Abstract
The mechanical behavior of granular materials such as sand is not well understood due to its complex solid/fluid-like behavior. In this paper, Mason sand was investigated to determine the grain-level Young’s modulus and hardness by nanoindentation, and the mesoscale behavior through X-ray tomography of a sample in compression. Mason sand specimen was confined in a polycarbonate tube and compressed in the axial direction at ten axial compressive strains up to -21.8 % while its microstructures were observed. The mesoscale deformations were determined by incremental digital volume correlation of reconstructed volumetric images. A procedure for characterization of internal force chains is developed. The minor principal strains and their principal directions were obtained and used to determine the formation and evolution of force chains.
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Hagerty MM, Hite DR, Ullrich CR, Hagerty DJ (1993) One-dimensional high-pressure compression of granular media. J Geotech Eng-ASCE 119:1–18
Yamamuro JA, Bopp PA, Lade PV (1996) One-dimensional compression of sands at high pressures. J Geotech Eng-ASCE 122:147–154
Vallejos JVJ (2008) Hydrostatic compression model for sandy soils. Can Geotech J 45:1169–1179
Rechenmacher AL, Finno RJ (2004) Digital image correlation to evaluate shear banding in dilative sands. Geotech Test J 27:13–22
Rechenmacher A, Abedi S, Chupin O, Orlando A (2011) Characterization of mesoscale instabilities in localized granular shear using digital image correlation. Acta Geotech 6:205–217
Arthur J, Menzies B (1972) Inherent anisotropy in a sand. Geotechnique 22:115–128
Lade PV, Prabucki M-J (1995) Softening and preshearing effects in sand. Soils Found 35:93–104
Wang Q, Lade PV (2001) Shear banding in true triaxial tests and its effect on failure in sand. J Eng Mech-ASCE 127:754–761
Pethica JB, Hutchings R, Oliver WC (1983) Hardness measurement at penetration depths as small as 20-nm. Philos Mag A 48:593–606
Pethica JB, Oliver WC (1987) Tip surface interactions in STM and AFM. Phys Scripta T19A:61–66
Oliver WC, Pharr GM (1992) An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments. J Mater Res 7:1564–1583
Liu Y, Varghese S, Ma J, Yoshino M, Lu H, Komanduri R (2008) Orientation effects in nanoindentation of single crystal copper. Int J Plast 24:1990–2015
Louis L, Wong T-F, Baud P (2007) Imaging strain localization by X-ray radiography and digital image correlation: Deformation bands in Rothbach sandstone. J Struct Geol 29:129–140
Daphalapurkar NP, Wang F, Fu B, Lu H, Komanduri R (2011) Determination of mechanical properties of sand grains by nanoindentation. Exp Mech 51:719–728
Wang F, Fu B, Luo H, Staggs S, Mirshams RA, Cooper WL, Park SY, Kim MJ, Hartley C and Lu H (2014) Characterization of the grain-level mechanical behavior of Eglin sand by nanoindentation. Exp Mech 54:871-884
Luo H, Cooper WL, Lu H (2014) Effects of particle size and moisture on the compressive behavior of dense Eglin sand under confinement at high strain rates. International Journal of Impact Engineering 65:40–55
Desrues J, Chambon R, Mokni M, Mazerolle F (1996) Void ratio evolution inside shear bands in triaxial sand specimens studied by computed tomography. Geotechnique 46:529–546
Al-Raoush R, Alshibli KA (2006) Distribution of local void ratio in porous media systems from 3D X-ray microtomography images. Physica A 361:441–456
Desrues J, Viggiani G (2004) Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry. Int J Numer Anal Met 28:279–321
Desrues J (2004) Tracking strain localization in geomaterials using computerized tomography, in: X-ray CT for Geomaterials, Otani J, Obara Y Eds, Balkema, pp 15–41
Alshibli K, Hasan A (2008) Spatial variation of void ratio and shear band thickness in sand using X-ray computed tomography. Geotechnique 58:249–257
Alshibli KA, Sture S, Costes NC, Frank ML, Lankton MR, Batiste SN, Swanson RA (2000) Assessment of localized deformations in sand using X-ray computed tomography. Geotech Test J 23:274–299
Otani J, Mukunoki T, Obara Y (2002) Characterization of failure in sand under triaxial compression using an industrial X-ray CT scanner. Int J Phys Model Geotech 2:15–22
Bari P, Bale H, Hanan JC (2012) Observing 3-D deformation of silica sand under in-situ quasi-static compression. Mech Mater 54:84–90
Hall S, Lenoir N, Viggiani G, Desrues J and Bésuelle P (2009) Strain localisation in sand under triaxial loading: characterisation by x-ray micro tomography and 3D digital image correlation. Proc 1st Int Symp On Compu Geomech (ComGeo 1), pp 239–247
Hall S, Bornert M, Desrues J, Pannier Y, Lenoir N, Viggiani G, Bésuelle P (2010) Discrete and continuum analysis of localised deformation in sand using X-ray μCT and volumetric digital image correlation. Geotechnique 60:315–322
Matsushima T, Uesugi K, Nakano T, Tsuchiyama A (2006) Visualization of grain motion inside a triaxial specimen by micro X-ray CT at SPring-8, in Advances in X-ray Tomography for Geomaterials (eds Desrues J, Viggiani G, Bésuelle P) ISTE. London UK ch 24:35–52
Matsushima T, Katagiri J, Uesugi K, Nakano T, Tsuchiyama A (2007) Micro X-Ray Ct At Spring-8 For Granular Mechanics in: Soil Stress–strain Behavior: Measurement, Modeling and Analysis (Solid Mechanics and Its Applications), Ling H, Callisto L. Leshchinsky D and Koseki J Eds, Netherlands, pp 225–234
