Computational Mechanics

, Volume 59, Issue 3, pp 419–441 | Cite as

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

  • Ante Buljac
  • Modesar Shakoor
  • Jan Neggers
  • Marc Bernacki
  • Pierre-Olivier Bouchard
  • Lukas Helfen
  • Thilo F. Morgeneyer
  • François Hild
Original Paper

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.

Keywords

Level set Microstructure meshing Multiscale analysis Volume correlation X-ray laminography 

References

  1. 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):4517–4525CrossRefGoogle Scholar
  2. 2.
    Bay B, Smith T, Fyhrie D, Saad M (1999) Digital volume correlation: three-dimensional strain mapping using X-ray tomography. Exp Mech 39:217–226CrossRefGoogle Scholar
  3. 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):939–950CrossRefGoogle Scholar
  4. 4.
    Besnard G, Hild F, Roux S (2006) “Finite-element” displacement fields analysis from digital images: application to Portevin-Le Châtelier bands. Exp Mech 46:789–803CrossRefGoogle Scholar
  5. 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, BerlinCrossRefGoogle Scholar
  6. 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):1401–1424CrossRefMATHGoogle Scholar
  7. 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 4:43–88Google Scholar
  8. 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):223–233CrossRefGoogle Scholar
  9. 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):444–453CrossRefGoogle Scholar
  10. 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):1613–1625CrossRefGoogle Scholar
  11. 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):289–305CrossRefGoogle Scholar
  12. 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 52:62–69CrossRefGoogle Scholar
  13. 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 84:175–187CrossRefGoogle Scholar
  14. 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 216:385–404CrossRefGoogle Scholar
  15. 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 217:701–715CrossRefGoogle Scholar
  16. 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):043702CrossRefGoogle Scholar
  17. 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):2245–2254CrossRefGoogle Scholar
  18. 18.
    Fritzen F, Forest S, Boehlke T, Kondo D, Kanit T (2012) Computational homogenization of elasto-plastic porous metals. Int J Plast 29:102–119CrossRefGoogle Scholar
  19. 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):4951–4976MathSciNetCrossRefMATHGoogle Scholar
  20. 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 99:2–15CrossRefGoogle Scholar
  21. 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):1977–1987CrossRefGoogle Scholar
  22. 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 103:558–572CrossRefGoogle Scholar
  23. 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 563:163–166CrossRefGoogle Scholar
  24. 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):170–173CrossRefGoogle Scholar
  25. 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. 26.
    Hild F, Roux S (2012) Comparison of local and global approaches to digital image correlation. Exp Mech 52(9):1503–1519CrossRefGoogle Scholar
  27. 27.
    Hütter G, Zybell L, Mühlich U, Kuna M (2013) Consistent simulation of ductile crack propagation with discrete 3D voids. Comput Mater Sci 80:61–70CrossRefGoogle Scholar
  28. 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):839–847CrossRefGoogle Scholar
  29. 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 144:118–141CrossRefGoogle Scholar
  30. 30.
    Kachanov L (1958) Time of the rupture process under creep conditions. Bull SSR Acad Sci 8:26–31 (in Russian)Google Scholar
  31. 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 56:177–195CrossRefGoogle Scholar
  32. 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):3960–3982CrossRefMATHGoogle Scholar
  33. 33.
    Kimmel R, Shaked D, Kiryati N, Bruckstein AM (1995) Skeletonization via distance maps and level sets. Comput Vis Image Underst 62(3):382–391CrossRefGoogle Scholar
  34. 34.
    Leclerc H, Périé J, Roux S, Hild F (2011) Voxel-scale digital volume correlation. Exp Mech 51(4):479–490CrossRefGoogle Scholar
  35. 35.
    Leclerc H, Périé J, Hild F, Roux S (2012) Digital volume correlation: what are the limits to the spatial resolution? Mech Ind 13:361–371CrossRefGoogle Scholar
  36. 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, ParisGoogle Scholar
  37. 37.
    Lemaitre J (1992) A course on damage mechanics. Springer, BerlinCrossRefMATHGoogle Scholar
  38. 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):959–970CrossRefGoogle Scholar
  39. 39.
