Skip to main content
SpringerLink
Log in

Numerical validation framework for micromechanical simulations based on synchrotron 3D imaging

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

A combined computational–experimental framework is introduced herein to validate numerical simulations at the microscopic scale. It is exemplified for a flat specimen with central hole made of cast iron and imaged via in-situ synchrotron laminography at micrometer resolution during a tensile test. The region of interest in the reconstructed volume, which is close to the central hole, is analyzed by digital volume correlation (DVC) to measure kinematic fields. Finite element (FE) simulations, which account for the studied material microstructure, are driven by Dirichlet boundary conditions extracted from DVC measurements. Gray level residuals for DVC measurements and FE simulations are assessed for validation purposes.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

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
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25

Similar content being viewed by others

References

  1. Babout L, Bréchet Y, Maire E, Fougères R (2004) On the competition between particle fracture and particle decohesion in metal matrix composites. Acta Mater 52(15):4517–4525

    Article  Google Scholar 

  2. Bay B, Smith T, Fyhrie D, Saad M (1999) Digital volume correlation: three-dimensional strain mapping using X-ray tomography. Exp Mech 39:217–226

    Article  Google Scholar 

  3. Beckman F, Grupp R, Haibel A, Huppmann M, Nöthe M, Pyzalla R, Reimers W, Schreyer A, Zettler R (2007) In-situ synchrotron X-ray microtomography studies of microstructure and damage evolution in engineering materials. Adv Eng Mater 9(11):939–950

    Article  Google Scholar 

  4. Besnard G, Hild F, Roux S (2006) “Finite-element” displacement fields analysis from digital images: application to Portevin-Le Châtelier bands. Exp Mech 46:789–803

    Article  Google Scholar 

  5. Boffi D, Brezzi F, Demkowicz LF, Durán RG, Falk RS, Fortin M (2008) Mixed finite elements, compatibility conditions, and applications, lecture notes in mathematics, vol 1939. Springer, Berlin

    Book  Google Scholar 

  6. Bonora N, Ruggiero A (2005) Micromechanical modeling of ductile cast iron incorporating damage. Part I: ferritic ductile cast iron. Int J Solids Struct 42(5–6):1401–1424

    Article  MATH  Google Scholar 

  7. Bornert M, Chaix J, Doumalin P, Dupré J, Fournel T, Jeulin D, Maire E, Moreaud M, Moulinec H (2004) Mesure tridimensionnelle de champs cinématiques par imagerie volumique pour l’analyse des matériaux et des structures. Inst Mes Métrol 4:43–88

    Google Scholar 

  8. Bouchard P, Bourgeon L, Lachapèle H, Maire E, Verdu C, Forestier R, Logé R (2008) On the influence of particle distribution and reverse loading on damage mechanisms of ductile steels. Mater Sci Eng A 496(1–2):223–233

    Article  Google Scholar 

  9. Bouterf A, Roux S, Hild F, Adrien J, Maire E (2014) Digital volume correlation applied to X-ray tomography images from spherical indentation tests on lightweight gypsum. Strain 50(5):444–453

    Article  Google Scholar 

  10. Buffière J, Maire E, Cloetens P, Lormand G, Fougères R (1999) Characterisation of internal damage in a MMCp using X-ray synchrotron phase contrast microtomography. Acta Mater 47(5):1613–1625

    Article  Google Scholar 

  11. Buffière J, Maire E, Adrien J, Masse J, Boller E (2010) In situ experiments with X ray tomography: an attractive tool for experimental mechanics. Exp Mech 50(3):289–305

    Article  Google Scholar 

  12. Bull D, Spearing S, Sinclair I, Helfen L (2013) Three-dimensional assessment of low velocity impact damage in particle toughened composite laminates using micro-focus X-ray computed tomography and synchrotron radiation laminography. Compos Part A 52:62–69

    Article  Google Scholar 

  13. Cao TS, Maire E, Verdu C, Bobadilla C, Lasne P, Montmitonnet P, Bouchard PO (2014) Characterization of ductile damage for a high carbon steel using 3D X-ray micro-tomography and mechanical tests—application to the identification of a shear modified GTN model. Comput Mater Sci 84:175–187

