Abstract
This article reviews the use of x-ray computed tomography (XRCT) to investigate the structure and properties of cellular solids. In the first section, the possibilities offered by XRCT are presented. Examples of tomographic images are shown for the three classes of material (polymers, metals, and ceramics). Different characterizations of cellular solids performed thanks to XRCT images are shown: calculation of morphological parameters, in situ and ex situ mechanical tests, and use of the tomographic images to perform finite element (FE) modeling. The second part of the paper presents the existing methods to create the meshes from tomographic images and highlights some interesting results from the FE simulations.
Similar content being viewed by others
References
L.J. Gibson and M.F. Ashby: Cellular Solids: Structure and Properties, 2nd ed. (Cambridge University Press, Cambridge, England, 1997), p. 510.
E. Maire: X-ray tomography applied to the characterization of highly porous materials. Annu. Rev. Mater. Res. 42, 7.1 (2012).
J.Y. Buffière, E. Maire, J. Adrien, J.P. Masse, and E. Boller: In situ experiments with x ray tomography: An attractive tool for experimental mechanics. Exp. Mech. 50, 289 (2010).
J. Baruchel, J.Y. Buffière, E. Maire, P. Merle, and G. Peix: X-Ray Tomography in Materials Science (Hermès Science Publications, Paris, France, 2000), p. 204.
S.R. Stock: Recent advances in x-ray microtomography applied to materials. Int. Mater. Rev. 53, 129 (2008).
F. Fischer, G.T. Lim, U.A. Handge, and V. Altstdt: Numerical simulations of mechanical properties of cellular materials using computing tomography analysis. J. Cell. Plast. 45, 441 (2009).
S. Youssef, E. Maire, and R. Gaertner: Finite element modeling of the actual structure of cellular material determined by X-ray tomography. Acta Mater. 53, 719 (2005).
P. Viot, D. Bernard, and E. Plougonven: Polymeric foam under dynamic loading by the use of the microtomographic technique. J. Mater. Sci. 42, 7202 (2007).
S. McDonald, G. Dedreuil-Monet, Y. Yao, A. Alderson, and P. Withers: In situ 3D X-ray microtomography study comparing auxetic and non-auxetic polymeric foams under tension. Phys. Status Solidi B 45, 248 (2011).
A. Burteau, F. N'Guyen, J.D. Bartout, S. Forest, Y. Bienvenu, S. Saberi, and D. Nauman: Impact of material processing and deformation on cell morphology and mechanical behavior of polyurethane and nickel foams. Int. J. Solids Struct. 49, 2714 (2012).
E. Maire, P. Colombo, J. Adrien, L. Babout, and L. Biasetto: Characterisation of the morphology of cellular ceramics by 3D image processing of X-ray tomography. J. Eur. Ceram. Soc. 27, 1973 (2007).
J. Zeschky, F. Goetz-Neuhoeffer, J. Neubauer, S.H. Jason Lo, B. Kummer, M. Scheffler, and P. Greil: Preceramic polymer derived cellular ceramics. Compos. Sci. Technol. 63, 2361 (2003).
S. Meille, M. Lombardi, J. Chevalier, and L. Montanaro: Mechanical properties of porous ceramics in compression: On the transition between elastic, brittle, and cellular behavior. J. Eur. Ceram. Soc. 32, 3959 (2012).
C. D'Angelo, A. Ortona, and P. Colombo: Finite elements analysis of reticulated ceramics under compression. Acta Mater. 60, 6692 (2012).
L. Zhang, J.M.F. Ferreira, S. Olhero, L. Courtois, E. Maire, T. Zhang, and J.C. Rauhe: 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 (2012).
D. Lacroix, A. Chateau, M.P. Ginebra, and J.A. Planell: Micro-finite element models of bone tissue-engineering scaffolds. Biomaterials 27, 5326 (2006).
