Statistical Characterization of Intragrain Misorientations at Large Strains Using High-Energy X-Ray Diffraction: Application to Hydrogen Embrittlement

  • Timothy J. H. LongEmail author
  • Matthew P. Miller
Thematic Section: 3D Materials Science
Part of the following topical collections:
  1. 3D Materials Science 2019


High-energy X-ray diffraction (HEXD) has become a powerful technique for studying deformation and failure in structural metals over the last two decades. In this work, we used multi-grain HEXD to investigate hydrogen embrittlement in polycrystalline nickel by quantifying the effects of solute hydrogen on the grain-scale plastic response. Five polycrystalline samples were probed: one undeformed control sample with no added hydrogen, one with no added hydrogen compressed in a high-pressure torsion (HPT) anvil, one with no hydrogen compressed and torqued by HPT, one charged with hydrogen compressed by HPT, and one with hydrogen compressed and torqued by HPT. Most current HEXD data reduction algorithms can only be used at strains less than 5–10%, while the largest strains in our samples exceed 21%. To process the data, we developed a new forward projection-based processing method to calculate discrete single grain orientation distributions (DSGODs) from the data. We used three statistics-based state variables to characterize the measured DSGODs. We found the grains in the two materials (hydrogen-charged and uncharged) had the same amount of intragrain misorientation, but how that misorientation was distributed in orientation space was different. We identified two types of grains in the hydrogen-charged samples, but only a single type in the uncharged samples. Our results suggest solute hydrogen does not affect all grains within a deforming aggregate equally. These mesoscale results and new state variables can help bridge the gap between micro- and macroscale observations of the effects of solute hydrogen on plasticity.


High-energy X-ray diffraction X-ray diffraction Misorientation Statistics Hydrogen embrittlement High-pressure torsion 



We would like to acknowledge the contributions of Dr. Ian Robertson (Department of Materials Science and Engineering, University of Wisconsin-Madison) and Dr. Shuai Wang (Department of Mechanical and Energy Engineering, Southern University of Science and Technology) for preparing the samples and performing the high-pressure torsion experiment. Dr. Akihide Nagao (JFE Steel Corporation) performed the high-pressure hydrogen charging and thermal desorption spectroscopy. We also thank the staff of the Cornell High Energy Synchrotron Source, especially Dr. Peter Ko (Cornell High Energy Synchrotron Source, Cornell University). We are also grateful for the assistance of Christopher Budrow (Sibley School of Mechanical and Aerospace Engineering, Cornell University) in performing the diffraction experiment, the help of Dr. Darren Pagan (Cornell High Energy Synchrotron Source, Cornell University) and Dr. Mark Obstalecki (Air Force Research Laboratory) in developing the indexing method, and the help of Dr. Kelly Nygren (Cornell High Energy Synchrotron Source, Cornell University) on hydrogen embrittlement.

Compliance with Ethical Standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


