Abstract
An incremental digital volume correlation (DVC) technique was developed to measure large nonlinear deformations on volumetric images acquired using X-ray micro-computed tomography (μ-CT). A series of bridging volumetric images are acquired during the loading of a specimen. The deformation in the neighboring images is sufficiently small to allow DVC calculation. The displacements are accumulated, and analyzed to determine their gradients for deformation measurements. The technique was applied for observation of internal deformations of Polymethacrylimide (PMI) foam, polymer bonded sugar (PBS), and granular materials in compression experiencing large nonlinear deformations. When PMI foam underwent compression, 17 states of the PMI were captured and large nonlinear deformations were observed. The PBS cylindrical specimen, in which sugar grains are embedded in hydroxylterminated polybutadiene (HTPB) binder matrix, was compressed up to 32 % of compressive strain without confinement. The debonding evolution was observed and discussed. On granular materials, a methodology was developed to determine for the force chains. These applications demonstrate that incremental DVC is a powerful technique for linking the microstructure with macroscopic mechanical behavior.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
B.K. Bay, T.S. Smith, D.P. Fyhrie, M. Saad, Digital volume correlation: three-dimensional strain mapping using X-ray tomography. Exp. Mech. 39(3), 217–226 (1999)
N. Lenoir, M. Bornert, J. Desrues, P. Bésuelle, G. Viggiani, Volumetric digital image correlation applied to X-ray microtomography images from triaxial compression tests on argillaceous rock. Strain 43(3), 193–205 (2007)
L. Liu, E.F. Morgan, Accuracy and precision of digital volume correlation in quantifying displacements and strains in trabecular bone. J. Biomech. 40(15), 3516–3520 (2007)
T.S. Smith, B.K. Bay, M.M. Rashid, Digital volume correlation including rotational degrees of freedom during minimization. Exp. Mech. 42(3), 272–278 (2002)
R. Zauel, Y.N. Yeni, B.K. Bay, X.N. Dong, D.P. Fyhrie, Comparison of the linear finite element prediction of deformation and strain of human cancellous bone to 3D digital volume correlation measurements. J. Biomech. Eng.Trans. ASME 128(1), 1–6 (2006)
O. Jirousek, I. Jandejsek, D. Vavrik, Evaluation of strain field in microstructures using micro-CT and digital volume correlation. J. Instrum. 6, C01039 (2011)
S.A. Maskarinec, C. Franck, D.A. Tirrell, G. Ravichandran, Quantifying cellular traction forces in three dimensions. Proc. Natl. Acad. Sci. 106(52), 22108 (2009)
C. Franck, S. Hong, S.A. Maskarinec, D.A. Tirrell, G. Ravichandran, Three-dimensional full-field measurements of large deformations in soft materials using confocal microscopy and digital volume correlation. Exp. Mech. 47(3), 427–438 (2007)
F. Forsberg, R. Mooser, M. Arnold, E. Hack, P. Wyss, 3D micro-scale deformations of wood in bending: synchrotron radiation mu CT data analyzed with digital volume correlation. J. Struct. Biol. 164(3), 255–262 (2008)
A. Germaneau, P. Doumalin, J.C. Dupre, Comparison between X-ray micro-computed tomography and optical scanning tomography for full 3D strain measurement by digital volume correlation. NDT & E Int. 41(6), 407–415 (2008)
F. Forsberg, C.R. Siviour, 3D deformation and strain analysis in compacted sugar using x-ray microtomography and digital volume correlation. Meas. Sci. Technol. 20(9), 095703 (2009)
S. Roux, F. Hild, P. Viot, D. Bernard, Three-dimensional image correlation from X-ray computed tomography of solid foam. Compos. A: Appl. Sci. Manuf. 39(8), 1253–1265 (2008)
F. Forsberg, M. Sjodahl, R. Mooser, E. Hack, P. Wyss, Full three-dimensional strain measurements on wood exposed to three-point bending: analysis by use of digital volume correlation applied to synchrotron radiation micro-computed tomography image data. Strain 46(1), 47–60 (2010)
Z. Hu, H. Luo, W. Young, H. Lu, Incremental digital volume correlation for large deformation measurement of PMI foam in compression, in ASME 2012 International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers, Houston, TX, 2012