    Article  Google Scholar 

  14. Cao TS, Bobadilla C, Montmitonnet P, Bouchard PO (2015) A comparative study of three ductile damage approaches for fracture prediction in cold forming processes. J Mater Process Technol 216:385–404

    Article  Google Scholar 

  15. Cheng Y, Laiarinandrasana L, Helfen L, Proudhon H, Klinkova O, Baumbach T, Morgeneyer T (2016) 3D damage micromechanisms in polyamide 6 ahead of a severe notch studied by in situ synchrotron laminography. Macromol Chem Phys 217:701–715

    Article  Google Scholar 

  16. Di Michiel M, Merino JM, Fernandez-Carreiras D, Buslaps T, Honkimäki V, Falus P, Martins T, Svensson O (2005) Fast microtomography using high energy synchrotron radiation. Rev Sci Instrum 76(4):043702

    Article  Google Scholar 

  17. Dong MJ, Prioul C, François D (1997) Damage effect on the fracture toughness of nodular cast iron: part I. Damage characterization and plastic flow stress modeling. Metall Mater Trans A 28(11):2245–2254

    Article  Google Scholar 

  18. Fritzen F, Forest S, Boehlke T, Kondo D, Kanit T (2012) Computational homogenization of elasto-plastic porous metals. Int J Plast 29:102–119

    Article  Google Scholar 

  19. Gruau C, Coupez T (2005) 3D tetrahedral, unstructured and anisotropic mesh generation with adaptation to natural and multidomain metric. Comput Methods Appl Mech Eng 194(48–49):4951–4976

    Article  MathSciNet  MATH  Google Scholar 

  20. Gurson A (1977) Continuum theory of ductile rupture by void nucleation and growth: part i—yield criterion and flow rules for porous ductile media. ASME J Eng Mater Technol 99:2–15

    Article  Google Scholar 

  21. Guvenilir A, Breunig T, Kinney J, Stock S (1997) Direct observation of crack opening as a function of applied load in the interior of a notched tensile sample of Al–Li 2090. Acta Mater 45(5):1977–1987

    Article  Google Scholar 

  22. Hannard F, Pardoen T, Maire E, Le Bourlot C, Mokso R, Simar A (2016) Characterization and micromechanical modelling of microstructural heterogeneity effects on ductile fracture of 6xxx aluminium alloys. Acta Mater 103:558–572

    Article  Google Scholar 

  23. Helfen L, Myagotin A, Pernot P, DiMichiel M, Mikulík P, Berthold A, Baumbach T (2006) Investigation of hybrid pixel detector arrays by synchrotron-radiation imaging. Nucl Inst Method Phys Res B 563:163–166

    Article  Google Scholar 

  24. Helfen L, Morgeneyer T, Xu F, Mavrogordato M, Sinclair I, Schillinger B, Baumbach T (2012) Synchrotron and neutron laminography for three-dimensional imaging of devices and flat material specimens. Int J Mater Res 2012(2):170–173

    Article  Google Scholar 

  25. Hild F, Bouterf A, Chamoin L, Mathieu F, Neggers J, Pled F, Tomičević Z, Roux S (2016) Toward 4D mechanical correlation. Adv Mech Simul Eng Sci 3(1):17. doi:10.1186/s40323-016-0070-z

  26. Hild F, Roux S (2012) Comparison of local and global approaches to digital image correlation. Exp Mech 52(9):1503–1519

    Article  Google Scholar 

  27. Hütter G, Zybell L, Mühlich U, Kuna M (2013) Consistent simulation of ductile crack propagation with discrete 3D voids. Comput Mater Sci 80:61–70

    Article  Google Scholar 

  28. Hütter G, Zybell L, Kuna M (2014) Size effects due to secondary voids during ductile crack propagation. Int J Solids Struct 51(3–4):839–847

    Article  Google Scholar 

  29. Hütter G, Zybell L, Kuna M (2015) Micromechanisms of fracture in nodular cast iron: from experimental findings towards modeling strategies—a review. Eng Fract Mech 144:118–141