  1. 1.
    Oddershede J, Camin B, Schmidt S, Mikkelsen LP, Sørensen HO, Lienert U, Poulsen HF, Reimers (2012) Measuring the stress field around an evolving crack in tensile deformed Mg AZ31 using three-dimensional X-ray diffraction. Acta Mater 60:3570–3580. CrossRefGoogle Scholar
  2. 2.
    Obstalecki M, Wong SL, Dawson PR, Miller MP (2014) Quantitative analysis of crystal scale deformation heterogeneity during cyclic plasticity using high-energy X-ray diffraction and finite-element simulation. Acta Mater 75:259–272. CrossRefGoogle Scholar
  3. 3.
    Bernier JV, Barton NR, Lienert U, Miller MP (2011) Far-field high-energy diffraction microscopy: a tool for intergranular orientation and strain analysis. J Strain Anal Eng Des 46:527–547. CrossRefGoogle Scholar
  4. 4.
    Schmidt S (2014) GrainSpotter: a fast and robust polycrystalline indexing algorithm. J Appl Crystallogr 47:276–284. CrossRefGoogle Scholar
  5. 5.
    Margulies L, Winther G, Poulsen HF (2001) In situ measurement of grain rotation during deformation of polycrystals. Science 291:2392–2394. CrossRefGoogle Scholar
  6. 6.
    Wang S, Nagao A, Edalati K, Horita Z, Robertson IM (2017) Influence of hydrogen on dislocation self-organization in Ni. Acta Mater 135:96–102. CrossRefGoogle Scholar
  7. 7.
    Oriani RA (1978) Hydrogen embrittlement of steels. Annu Rev Mater Sci 8:327–357. CrossRefGoogle Scholar
  8. 8.
    Barton NR, Dawson PR (2001) A methodology for determining average lattice orientation and its application to the characterization of grain substructure. Metall Mater Trans A 32:1967–1975. CrossRefGoogle Scholar
  9. 9.
    Glez Jean Christophe, Driver Julian (2001) Orientation distribution analysis in deformed grains. J Appl Crystallogr 34:280–288. CrossRefGoogle Scholar
  10. 10.
    Ferreira PJ, Robertson IM, Birnbaum HK (1998) Hydrogen effects on the interaction between dislocations. Acta Mater 46:1749–1757. CrossRefGoogle Scholar
  11. 11.
    Robertson IM (1999) The effect of hydrogen on dislocation dynamics. Eng Fract Mech 64:649–673. CrossRefGoogle Scholar
  12. 12.
    Martin ML, Sofronis P, Robertson IM, Awane T, Murakami Y (2013) A microstructural based understanding of hydrogen-enhanced fatigue of stainless steels. Int J Fatigue 57:28–36. CrossRefGoogle Scholar
  13. 13.
    Wang S, Martin ML, Sofronis P, Ohnuki S, Hashimoto N, Robertson IM (2014) Hydrogen-induced intergranular failure of iron. Acta Mater 69:275–282. CrossRefGoogle Scholar
  14. 14.
    Knowles JK (1998) Linear vector spaces and cartesian tensors. Oxford University Press, New YorkGoogle Scholar
  15. 15.
    Frank C (1988) Orientation mapping: 1987 MRS fall meeting Von Hipple award lecture. MRS Bull 13:24–31. CrossRefGoogle Scholar
  16. 16.
    Poulsen H (2004) Three-dimensional X-ray diffraction microscopy: mapping polycrystals and their dynamics. Springer-Verlag, BerlinCrossRefGoogle Scholar
  17. 17.
    Suter RM, Hennessy D, Xiao C, Lienert U (2006) Forward modeling method for microstructure reconstruction using X-ray diffraction microscopy: single-crystal verification. Rev Sci Instrum 77:12905–12912. CrossRefGoogle Scholar
  18. 18.
    Cullity BD, Stock SR (2013) Elements of X-ray diffraction, 3rd edn. Pearson Education Limited, LondonGoogle Scholar
  19. 19.
    Pagan DC, Miller MP (2016) Determining heterogeneous slip activity on multiple slip systems from single crystal orientation pole figures. Acta Mater 116:200–211. CrossRefGoogle Scholar
  20. 20.
    Oddershede J, Schmidt S, Poulsen HF, Sørensen HO, Wright J, Reimers W (2010) Determining grain resolved stresses in polycrystalline materials using three-dimensional X-ray diffraction. J Appl Crystallogr 43:539–549. CrossRefGoogle Scholar
  21. 21.
    Wong SL, Park JS, Miller MP, Dawson PR (2013) A framework for generating synthetic diffraction images from deforming polycrystals using crystal-based finite element formulations. Comput Mater Sci 77:456–466. CrossRefGoogle Scholar
  22. 22.
    Nye JF (1953) Some geometrical relations in dislocated crystals. Acta Metall 1:153–162. CrossRefGoogle Scholar
  23. 23.
    Hansen P, Sørensen H, Sükösd Z, Poulsen H (2009) Reconstruction of single-grain orientation distribution functions for crystalline materials. SIAM J Imaging Sci 2:593–613. CrossRefGoogle Scholar
  24. 24.
    Pagan DC, Obstalecki M, Park JS, Miller MP (2018) Analyzing shear band formation with high resolution X-ray diffraction. Acta Mater 147:133–148. CrossRefGoogle Scholar
  25. 25.
    Barton NR, Bernier JV (2012) A method for intragranular orientation and lattice strain distribution determination. J Appl Crystallogr 45:1145–1155. CrossRefGoogle Scholar
  26. 26.
    Johnson WH (1874) On some remarkable changes produced in iron and steel by the action of hydrogen and acids. Proc R Soc Lond 23:168–179. CrossRefGoogle Scholar
  27. 27.
    Nagao A, Dadfarnia M, Sofronis P, Robertson I (2016) Hydrogen embrittlement: mechanisms. In: Totten G, Colas R (eds) Encyclopedia of iron, steel, and their alloys. CRC Press, Boca Raton, pp 1768–1784CrossRefGoogle Scholar
  28. 28.
    Miresmaeili R, Ogino M, Nakagawa T, Kanayama H (2010) A coupled elastoplastic-transient hydrogen diffusion analysis to simulate the onset of necking in tension by using the finite element method. Int J Hydrog Energy 35:1506–1514. CrossRefGoogle Scholar
  29. 29.
    Barrera O, Tarleton E, Tang HW, Cocks ACF (2016) Modeling the coupling between hydrogen diffusion and the mechanical behaviour of metals. Comput Mater Sci 122:219–228. CrossRefGoogle Scholar
  30. 30.
    Zhilyaev AP, McNelley TR, Langdon T (2008) Using high-pressure torsion for metal processing: fundamentals and applications. Prog Mater Sci 53:893–979. CrossRefGoogle Scholar
  31. 31.
    Valiev RZ, Estrin Y, Horita Z, Langdon TG, Zechetbauer MJ, Zhu YT (1996) Structure and deformaton behaviour of Armco iron subjected to severe plastic deformation. Acta Mater 44:4705–4712. CrossRefGoogle Scholar
  32. 32.
    Barton NR, Boyce DE, Dawson PR (2002) Pole figure inversion using finite elements over Rodrigues space. Textures Microstruct 35:113–144. CrossRefGoogle Scholar
  33. 33.
    MathWorks (2017) MATLAB Documentation: bwconncomp. MathWorks, Natick, MA. Accessed 30 Aug 2017
  34. 34.
    Humbert H, Gey N, Muller J, Esling C (1996) Determination of a mean orientation from a cloud of orientations. application to electron back-scattering pattern measurements. J Appl Crystallogr 29:662–666. CrossRefGoogle Scholar
  35. 35.
    Cramér H (1955) The elements of probability theory and some of its applications. Wiley, New YorkCrossRefGoogle Scholar
  36. 36.
    Westfall PH (2014) Kurtosis as Peakedness, 1905–2014. R.I.P. Am Stat 68:191–195. CrossRefGoogle Scholar
  37. 37.
    Muirhead RJ (1982) Aspects of multivariate statistical theory. Wiley, Hoboken, pp 1–49CrossRefGoogle Scholar
  38. 38.
    Lloyd S (1982) Least squares quantization in PCM. IEEE Trans Inf Theory 28:129–137. CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society 2019

Authors and Affiliations

  1. 1.Department of Materials Science and EngineeringCornell UniversityIthacaUSA
  2. 2.Sibley School of Mechanical and Aerospace EngineeringCornell UniversityIthacaUSA

Personalised recommendations