Journal of Materials Science

, Volume 53, Issue 9, pp 6390–6402 | Cite as

Determination of the fibre orientation distribution of a mineral wool network and prediction of its transverse stiffness using X-ray tomography

  • Lucie ChapelleEmail author
  • Allan Lyckegaard
  • Yukihiro Kusano
  • Carsten Gundlach
  • Mathilde Rosendahl Foldschack
  • Dorthe Lybye
  • Povl Brøndsted


A method to determine the orientation and diameter distributions of mineral wool fibre networks using X-ray tomography and image analysis is presented. The method is applied to two different types of mineral wool: glass wool and stone wool. The orientation information is obtained from the computation of the structure tensor, and the diameter is estimated by applying a greyscale granulometry. The results of the image analysis indicate the two types of fibres are distributed in a 2D planar arrangement with the glass wool fibres showing a higher degree of planarity than the stone wool fibres. The orientation information is included in an analytical model based on a Euler–Bernoulli beam approximation. The model enables prediction of the transverse stiffness. It is indicated that the glass wool transverse stiffness is lower than the stone wool transverse stiffness. Comparison with experimental results confirms the assumption that the underlying deformation mechanism of mineral wool is the bending of fibre segments between bonds.



Financial support from CINEMA: “the allianCe for ImagiNg of Energy MAterials”, DSF-Grant No. 1305-00032B under “The Danish Council for Strategic Research” and from Innovationsfonden is gratefully acknowledged. The authors thank the 3D Imaging Centre at The Technical University of Denmark for the acquisition of the X-ray CT scans and Jesper Asgaard Bøtner for helping with the SEM diameter analyses.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest.


