[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content

Advertisement

Springer Nature Link
Log in

X-ray CT imaging and finite element computations of the elastic properties of a rigid organic foam compared to experimental measurements: insights into foam variability

  • Original Paper
  • Published:
Journal of Materials Science Aims and scope Submit manuscript

Abstract

A combined computational/experimental technique was developed to analyze the compressive elastic properties of a rigid organic foam. This technique combines X-ray computed tomography, image analysis, and large-scale finite element computations utilizing a new numerical technique. Predictions of Young’s modulus were validated with uniaxial compression testing. Good agreement was obtained between imaging/finite element computations and experimental mechanical measurements within experimental error, and the limited knowledge existing on the solid material comprising the backbone of the foam. Using the new combined experimental/theoretical procedures, it was found that the predicted Young’s modulus of the solid backbone differed by more than a factor of 100 % between two different grades of the foam, in accordance with the findings of other researchers. A significant variability of the backbone modulus was also found within the same grade. Density measurements identified the variability between different grades of foam and different as-received sample thicknesses within the same grade of foam.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

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

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Notes

  1. Certain commercial equipment and/or materials are identified in this report in order to adequately specify the experimental procedure. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the equipment and/or materials used are necessarily the best available for the purpose.

References

  1. Gibson LJ, Ashby MF (1997) Cellular Solids: Structure and Properties, 2nd edn. Cambridge University Press, Cambridge

    Book  Google Scholar 

  2. Rice RW (1998) Porosity of ceramics. Marcel Dekker Inc, New York

    Google Scholar 

  3. Gibson LJ (2000) Mechanical behavior of metallic foams. Annu Rev Mater Sci 30:191–227. doi:10.1146/annurev.matsci.30.1.191

    Article  Google Scholar 

  4. Roberts AP, Garboczi EJ (2000) Elastic properties of model porous ceramics. J Amer Ceram Soc 83:3041–3048

    Article  Google Scholar 

  5. Roberts AP, Garboczi EJ (2002) Elastic properties of model random three-dimensional open-cell solids. J Mech Phys Solids 50:33–55

    Article  Google Scholar 

  6. Roberts AP, Garboczi EJ (2001) Elastic moduli of model random three-dimensional closed-cell cellular solids. Acta Mater 49:189–197

    Article  Google Scholar 

  7. Guessasma S, Babin P, Della Valle G, Dendievel R (2008) Relating cellular structure of open solid food foams to their Young’s modulus: finite element calculation. Int J Solids Struct 45:2881–2896

    Article  Google Scholar 

  8. Jang WY, Kraynik AM, Kyriakides S (2008) On the microstructure of open-cell foams and its effect on elastic properties. Int J Solids Struct 45:1845–1875

    Article  Google Scholar 

  9. Kak AC, Slaney M (2001) Principles of computerized tomographic imaging. SIAM, New York

    Book  Google Scholar 

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

    Article  Google Scholar 

  11. Maire E, Fazekas A, Salvo L, Dendievel R, Youssef S, Cloetens P, Letang JM (2003) X-ray tomography applied to the characterization of cellular materials: related finite element modeling problems. Compos Sci Technol 63:2431–2443

    Article  Google Scholar 

  12. Ulrich D, van Rietbergen B, Weinans H, Ruegsegger P (1998) Finite element analysis of trabecular bone structure: a comparison of image-based meshing techniques. J Biomech 31:1187–1192. doi:10.1016/S0021-9290(89)00118-3

    Article  Google Scholar 

  13. Arns CH, Knackstedt MA, Pinczewski WV, Garboczi EJ (2002) Computation of linear elastic properties from microtomographic images: methodology and agreement between theory and experiment. Geophysics 67(5):1396–1405. doi:10.1190/1.1512785