    Article  Google Scholar 

  30. Kachanov L (1958) Time of the rupture process under creep conditions. Bull SSR Acad Sci 8:26–31 (in Russian)

    Google Scholar 

  31. Kahziz M, Morgeneyer T, Maziere M, Helfen L, Bouaziz O, Maire E (2016) In situ 3D synchrotron laminography assessment of edge fracture in DP steels: quantitative and numerical analysis. Exp Mech 56:177–195

    Article  Google Scholar 

  32. Kanit T, N’Guyen F, Forest S, Jeulin D, Reed M, Singleton S (2006) Apparent and effective physical properties of heterogeneous materials: representativity of samples of two materials from food industry. Comput Method Appl Mech Eng 195(33–36):3960–3982

    Article  MATH  Google Scholar 

  33. Kimmel R, Shaked D, Kiryati N, Bruckstein AM (1995) Skeletonization via distance maps and level sets. Comput Vis Image Underst 62(3):382–391

    Article  Google Scholar 

  34. Leclerc H, Périé J, Roux S, Hild F (2011) Voxel-scale digital volume correlation. Exp Mech 51(4):479–490

    Article  Google Scholar 

  35. Leclerc H, Périé J, Hild F, Roux S (2012) Digital volume correlation: what are the limits to the spatial resolution? Mech Ind 13:361–371

    Article  Google Scholar 

  36. Leclerc H, Neggers J, Mathieu F, Roux S, Hild F (2015) Correli 3.0. IDDN.FR.001.520008.000.S.P.2015.000.31500, Agence pour la Protection des Programmes, Paris

  37. Lemaitre J (1992) A course on damage mechanics. Springer, Berlin

    Book  MATH  Google Scholar 

  38. Limodin N, Réthoré J, Adrien J, Buffière J, Hild F, Roux S (2011) Analysis and artifact correction for volume correlation measurements using tomographic images from a laboratory X-ray source. Exp Mech 51(6):959–970

    Article  Google Scholar 

  39. Ludwik P (1909) Elemente der technologischen Mechanik. Springer, Leipzig

    Book  MATH  Google Scholar 

  40. Maire E, Withers PJ (2014) Quantitative X-ray tomography. Int Mater Rev 59(1):1–43

    Article  Google Scholar 

  41. Mathieu F, Leclerc H, Hild F, Roux S (2015) Estimation of elastoplastic parameters via weighted FEMU and integrated-DIC. Exp Mech 55(1):105–119

    Article  Google Scholar 

  42. Maurel V, Helfen L, N’Guyen F, Köster A, Di Michiel M, Baumbach T, Morgeneyer T (2012) Three-dimensional investigation of thermal barrier coatings by synchrotron-radiation computed laminography. Scr Mater 66:471–474

    Article  Google Scholar 

  43. Morgeneyer T, Besson J, Proudhon H, Starink M, Sinclair I (2009) Experimental and numerical analysis of toughness anisotropy in AA2139 Al-alloy sheet. Acta Mater 57(13):3902–3915

    Article  Google Scholar 

  44. Morgeneyer T, Helfen L, Mubarak H, Hild F (2013) 3D digital volume correlation of synchrotron radiation laminography images of ductile crack initiation: an initial feasibility study. Exp Mech 53(4):543–556

    Article  Google Scholar 

  45. Myagotin A, Voropaev A, Helfen L, Hänschke D, Baumbach T (2013) Efficient volume reconstruction for parallel-beam computed laminography by filtered backprojection on multi-core clusters. IEEE Trans Image Process 22(12):5348–5361

    Article  Google Scholar 

  46. Needleman A, Tvergaard V (1984) An analysis of ductile rupture in notched bars. J Mech Phys Solids 32(6):461–490

    Article  Google Scholar 

  47. Odin G, Savoldelli C, Bouchard PO, Tillier Y (2010) Determination of Young’s modulus of mandibular bone using inverse analysis. Med Eng Phys 32(6):630–637

    Article  Google Scholar 

  48. Osher S, Sethian JA (1988) Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations. J Comput Phys 79(1):12–49

    Article  MathSciNet  MATH  Google Scholar 

  49. Proudhon H, Li J, Reischig P, Guéninchault N, Forest S, Ludwig W (2016) Coupling diffraction contrast tomography with the finite element method. Adv Eng Mater 18(6):903–912

