Deformation of granular texture media studied by X-ray CT & 3D DIC at the continuous and microstructure scales

Transcription

1 Deformation of granular texture media studied by X-ray CT & 3D DIC at the continuous and microstructure scales N. Lenoir, S.A. Hall, J. Desrues, G. Viggiani and P. Bésuelle (Laboratoire 3S-R) Michel Bornert and Yannick Pannier (LMS)

2 Outline 1 - Background and motivations 2 - Experiment 3 Classic (continuum) DIC approach 4 - Discrete DIC approach 5 - Conclusions & perspectives

3 Outline 1 - Background and motivations 2 - Experiment 3 Classic (continuum) DIC approach 4 - Discrete DIC approach 5 - Conclusions & perspectives

4 Background and motivations Study of the strain localisation in geomaterials Ireland San Andreas Triaxial (J. Desrues) Application fields: Rock fracturation: permeability evolution in reservoirs Underground radioactive waste disposal CO 2 storage etc

5 Background and motivations Why in-situ tomography and DIC? In conventional material testing specimen response is characterized only globally BUT once it s localised need to explore the full 3D field of deformation in-situ X-ray CT Only X-ray CT can be not enough need of Digital Image Correlation

6 Background and motivations ~65 mm 2 images of specimen at different loading (2D - photos of surface / 3D - tomograms) Vector-displacement field with sub-pixel accuracy ([dx, dy] / [dx, dy, dz]) x-displacement 8 Number of pixels 0 z-displacement 0-8 Number of pixels Search in 2D/3D for best correlation displacement vector (integer - pixel) Continuum hypothesis Sub-pixel refinement strain analysis (ε ij ) Max. shear strain Strain in-house codes TomoWarp / PhotoWarp (3D/2D) developed by S.A Hall (Laboratoire 3S-R)

7 Background and motivations Why in-situ tomography and DIC? In conventional material testing specimen response is characterized only globally BUT once it s localised need to explore the full 3D field of deformation in-situ X-ray CT Only X-ray CT can be not enough need of Digital Image Correlation Works well on continuous media Deviateur (MPa) Déformation axiale Shear strain X-ray CT Example of a clayey rock Lenoir et al. (2007)

8 Background and motivations And for granular materials?? If the granular material is seen as a continuous media, YES Triaxial test on Yamazuna sand Dry, undrained, 50kPa, d 50 =0.5mm Spatial resolution: 73x73x300µm A-B B-C C-D Incremental shear strain fields Force (kgf) 1 B A kPa 4 C D 50kPa Initial Displacement (mm) 50 mm X-ray CT at peak If the granular material is seen as a discrete media,???????

9 Objectives of this study Studying experimentally geomaterials as materials with a microstructure from diffuse to localized deformation i.e study the texture (#grains and their arrangement) and its evolution Imaging material evolution and deformation processes with grainscale resolution for a sand undergoing triaxial compression Combining 3D in-situ synchrotron x-ray microtomography 3D-volumetric digital image correlation (DIC) Continuum approach (strain localisation) Discrete approach (full 3D grain kinematics) Within the MicroModex project, a project funded by the National french Agency for Research (ANR) project n ANR05-BLAN-0192

10 Previously Some studies exist for characterizing particles kinematics in 3D with in situ X-ray CT experiment BUT on man-made materials Alshibli et al. (2006) Chang et al. (2003) And for real granular material like sand?

11 Previously 2D-DIC (a) (c) (b) (d) Matshushima et al. (2006) Due to some error in grain identification process, however, it is in fact difficult to obtain the perfect correspondence between the different stages. It is therefore necessary to develop some additional specific algorithms to overcome this problem. (Matshushima et al. 2006) Need to develop specific method for real particles

12 Outline 1 - Background and motivations 2 - Experiment 3 - Classic/continuum DIC approach 4 - Discrete DIC approach 5 - Conclusions & perspectives

13 Experimental set-up Triaxial set-up specifically designed for performing in situ tests on a synchrotron beamline. Experiments were carried out at the highenergy beamline ID15A at ESRF, Grenoble (European Synchrotron Radiation Facility) Key advantages: Short scanning time High resolution Acquisition of entire specimen took less than 12 min (4 scans of overlapping vertical sections) Voxel size in the reconstructed volume is 14 x 14 x 14 µm 3 Typical image is 1020x1020x1570 voxels

14 Experimental set-up Viggiani et al.(2004) ; Lenoir et al. (2007) in situ µtomography triaxial system X-ray beam Displacement load Pore pressure Sample 11mm h22mm Detector Confinement cell in plexi, capacity 1MPa Axial loading, 7.5kN, 1µm/min Drained/undrained conditions