    Article  Google Scholar 

  14. Elliott JA, Windle AH, Hobdell JR, Eeckhaut G, Oldman RJ, Ludwig W, Boller E, Cloetens P, Baruchel J (2002) In-situ deformation of an open-cell flexible polyurethane foam characterised by 3D computed microtomography. J Mater Sci 37:1547–1555. doi:10.1023/A:1014920902712

    Article  Google Scholar 

  15. Patterson BM, Henderson K, Smith Z, Zhang D, and Giguere P (2012) Application of Micro-CT to In-situ Foam Compression and Numerical Modeling. Microscopy and Analysis Tomography and Image Analysis Supplement, March 2012

  16. Hangai Y, Yamaguchi R, Takahashi S, Utsunomiya T, Kuwazuru O, Yoshikawa N (2013) Deformation behaviour estimation of aluminum foam by X-ray CT image-based finite element analysis. Metall Mater Trans A 44(4):1880–1886

    Article  Google Scholar 

  17. Zhang L, Ferreira JMF, Olhere S, Courtois L, Zhang T, Maire E, Rauhe JC (2012) Modeling the mechanical properties of optimally processed cordierite-mullite-alumina ceramic foams by X-ray computed tomography and finite element analysis. Acta Mater 60:4235–4246

    Article  Google Scholar 

  18. Knackstedt MA, Arns CH, Saadatfar M, Sended TJ, Limaye A, Sakellariou A, Sheppard AP, Sok RM, Schrof W, Steininger H (2006) Elastic and transport properties of cellular solids derived from three-dimensional tomographic images. Proc R Soc A 462:2833–2862. doi:10.1098/rspa.2006.1657

    Article  Google Scholar 

  19. Caty O, Maire E, Youssef S, Bouchet R (2008) Modeling the properties of closed-cell cellular materials from tomography images using finite shell elements. Acta Mater 56:5524–5534. doi:10.1016/j.actamat.2008.07.023

    Article  Google Scholar 

  20. Babin P, Della Valle G, Dendievel R, Lassoued N, Salvo L (2005) Mechanical properties of bread crumbs from tomography based finite element simulations. J Mater Sci 40:5867–5873. doi:10.1007/s10853-005-5021-x

    Article  Google Scholar 

  21. Tsafnat N, Tsafnat G, Jones AS (2008) Micro-finite element modelling of coke blends using X-ray microtomography. Fuel 87:2983–2987. doi:10.1016/j.fuel.2008.03.027

    Article  Google Scholar 

  22. Amsellem O, Madi K, Borit F, Jeulin D, Guipont V, Jeandin M, Boller E, Pauchet F (2008) Two-dimensional (2D) and three-dimensional (3D) analyses of plasma-sprayed alumina microstructures for finite-element simulation of Young’s modulus. J Mater Sci 43:4091–4098. doi:10.1007/s10853-007-2239-9

    Article  Google Scholar 

  23. Veyhl C, Belova IV, Murch GE, Fiedler T (2011) Finite element analysis of the mechanical properties of cellular aluminum based on micro-computed tomography. Mater Sci Eng A 528:4550–4555. doi:10.1016/j.msea.2011.02.031

    Article  Google Scholar 

  24. Youssef S, Maire E, Gaertner R (2005) Finite element modelling of the actual structure of cellular materials determined by X-ray tomography. Acta Materiala 53:719–730. doi:10.1016/j.actamat.2004.10.024

    Article  Google Scholar 

  25. Maire E, Colombo P, Adrien J, Babout L, Biasetto L (2007) Characterization of the morphology of cellular ceramics by 3D image processing of X-ray tomography. J Eur Ceram Soc 27:1973–1981

    Article  Google Scholar 

  26. Garboczi EJ, Kushch VI (2015) Computing elastic moduli on 3-D X-ray computed tomography image stacks. J Mech Phys Solids 76:84–97

    Article  Google Scholar 

  27. http://www.rohacell.com. Accessed 14 Oct 2014

  28. Flores-Johnson EA, Li QM, Mines RAW (2008) Degradation of elastic modulus of progressively-crushable foams in uniaxial compression. J Cell Plast 44:415–434

