Journal of Materials Science

, Volume 51, Issue 3, pp 1234–1250 | Cite as

Development of an in situ method for measuring elastic and total strain fields at the grain scale with an estimation of accuracy

  • Wang Chow
  • Denis Solas
  • Guillaume Puel
  • Thierry Baudin
  • Véronique Aubin
Multiscale Modeling and Experiment


Identifying the parameters of a crystal plasticity model requires the use of grain scale experimental data. The objective of our work is to develop a robust procedure to identify the model using information at the scale of the crystals. In this study, an in situ experimental measurement has been developed for the parameter identification of crystal plasticity models. During the experimental stage, the total \({\left( \epsilon ^t\right) }\) and elastic \({\left( \epsilon ^e\right) }\) strain fields of an Al-alloy specimen with around 12 grains were measured at the same time. The total strain fields were determined by digital image correlation. For this, a speckle-painting was applied on the sample surface which was tracked to derive the total deformation of the specimen surface under loading. The elastic strains were calculated from X-ray diffraction measurements. Yet certain experimental difficulties had to be solved in order to achieve these simultaneous measurements. Besides results and analysis, the corresponding uncertainties during each measurement were quantified as well.


Strain Field Digital Image Correlation Representative Volume Element Crystal Plasticity Model Digital Image Correlation Measurement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Abdul-Latif A, Dingli J, Saanouni K (1998) Modeling of complex cyclic inelasticity in heterogeneous polycrystalline microstructure. Mech Mater 30(4):287–305CrossRefGoogle Scholar
  2. 2.
    Badulescu C, Grédiac M, Haddadi H, Mathias JD, Balandraud X, Tran HS (2011) Applying the grid method and infrared thermography to investigate plastic deformation in aluminium multicrystal. Mech Mater 43(1):36–53CrossRefGoogle Scholar
  3. 3.
    Barbe F, Decker L, Jeulin D, Cailletaud G (2001) Intergranular and intragranular behavior of polycrystalline aggregates. part 1: finite element model. Int J Plast 17(4):513–536CrossRefGoogle Scholar
  4. 4.
    Barbe F, Forest S, Cailletaud G (2001) Intergranular and intragranular behavior of polycrystalline aggregates.part 2: results. Int J Plast 17(4):537–563CrossRefGoogle Scholar
  5. 5.
    Brahme A, Alvi M, Saylor D, Fridy J, Rollett A (2006) 3D reconstruction of microstructure in a commercial purity aluminium. Viewpoint set no. 41 3D characterization and analysis of materials organized by G. Spanos. Scr Mater 55(1):75–80CrossRefGoogle Scholar
  6. 6.
    Cédat D, Fandeur O, Rey C, Raabe D (2012) Polycrystal model of the mechanical behavior of a Mo-TiC30vol.% metal-ceramic composite using a 3D microstructure map obtained by a dual beam FIB-SEM. Acta Mater 60:1623–1632CrossRefGoogle Scholar
  7. 7.
    Chow W, Solas D, Puel G, Perrin E, Baudin T, Aubin V (2014) Measurement of complementary strain fields at the grain scale. Adv Mater Res 996:64–69CrossRefGoogle Scholar
  8. 8.
    Crostack HA, Reimers W, Eckold G (1989) Analysis of the plastic deformation in single grains of polycrystalline materials. In: Beck G, Denis S, Simon A (eds) International conference on residual stresses. Springer, Netherlands, p 190CrossRefGoogle Scholar
  9. 9.
    De Jaeger J, Solas D, Baudin T, Fandeur O, Schmitt JH, Rey C (2012) Inconel 718 single and multipass modelling of hot forging. Superalloys 2012. Wiley, New York, pp 663–672Google Scholar
  10. 10.
    Eberl F (2000) Second order heterogeneities in a multicrystal: experimental developments using X-ray diffraction and comparaison with finite element model. Ph.D. thesis, ENSAM, CER de Paris, France (2000)Google Scholar
  11. 11.
    Eshelby JD (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc R Soc Lond A 241(1226):376–396CrossRefGoogle Scholar
  12. 12.
    Evrard P, Alvarez-Armas I, Aubin V, Degallaix S (2010) Polycrystalline modeling of the cyclic hardening/softening behavior of an austenitic-ferritic stainless steel. Mech Mater 42(4):395–404CrossRefGoogle Scholar
  13. 13.
    Evrard P, Aubin V, Pilvin P, Degallaix S, Kondo D (2008) Implementation and validation of a polycrystalline model for a bi-phased steel under non-proportional loading paths. Mech Res Commun 35(5):336–343CrossRefGoogle Scholar
  14. 14.
    Evrard P, Bartali AE, Aubin V, Rey C, Degallaix S, Kondo D (2010) Influence of boundary conditions on bi-phased polycrystal microstructure calculation. Int J Solids Struct 47(16):1979–1986CrossRefGoogle Scholar
  15. 15.
    Guilhem Y, Basseville S, Curtit F, Stphan JM, Cailletaud G (2013) Numerical investigations of the free surface effect in three-dimensional polycrystalline aggregates. Comput Mater Sci 70:150–162CrossRefGoogle Scholar