15 Experiment on Hostun sand (S28) Dry triaxial test, loose conditions (e 0 =0.95) P confinement = 100 kpa Fine-grained, angular siliceous sand d µm Sample dimensions: Ø11 x h22 mm X-ray tomography scans: 1-7 Spatial resolution : 14 x 14 x 14 µm 3 Mean grain size 20 voxels Volume of a grain 5500 voxels Total number of grains Small but remains mechanically pertinent

16 q (kpa) Experiment on Hostun sand (S28) Strain

17 Outline 1 - Background and motivations 2 - Experiment 3 Classic (continuum) DIC approach 4 - Discrete DIC approach 5 - Conclusions & perspectives

18 Classic 3D-DIC (continuum approach) Does the classic (i.e.continuum approach) 3D-DIC work on a granular material seen as discrete? 3D-DIC spacing of DIC grid = 20 voxels correlation domain = 20 voxels 3 mean grain size Analysis on the entire specimen in 3D Incremental analysis look at deformation at different stages of the test and thus identify development of strain localization Results presented for just a vertical slice through the 3D volume, perpendicular to the evolving band

19 3D-DIC displacement field q (kpa) Strain U x U y U z Even under a continuum assumption, 3D volumetric DIC works well on granular materials!! Y X Z

20 q (kpa) 3D-DIC strain field Strain Before peak - distributed localisations Begins to organise in 4-5 and definitely localising in 5-6 (before peak) Non-uniformity of strain in the band Need to go to the grain scale Y Z X

21 Outline 1 - Background and motivations 2 - Experiment 3 Classic (continuum) DIC approach 4 - Discrete DIC approach 5 - Conclusions & perspectives

22 Discrete 3D DIC Classic DIC initial estimate of [dx,dy,dz] for each grain Discrete DIC Image segmentation grain-mask to define grain-shape correlation domains (3 voxels expansion to capture grain boundary) - Grain shape correlation domain centred on each grain (from ) - Initial estimate of displacements from classic DIC results (from ) sub-voxel refinement (6 parameters: 3 displ. + 3 rotations) full grain kinematics for each grain ( X ) X T( X ) R. ( X X ) Φ =

23 Segmentation Segmentation by 3D watershed method implemented in the software Visilog (NOESIS) Number of grains in whole specimen: # Typical volume of one grain: # 5500 voxels CT image Segmentation Segmented image

24 Discrete 3D DIC Classic DIC initial estimate of [dx,dy,dz] for each grain Discrete DIC Image segmentation grain-mask to define grain-shape correlation domains (3 voxels expansion to capture grain boundary) - Grain shape correlation domain centred on each grain (from ) - Initial estimate of displacements from classic DIC results (from ) sub-voxel refinement (6 parameters: 3 displ. + 3 rotations) full grain kinematics for each grain ( X ) X T( X ) R. ( X X ) Φ =

25 Discrete 3D DIC : first results - Analysis of 2 large increments : step 1-5 and 1-7 q (kpa) - Work done on the medium part of the specimen (half of the specimen volume) - 850x850x795 voxels - > grains - All results are presented on the mask provided by the segmentation of the specimen image at the initial step (step 1) Strain Y Z X

26 3D grain rotation and displacement field (Results filtered to remove grains with wrong large rotation angles) Step 1 5 Y X Grain rotation (radians) reconstructed displacement field dz (# voxels) Z

27 3D grain displacement field Step 1 5 Y X reconstructed displacement field dx (# voxels) reconstructed displacement field dy (# voxels) Z (Results filtered to remove grains with wrong large rotation angles)

28 Grain contact kinematics Continuity of displacement Discontinuity of displacement analysis is ongoing reconstructed displacement field dz (# voxels)

29 Grain rotations Total grain rotation angles obtained by discrete approach before and after peak (radians) large rotations after peak i.e. when the shear band fully develops

30 Comparison continuum/discrete Grain rotation angle obtained by discrete approach Shear strain obtained by continuum approach (rad) Zone analyzed by discrete approach Main rotation after peak i.e. when the shear band is fully developed Number of grains whithin the shear band in accordance with previous works

31 Conclusions and perspectives In-situ micro-tomography of triaxial tests is a powerful tool to investigate strain localisation in geomaterials However, to really characterise strain evolution need 3Dvolumetric Digital Image Correlation techniques Have shown the faisability of fully characterizing sand texture and its evolution Able to measure large rotation Future : Complete post-traitement (grain contacts, specific area, comparaison with simulation, etc) Complete set of triaxial thanks to our new in-house x-ray tomography facility (less noisy images, different mode of sollication like confinement pressure, density, etc) Results published soon in a special issue of Géotechnique named Soil Mechanics at the Grain Scale, Desrues et al. 2010

32 In house X-ray CT scanner X-ray CT scanner specifically designed for our 2 main objectives: multiscale and in situ experiment Triaxial set-up ready for a complete set of tests in our in-house scanner

33 In house X-ray CT scanner Synchrotron, spatial resolution 14 µm 3 In house, spatial resolution 18 µm 3