Peters JF, Muthuswamy M, Wibowo J, Tordesillas A (2005) Characterization of force chains in granular material. Phys Rev E 72:041307
Azéma E, Radjaï F (2012) Force chains and contact network topology in sheared packings of elongated particles. Phys Rev E 85:031303
Tordesillas A, Walker DM, Lin Q (2010) Force cycles and force chains. Phy Rev E 81:011302
Hartley RR, Behringer RP (2003) Logarithmic rate dependence of force networks in sheared granular materials. Nature 421:928–931
Rechenmacher A, Abedi S, Chupin O (2010) Evolution of force chains in shear bands in sands. Geotechnique 60:343–351
Majmudar TS, Behringer RP (2005) Contact force measurements and stress-induced anisotropy in granular materials. Nature 435:1079–1082
Sutton MA, Wolters WJ, Peters WH, Ranson WF, McNeill SR (1983) Determination of displacements using an improved digital correlation method. Image Vision Comput 1:133–139
Lu H, Cary P (2000) Deformation measurements by digital image correlation: Implementation of a second-order displacement gradient. Exp Mech 40:393–400
Hu Z, Luo H, Du Y, Lu H (2013) Fluorescent stereo microscopy for 3D surface profilometry and deformation mapping. Optical Express 21:11808–11818
Bay BK, Smith TS, Fyhrie DP, Saad M (1999) Digital volume correlation: three-dimensional strain mapping using X-ray tomography. Exp Mech 39:217–226
Lenoir N, Bornert M, Desrues J, Bésuelle P, Viggiani G (2007) Volumetric digital image correlation applied to X-ray microtomography images from triaxial compression tests on argillaceous rock. Strain 43:193–205
Liu L, Morgan EF (2007) Accuracy and precision of digital volume correlation in quantifying displacements and strains in trabecular bone. J Biomech 40:3516–3520
Smith TS, Bay BK, Rashid MM (2002) Digital volume correlation including rotational degrees of freedom during minimization. Exp Mech 42:272–278
Zauel R, Yeni YN, Bay BK, Dong XN, Fyhrie DP (2006) Comparison of the linear finite element prediction of deformation and strain of human cancellous bone to 3D digital volume correlation measurements. J Biomech Eng-T Asme 128:1–6
Forsberg F, Mooser R, Arnold M, Hack E, Wyss P (2008) 3D micro-scale deformations of wood in bending: Synchrotron radiation mu CT data analyzed with digital volume correlation. J Struct Biol 164:255–262
Forsberg F, Sjodahl M, Mooser R, Hack E, Wyss P (2010) 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 46:47–60
Roux S, Hild F, Viot P, Bernard D (2008) Three-dimensional image correlation from X-ray computed tomography of solid foam. Compos Part A-Appl S 39:1253–1265
Hu Z, Luo H, Young W, Lu H (2012) Incremental digital volume correlation for large deformation measurement of PMI foam in compression ASME 2012 Int Mech Eng Cong Exp Houston. TX 721–726
Hu Z, Luo H and Lu H (2014) Observation of the microstructural evolution in a structural polymeric foam using incremental digital volume correlation in: Jin H, Sciammarella C, Yoshida S and Lamberti L (eds) Advancement of Optical Methods in Experimental Mechanics, Volume 3 Springer International Publishing, pp 159–166
Forsberg F and Siviour CR (2009) 3D deformation and strain analysis in compacted sugar using x-ray microtomography and digital volume correlation. Meas Sci Technol 20Artn 095703
Hu Z, Luo H, Bardenhagen SG, Siviour CR, Armstrong RW, Lu H (2014) Internal deformation measurement of polymer bonded sugar in compression by digital volume correlation of in-situ tomography. Exp Mech. doi:10.1007/s11340-014-9856-4 (online)
Bruck HA, McNeill SR, Sutton MA, Peters WH (1989) Digital image correlation using newton–raphson method of partial-differential correlation. Exp Mech 29:261–267
Vendroux G, Knauss WG (1998) Submicron deformation field measurements: Part 2. Improved digital image correlation. Exp Mech 38:86–92
Luu L, Wang Z, Vo M, Hoang T, Ma J (2011) Accuracy enhancement of digital image correlation with B-spline interpolation. Opt Lett 36:3070–3072
Keys R (1981) Cubic convolution interpolation for digital image processing. Acou Speec Signal Proc IEEE Tran 29:1153–1160
Gates M, Heath MT, Lambros J (2014) High-performance hybrid CPU and GPU parallel algorithm for digital volume correlation. Int J High Perform C. doi:10.1177/1094342013518807 (online)
Blatt H, Tracy RJ and Owens B (1996) Petrology-Igneous. Sedimentary, and Metamorphic: WH Freeman &Co, New York: 377–380
Meyer F (1994) Topographic distance and watershed lines. Signal Process 38:113–125
ASTM (2009) Particle-size distribution (gradation) of soils using sieve analysis ASTM committee D18 on soil and rock. ASTM International, West Conshohocken
Acknowledgments
We acknowledge the support of ONR MURI grant N00014-11-1-0691 and US Army grant W91CRB-13-C-0037. We also thank NSF CMMI-1031829 and ECCS-1307997, and Louis A. Beercherl Jr. Chair for additional support.
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Hu, Z., Du, Y., Luo, H. et al. Internal Deformation Measurement and Force Chain Characterization of Mason Sand under Confined Compression using Incremental Digital Volume Correlation. Exp Mech 54, 1575–1586 (2014). https://doi.org/10.1007/s11340-014-9915-x
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DOI: https://doi.org/10.1007/s11340-014-9915-x