  1. 1.
    Baudequin M, Ryschenkow G, Roux S et al (1999) Non-linear elastic behavior of light fibrous materials. Eur Phys J B Condens Matter Complex Syst 12:157–162. CrossRefGoogle Scholar
  2. 2.
    Buffiere J-Y, Maire E, Adrien J et al (2010) In situ experiments with X ray tomography: an attractive tool for experimental mechanics. Exp Mech 50:289–305. CrossRefGoogle Scholar
  3. 3.
    James JP, Choi H-W, Pharoah JG (2012) X-ray computed tomography reconstruction and analysis of polymer electrolyte membrane fuel cell porous transport layers. Int J Hydrog Energy 37:18216–18230. CrossRefGoogle Scholar
  4. 4.
    Pfrang A, Didas S, Tsotridis G (2013) X-ray computed tomography of gas diffusion layers of PEM fuel cells: segmentation of the micro porous layer. J Power Sour 235:81–86CrossRefGoogle Scholar
  5. 5.
    Tran H, Doumalin P, Delisee C et al (2012) 3D mechanical analysis of low-density wood-based fiberboards by X-ray microcomputed tomography and digital volume correlation. J Mater Sci 48:3198–3212. CrossRefGoogle Scholar
  6. 6.
    Maire E, Colombo P, Adrien J et al (2007) Characterization of the morphology of cellular ceramics by 3D image processing of X-ray tomography. J Eur Ceram Soc 27:1973–1981. CrossRefGoogle Scholar
  7. 7.
    Gaiselmann G, Manke I, Lehnert W, Schmidt V (2013) Extraction of curved fibers from 3D data. Image Anal Stereol 32:57–63. CrossRefGoogle Scholar
  8. 8.
    Pandita S, Verpoest I (2003) Prediction of the tensile stiffness of weft knitted fabric composites based on X-ray tomography images. Compos Sci Technol 63:311–325. CrossRefGoogle Scholar
  9. 9.
    Badel P, Sallé EV, Maire E, Boisse P (2009) Simulation and tomography analysis of textile composite reinforcement deformation at the mesoscopic scale. Int J Mater Form 2:189–192. CrossRefGoogle Scholar
  10. 10.
    Pazmino J, Carvelli V, Lomov SV (2014) Formability of a non-crimp 3D orthogonal weave E-glass composite reinforcement. Compos Part A Appl Sci Manuf 61:76–83. CrossRefGoogle Scholar
  11. 11.
    Zeng X, Brown LP, Endruweit A et al (2014) Geometrical modelling of 3D woven reinforcements for polymer composites: prediction of fabric permeability and composite mechanical properties. Compos Part A Appl Sci Manuf 56:150–160. CrossRefGoogle Scholar
  12. 12.
    Straumit I, Lomov SV, Wevers M (2015) Composites: part A quantification of the internal structure and automatic generation of voxel models of textile composites from X-ray computed tomography data. Compos Part A 69:150–158. CrossRefGoogle Scholar
  13. 13.
    Thibault X, Bloch J-F (2002) Structural analysis by X-Ray microtomography of a strained nonwoven papermaker felt. Text Res J 72:480–485. CrossRefGoogle Scholar
  14. 14.
    Viguié J, Latil P, Orgéas L et al (2013) Finding fibres and their contacts within 3D images of disordered fibrous media. Compos Sci Technol 89:202–210. CrossRefGoogle Scholar
  15. 15.
    Eberhardt CN, Clarke AR (2002) Automated reconstruction of curvilinear fibres from 3D datasets acquired by X-ray microtomography. J Microsc 206:41–53. CrossRefGoogle Scholar
  16. 16.
    Tausif M, Duffy B, Grishanov S et al (2014) Three-dimensional fiber segment orientation distribution using X-Ray microtomography. Microsc Microanal 20:1–10. CrossRefGoogle Scholar
  17. 17.
    Rolland du Roscoat S, Bloch J-F, Thibault X (2005) Synchrotron radiation microtomography applied to investigation of paper. J Phys D Appl Phys 38:A78–A84. CrossRefGoogle Scholar
  18. 18.
    Aronsson M (2002) Estimating fibre twist and aspect ratios in 3D voxel volumes. In: 16th International conference on pattern recognitionGoogle Scholar
  19. 19.
    Rolland du Roscoat S, Decain M, Thibault X et al (2007) Estimation of microstructural properties from synchrotron X-ray microtomography and determination of the REV in paper materials. Acta Mater 55:2841–2850. CrossRefGoogle Scholar
  20. 20.
    Marulier C, Dumont PJJ, Orgéas L et al (2012) Towards 3D analysis of pulp fibre networks at the fibre and bond levels. Nord Pulp Pap Res J Pap Phys 28:245–255CrossRefGoogle Scholar
  21. 21.
    Marulier C, Dumont PJJ, Orgéas L et al (2015) 3D analysis of paper microstructures at the scale of fibres and bonds. Cellulose 22:1517–1539. CrossRefGoogle Scholar
  22. 22.
    Geiss RH, Rice KP, Keller RR et al (2009) Three dimensional analysis of a compression test on stone wool. Acta Mater 57:3310–3320CrossRefGoogle Scholar
