Skip to main content
Log in

Quantitative Study of Residual Strain and Geometrically Necessary Dislocation Density Using HR-EBSD Method

  • Research paper
  • Published:
Experimental Mechanics Aims and scope Submit manuscript

Abstract

Background

Optical metrology is widely used to measure materials’ deformation and mechanical properties but current fundamental research requires more precise measurement of microstructure and deformation in internal materials. Electron backscattered diffraction (EBSD) technique measures crystal orientation in individual grain and high resolution EBSD (HR-EBSD) method provides information about residual strain and GND density.

Objective

Deformation of two stainless steels Nitronic 60 and Tristelle 5183 with different proportions of ferrite and carbides are characterised.

Methods

Push-release bend testing was used to provide progressive increasing bending stress in two iron-based material samples. HR-EBSD and high resolution digital image correlation (HR-DIC) methods characterised residual strain, GND density and plastic strain distributions in each sample.

Results

Nitronic 60 and Tristelle 5183 were deformed and obtained 3.8% and 0.9% plastic strain Ɛxx. High GND densities distributed neighbouring grain boundaries in Nitronic 60 while high GND densities distributed around carbides, especially intragranular carbides in Tristelle 5183.

Conclusions

HR-EBSD and HR-DIC quantitative characterised deformation in two iron-based alloys, grain/twin boundaries and carbides resulted in GND density increase, promoted work hardening and accumulated high residual elastic strain. Heterogeneous grain/carbide size distribution leaded to stress concentration and cause carbide decohesion and brittle fracture of sample.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Rastogi P (2015) Digital optical measurement techniques and applications. Artech House

  2. Li X, Xie H, Kang Y, Wu XJAMSS (2010) A brief review and prospect of experimental solid mechanics in China. 23(6):498–548

  3. Sirohi R (2018) Optical methods of measurement: wholefield techniques. CRC Press

    Book  Google Scholar 

  4. Wang Q, Ri S, Maenosono A, Tanaka Y, Koyama M (2019) 1-second-resolved strain mapping in Ti-6Al-4V alloys during dwell fatigue in SEM by video sampling moiré. Mech Mater 133:63–70

    Article  Google Scholar 

  5. Qiu W, Li Q, Lei Z-K, Qin Q-H, Deng W-L (2013) Kang Y-LJC. The use of a carbon nanotube sensor for measuring strain by micro-Raman spectroscopy 53:161–168

    Google Scholar 

  6. Ferraro JR (2003) Introductory raman spectroscopy. Elsevier

    Google Scholar 

  7. Popov MN, Spitaler J, Veerapandiyan VK, Bousquet E, Hlinka J, Deluca MJnCM (2020) Raman spectra of fine-grained materials from first principles. 6(1):1–7

  8. Movasaghi Z, Rehman S, Rehman IUJASR (2007) Raman spectroscopy of biological tissues. 42(5):493–541

  9. Dresselhaus MS, Dresselhaus G, Saito R, Jorio AJPr (2005) Raman spectroscopy of carbon nanotubes. 409(2):47–99

  10. Malard L, Pimenta MA, Dresselhaus G, Dresselhaus MJPr (2009) Raman spectroscopy in graphene. 473(5–6):51–87

  11. Bai Y, Zhang R, Ye X, Zhu Z, Xie H, Shen B, Cai D, Liu B, Zhang C, Jia ZJNn (2018) Carbon nanotube bundles with tensile strength over 80 GPa. 13(7):589–595

  12. Li JF, Huang YF, Ding Y, Yang ZL, Li SB, Zhou XS, Fan FR, Zhang W, Zhou ZY, Ren BJn (2010) Shell-isolated nanoparticle-enhanced Raman spectroscopy. 464(7287):392–395

  13. Qiu W, Cheng C-L, Liang R-R, Zhao C-W, Lei Z-K, Zhao Y-C, Ma L-L, Xu J, Fang H-J, Kang Y-LJAMS (2016) Measurement of residual stress in a multi-layer semiconductor heterostructure by micro-Raman spectroscopy. 32(5):805–812

  14. Stuart BJKOeoct (2000) Infrared spectroscopy

  15. Mantsch HH, Chapman D (1996) Infrared spectroscopy of biomolecules. Wiley-Liss New York

  16. Qazilbash MM, Brehm M, Chae B-G, Ho P-C, Andreev GO, Kim B-J, Yun SJ, Balatsky A, Maple M, Keilmann FJS (2007) Mott transition in VO2 revealed by infrared spectroscopy and nano-imaging. 318(5857):1750–1753

