Abstract
Probing the strain locally and throughout the bulk of various materials has long been of interest in Materials Science. This article presents a general methodology for assessing the plastic strain in terms of the displacement gradient tensor throughout the bulk of opaque samples. The method relies on a homogenous distribution of marker particles throughout the bulk of a sample, markers which are detected through the application of synchrotron X-ray tomography. Making use of the morphology of individual markers, motion of individual markers is tracked during deformation allowing the local displacement field to be determined throughout the bulk. The local displacement gradient tensor is derived from the displacement field. Spatial resolution is directly related to marker particle density in the sample, here 30 μm. The accuracy of the displacement gradient tensor calculation is dependent on the accuracy with which each marker position is determined and is shown to be in the range from 0.005 to 0.012.
Similar content being viewed by others
References
Sachs G, Eisbein, W (1931) Kraftbedarf und fließvorgänge beim stangenpressen. Deutsche Materialprüfungsanstalten Mitteilungen 16:67–96.
Devenpeck ML, Richmond, O (1965) Strip-drawing experiments with a sigmoidal die profile. J Eng Ind Strony 85:425–428.
Beynon JH, Sellars MC (1985) Strain distribution patterns during plane strain compression. J Test Eval 13:28–38.
Liu YL, Fischer G (1997) In situ measurement of local strain in a metal matrix composite by the object grating technique. Scr Mater 36:1187–1194.
Schroeter BM, McDowell DL (2003) Measurement of deformation fields in polycrystalline ofhc copper. Int J Plast 19:1355–1376.
Humphreys FJ, Prangnell PB, Bowen JR, Gholinia A, Harris C (1999) Developing stable fine-grain microstructures by large strain deformation. Philos Trans R Soc London A 357:1663–1681.
Jordan EH, Ochi SCU, Pease D, Budnick JI (1994) Microradiographic strain measurements using markers. Exp Mech 34:155–165.
Allais L, Bornert M, Bretheau T, Caldemaison D. (1994) Experimental characterization of the local strain field in a heterogeneous elastoplastic material. Acta metall mater 42:3865–3880.
Soppa E, Doumalin P, Binkele P, Wiesendanger T, Bornert M, Schmauder S (2001) Experimental and numerical characterization of in-plane deformation in two-phase materials. Comput Mater Sci 21:261–275.
Tanaka Y, Yang J-M, Liu YF, Kagawa Y (2007) Characterization of nanoscale deformation in a discontinuously reinforced titanium composite using afm and nanolithography. Scr Mater 56:209–212.
Crostack HA, Fischer G, Soppa E, Schmauder S, Liu YL (2001) Localization of strain in metal-matrix composites studied by a scanning electron microscope-based grating method. J Microsc 201:171–178.
Tong W (2004) Plastic surface strain mapping. Exp Mech 44:502–511.
Quinta Da Fonseca J, Mummery PM, Withers PJ (2005) Full-field strain mapping by optical correlation of micrographs acquired during deformation. J Microsc 218:9–21.
Vendroux G, Schmidt N, Knauss WG (1998) Submicron deformation field measurements: part 3. Demonstration of deformation determinations. Exp Mech 38:154–160.
Zhang N, Tong Wei (2004) An experimental study on grain deformation and interactions in an Al-0.5% Mg multicrystal. Int J Plast 20:523–542.
Kak AC, Slaney M (2001) Principles of Computerized Tomographic Imaging. Society of Industrial and Applied Mathematics.
Salvo L, Cloetens P, Maire E, Zabler S, Blandin JJ, Buffiere JY, Ludwig W, Boller E, Bellet D, Josserond C (2003) X-ray micro-tomography an attractive characterisation technique in materials science. Nucl Instrum Methods Phys Res B 200:273–286.
Schroer, CG, Cloetens P, Rivers M, Snigirev A, Takeuchi A, Yun W (2004) High-resolution 3D imaging microscopy using hard X-rays. MRS bull strony 157–165.
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.
Verhulp E, van Rietbergen B, Huiskes R (2004) A three-dimensional image correlation technique for strain measurements in microstructures. J Biomech 37:1313–1320.
McDonald SA, Schneider LCR, Cocks, ACF, Withers, PJ (2006) Particle movement during the deep penetration of a granular material studied by X-ray microtomography. Scr Mater 54:191–196.
Toda H, Sinclair I, Buffiere JY, Maire E, Khor KH, Gregson P, Kobayashi T (2004) A 3d measurement procedure for internal local crack driving forces via synchrotron X-ray radiation. Acta Mater 52:1305–1317.
Ohgaki T, Toda H, Kobayashi M, Uesugi K, Niinomi M, Akahori T, Kobayash T, Makii K, Aruga Y (2006) In situ observations of compressive behaviour of aluminium foams by local tomography using high-resolution X-rays. Philos Mag 86:4417–4438.
Yang C-Y , Fu X-Y (2004) Development and validation of a material-labeling method for powder process characterization using X-ray computed tomography. Powder Technol 146:10–19.
Nielsen SF, Poulsen HF, Beckmann F, Thorning C, Wert JA (2003) Measurements of plastic displacement gradient components in three dimensions using marker particles and synchrotron X-ray absorption microtomography. Acta Mater 51:2407–2415.
Haldrup K, Nielsen SF, Beckmann F, Wert JA (2006) Inhomogeneous plastic flow investigated by X-ray absorption micro-tomography of an aluminium alloy containing marker particles. J Microsc 222:28–35.
Haldrup K, Nielsen SF, Beckmann F, Wert JA (2005) Plastic strain measurements: from 2D to 3D. Mater Sci Technol 21:1428–1431.
Cloetens P, Ludwig W, Baruchel J, Van Dyck D, Van Landuyt J, Guigay JP, Schlenker M (1999) Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays. Appl Phys Lett 75:1912–1914.
Jeremic B, Scheuermann G, Frey J, Yang Z, Hamann B, Joy KI, Hagen H (2002) Tensor visualizations in computational geomechanics. Intl J Numer Anal Methods Geomech 26: 925–944.
Haldrup K, Beckmann F, Nielsen SF, Wert JA (2007) Experimental determination of strain partitioning among individual grains in the bulk of an aluminum multicrystal. Mater Charact. (accepted for publication).
Author information
Authors and Affiliations
Corresponding author
Additional information
The software implementation of the procedures and algorithms presented in this work has been collected to form the “3Dstrain” program package which is intended to be free for use by the scientific community. It is available at http://synchsoftware.risoe.dk under GNU General Public License.
Rights and permissions
About this article
Cite this article
Haldrup, K., Nielsen, S.F. & Wert, J.A. A General Methodology for Full-Field Plastic Strain Measurements Using X-ray Absorption Tomography and Internal Markers. Exp Mech 48, 199–211 (2008). https://doi.org/10.1007/s11340-007-9079-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11340-007-9079-z