C. Renghini, A. Giuliani, S. Mazzoni, F. Brun, E. Larsson, F. Baino, and C. Vitale-Brovarone: Microstructural characterization and in vitro bioactivity of porous glass-ceramic scaffolds for bone regeneration by synchrotron radiation X-ray microtomography. J. Eur. Ceram. Soc. DOI: 10.1016/j.jeurceramsoc.2012.10.016.
Y. Okanoue, M. Ikeuchi, R. Takemasa, T. Tani, T. Matsumoto, M. Sakamoto, and M. Nakasu: Comparison of in vivo bioactivity and compressive strength of a novel superporous hydroxyapatite with beta-tricalcium phosphate. Arch. Orthop. Trauma Surg. 132, 1603 (2012).
G. Gioux, T.M. McCormack, and L.J. Gibson: Failure of aluminum foams under multiaxial loads. Inter. J. Mech. Sci. 42, 1097 (2000).
I. Jeon, T. Asahina, K.J. Kang, S. Im, and T.J. Lu: Finite element simulation of the plastic collapse of closed-cell aluminum foams with X-ray computed tomography. Mech. Mater. 42, 227 (2010).
N. Michailidis, F. Stergioudi, H. Omar, D. Papadopoulos, and D.N. Tsipas: Experimental and FEM analysis of the material response of porous metals imposed to mechanical loading. Colloids Surf., A 382, 124 (2011).
C. Veyhl, I.V. Belova, G.E. Murch, A. Oschner, and T. Fiedler: On the mesh dependence of non-linear mechanical finite element analysis. Finite Elem. Anal. Des. 46, 371 (2010).
T. Guillén, Q.H. Zhang, G. Tozzi, A. Orhndorf, H.J. Christ, and J. Tong: Compressive behavior of bovine cancellous bone and bone analogous materials, microCT characterisation and FE analysis. J. Mech. Behav. Biomed. Mater. 4, 1452 (2011).
O. Caty, E. Maire, S. Youssef, and R. Bouchet: Modeling the properties of closed-cell cellular materials from tomography images using finite shell elements. Acta Mater. 56, 5524 (2008).
P. Lhuissier, L. Salvo, and Y. Bréchet: Quasistatic mechanical behavior of stainless steel hollow sphere foam: Macroscopic properties and damage mechanisms followed by X-ray tomography. Mater. Lett. 63, 1113 (2009).
R. Singh, P.D. Lee, T.C. Lindley, C. Kohlhauser, C. Hellmich, M. Bram, T. Imwinkelried, and R.J. Dashwood: Characterization of the deformation behavior of intermediate porosity interconnected Ti foams using micro-computed tomography and direct finite element modeling. Acta Biomater. 6, 2342 (2010).
M. Saadatfar, F. Garcia-Moreno, S. Hutzler, A.P. Sheppard, M.A. Knackestedt, J. Banhart, and D. Weaire: Imaging of metallic foams using X-ray micro-CT. Colloids Surf., A 344, 107 (2009).
S. Van Bael, G. Kerckhofs, M. Moesen, G. Pyka, J. Schrooten, and J.P. Kruth: Micro-CT-based improvement of geometrical and mechanical controllability of selective laser melted Ti6Al4V porous structures. Mater. Sci. Eng., A 528, 7423 (2011).
F. Tariq, R. Haswell, P.D. Lee, and D.W. McComb: Characterization of hierarchical pore structures in ceramics using multiscale tomography. Acta Mater. 59, 2109 (2011).
Morph: IMorph [online]. Available on: <www.imorph.com>.
L. Brabant, J. Vlassenbroeck, Y. De Witte, V. Cnudde, M.N. Boone, J. Dewanckele, and L. Van Hoorebeke: Three-dimensional analysis of high-resolution X-ray computed tomography data with Morpho+. Microsc. Microanal. 17, 252 (2011).
H. Toda, T. Kobayashi, M. Niimoni, T. Ohgaki, M. Kobayashi, M. Kuroda, T. Akahori, K. Uesugi, K. Makii, and Y. Aruga: Quantitative assessment of microstructure and its effect on compressive behavior of aluminum foams via high resolution synchrotron X-ray tomography. Metall. Mater. Trans. A 37, 1211 (2006).
