fully austenitic high-manganese steel using three dimensional data. Acta Mater 70:281–289. https://doi.org/10.1016/j.actamat.2014.02.038

    Article  Google Scholar 

  13. Jones R, Randle V, Engelberg D, Marrow TJ (2009) Five-parameter grain boundary analysis of a grain boundary–engineered austenitic stainless steel. J Microsc 233:417–422. https://doi.org/10.1111/j.1365-2818.2009.03129.x

    Article  Google Scholar 

  14. Gertsman VY, Bruemmer SM (2001) Study of grain boundary character along intergranular stress corrosion crack paths in austenitic alloys. Acta Mater 49:1589–1598. https://doi.org/10.1016/S1359-6454(01)00064-7

    Article  Google Scholar 

  15. Jones R, Randle V (2010) Sensitisation behaviour of grain boundary engineered austenitic stainless steel. Mater Sci Eng A 527:4275–4280. https://doi.org/10.1016/j.msea.2010.03.058

    Article  Google Scholar 

  16. Shi F, Tian PC, Jia N et al (2016) Improving intergranular corrosion resistance in a nickel-free and manganese-bearing high-nitrogen austenitic stainless steel through grain boundary character distribution optimization. Corros Sci 107:49–59. https://doi.org/10.1016/j.corsci.2016.02.019

    Article  Google Scholar 

  17. Tokita S, Kokawa H, Sato YS, Fujii HT (2017) In situ EBSD observation of grain boundary character distribution evolution during thermomechanical process used for grain boundary engineering of 304 austenitic stainless steel. Mater Charact 131:31–38. https://doi.org/10.1016/j.matchar.2017.06.032

    Article  Google Scholar 

  18. Feng W, Yang S, Yan Y (2017) Dependence of grain boundary character distribution on the initial grain size of 304 austenitic stainless steel. Philos Mag 97:1057–1070. https://doi.org/10.1080/14786435.2017.1288943

    Article  Google Scholar 

  19. Hu C, Xia S, Li H et al (2011) Improving the intergranular corrosion resistance of 304 stainless steel by grain boundary network control. Corros Sci 53:1880–1886. https://doi.org/10.1016/j.corsci.2011.02.005

    Article  Google Scholar 

  20. Murr LE, Wong GI, Horylev RJ (1973) Measurement of interfacial free energies and associated temperature coefficients in 304 stainless steel. Acta Metall 21:595–604. https://doi.org/10.1016/0001-6160(73)90068-0

    Article  Google Scholar 

  21. Saylor DM, Rohrer GS (2001) Evaluating anisotropic surface energies using the capillarity vector reconstruction method. Interface Sci 9:35–42. https://doi.org/10.1023/A:1011262628243

    Article  Google Scholar 

  22. Holm EA, Olmsted DL, Foiles SM (2010) Comparing grain boundary energies in face-centered cubic metals: Al, Au, Cu and Ni. Scr Mater 63:905–908. https://doi.org/10.1016/j.scriptamat.2010.06.040

    Article  Google Scholar 

  23. Olmsted DL, Foiles SM, Holm EA (2009) Survey of computed grain boundary properties in face-centered cubic metals: I. Grain boundary energy. Acta Mater 57:3694–3703. https://doi.org/10.1016/j.actamat.2009.04.007

    Article  Google Scholar 

  24. Rohrer GS, Holm EA, Rollett AD et al (2010) Comparing calculated and measured grain boundary energies in nickel. Acta Mater 58:5063–5069. https://doi.org/10.1016/j.actamat.2010.05.042

    Article  Google Scholar 

  25. Holm EA, Rohrer GS, Foiles SM et al (2011) Validating computed grain boundary energies in fcc metals using the grain boundary character distribution. Acta Mater 59:5250–5256. https://doi.org/10.1016/j.actamat.2011.05.001

    Article  Google Scholar 

  26. Shibuta Y, Takamoto S, Suzuki T (2008) A molecular dynamics study of the energy and structure of the symmetric tilt boundary of iron. ISIJ Int 48:1582–1591. https://doi.org/10.2355/isijinternational.48.1582

    Article  Google Scholar 

  27. Finnis MW, Sinclair JE (1984) A simple empirical N-body potential for transition metals. Philos Mag A 50:45–55. https://doi.org/10.1080/01418618408244210