  17. Barth AJBeBA-B (2007) Infrared spectroscopy of proteins. 1767(9):1073–1101

  18. Jiang Z, Henriksen EA, Tung L, Wang Y-J, Schwartz M, Han MY, Kim P, Stormer HLJPrl (2007) Infrared spectroscopy of Landau levels of graphene. 98(19):197403

  19. Guinier A (1994) X-ray diffraction in crystals, imperfect crystals, and amorphous bodies. Courier Corporation

  20. Klug HP, Alexander LE (1974) X-ray diffraction procedures: for polycrystalline and amorphous materials

  21. Li Z, Lu C, Xia Z, Zhou Y, Luo ZJC (2007) X-ray diffraction patterns of graphite and turbostratic carbon 45(8):1686–1695

    Google Scholar 

  22. Tonouchi MJNp (2007) Cutting-edge terahertz technology. 1(2):97–105

  23. Siegel PHJITomt, techniques (2002) Terahertz technology. 50(3):910–928

  24. Beard MC, Turner GM, Schmuttenmaer CA (2002) Terahertz spectroscopy. ACS Publications

  25. Krivoglaz MA (2012) X-ray and neutron diffraction in nonideal crystals. Springer Science & Business Media

  26. Bacon GE (1975) Neutron diffraction. 3

  27. Trucano P, Chen RJN (1975) Structure of graphite by neutron diffraction 258(5531):136–137

    Google Scholar 

  28. Wenk H, Lutterotti L, Vogel SJPD (2010) Rietveld texture analysis from TOF neutron diffraction data 25(3):283–296

    Google Scholar 

  29. Wang Z, Denlinger E, Michaleris P, Stoica AD, Ma D, Beese AMJM, Design (2017) Residual stress mapping in Inconel 625 fabricated through additive manufacturing: Method for neutron diffraction measurements to validate thermomechanical model predictions. 113:169–177

  30. Allen A, Hutchings M, Windsor C, Andreani CJAiP (1985) Neutron diffraction methods for the study of residual stress fields. 34(4):445–473

  31. Hutchings MT (2005) Introduction to the characterization of residual stress by neutron diffraction. CRC Press

    Book  Google Scholar 

  32. Sunde M, Serpell LC, Bartlam M, Fraser PE, Pepys MB, Blake CCJJomb (1997) Common core structure of amyloid fibrils by synchrotron X-ray diffraction. 273(3):729–739

  33. Sokolov AA, Ternov IMJs (1966) Synchrotron radiation

  34. Schoenlein R, Chattopadhyay S, Chong H, Glover T, Heimann P, Shank C, Zholents A, Zolotorev MJS (2000) Generation of femtosecond pulses of synchrotron radiation 287(5461):2237–2240

    Google Scholar 

  35. Randle V, Engler O (2000) Introduction to texture analysis: macrotexture, microtexture and orientation mapping. CRC Press

    Book  Google Scholar 

  36. OxfordInstrument. http://www.ebsd.com/10-ebsd-explained

  37. Wilkinson AJ, Britton TB (2012) Strains, planes, and EBSD in materials science. Mater Today 15(9):366–376

    Article  Google Scholar 

  38. Schwartz AJ, Kumar M, Adams BL, Field DP (2009) Electron backscatter diffraction in materials science, vol 2. Springer

    Book  Google Scholar 

  39. Wilkinson AJ, Meaden G, Dingley DJ (2013) High resolution mapping of strains and rotations using electron backscatter diffraction. Mater Sci Technol 22(11):1271–1278. https://doi.org/10.1179/174328406x130966

    Article  Google Scholar 

  40. Wilkinson AJ, Meaden G, Dingley DJ (2006) High-resolution elastic strain measurement from electron backscatter diffraction patterns: new levels of sensitivity. Ultramicroscopy 106(4–5):307–313. https://doi.org/10.1016/j.ultramic.2005.10.001

    Article  Google Scholar 

  41. Jiang J, Britton TB, Wilkinson AJ (2012) Accumulation of geometrically necessary dislocations near grain boundaries in deformed copper. Philos Mag Lett 92(11):580–588

    Article  Google Scholar 

  42. Britton TB, Wilkinson AJ (2012) Stress fields and geometrically necessary dislocation density distributions near the head of a blocked slip band. Acta Mater 60(16):5773–5782

    Article  Google Scholar 

  43. Kacher J, Landon C, Adams BL, Fullwood D (2009) Bragg’s Law diffraction simulations for electron backscatter diffraction analysis. Ultramicroscopy 109(9):1148–1156

