Advertisement

International Journal of Material Forming

, Volume 11, Issue 3, pp 341–355 | Cite as

Comparison of 2 methodologies developed for the determination of residual stresses through X-ray diffraction: application to a textured hcp titanium alloy

  • S. Dufrenoy
  • T. Chauveau
  • I. Lemaire-Caron
  • R. Brenner
  • B. Bacroix
SI: Modeling Materials and Processes, in Memory of Professor José J. Grácio

Abstract

For polycrystalline materials, the experimental determination of residual stresses neglects the so-called 2nd order fluctuations arising from e.g. plastic or thermal incompatibilities from grain to grain. This constitutes a serious limitation of the classical measurements methods, since these 2nd residual stresses are known to have a major influence on the mechanical behavior of metallic alloys, especially if these are strongly textured. In the present paper, a new methodology for the treatment of the measured data is described and compared to classical ones. In order to do so, the simulation of a tensile test is performed using a self-consistent elasto-plastic model, in order to constitute a virtual experimental data set. The 1st and 2nd order stresses are extracted from the simulation for various macroscopic stress levels. Two approaches (the classical sin2ψ method and a method based on the simultaneous analysis of several X-ray diffraction peaks) are then used to quantify the 1st order stresses from these “experimental” data. It is clearly shown that the method based on multi-peak analysis allows to minimize the error made by neglecting the so-called 2nd order stresses and leads to a better quantitative estimation of the 1st order stresses.

Keywords

Residual stresses Hcp structure Titanium alloys Self-consistent model X-ray diffraction (XRD) 

Notes

Acknowledgements

Fruitful discussions about residual stresses with D. Aliaga and N. Guillemot from Airbus Helicopters are acknowledged.

Compliance with ethical standards

Funding

The authors would like to thank the Conseil Général de Seine St Denis (CG93) for the attribution of a PhD fellowship to S. Dufrenoy.