    Article  Google Scholar 

  50. Quan DL, Toulorge T, Marchandise E, Remacle JF, Bricteux G (2014) Anisotropic mesh adaptation with optimal convergence for finite elements using embedded geometries. Comput Method Appl Mech Eng 268:65–81

    Article  MathSciNet  MATH  Google Scholar 

  51. Rabotnov Y (1963) On the equations of state for creep. McMillan, New York

    Google Scholar 

  52. Rannou J, Limodin N, Réthoré J, Gravouil A, Ludwig W, Baïetto M, Buffière J, Combescure A, Hild F, Roux S (2010) Three dimensional experimental and numerical multiscale analysis of a fatigue crack. Comput Method Appl Mech Eng 199:1307–1325

    Article  MATH  Google Scholar 

  53. Reischig P, Helfen L, Wallert A, Baumbach T, Dik J (2013) Non-invasive, three-dimensional X-ray imaging of paint layers. Appl Phys A 111:983–995

    Article  Google Scholar 

  54. Resk H, Delannay L, Bernacki M, Coupez T, Logé R (2009) Adaptive mesh refinement and automatic remeshing in crystal plasticity finite element simulations. Model Simul Mater Sci Eng 17(7):075,012

    Article  Google Scholar 

  55. Roth C, Mohr D (2016) Ductile fracture experiments with locally proportional loading histories. Int J Plast 79:328–354

    Article  Google Scholar 

  56. Roux S, Hild F, Viot P, Bernard D (2008) Three dimensional image correlation from X-ray computed tomography of solid foam. Compos Part A 39(8):1253–1265

    Article  Google Scholar 

  57. Roux E, Bernacki M, Bouchard PO (2013) A level-set and anisotropic adaptive remeshing strategy for the modeling of void growth under large plastic strain. Comput Mater Sci 68:32–46

    Article  Google Scholar 

  58. Shakoor M, Bernacki M, Bouchard PO (2015) A new body-fitted immersed volume method for the modeling of ductile fracture at the microscale: analysis of void clusters and stress state effects on coalescence. Eng Fract Mech 147:398–417

    Article  Google Scholar 

  59. Shakoor M, Scholtes B, Bouchard PO, Bernacki M (2015) An efficient and parallel level set reinitialization method—application to micromechanics and microstructural evolutions. Appl Math Model 39(23–24):7291–7302

    Article  MathSciNet  Google Scholar 

  60. Shakoor M, Bouchard PO, Bernacki M (2016) An adaptive level-set method with enhanced volume conservation for simulations in multiphase domains. Int J Numer Method Eng. doi:10.1002/nme.5297

  61. Smith T, Bay B, Rashid M (2002) Digital volume correlation including rotational degrees of freedom during minimization. Exp Mech 42(3):272–278

    Article  Google Scholar 

  62. Sukumar N, Chopp D, Moës N, Belytschko T (2001) Modeling holes and inclusions by level sets in the extended finite-element method. Comput Method Appl Mech Eng 190(46–47):6183–6200

    Article  MathSciNet  MATH  Google Scholar 

  63. Sussman M, Fatemi E, Smereka P, Osher S (1998) An improved level set method for incompressible two-phase flows. Comput Fluid 27(5–6):663–680

    Article  MATH  Google Scholar 

  64. Taillandier-Thomas T, Roux S, Morgeneyer T, Hild F (2014) Localized strain field measurement on laminography data with mechanical regularization. Nucl Inst Method Phys Res B 324:70–79

    Article  Google Scholar 

  65. Tang S, Kopacz AM, Chan O’Keeffe S, Olson GB, Liu WK (2013) Three-dimensional ductile fracture analysis with a hybrid multiresolution approach and microtomography. J Mech Phys Solid 61(11):2108–2124

    Article  Google Scholar 

  66. Tomičević Z, Hild F, Roux S (2013) Mechanics-aided digital image correlation. J Strain Anal 48:330–343

    Article  Google Scholar 

  67. Tomičević Z, Kodvanj J, Hild F (2016) Characterization of the nonlinear behavior of nodular graphite cast iron via inverse identification—analysis of uniaxial tests. Eur J Mech 59:140–154