J.L. Grenestedt and K. Tanaka: Influence of cell shape variations on elastic stiffness of closed cell cellular solids. Scr. Mater. 40, 71 (1999).
N.A. Fleck, O.B. Olurin, C. Chen, and M.F. Ashby: The effect of hole size upon the strength of metallic and polymeric foams. J. Mech. Phys. Solids 49, 2015 (2001).
E. Maire, A. Fazekas, L. Salvo, R. Dendievel, S. Youssef, P. Cloetens, and J.M. Létang: X-ray tomography applied to the characterization of cellular materials. Related finite element modeling problems. Compos. Sci. Technol. 63, 2431 (2003).
C. Berre, S.L. Fok, P.M. Mummery, J. Ali, B.J. Marsden, T.J. Marrow, and G.B. Neighbour: Failure analysis of the effects of porosity in thermally oxidised nuclear graphite using finite element modeling. J. Nucl. Mater. 381, 1 (2008).
M. Saadatfar, C.H. Arns, M.A. Knackstedt, and T. Senden: Mechanical and transport properties of polymeric foams derived from 3D images. Colloids Surf., A 263, 284 (2005).
E.J. Garboczi and A.R. Day: An algorithm for computing the effective linear elastic properties of heterogeneous materials: Three-dimensional results for composites with equal phase poisson ratios. J. Mech. Phys. Solids 43, 349 (1995).
C.H. Arns, M.A. Knackstedt, W. Val Pinczewski, and E.J. Garboczi: Computation of linear elastic properties from microtomographic images: Methodology and agreement between theory and experiment. Geophysics 67, 1396 (2002).
T. Fiedler, S.M.H. Hosseini, I.V. Belova, G.E. Murch, and A. Ochsner: A refined finite element analysis on the thermal conductivity of perforated hollow sphere structures. Comp. Mater. Sci. 47, 314 (2009).
A.P. Roberts and E.J. Garboczi: Elastic moduli of model random three-dimensional closed-cell cellular solids. Acta Mater. 49, 189 (2001).
J. Escoda, F. Willot, D. Jeulin, J. Sanahuja, and C. Toulemonde: Estimation of local stresses and elastic properties of a mortar sample by FFT computation of fields on a 3D image. Cem. Concr. Res. 41, 542 (2011).
J.A. Elliott, A.H. Windle, J.R. Hobdell, G. Eeckhaut, R.J. Oldman, W. Ludwig, E. Boller, P. Cloetens, and J. Baruchel: In-situ deformation of an open-cell flexible polyurethane foam characterized by 3D computed tomography. J. Mater. Sci. 37, 1547 (2002).
D. Ulrich, B. Van Rietbergen, H. Weinans, and P. Rüegsegger: Finite element analysis of trabecular bone structure: A comparison of image-based meshing techniques. J. Biomech. 31, 1187 (1998).
M. Vesenjak, C. Veyhl, and T. Fiedler: Analysis of anisotropy and strain rate sensitivity of open-cell metal foam. Mater. Sci. Eng., A 541, 105 (2012).
V. Marcadon, C. Davoine, B. Passilly, D. Boivin, F. Popoff, A. Rafray, and S. Kruch: Mechanical behavior of hollow-tube stackings: Experimental characterization and modeling of the role of their constitutive material behavior. Acta Mater. 60, 5626, (2012).
C. Sandino, J.A. Planell, and D. Lacroix: A finite element study of mechanical stimuli in scaffolds for bone tissue engineering. J. Biomech. 41, 1005 (2008).
C. Barbier, R. Dendievel, and D. Rodney: Numerical study of 3D-compressions of entangled materials. Comp. Mater. Sci. 45, 593 (2009).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Petit, C., Meille, S. & Maire, E. Cellular solids studied by x-ray tomography and finite element modeling–a review. Journal of Materials Research 28, 2191–2201 (2013). https://doi.org/10.1557/jmr.2013.97
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1557/jmr.2013.97