  23. 23.
    Maire E, Adrien J, Hild F, et al (2013) Digital X-ray tomography volume correlation of Rockwool during compression. In: Conference Proceedings of the society for experimental mechanics, pp 291–298Google Scholar
  24. 24.
    Couprie M, Meulenyzer S, Salem MA et al (2014) Fibre analysis in 3D materials and process validation on artificial data. J Microsc 255:78–88. Google Scholar
  25. 25.
    Tan JC, Elliott JA, Clyne TW (2006) Analysis of tomography images of bonded fibre networks to measure distributions of fibre segment length and fibre orientation. Adv Eng Mater 8:495–500. CrossRefGoogle Scholar
  26. 26.
    Gibson LJ, Ashby MF, Schajer GS, Robertson CI (1982) The Mechanics of Two-Dimensional Cellular Materials. Proc R Soc Lond A Math Phys Eng Sci 382:25–42CrossRefGoogle Scholar
  27. 27.
    Mezeix L, Bouvet C, Huez J, Poquillon D (2009) Mechanical behavior of entangled fibers and entangled cross-linked fibers during compression. J Mater Sci 44:3652–3661. CrossRefGoogle Scholar
  28. 28.
    Clyne TW, Markaki AE, Tan JC (2005) Mechanical and magnetic properties of metal fibre networks, with and without a polymeric matrix. Compos Sci Technol 65:2492–2499. CrossRefGoogle Scholar
  29. 29.
    Bigün J, Granlund GH, Wiklund J (1991) Multidimensional orientation estimation with applications to texture analysis and optical flow. IEEE Trans Pattern Anal Mach Intell 13:775–790. CrossRefGoogle Scholar
  30. 30.
    Weickert J (1995) Multiscale texture enhancement. In: Proceedings computer analysis of images and patterns, 6th international conference, CAIP’95 Prague, Czech Republic, Sept 6–8, 1995, pp 230–237Google Scholar
  31. 31.
    Köthe U (2003) Edge and junction detection with an improved structure tensor. Ger Assoc Pattern Recognit. Google Scholar
  32. 32.
    Budde MD, Frank JA (2012) Examining brain microstructure using structure tensor analysis of histological sections. Neuroimage 63:1–10. CrossRefGoogle Scholar
  33. 33.
    Van Vliet LJ, Faas FGA (2006) Multi-orientation analysis by decomposing the structure tensor and clustering. Proc Int Conf Pattern Recognit 3:856–860. Google Scholar
  34. 34.
    Scharr H, Black MJ, Haussecker H (2003) Image statistics and anisotropic diffusion. In: Proceedings ninth IEEE international conference on computer vision, vol 2. IEEE, pp 840–847Google Scholar
  35. 35.
    Moreno R, Borga M (2012) Estimation of trabecular thickness in gray-scale images through granulometric analysis. In: SPIE 8314: medical imaging. San DiegoGoogle Scholar
  36. 36.
    Standfest G, Kranzer S, Petutschnigg A, Dunky M (2010) Determination of the microstructure of an adhesive-bonded medium density fiberboard (MDF) using 3-D sub-micrometer computer tomography. J Adhes Sci Technol 24:1501–1514. CrossRefGoogle Scholar
  37. 37.
    Peyrega C, Jeulin D, Delisée C, Lux J (2009) 3D morphological modelling of a random fibrous network. Image Anal Stereol 28:129–141CrossRefGoogle Scholar
  38. 38.
    Lux J, Ahmadi A, Gobbé C, Delisée C (2006) Macroscopic thermal properties of real fibrous materials: volume averaging method and 3D image analysis. Int J Heat Mass Transf 49:1958–1973. CrossRefGoogle Scholar
  39. 39.
    Redenbach C, Vecchio I (2011) Statistical analysis and stochastic modelling of fibre composites. Compos Sci Technol 71:107–112. CrossRefGoogle Scholar
  40. 40.
    Komori T, Makishima K (1979) Geometrical expressions of spaces in anisotropic fiber assemblies. Text Res J 49:550–555. CrossRefGoogle Scholar
  41. 41.
    Komori T, Makishima K (1977) Numbers of fiber-to-fiber contacts in general fiber assemblies. Text Res J 47:13–17. CrossRefGoogle Scholar
  42. 42.
    Makishima A, Mackenzie JD (1975) Calculation of bulk modulus, shear modulus and Poisson’s ratio of glass. J Non Cryst Solids 17:147–157. CrossRefGoogle Scholar
  43. 43.
    Koenig AR, Hamilton RD, Laskowski TE et al (1993) Fiber diameter measurement of bulk man-made vitreous fiber. Anal Chim Acta 280:289–298. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.ROCKWOOL International A/SHedehuseneDenmark
  2. 2.Xnovo Technology ApSKøgeDenmark
  3. 3.Department of Wind EnergyTechnical University of DenmarkRoskildeDenmark
  4. 4.Department of PhysicsTechnical University of DenmarkKgs. LyngbyDenmark

Personalised recommendations