    Article  Google Scholar 

  29. Li QM, Mines RAW (2002) Strain measures for rigid crushable foam in uniaxial compression. Strain 38:132–140

    Article  Google Scholar 

  30. Li QM, Magkiriadis I, Harrigan JJ (2006) Compressive strain at the onset of densification of cellular solids. J Cell Plast 42:371–392

    Article  Google Scholar 

  31. Li QM, Mines RAW, Birch RS (2000) The crush behavior of Rohacell-51 WF structural foam. Inter J Solids Struct 37:6321–6341

    Article  Google Scholar 

  32. Gibson LJ, Ashby MF (1982) The mechanics of three-dimensional cellular materials. Proc R Soc Lond A 382:43–59

    Article  Google Scholar 

  33. Maiti SK, Gibson LJ, Ashby MF (1984) Deformation and energy absorption diagrams for cellular solids. Acta Metal 32:1963–1975

    Article  Google Scholar 

  34. Maiti SK, Ashby MF, Gibson LF (1984) Fracture toughness of brittle cellular solids. Scr Metall 18:213–217

    Article  Google Scholar 

  35. Wang J, Wang H, Chen X, Yu Y (2010) Experimental and numerical study of the elastic properties of PMI foams. J Mater Sci 45:2688–2695. doi:10.1007/s10853-010-4250-9

    Article  Google Scholar 

  36. Daphalapurkar NP, Hanan JC, Phelps NB, Bale H, Lu H (2008) Tomography and simulation of microstructure evolution of a closed-cell polymer foam in compression. Mech Adv Mater Struct 15:594–611

    Article  Google Scholar 

  37. Bhat BT, Wang TG (1990) A comparison of mechanical properties of some foams and honeycombs. J Mater Sci 25:5157–5162. doi:10.1007/BF00580144

    Article  Google Scholar 

  38. Arezoo S, Tagarielli VL, Petrinic N, Reed JM (2011) The mechanical response of Rohacell foams at different length scales. J Mater Sci 46:6864–6870. doi:10.1007/s10853-011-5649-7

    Google Scholar 

  39. Kak AC, Slandy M (1988) Principles of computerized tomographic imaging. IEEE Press, New York

    Google Scholar 

  40. Miller JD, Lin CL (2004) Three-dimensional analysis of particulates in mineral processing systems by cone-beam x-ray microtomography. Miner Metall. Process 21(3):113–124

    Google Scholar 

  41. Yu H, Cao G, Burk L, Lee Y, Lu J, Santago P, Zhou O, Wang G (2009) Compressive sampling based interior reconstruction for dynamic carbon nanotube micro-CT. J X-Ray Sci Technol 17:295–303. doi:10.3233/XST-2009-0230

    Google Scholar 

  42. Cho S, Bian J, Pelizzari CA, Chen CT, He TC, Pan X (2007) Region-of-interest image reconstruction in circular cone-beam microCT. Med Phys 34:4923–4933. doi:10.1118/1.2804924

    Article  Google Scholar 

  43. Videla AR, Lin CL, Miller JD (2006) Watershed functions applied to a 3Dd image segmentation problem for the analysis of packed particle beds. Part Sys Charact 23:237–245

    Article  Google Scholar 

  44. Patterson BM, Escobedo-Diaz JP, Cerreta E, Dennis-Koller D (2012) Dimensional quantification of embedded voids or objects in three dimensions using X-ray tomography. Microsc Microanal 18(2):390–398

    Article  Google Scholar 

  45. Schlimper R, Rinker M, Schäuble R (2009) Prediction of material behaviour of closed cell rigid foams via mesoscopic modelling, In: Proceedings of the International Committee on Composite Materials Meeting: ICCM 17, 27–31 July 2009, Edinburgh, Scotland, UK