    Google Scholar 

  68. Ueda T, Helfen L, Morgeneyer TF (2014) In situ laminography study of three-dimensional individual void shape evolution at crack initiation and comparison with Gurson–Tvergaard–Needleman-type simulations. Acta Mater 78:254–270

    Article  Google Scholar 

  69. Verhulp E, van Rietbergen B, Huiskes R (2004) A three-dimensional digital image correlation technique for strain measurements in microstructures. J Biomech 37(9):1313–1320

    Article  Google Scholar 

  70. Wagoner RH, Chenot JL (2001) Metal forming analysis. Cambridge University Press, Cambridge

    Book  Google Scholar 

  71. Xu F, Helfen L, Baumbach T, Suhonen H (2012) Comparison of image quality in computed laminography and tomography. Opt Exp 20:794–806

    Article  Google Scholar 

  72. Young PG, Beresford-West TBH, Coward SRL, Notarberardino B, Walker B, Abdul-Aziz A (2008) An efficient approach to converting three-dimensional image data into highly accurate computational models. Philos Trans Ser A 366(1878):3155–3173

    Article  MathSciNet  Google Scholar 

  73. Zhang K, Bai J, François D (1999) Ductile fracture of materials with high void volumefraction. Int J Solids Struct 36(23):3407–3425

    Article  MATH  Google Scholar 

  74. Zhang Y, Bajaj C, Sohn BS (2005) 3D finite element meshing from imaging data. Comput Method Appl Mech Eng 194(48–49):5083–5106

    Article  MATH  Google Scholar 

  75. Zybell L, Hütter G, Linse T, Mühlich U, Kuna M (2014) Size effects in ductile failure of porous materials containing two populations of voids. Eur J Mech 45:8–19

    Article  Google Scholar 

Download references

Acknowledgements

This study was performed within the COMINSIDE project funded by the French Agence Nationale de la Recherche (ANR-14-CE07-0034-02 Grant). We also acknowledge the European Synchrotron Radiation Facility for provision of beamtime at beamline ID15, experiment MA 1932. It is also a pleasure to acknowledge the support of BPI France (“DICCIT” project), and of the Carnot M.I.N.E.S institute (“CORTEX” project). M. Kuna, L. Zybell and M. Horn from IMFD, TU Freiberg are thanked for materials supply and machining as well as for scientific discussions.

Author information

Authors and Affiliations

  1. Laboratoire de Mécanique et Technologie (LMT), ENS Paris-Saclay/CNRS/Univ. Paris-Saclay, 61 avenue du Président Wilson, 94235, Cachan Cedex, France

    Ante Buljac, Jan Neggers & François Hild

  2. MINES ParisTech, PSL Research University, Centre des Matériaux, CNRS UMR 7633, BP 87, 91003, Evry, France

    Ante Buljac & Thilo F. Morgeneyer

  3. MINES ParisTech, PSL - Research University, CEMEF - Centre de mise en forme des matériaux, CNRS UMR 7635, CS 10207 rue Claude Daunesse, 06904, Sophia Antipolis Cedex, France

    Modesar Shakoor, Marc Bernacki & Pierre-Olivier Bouchard

  4. ANKA/Institute for Photon Science and Synchrotron Radiation Karlsruhe Institute of Technology (KIT), 76131, Karlsruhe, Germany

    Lukas Helfen

  5. European Synchrotron Radiation Facility (ESRF), 38043, Grenoble, France

    Lukas Helfen

Authors
  1. Ante Buljac
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Modesar Shakoor
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jan Neggers
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Marc Bernacki
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Pierre-Olivier Bouchard
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Lukas Helfen
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Thilo F. Morgeneyer
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. François Hild
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to François Hild.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Buljac, A., Shakoor, M., Neggers, J. et al. Numerical validation framework for micromechanical simulations based on synchrotron 3D imaging. Comput Mech 59, 419–441 (2017). https://doi.org/10.1007/s00466-016-1357-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-016-1357-0

Keywords

Search

Navigation