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Identification of the local mechanical properties of an
inorganic fiber‐based material using X‐ray computed micro tomography and distinct elements method
Hauss G., Bernard D., Dedecker F., Couprie M., Meulenyzer S., Pourcel F.
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Outline
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• Fiber‐based material• Experimental settings• Image processing• Fibers labelling and contacts extraction• Distinct Element Modeling (PFC3D) • Numerical results• Conclusions and perspectives
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Fiber‐based material
• Sample shape
Sound state (25 µm/px)
D
e
D ~ 52 mme ~ 12 mm
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Fiber‐based material
• Compression test
Compressive testV = 50 µm/min
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Experimental settings
• Microtomographic apparatus
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Nanotom, Phoenix X‐Ray©GE ©
CMOS Detector2304*2304 px50 µm/px
Spinning mandrel
X‐Ray TubeW or Mo target
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Experimental settings
• In‐situ device
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Experimental settings
• Experimental settings
Z = 170 mmZD = 340 mmpxSize = 25 µmN = 2500t = 1 sU = 100 kVI = 240 µA
DetectorSource
Spinningmandrel
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Experimental settings
• Experimental process
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Image processing
• Global procedure
Data reconstruction using a Beam Hardenningcorrection
Median filter 3*3*3
Grey level normalization Thresholding
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Image processing
• Usable data setStep 01
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Image processing
• Usable data setStep 04
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Image processing
• Usable data setStep 06
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Image processing
• Usable data setStep 10
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Fibers labeling and contacts extraction
• Fibers labeling
14[1] John Chaussard, Michel Couprie, and Hugues Talbot. A discrete lambda‐medial axis. In 15th Discrete Geometry for Computer Imagery (DGCI’09), Lecture Notes in Computer Science, pages 1–12, 2009. To appear.[2] F. Chazal and A. Lieutier. The lambda medial axis. Graphical Models, 67(4) :304–331, 2005.
Elbow detection
Contacts detection3D Image (i) Skeleton (i) Fibers labeling (i)
3D Image (i+1) Skeleton (i+1)
Fibers labeling (i+1)
IDENTIFICATION ?
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Fibers identification: Image i, skeleton i
Fibers labeling and contacts extraction
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Fibers identification: Image i+1, skeleton i
Fibers labeling and contacts extraction
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Fibers labeling and contacts extraction
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Fibers identification: Intersection image i+1, skeleton i
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Fibers identifications: Labeling i+1
Fibers labeling and contacts extraction
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Node tracking: Displacement of labelized nodes
Fibers labeling and contacts extraction
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Fibers labeling and contacts extraction
• Fibers labeling Image data:‐Voxel size‐Fiber size (Vox.)‐Fiber radius (Vox.)
Skeleton data‐Fiber ID‐Upper Fiber ID‐Spline equation (3rd order)
SKELETONIZATION + IDENTIFICATION
20[1] John Chaussard, Michel Couprie, and Hugues Talbot. A discrete lambda‐medial axis. In 15th Discrete Geometry for Computer Imagery (DGCI’09), Lecture Notes in Computer Science, pages 1–12, 2009. To appear.[2] F. Chazal and A. Lieutier. The lambda medial axis. Graphical Models, 67(4) :304–331, 2005.
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Fibers labeling and contacts extraction
• Contacts extraction
Contact description‐ Contact ID‐Fiber 1 ID in contact + length of contact (S1‐S2)‐Fiber 2 ID in contact + length of contact (S’1‐S’2)
PROJECTION
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Contacts:
Surface area of intersection of 2 labelised fibers
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Distinct Element Modeling
• Fibers and contacts modeling
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Fibers = clusters of particles Inter‐ and intra‐fiber contacts
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Distinct Element Modeling
• Contacts definitions
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Parallel bond model
Incremental linear law
Intra‐fiber (2 successive particles) and detected1 inter‐fiber contacts modeling contacts bonded !