    Article  Google Scholar 

  44. Adams BL, Kacher J (2010) EBSD-based microscopy: Resolution of dislocation density. Computers, Materials, & Continua 14(3):185–196

    Google Scholar 

  45. Abuzaid W, Sehitoglu H, Lambros J (2013) Plastic strain localization and fatigue micro-crack formation in Hastelloy X. Mater Sci Eng, A 561:507–519

    Article  Google Scholar 

  46. Yan D, Tasan CC, Raabe D (2015) High resolution in situ mapping of microstrain and microstructure evolution reveals damage resistance criteria in dual phase steels. Acta Mater 96:399–409

    Article  Google Scholar 

  47. Ocken H (1995) The galling wear resistance of new iron-base hardfacing alloys: a comparison with established cobalt-and nickel-base alloys. Surf Coat Technol 76:456–461

    Article  Google Scholar 

  48. Sulley J, Stewart D (2016) HIPed Hard Facings for Nuclear Applications: Materials, Key Potential Defects and Mitigating Quality Control Measures. In: 2016 24th International Conference on Nuclear Engineering, 2016. American Society of Mechanical Engineers, pp V001T003A034-V001T003A034

  49. Zhao C, Stewart D, Jiang J, Dunne FP (2018) A comparative assessment of iron and cobalt-based hard-facing alloy deformation using HR-EBSD and HR-DIC. Acta Mater 159:173–186

    Article  Google Scholar 

  50. Cockeram B (2000) Corrosion resistance and electrochemical potentiokinetic reactivation testing of some iron-based hardfacing alloys. Corrosion 56(8):849–859

    Article  Google Scholar 

  51. Hansen N (2004) Hall-Petch relation and boundary strengthening. Scripta Mater 51(8):801–806

    Article  Google Scholar 

  52. Pan B, Qian K, Xie H, Asundi A (2009) Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. Meas Sci Technol 20(6):062001

    Article  Google Scholar 

  53. Wan V, Cuddihy M, Jiang J, MacLachlan D, Dunne F (2016) An HR-EBSD and computational crystal plasticity investigation of microstructural stress distributions and fatigue hotspots in polycrystalline copper. Acta Mater 115:45–57

    Article  Google Scholar 

  54. Hunsche A, Neumann P (1986) Quantitative measurement of persistent slip band profiles and crack initiation. Acta Metall 34(2):207–217

    Article  Google Scholar 

  55. Sangid MD, Maier HJ, Sehitoglu H (2011) A physically based fatigue model for prediction of crack initiation from persistent slip bands in polycrystals. Acta Mater 59(1):328–341

    Article  Google Scholar 

  56. Wang S, Kalácska S, Maeder X, Michler J, Giuliani F (2019) Britton TBJSM. The effect of δ-hydride on the micromechanical deformation of a Zr alloy studied by in situ high angular resolution electron backscatter diffraction 173:101–105

    Google Scholar 

  57. Jun TS, Zhang Z, Dunne FP, Britton TB Evaluation of Local Rate Sensitivity in a Dwell‐Sensitive Ti6242 Using Micropillar Compression. In: Proceedings of the 13th World Conference on Titanium, 2016. Wiley Online Library, pp 498–498

  58. Arsenlis A, Parks D (1999) Crystallographic aspects of geometrically-necessary and statistically-stored dislocation density. Acta Mater 47(5):1597–1611

    Article  Google Scholar 

  59. Kysar J, Saito Y, Oztop M, Lee D, Huh W (2010) Experimental lower bounds on geometrically necessary dislocation density. Int J Plast 26(8):1097–1123

    Article  Google Scholar 

  60. Hall E (1951) The deformation and ageing of mild steel: III discussion of results. Proc Phys Soc London, Sect B 64(9):747

    Article  Google Scholar 

Download references

Acknowledgements

Thanks for the financial support of the National Natural Science Foundation of China (grant numbers 11632010). C. Zhao acknowledge the financial support by the China Scholarship Council (CSC), Rolls-Royce and Imperial College London. C. Zhao want to express thanks to Prof Fionn Dunne, Dr Ben Britton and Dr Jun Jiang for helpful discussions on the experiments.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to X. Li.

Ethics declarations

Conflict of Interests

The authors have no conflicts of interest to declare that are relevant to the content of this article. The research did not involve any human participants and/or animals.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, C., Li, X. Quantitative Study of Residual Strain and Geometrically Necessary Dislocation Density Using HR-EBSD Method. Exp Mech 61, 1281–1290 (2021). https://doi.org/10.1007/s11340-021-00741-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11340-021-00741-6

Keywords

Navigation