    Article  Google Scholar 

  28. Wang P, Xu S, Liu J et al (2017) Atomistic simulation for deforming complex alloys with application toward TWIP steel and associated physical insights. J Mech Phys Solids 98:290–308. https://doi.org/10.1016/j.jmps.2016.09.008

    Article  Google Scholar 

  29. Pierce DT, Jiménez JA, Bentley J et al (2014) The influence of manganese content on the stacking fault and austenite/ε-martensite interfacial energies in Fe–Mn–(Al–Si) steels investigated by experiment and theory. Acta Mater 68:238–253. https://doi.org/10.1016/j.actamat.2014.01.001

    Article  Google Scholar 

  30. Chamati H, Papanicolaou NI, Mishin Y, Papaconstantopoulos DA (2006) Embedded-atom potential for Fe and its application to self-diffusion on Fe(100). Surf Sci 600:1793–1803. https://doi.org/10.1016/j.susc.2006.02.010

    Article  Google Scholar 

  31. Allain S, Chateau J-P, Bouaziz O et al (2004) Correlations between the calculated stacking fault energy and the plasticity mechanisms in Fe–Mn–C alloys. Mater Sci Eng A 387:158–162. https://doi.org/10.1016/j.msea.2004.01.059

    Article  Google Scholar 

  32. Bulatov VV, Reed BW, Kumar M (2014) Grain boundary energy function for fcc metals. Acta Mater 65:161–175. https://doi.org/10.1016/j.actamat.2013.10.057

    Article  Google Scholar 

  33. Ratanaphan S, Olmsted DL, Bulatov VV et al (2015) Grain boundary energies in body-centered cubic metals. Acta Mater 88:346–354. https://doi.org/10.1016/j.actamat.2015.01.069

    Article  Google Scholar 

  34. Ratanaphan S, Boonkird T, Sarochawikasit R et al (2017) Atomistic simulations of grain boundary energies in tungsten. Mater Lett 186:116–118. https://doi.org/10.1016/j.matlet.2016.09.104

    Article  Google Scholar 

  35. Sato K, Ichinose M, Hirotsu Y, Inoue Y (1989) Effects of deformation induced phase transformation and twinning on the mechanical properties of austenitic Fe–Mn–Al alloys. ISIJ Int 29:868–877. https://doi.org/10.2355/isijinternational.29.868

    Article  Google Scholar 

  36. Plimpton SJ (2007) Large-scale atomic/molecular massively parallel simulator. Sandia Natl Lab

  37. Foiles SM (2010) Temperature dependence of grain boundary free energy and elastic constants. Scr Mater 62:231–234. https://doi.org/10.1016/j.scriptamat.2009.11.003

    Article  Google Scholar 

  38. Gupta D (2003) Diffusion, solute segregations and interfacial energies in some material: an overview. Interface Sci 11:7–20. https://doi.org/10.1023/A:1021570503733

    Article  Google Scholar 

  39. Morawiec A, Glowinski K (2013) On “macroscopic” characterization of mixed grain boundaries. Acta Mater 61:5756–5767. https://doi.org/10.1016/j.actamat.2013.06.019

    Article  Google Scholar 

  40. Glowinski K (2014) On identification of symmetric and improperly quasi-symmetric grain boundaries. J Appl Crystallogr 47:726–731. https://doi.org/10.1107/S160057671400435X

    Article  Google Scholar 

  41. Ratanaphan S, Raabe D, Sarochawikasit R et al (2017) Grain boundary character distribution in electroplated nanotwinned copper. J Mater Sci 52:4070–4085. https://doi.org/10.1007/s10853-016-0670-5

    Article  Google Scholar 

  42. Davison AC, Hinkley DV (1997) Bootstrap methods and their application. Cambridge University Press, Cambridge

    Book  Google Scholar 

  43. Li J, Dillon SJ, Rohrer GS (2009) Relative grain boundary area and energy distributions in nickel. Acta Mater 57:4304–4311. https://doi.org/10.1016/j.actamat.2009.06.004

    Article  Google Scholar 

  44. Saylor DM, Morawiec A, Rohrer GS (2003) The relative free energies of grain boundaries in magnesia as a function of five macroscopic parameters. Acta Mater 51:3675–3686. https://doi.org/10.1016/S1359-6454(03)00182-4

    Article  Google Scholar 

  45. Beladi H, Rohrer GS (2013) The relative grain boundary area and energy distributions in a ferritic steel determined from three-dimensional electron backscatter diffraction maps. Acta Mater 61:1404–1412. https://doi.org/10.1016/j.actamat.2012.11.017