Cracks (inter‐ and intra‐fiber) and non detected2 inter‐fiber contacts modeling
PB
1 Inter‐fibers contacts detected on real image2 Inter‐fibers contacts non detected on real image
25.0_
*
)*_(*
21
21
2intra
radpbkkkkk
Rradpbkk
nn
nncontactn
part
contactn
n
0
00
si , 0 si, )(*
uuFuuuukF
nn
nnnn
1 Overlap : Overlap :
0
00
tutu
n
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Numerical results
• Assumptions and parameters to calibrate
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Modeling hypothesis
Fibers deformation rather than inter‐fibers contacts deformation (experimental observations)
K intra‐fibers < K inter‐fibers Same stiffness before and after fracture
K inter‐fibers after fracture = K intra fibers before fracture
Parameters to calibrate
Kpart K intra‐fiber
Rm intra : Intra‐fibers strengthRm inter : Inter‐fibers strength
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Numerical results
• Particle stiffness global fitting procedure (infinite strengths elastic behavior)
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Numerical compression test
Kpart = 160 kN/m
E = 56 MPa
Experimental compression test
E = 56 MPaF = 1130 N
Vertical displacement (mm)
Stre
ngth
(kN
)
Vertical displacement (mm)
Stre
ngth
(kN
)
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Numerical results
• Ultimate strength fitting procedure
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Fmax = 1100 N
Rm intra = 10 MpaRm inter = 50 Mpa
Numerical compression testExperimental compression tests
Strength vs. displacement curve
Displacement (mm)
Strength
(N)
Stre
gnth
(kN
)Displacement (mm)
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Numerical results
• Rm influences on strength‐displacement curves
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Rm intra = 40 MPaRm inter = 40 MPa Fmax = 1100 N
Rm intra = 80 MPaRm inter = 40 MPa Fmax = 1100 N
Rm intra = 40 MPaRm inter = 80 MPa Fmax = 2200 N
brittle failure
Vertical displacement (mm)
Com
pres
sive
str
engt
h (k
N)
ductile failure
Vertical displacement (mm)
Com
pres
sive
str
engt
h (k
N)
brittle failure
Vertical displacement (mm)
Com
pres
sive
str
engt
h (k
N)
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Numerical results
• Modeling of sample deformation
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Simulated fibers displacements Comparison with experimental data
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Conclusions
• Original and efficient individual fiber tracking procedure
• 3D images to Distinct Element Method data conversion
• Parameters fitting procedure for a good modeling of the macroscopic mechanical behavior
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Perspectives
• Local properties consideration– Identification of local mechanical properties around favorable cracks sites
– Local variability included to model: • Volume: Stochastic distribution of defects along fiber• Punctual: Singular defects localization
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Fiber porosity Punctual defect
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Thank you for your attention
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Conclusions
• Fitting procedures using real image data set: – Excellent modeling of the initial sample (geometry)
– Calibration of the micro mechanical parameters (considering few assumptions)
• Good modeling of the macroscopic mechanical behavior
• In the real life, high local variability of micro parameters (stiffness and strength)
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Question LAFARGE
• Qu’a‐t‐on le droit de dire sur l’échantillon ?
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Question ESIEE
• Comment est choisi le critère de taille minimale des nouvelles fibres dans la phase d’identification (diapo 18)?
• Comment la taille du contact et sa position sont elles déterminées ?
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Question ITASCA
• Pour les contacts intra‐fibre:La loi de répulsion par contact élastique linéaire est elle toujours active ?
Si tu parles du fait que 2 particules qui se chevauchent, doivent en théorie s’écarter, alors non la loi de répulsion est désactivée pour éviter ce phénomène. On base le comportement sur des lois élastiques purement incrémentales.
La loi parallel bond est elle constante lors de la déformation des fibres ?
Les propriétés locales des PB sont constantes tout au long du calcul (quelque soit la déformation). Elles dépendent par contre du type de contact inter ou intra‐fibre.
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Question ITASCA• Pour les contacts inter‐fibre:Comment est définie la loi parallel bond par rapport aux zones de contact
observées (redistribution de l’aire de contact) ?Je ne suis pas certain de bien comprendre la question. Ce qui est sur c’est que nous n’avons pas
pris en compte l’aire du contact, mais simplement la coordonnée linéique de contact le long des 2 fibres
Comment est définie la zone de contact ?Chaque fibre est représentée par son équation paramétrique. La zone de contact d’une fibre avec
ses voisines est définie sur un intervalle [T1;T2] de son équation paramètrique
Conservation du volume de recouvrement entre les deux fibres qui impose un intervalle de contact ajusté.
Ou conservation de l’abscisse curviligne du contact qui impose un nouveau volume de contact ?
On conserve l’abscisse curviligne du contact entre les 2 fibres. Aucune information sur le volume du contact n’a été intégrée !
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Question ITASCA
• Interprétation des résultats:Les rigidités locales sont elles utilisées pour remonter aux données matériau ?
Le calage des rigidités locales a permis de reproduire le comportement macroscopique du matériau (sous essai de compression). Par contre, il n’a pas été possible à ce stade de considérer des propriétés locales différentes pour reproduire les déplacements locaux des fibres
Rigidité particule Module d’Young du matériau.La conclusion est un peu rapide, car ici la rigidité des particules n’intervient que lorsque les
liaisons PB se cachent (rupture d’une fibre ou d’un contact inter‐fibres). Avant cela, le module d’Young du matériau dépend directement de la rigidité des PB inter et intra fibres.
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Numerical results
• Fitting procedure using real image data set
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Conclusion
• What has been done.• What could be done to enhance the results.
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Question LAFARGE
• Qu’a‐t‐on le droit de dire sur l’échantillon ?
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Question ESIEE
• Comment est choisi le critère de taille minimale des nouvelles fibres dans la phase d’identification (diapo 18)?
• Comment la taille du contact et sa position sont elles déterminées ?
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Question ITASCA
• Pour les contacts intra‐fibre:La loi de répulsion par contact élastique linéaire est elle toujours active ?
La loi parallel bond est elle constante lors de la déformation des fibres ?
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Question ITASCA
• Pour les contacts inter‐fibre:Comment est définie la loi parallel bond par rapport aux zones de contact observées (redistribution de l’aire de contact) ?
Comment est définie la zone de contact ?Conservation du volume de recouvrement entre les deux fibres qui impose un intervalle de contact ajusté.
Ou conservation de l’abscisse curviligne du contact qui impose un nouveau volume de contact ?
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Question ITASCA
• Interprétation des résultats:Les rigidités locales sont elles utilisées pour remonter aux données matériau ?
Rigidité particule Module d’Young du matériau.