Z. Hu, H. Luo, H. Lu, Observation of the Microstructural Evolution in a Structural Polymeric Foam Using Incremental Digital Volume Correlation, in Advancement of Optical Methods in Experimental Mechanics, ed. by H. Jin et al., vol. 3 (Springer, Cham, 2014), pp. 159–166
S. Hall, M. Bornert, J. Desrues, Y. Pannier, N. Lenoir, G. Viggiani, P. Bésuelle, Discrete and continuum analysis of localised deformation in sand using X-ray mu CT and volumetric digital image correlation. Geotechnique 60(5), 315–322 (2010)
Z. Hu, Y. Du, H. Luo, B. Zhong, H. Lu, Internal deformation measurement and force chain characterization of mason sand under confined compression using incremental digital volume correlation. Exp. Mech. 54(9), 1575–1586 (2014)
Z. Hu, H. Luo, S.G. Bardenhagen, C.R. Siviour, R.W. Armstrong, H. Lu, Internal deformation measurement of polymer bonded sugar in compression by digital volume correlation of in-situ tomography. Exp. Mech. 55(1), 289–300 (2015)
J. Rannou, N. Limodin, J. Réthoré, A. Gravouil, W. Ludwig, M.C. Baïetto-Dubourg, J.Y. Buffière, A. Combescure, F. Hild, S. Roux, Three dimensional experimental and numerical multiscale analysis of a fatigue crack. Comput. Methods Appl. Mech. Eng. 199(21–22), 1307–1325 (2010)
J. Carroll, C. Efstathiou, J. Lambros, H. Sehitoglu, B. Hauber, S. Spottswood, R. Chona, Investigation of fatigue crack closure using multiscale image correlation experiments. Eng. Fract. Mech. 76(15), 2384–2398 (2009)
B.K. Bay, Methods and applications of digital volume correlation. J. Strain Anal. Eng. Des. 43(8), 745–760 (2008)
E. Verhulp, B. Rietbergen, R. Huiskes, A three-dimensional digital image correlation technique for strain measurements in microstructures. J. Biomech. 37(9), 1313–1320 (2004)
J. Rethore, S. Roux, F. Hild, From pictures to extended finite elements: extended digital image correlation (X-DIC). Compt. Rendus Mec. 335(3), 131–137 (2007)
J. Rethore, J.P. Tinnes, S. Roux, J.Y. Buffiere, F. Hild, Extended three-dimensional digital image correlation (X3D-DIC). Compt. Rendus Mec. 336(8), 643–649 (2008)
H. Leclerc, J.N. Perie, S. Roux, F. Hild, Voxel-scale digital volume correlation. Exp. Mech. 51(4), 479–490 (2011)
K. Haldrup, S. Nielsen, L. Mishnaevsky Jr, F. Beckmann, J. A. Wert, 3-dimensional strain fields from tomographic measurements. Proc. SPIE 6318, Developments in X-Ray Tomography V, 63181B (2006). doi: 10.1117/12.679043
M. Kobayashi, H. Toda, Y. Kawai, T. Ohgaki, K. Uesugi, D.S. Wilkinson, T. Kobayashi, Y. Aoki, M. Nakazawa, High-density three-dimensional mapping of internal strain by tracking microstructural features. Acta Mater. 56(10), 2167–2181 (2008)
M. Gates, J. Lambros, M.T. Heath, Towards high performance digital volume correlation. Exp. Mech. 51(4), 491–507 (2011)
M. Gates, M.T. Heath, J. Lambros, High-performance hybrid CPU and GPU parallel algorithm for digital volume correlation. Int. J. High Perform. Comput. Appl. 29, 92–106 (2014). doi: 1094342013518807
Z. Hu, H. Xie, H. Lu, J. Gao, An approach to running digital volume correlation on personal computer, in 16th International Conference on Experimental Mechanics, Cambridge, UK, 2014
M. Anwander, B.G. Zagar, B. Weiss, H. Weiss, Noncontacting strain measurements at high temperatures by the digital laser speckle technique. Exp. Mech. 40(1), 98–105 (2000)
B. Grant, H. Stone, P. Withers, M. Preuss, High-temperature strain field measurement using digital image correlation. J. Strain Anal. Eng. Des. 44(4), 263 (2009)
R. Keys, Cubic convolution interpolation for digital image processing. IEEE Trans. Acoust. Speech Signal Process. 29(6), 1153–1160 (1981)
E.A. Flores-Johnson, Q.M. Li, R.A.W. Mines, Degradation of elastic modulus of progressively crushable foams in uniaxial compression. J. Cell. Plast. 44(5), 415–434 (2008)
L. Babout, W. Ludwig, E. Maire, J.Y. Buffière, Damage assessment in metallic structural materials using high resolution synchrotron X-ray tomography. Nucl. Instrum. Methods Phys. Res., Sect. B 200, 303–307 (2003)