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Withers PJ (2007) Residual stress and its role in failure. Rep Prog Phys 70(12):2211CrossRefGoogle Scholar
  2. 2.
    Bretheau T, Castelnau O (2006), Les contraintes résiduelles : d'où viennent-elles ? Comment les caractériser ?, in Rayons X et Matière. Lavoisier. p. 123–153Google Scholar
  3. 3.
    Noyan IC, Cohen JB (1985) An X-ray diffraction study of the residual stress-strain distributions in shot-peened two-phase brass. Mater Sci Eng 75(1):179–193CrossRefGoogle Scholar
  4. 4.
    Turner PA, Tomé CN (1994) A study of residual stresses in Zircaloy-2 with rod texture. Acta Metall Mater 42(12):4143–4153CrossRefGoogle Scholar
  5. 5.
    Baczmański A, Hfaiedh N, François M, Wierzbanowski K (2009) Plastic incompatibility stresses and stored elastic energy in plastically deformed copper. Mater Sci Eng A 501(1–2):153–165CrossRefGoogle Scholar
  6. 6.
    Turner PA, Christodoulou N, Tomé CN (1995) Modeling the mechanical response of rolled Zircaloy-2. Int J Plast 11(3):251–265CrossRefGoogle Scholar
  7. 7.
    Afnor, J. Non-destructive Testing — Test Method for Residual Stress analysis by X-ray Diffraction. AFNORGoogle Scholar
  8. 8.
    Pang JWL, Holden TM, Mason TE (1998) In situ generation of intergranular strains in an Al7050 alloy. Acta Mater 46(5):1503–1518CrossRefGoogle Scholar
  9. 9.
    Clausen B, Lorentzen T, Bourke MAM, Daymond MR (1999) Lattice strain evolution during uniaxial tensile loading of stainless steel. Mater Sci Eng A 259(1):17–24CrossRefGoogle Scholar
  10. 10.
    Zhu KY, Bacroix B, Chauveau T, Chaubet D, Castelnau O (2009) Texture evolution and associated nucleation and growth mechanisms during annealing of a Zr alloy. Metall Mater Trans A Phys Metall Mater Sci 40A(10):2423–2434CrossRefGoogle Scholar
  11. 11.
    Kroner E (1958) Berechnung der Elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls. Z Phys 151(4):504–518CrossRefGoogle Scholar
  12. 12.
    Hutchinson J (1970) Elastic-plastic behaviour of polycrystalline metals and composites. Proceedings of the Royal Society of London Series a-Mathematical and Physical Sciences, 319(1537): 247-&Google Scholar
  13. 13.
    Tome CN, Christodoulou N, Turner PA, Miller MA, Woo CH, Root J, Holden TM (1996) Role of internal stresses in the transient of irradiation growth of Zircaloy-2. J Nucl Mater 227(3):237–250CrossRefGoogle Scholar
  14. 14.
    Gloaguen D, Berchi T, Girard E, Guillén R (2007) Measurement and prediction of residual stresses and crystallographic texture development in rolled Zircaloy-4 plates: X-ray diffraction and the self-consistent model. Acta Mater 55(13):4369–4379CrossRefGoogle Scholar
  15. 15.
    Baczmański A, Wierzbanowski K, Lipiński P, Helmholdt RB, Ekambaranathan G, Pathiraj B (1994) Examination of the residual stress field in plastically deformed polycrystalline material. Philos Mag A 69(3):437–449CrossRefGoogle Scholar
  16. 16.
    Jeong GS, Allen DH, Lagoudas DC (1994) Residual stress evolution due to cool down in viscoplastic metal matrix composites. Int J Solids Struct 31(19):2653–2677CrossRefzbMATHGoogle Scholar
  17. 17.
    Turner PA, Tomé CN (1993) Self-consistent modeling of visco-elastic polycrystals: application to irradiation creep and growth. J Mech Phys Solids 41(7):1191–1211CrossRefzbMATHGoogle Scholar
  18. 18.
    Zecevic M, Knezevic M, Beyerlein IJ, Tomé CN (2015) An elasto-plastic self-consistent model with hardening based on dislocation density, twinning and de-twinning: application to strain path changes in HCP metals. Mater Sci Eng A 638:262–274CrossRefGoogle Scholar
  19. 19.
    Yoshida K, Brenner R, Bacroix B, Bouvier S (2011) Micromechanical modeling of the work-hardening behavior of single- and dual-phase steels under two-stage loading paths. Mater Sci Eng A 528:1037–1046CrossRefGoogle Scholar
  20. 20.
    Benmhenni N, Bouvier S, Brenner R, Chauveau T, Bacroix B (2013) Micromechanical modelling of monotonic loading of CP alpha-Ti: correlation between macroscopic and microscopic behaviour. Mater Sci Eng A 573:222–233CrossRefGoogle Scholar
  21. 21.
    Fisher ES, REnken CJ (1964) Single-crystal elastic moduli and the hcp -> bcc transformation in Ti; Zr and Hf. Phys Rev 165(2A):482–500CrossRefGoogle Scholar
  22. 22.
    Guillemot N, Winter M, Souto-Lebel A, Lartigue C, Billardon R (2011) 3D heat transfer analysis for a hybrid approach to predict residual stresses after ball-end milling. Procedia Eng 19:125–131CrossRefGoogle Scholar
  23. 23.
    Webster GA, Wimpory RC (2001) Non-destructive measurement of residual stress by neutron diffraction. J Mater Process Technol 117(3):395–399CrossRefGoogle Scholar
  24. 24.
    Daymond MR, Withers PJ (1996) A new stroboscopic neutron diffraction method for monitoring materials subjected to cyclic loads: thermal cycling of metal matrix composites. Scr Mater 35(6):717–720CrossRefGoogle Scholar
  25. 25.
    Ligot J, Welzel U, Lamparter P, Vermeulen AC, Mittemeijer EJ (2005) Stress analysis of polycrystalline thin films and surface regions by X-ray diffraction. J Appl Crystallogr 38(1):1–29CrossRefGoogle Scholar
  26. 26.
    Dufrenoy, S., B. Bacroix, C. Th., I. Lemaire, N. Guillemot, and G. Thomas (2015) Influence of surface integrity on fatigue limit: Ti-10V-2Fe-3Al titanium application. In 13th World Conference on Titanium. San Diego, USA: TMSGoogle Scholar
  27. 27.
    Belkhabbaz, A., R. Brenner, N. Rupin, B. Bacroix, and J. Fonseca (2011) Prediction of the overall behavior of a 3D microstructure of austenitic steel by using FFT numerical scheme, in 11th International Conference on the Mechanical Behavior of Materials. M. Guagliano and L. Vergani, (Eds), 1883–1888Google Scholar
  28. 28.
    Dufrenoy S, Chauveau T, Brenner R, Fontugne C, Bacroix B (2014) Modeling methodology for stress determination by XRD in polycrystalline materials. Residual Stresses Ix 996:106–111Google Scholar
  29. 29.
    Daymond MR, Tome CN, Bourke MAM (2000) Measured and predicted intergranular strains in textured austenitic steel. Acta Mater 48(2):553–564CrossRefGoogle Scholar
  30. 30.
    Jeong Y, Gnäupel-Herold T, Barlat F, Iadicola M, Creuziger A, Lee M-G (2015) Evaluation of biaxial flow stress based on elasto-viscoplastic self-consistent analysis of X-ray diffraction measurements. Int J Plast 66:103–118CrossRefGoogle Scholar
  31. 31.
    Baczmański A, Braham C (2004) Elastoplastic properties of duplex steel determined using neutron diffraction and self-consistent model. Acta Mater 52(5):1133–1142CrossRefGoogle Scholar
  32. 32.
    Gloaguen D, Fajoui J, Girault B (2014) Residual stress fields analysis in rolled Zircaloy-4 plates: grazing incidence diffraction and elastoplastic self-consistent model. Acta Mater 71:136–144CrossRefGoogle Scholar

Copyright information

© Springer-Verlag France 2017

Authors and Affiliations

  • S. Dufrenoy
    • 1
    • 2
  • T. Chauveau
    • 1
  • I. Lemaire-Caron
    • 2
  • R. Brenner
    • 3
  • B. Bacroix
    • 1
  1. 1.LSPM - CNRSVilletaneuseFrance
  2. 2.QUARTZ, EA7393Saint OuenFrance
  3. 3.Institut Jean Le Rond d’Alembert, CNRS - Université Pierre et Marie Curie, UMR 7190ParisFrance

Personalised recommendations