  16. 16.
    Hild F, Roux S (2008) Correliq4: a software for ”finite-element” displacement field measurements by digital image correlation. Internal report 269, ENS, CachanGoogle Scholar
  17. 17.
    Jiang J, Britton TB, Wilkinson AJ (2013) Mapping type III intragranular residual stress distributions in deformed copper polycrystals. Acta Mater 61(15):5895–5904CrossRefGoogle Scholar
  18. 18.
    Kanit T, Forest S, Galliet I, Mounoury V, Jeulin D (2003) Determination of the size of the representative volume element for random composites: statistical and numerical approach. Int J Solids Struct 40(1314):3647–3679CrossRefGoogle Scholar
  19. 19.
    Koga N, Nakada N, Tsuchiyama T, Takaki S, Ojima M, Adachi Y (2012) Distribution of elastic strain in a pearlite structure. Scr Mater 67(4):400–403CrossRefGoogle Scholar
  20. 20.
    Kroner E (1958) Berechnung der elastischen konstanten des vielkristalls aus den konstanten des einkristalls. Z Phys 151(4):504–518CrossRefGoogle Scholar
  21. 21.
    Lebensohn R, Canova G (1997) A self-consistent approach for modelling texture development of two-phase polycrystals: application to titanium alloys. Acta Mater 45(9):3687–3694CrossRefGoogle Scholar
  22. 22.
    Li Y, Bompard P, Rey C, Aubin V (2012) Polycrystalline numerical simulation of variable amplitude loading effects on cyclic plasticity and microcrack initiation in austenitic steel 304L. Int J Fatigue 42:71–81CrossRefGoogle Scholar
  23. 23.
    Ludwig W, King A, Reischig P, Herbig M, Lauridsen EM, Schmidt S, Proudhon H, Forest S, Cloetens P, Du Roscoat SR et al (2009) New opportunities for 3D materials science of polycrystalline materials at the micrometre lengthscale by combined use of X-ray diffraction and X-ray imaging. Mater Sci Eng 524(1):69–76CrossRefGoogle Scholar
  24. 24.
    Martin G, Sinclair C, Schmitt JH (2013) Plastic strain heterogeneities in an Mg-1Zn-0.5Nd alloy. Scr Mater 68:695–698CrossRefGoogle Scholar
  25. 25.
    Marty B, Moretto P, Gergaud P, Lebrun J, Ostolaza K, Ji V (1997) X-ray study on single crystal superalloy SRR99: mismatch gamma/gamma’, mosaicity and internal stress. Acta Mater 45(2):791–800CrossRefGoogle Scholar
  26. 26.
    Molinari A, Ahzi S, Kouddane R (1997) On the self-consistent modeling of elastic-plastic behavior of polycrystals. Mech Mater 26(1):43–62CrossRefGoogle Scholar
  27. 27.
    Ortner B (1986) The choice of lattice planes in X-ray strain measurements of single crystals. Adv X-ray Anal 29:113–118Google Scholar
  28. 28.
    Ortner B (1986) Simultaneous determination of the lattice constant and elastic strain in cubic single crystal. Adv X-ray Anal 29:387–394Google Scholar
  29. 29.
    Petit J, Bornert M, Hofmann F, Robach O, Micha J, Ulrich O, Bourlot CL, Faurie D, Korsunsky A, Castelnau O (2012) Combining laue microdiffraction and digital image correlation for improved measurements of the elastic strain field with micrometer spatial resolution. Symposium on full-field measurements and identification in solid mechanics. Procedia (IUTAM) 4(0):133–143CrossRefGoogle Scholar
  30. 30.
    Saai A (2008) Physical model of the plasticity of a metal crystal CFC subjected to alternating loads: contribution to the definition of multiscale modeling of shaping metal. Ph.D. thesis, University of Savoie, FranceGoogle Scholar
  31. 31.
    Saai A, Louche H, Tabourot L, Chang HJ (2010) Experimental and numerical study of the thermo-mechanical behavior of Al bi-crystal in tension using full field measurements and micromechanical modeling. Mech Mater 42:275–292CrossRefGoogle Scholar
  32. 32.
    Schmid E, Boas W (1951) Plasticity of crystals. Springer, New YorkGoogle Scholar
  33. 33.
    Schwartz J, Fandeur O, Rey C (2010) Fatigue crack initiation modelling of 316LN steel based on non local plasticity theory. Proc Eng 2(1):1353–1362CrossRefGoogle Scholar
  34. 34.
    St-Pierre L, Héripré E, Dexet M, Crépin J, Bertolino G, Bilger N (2008) 3D simulations of microstructure and comparison with experimental microstructure coming from O.I.M analysis. Int J Plast 24(9):1516–1532CrossRefGoogle Scholar
  35. 35.
    Zeghadi A (2007) N’guyen, F., Forest, S., Gourgues, A.F., Bouaziz, O.: ensemble averaging stress–strain fields in polycrystalline aggregates with a constrained surface microstructure—part 1: anisotropic elastic behaviour. Philos Mag 87(8–9):1401–1424CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Wang Chow
    • 1
  • Denis Solas
    • 2
  • Guillaume Puel
    • 1
  • Thierry Baudin
    • 2
  • Véronique Aubin
    • 1
  1. 1.MSSMat, UMR CNRS 8579, CentraleSupélec, Univ Paris-SaclayChâtenay-MalabryFrance
  2. 2.ICMMO, UMR CNRS 8182, Univ Paris Sud, Univ Paris-SaclayOrsayFrance

Personalised recommendations