    Ludwik P (1909) Elemente der technologischen Mechanik. Springer, LeipzigCrossRefMATHGoogle Scholar
  40. 40.
    Maire E, Withers PJ (2014) Quantitative X-ray tomography. Int Mater Rev 59(1):1–43CrossRefGoogle Scholar
  41. 41.
    Mathieu F, Leclerc H, Hild F, Roux S (2015) Estimation of elastoplastic parameters via weighted FEMU and integrated-DIC. Exp Mech 55(1):105–119CrossRefGoogle Scholar
  42. 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 66:471–474CrossRefGoogle Scholar
  43. 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):3902–3915CrossRefGoogle Scholar
  44. 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):543–556CrossRefGoogle Scholar
  45. 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):5348–5361CrossRefGoogle Scholar
  46. 46.
    Needleman A, Tvergaard V (1984) An analysis of ductile rupture in notched bars. J Mech Phys Solids 32(6):461–490CrossRefGoogle Scholar
  47. 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):630–637CrossRefGoogle Scholar
  48. 48.
    Osher S, Sethian JA (1988) Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations. J Comput Phys 79(1):12–49MathSciNetCrossRefMATHGoogle Scholar
  49. 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):903–912CrossRefGoogle Scholar
  50. 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 268:65–81MathSciNetCrossRefMATHGoogle Scholar
  51. 51.
    Rabotnov Y (1963) On the equations of state for creep. McMillan, New YorkGoogle Scholar
  52. 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 199:1307–1325CrossRefMATHGoogle Scholar
  53. 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 111:983–995CrossRefGoogle Scholar
  54. 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):075,012CrossRefGoogle Scholar
  55. 55.
    Roth C, Mohr D (2016) Ductile fracture experiments with locally proportional loading histories. Int J Plast 79:328–354CrossRefGoogle Scholar
  56. 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):1253–1265CrossRefGoogle Scholar
  57. 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 68:32–46CrossRefGoogle Scholar
  58. 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 147:398–417CrossRefGoogle Scholar
  59. 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):7291–7302MathSciNetCrossRefGoogle Scholar
  60. 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. 61.
    Smith T, Bay B, Rashid M (2002) Digital volume correlation including rotational degrees of freedom during minimization. Exp Mech 42(3):272–278CrossRefGoogle Scholar
  62. 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):6183–6200MathSciNetCrossRefMATHGoogle Scholar
  63. 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):663–680CrossRefMATHGoogle Scholar
  64. 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 324:70–79CrossRefGoogle Scholar
  65. 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):2108–2124CrossRefGoogle Scholar
  66. 66.
    Tomičević Z, Hild F, Roux S (2013) Mechanics-aided digital image correlation. J Strain Anal 48:330–343CrossRefGoogle Scholar
  67. 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 59:140–154Google Scholar
  68. 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 78:254–270CrossRefGoogle Scholar
  69. 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):1313–1320CrossRefGoogle Scholar
  70. 70.
    Wagoner RH, Chenot JL (2001) Metal forming analysis. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  71. 71.
    Xu F, Helfen L, Baumbach T, Suhonen H (2012) Comparison of image quality in computed laminography and tomography. Opt Exp 20:794–806CrossRefGoogle Scholar
  72. 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):3155–3173MathSciNetCrossRefGoogle Scholar
  73. 73.
    Zhang K, Bai J, François D (1999) Ductile fracture of materials with high void volumefraction. Int J Solids Struct 36(23):3407–3425CrossRefMATHGoogle Scholar
  74. 74.
    Zhang Y, Bajaj C, Sohn BS (2005) 3D finite element meshing from imaging data. Comput Method Appl Mech Eng 194(48–49):5083–5106CrossRefMATHGoogle Scholar
  75. 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 45:8–19CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Laboratoire de Mécanique et Technologie (LMT), ENS Paris-Saclay/CNRS/Univ. Paris-SaclayCachan CedexFrance
  2. 2.MINES ParisTech, PSL Research University, Centre des Matériaux, CNRS UMR 7633EvryFrance
  3. 3.MINES ParisTech, PSL - Research University, CEMEF - Centre de mise en forme des matériaux, CNRS UMR 7635Sophia Antipolis CedexFrance
  4. 4.ANKA/Institute for Photon Science and Synchrotron Radiation Karlsruhe Institute of Technology (KIT)KarlsruheGermany
  5. 5.European Synchrotron Radiation Facility (ESRF)GrenobleFrance

Personalised recommendations