    Article  Google Scholar 

  46. Ratanaphan S, Yoon Y, Rohrer GS (2014) The five parameter grain boundary character distribution of polycrystalline silicon. J Mater Sci 49:4938–4945. https://doi.org/10.1007/s10853-014-8195-2

    Article  Google Scholar 

  47. Gruber J, George DC, Kuprat AP et al (2005) Effect of anisotropic grain boundary properties on grain boundary plane distributions during grain growth. Scr Mater 53:351–355. https://doi.org/10.1016/j.scriptamat.2005.04.004

    Article  Google Scholar 

  48. Beladi H, Rohrer GS (2013) The distribution of grain boundary planes in interstitial free steel. Metall Mater Trans A 44:115–124. https://doi.org/10.1007/s11661-012-1393-0

    Article  Google Scholar 

  49. Ratanaphan S (2013) Grain boundary character distributions in isostructural materials. Ph.D. thesis, Dep Mater Sci Eng Carnegie Mellon Univ

  50. Cantwell PR, Tang M, Dillon SJ et al (2014) Grain boundary complexions. Acta Mater 62:1–48. https://doi.org/10.1016/j.actamat.2013.07.037

    Article  Google Scholar 

  51. Raabe D, Herbig M, Sandlöbes S et al (2014) Grain boundary segregation engineering in metallic alloys: a pathway to the design of interfaces. Curr Opin Solid State Mater Sci 18:253–261. https://doi.org/10.1016/j.cossms.2014.06.002

    Article  Google Scholar 

  52. Kuzmina M, Ponge D, Raabe D (2015) Grain boundary segregation engineering and austenite reversion turn embrittlement into toughness: example of a 9 wt.% medium Mn steel. Acta Mater 86:182–192. https://doi.org/10.1016/j.actamat.2014.12.021

    Article  Google Scholar 

  53. Deng Y, Tasan CC, Pradeep KG et al (2015) Design of a twinning-induced plasticity high entropy alloy. Acta Mater 94:124–133. https://doi.org/10.1016/j.actamat.2015.04.014

    Article  Google Scholar 

  54. Frolov T, Olmsted DL, Asta M, Mishin Y (2013) Structural phase transformations in metallic grain boundaries. Nat Commun 4:1899. https://doi.org/10.1038/ncomms2919

    Article  Google Scholar 

  55. Frolov T, Asta M, Mishin Y (2015) Segregation-induced phase transformations in grain boundaries. Phys Rev B 92:020103. https://doi.org/10.1103/PhysRevB.92.020103

    Article  Google Scholar 

  56. Kurtuldu G, Sicco A, Rappaz M (2014) Icosahedral quasicrystal-enhanced nucleation of the fcc phase in liquid gold alloys. Acta Mater 70:240–248. https://doi.org/10.1016/j.actamat.2014.02.037

    Article  Google Scholar 

  57. Thomas SL, Chen K, Han J et al (2017) Reconciling grain growth and shear-coupled grain boundary migration. Nat Commun 8:1764. https://doi.org/10.1038/s41467-017-01889-3

    Article  Google Scholar 

  58. Homer ER, Patala S, Priedeman JL (2015) Grain boundary plane orientation fundamental zones and structure-property relationships. Sci Rep 5:15476. https://doi.org/10.1038/srep15476

    Article  Google Scholar 

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Acknowledgements

S.R. acknowledges the financial supports provided by the Skill Development Grant, King Mongkut’s University of Technology Thonburi (KMUTT), Research Strengthening Project of the Faculty of Engineering, KMUTT, and the Thailand Research Fund and Office of the Higher Education Commission (MRG6080253). G.S.R. acknowledges support from the National Science Foundation under grant DMR 1628994. The simulating machine supported by the Innovative Software and Computing Center at KMUTT. We also thank Prof. Tawee Tunkasiri and Prof. Poom Kumam for critical comment and suggestion, Dr. David Olmsted for the code used for grain boundary energy calculation, and Dr. Lucas Hale for iprPy calculation framework and the Interatomic Potential Repository Project (NIST).

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Correspondence to Sutatch Ratanaphan.

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Ratanaphan, S., Sarochawikasit, R., Kumanuvong, N. et al. Atomistic simulations of grain boundary energies in austenitic steel. J Mater Sci 54, 5570–5583 (2019). https://doi.org/10.1007/s10853-018-03297-4

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