J.Y. Buffiere, E. Ferrie, H. Proudhon, W. Ludwig, Three-dimensional visualisation of fatigue cracks in metals using high resolution synchrotron X-ray micro-tomography. Mater. Sci. Technol. 22(9), 1019–1024 (2006)
M.A. Dudek, L. Hunter, S. Kranz, J.J. Williams, S.H. Lau, N. Chawla, Three-dimensional (3D) visualization of reflow porosity and modeling of deformation in Pb-free solder joints. Mater. Charact. 61(4), 433–439 (2010)
N. Daphalapurkar, J. Hanan, N. Phelps, H. Bale, H. Lu, Tomography and simulation of microstructure evolution of a closed-cell polymer foam in compression. Mech. Adv. Mater. Struct. 15(8), 594–611 (2008)
A. Sassov, E. Buelens, Micro-CT for Polymers and Composite Materials, in Functional Materials, ed. by K. Grassie, E. Teuckhoff, G. Wegner, J. Haußelt, H. Hanselka (Wiley, Weinheim, 2006), pp. 374–377
B.M. Patterson, K. Henderson, Z. Smith, D. Zhang, P. Giguere, Applications of micro-CT to in-situ foam compression and numerical modeling. Microsc. Anal. S4–7 (2012)
P.R. Laity, C.R. Siviour, P.D. Church, W.G. Proud, High strain rate characterisation of a polymer bonded sugar, in Shock Compression of Condensed Matter—2005, Pts 1 and 2, ed. by M.D. Furnish, et al.(2006), pp. 905–908
C. Siviour, P. Laity, W. Proud, J. Field, D. Porter, P. Church, P. Gould, W. Huntingdon-Thresher, High strain rate properties of a polymer-bonded sugar: their dependence on applied and internal constraints. Proc. R. Soc. A Math. Phys. Eng. Sci. 464(2093), 1229–1255 (2008)
J. Desrues, R. Chambon, M. Mokni, F. Mazerolle, Void ratio evolution inside shear bands in triaxial sand specimens studied by computed tomography. Geotechnique 46(3), 529–546 (1996)
R. Al-Raoush, K.A. Alshibli, Distribution of local void ratio in porous media systems from 3D X-ray microtomography images. Phys. A Stat. Mech. Appl. 361(2), 441–456 (2006)
J. Desrues, G. Viggiani, Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry. Int. J. Numer. Anal. Methods Geomech. 28(4), 279–321 (2004)
J. Desrues, Tracking strain localization in geomaterials using computerized tomography. in X-ray CT for Geomaterials (2004), pp. 15–41
K. Alshibli, A. Hasan, Spatial variation of void ratio and shear band thickness in sand using X-ray computed tomography. Geotechnique 58(4), 249–257 (2008)
K.A. Alshibli, S. Sture, N.C. Costes, M.L. Frank, M.R. Lankton, S.N. Batiste, R.A. Swanson, Assessment of localized deformations in sand using X-ray computed tomography. ASTM Geotech. Test. J. 23(3), 274–299 (2000)
J. Otani, T. Mukunoki, Y. Obara, Characterization of failure in sand under triaxial compression using an industrial X-ray CT scanner. Int. J. Phys. Model. Geotech. 2(1), 15–22 (2002)
P. Bari, H. Bale, J.C. Hanan, Observing 3-D deformation of silica sand under in-situ quasi-static compression. Mech. Mater. 54, 84–90 (2012)
S. Hall, N. Lenoir, G. Viggiani, J. Desrues, P. Bésuelle, Strain localisation in sand under triaxial loading: characterisation by x-ray micro tomography and 3D digital image correlation, in Proceedings of the 1st Int. Symp. on Computational Geomechanics (ComGeo 1), 2009
J.F. Peters, M. Muthuswamy, J. Wibowo, A. Tordesillas, Characterization of force chains in granular material. Phys. Rev. E 72(4), 041307 (2005)
Acknowledgements
HL acknowledges the support of ONR MURI 0014-11-1-0691, AFOSR FA9550-14-1-0227, US Army W91CBR-13-C-0037, DOE NEUP 09-416, and NSF ECCS-1459044 and CMMI-1031829. HL also thanks the Louis A. Beecherl Chair for additional support.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 The Society for Experimental Mechanics, Inc.
About this paper
Cite this paper
Hu, Z., Luo, H., Du, Y., Lu, H. (2016). Correlation of Microscale Deformations to Macroscopic Mechanical Behavior Using Incremental Digital Volume Correlation of In-Situ Tomography. In: Jin, H., Yoshida, S., Lamberti, L., Lin, MT. (eds) Advancement of Optical Methods in Experimental Mechanics, Volume 3. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-22446-6_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-22446-6_16
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-22445-9
Online ISBN: 978-3-319-22446-6
eBook Packages: EngineeringEngineering (R0)