  46. The Fiji software, found at http://fiji.sc/Fiji, which is a version of the NIH software ImageJ, located at http://imagej.nih.gov/ij/

  47. Elias H-G (1984) Macromolecules: structure and properties, 2nd edn. Plenum Press, New York

    Book  Google Scholar 

  48. Chen CP, Anderson WB, Lakes RS (1994) Relating the properties of the foam to the properties of the solid from which it is made. Cell Polym 13:16–32

    Google Scholar 

  49. Garboczi EJ, Day AR (1995) An algorithm for computing the effective linear elastic properties of heterogeneous materials: 3-D results for composites with equal phase Poisson ratios. J Mech Phys Solids 43:1349–1362

    Article  Google Scholar 

  50. Garboczi EJ (1998) Finite element and finite difference programs for computing the linear electric and elastic properties of digital images of random materials. NIST Internal Report 6269, U.S. Department of Commerce, Gaithersburg, Maryland

  51. Bohn RB, Garboczi EJ (2003) User manual for finite element and finite difference programs: A parallel version of NIST IR 6269. NIST Internal Report 6997, U.S. Department of Commerce, Gaithersburg, Maryland

  52. Garboczi EJ, Douglas JF, Bohn RB (2006) A hybrid finite element-analytical method for determining the intrinsic elastic moduli of particles having moderately extended shapes and a wide range of elastic properties. Mech Mater 38:786–800

    Article  Google Scholar 

  53. Kushch VI (2013) Micromechanics of composites: multipole expansion approach. Elsevier, Amsterdam

    Google Scholar 

  54. ASTM D1621 - 10 Standard Test Method for Compressive Properties of Rigid Cellular Plastics, ASTM Subcommittee D20.22, Book of Standards Volume: 08.01 (ASTM, West Conshohocken, PA)

  55. Roberts AP, Garboczi EJ (2002) Computation of the linear elastic properties of random porous materials with a wide variety of microstructure. Proc Royal Soc 458:1033–1054

    Article  Google Scholar 

  56. Tranchida D, Piccarolo S, Loos J, Alexeev A (2006) Accurately evaluating Young’s modulus of polymers through nanoindentations: a phenomenological correction factor to the Oliver and Pharr procedure. Appl Phys Lett 89:171905-1–171905-3

    Article  Google Scholar 

  57. Kaufman JD, Klapperich CM (2009) Surface detection errors cause overestimation of the modulus in nanoindentation on soft materials. J Mech Behav Biomed Mater 2:312–317. doi:10.1016/j.jmbbm.2008.08.004

    Article  Google Scholar 

  58. Thorpe MF, Jasiuk I (1992) New results in the theory of elasticity for two-dimensional composites. Proc Roy Soc Lond A 438:531–544

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Corporate Innovation Center, USG Corporation, Libertyville, IL, USA

    K. Natesaiyer, C. Chan, S. Sinha-Ray & D. Song

  2. Department of Mechanical & Industrial Engineering, University of Illinois at Chicago, Chicago, IL, USA

    S. Sinha-Ray

  3. Department of Metallurgical Engineering, University of Utah, Salt Lake City, UT, USA

    C. L. Lin & J. D. Miller

  4. Applied Chemicals and Materials Division, NIST, Boulder, CO, USA

    E. J. Garboczi

  5. Materials and Structural Systems Division, NIST, Gaithersburg, MD, USA

    A. M. Forster

Authors
  1. K. Natesaiyer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Chan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Sinha-Ray
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. D. Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. C. L. Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. J. D. Miller
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. E. J. Garboczi
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. A. M. Forster
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. J. Garboczi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Natesaiyer, K., Chan, C., Sinha-Ray, S. et al. X-ray CT imaging and finite element computations of the elastic properties of a rigid organic foam compared to experimental measurements: insights into foam variability. J Mater Sci 50, 4012–4024 (2015). https://doi.org/10.1007/s10853-015-8958-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10853-015-8958-4

Keywords

Search

Navigation