Studying thermomechanical properties of thermostructural composites using X-ray microcomputed tomography

Studying thermomechanical properties of thermostructural composites using X-Ray

computed micro-tomography

O.Caty1, E.Rohmer1, C.Lorrette1,2, G.L.Vignoles1, G.Couégnat1, M.Charron1

- University of Bordeaux -

1 LCTS Laboratoire des Composites ThermoStructuraux

2 CEA centre de Saclay – Commissariat à l’Energie Atomique et aux Energies Alternatives

Avizo EUGM 2012 – 30 mai au 1er juin 2012 - Bordeaux

O.CATY et al. - μCT / Thermostructural composites – Avizo2012 [email protected]

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Outline • Motivation

• C/C composites– 3D images– Thermomechanical models

• Tubular shaped SiC/SiC– Image analysis– Mechanical models


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Motivation• Material : C or SiC composites

+ High temperature+ Low CTE coeff. of thermal exp.+ Mechanical properties

• Applications (highly demanding conditions)+ Nuclear power plants (fuel confinement – Tokamak plasma-facing components)

+ Aerospace technology (ArianeV boosters, Jet engine divergent, Atmospheric reentry heat shield parts, Aircraft brakes…)

• Predict thermo mechanical properties– Materials are highly structured (woven materials)– Behavior is linked to the 3D geometry

Objective : predict the material behavior


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Developed method(s)• Scan the material

– X-ray μCT– Visualisation in 3D (Avizo std.)

• Work on images– Pores and cracks : determine density,

shape and position– Matrix and fibers : determine orientation,

density, shape and pattern of the weaving– Mesh the image

• Calculate the thermomechanical behavior – Using the mesh – With elements enriched (density,

orientation… calculated on μCT images).


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C/C compositesμCT images : - Phoenix XRay – Nanotom

- Laboratory Micro/nano CT system

- Resolution : 5 μm

- Woven plies (X-Y directions)

- Stacked and stitched in Z direction

- > Complex geometry :

- Tangled phases (yarn, matrix, pores) hard to label

X-Z 3D

X-Y Y-Z


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C/C compositesSolution :

- Use directly the voxel as the structural element (Finite element for calculation)

- Enrich the elements by the direction of fibers and the density (both measured on the image)

μCT 3D image… … is meshed using the voxel as FE…

…FE density…

… and orientations enrich the model…

…calculation of thermal dilation

- Avizo for image visualization (3D image, density, orientations)- ImageJ for data translation- Zebulon or Coda for FE calculation


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C/C compositesMeasure the density

Porosity

Porosity & material

MaterialMaterials properties

Relative density


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C/C compositesMeasure the fiber directions :

- Image structure tensor

- Image Hessian matrix

2 2 2

2

2 2 2

2

2 2 2

2

e

I I Ix x y x zI I IH

y x y y zI I I

z x z y z

- Where I is the Grey level of the pixel

- x, y and z are the image direction

- Derivatives calculated by centred finite difference method – ie :

- Mask applied

2

2

( , ) ( 1, ) 2 ( , ) ( 1, )I x y I x y I x y I x yx

- Calculate eigenvalues and eigenvectors of the Hessian matrix

- The eigenvector associated with the minimum egeinvalue

- > represents the minimum grey level variation

- > material (fibers) direction.


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C/C compositesMeasurement of the fiber directions :

x

y

z

z

y

x

X orientation

Z orientation

Y orientation


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C/C compositesCalculation - T=1500°C:

Mesh

Density

Directions - Calculated global thermal dilation : εyy= 0.7%

- Visualization of the effect on the structure : local variations & stresses


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C/C compositesConclusion

- Complex architecture -> use voxel as finite element

- Enrich elements with measures on images (direction and density)

- Avizo very useful for 3D visualization (grey scale images, combination of orientation field images)

Next :

tubular shaped SiC/SiC- More easy to label

- Unstructured meshes based on image segmentation (reconstruction or direct mesh)


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Tubular shaped SiC/SiC

- Laboratory Micro/nano CT system

- Resolution : 10 μm

X-Y 3D - int 3D - ext

X-Z

- Braided tubular fabrics

- 2 stacks- Dry and infiltrated materials available- Phases and weaving relatively easy to analyze


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Tubular shaped SiC/SiC1st Solution :

- Polar to Cartesian transformation

- Analyze the weaving pattern by locating and marking the path

- Encode the path to reconstruct a finite element model


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Tubular shaped SiC/SiC1st Solution :

- Polar to Cartesian transformation

- Analyze the weaving pattern by locating and marking the path

- Encode the path to reconstruct a finite element model

Color = orientation


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Tubular shaped SiC/SiC2nd solution :

- Mesh the image directly with Avizo (unstructured tetrahedrons)

- Enrich the elements with measurements on images (density & orientations)

μCT 3D image… … is meshed using Avizo…

…orientations…

… and density enrich the model…

…calculation of compressive behavior


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Tubular shaped SiC/SiCMeshing the image with Avizo :

μCT 3D image of a dry tube …

…A marching cubes algorithm is applied…

…simplification (max distance criterion)…

(To mesh the surface)

…is labeled…

(Tetrahedra)

…the label is dilated…(To simulate the matrix)

…simplification (nbr of triangles criterion)…

…apply an advancing front algorithm…

(Homogeneous triangles)

(To extract the SiC Yarns)

(triangles adapted to curvature)


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Tubular shaped SiC/SiC

Determination of center of gravity of tetrahedra

Reading orientations & density in voxels

(same methods as in CC composites)

Calculation(compressive BC)

Affect local informations :


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Tubular shaped SiC/SiCResults :

Measured by digital image correlation

Initial μCT

Calculated deformation

Ecalculated= 180 GPa

Emeasured= 177 GPa

εzz


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Tubular shaped SiC/SiCConclusions

= Less complex architecture -> 2 solutions

- 1st solution : analyze & encode the weaving path to reconstruct a finite element model

- Weaving hard to analyze, to reconstruct and to calculate. But accurate method.

- 2nd solution : mesh the image with Avizo & enrich the elements with measurements on images (density & orientations)

- Thanks to Avizo package, mesh is easy to produce.

- Calculation very efficient and accurate (close to experimental results)


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Conclusions/perspectives

• Calculations based on the real material

• Very accurate methods – halfway methods between experimental and modeling

• Useful to understand and predict thermostructural composites behavio

• Importance of the knowledge of micro-scale mechanical properties

• Avizo® mostly used for 3D observation (density, geometry, orientations) and meshing.


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Acknowledgements

• Industrial partners :– Safran Herakles (SPS) : A.Dekeyrel,

B.Delperier, B.Reignier, C.Descamps– CEA Saclay : C.Sauder

• Students :– T.Agulhon, M.Genin, N.Siefert


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Thank you for your attention

Studying thermomechanical properties of thermostructural composites using X-Ray micro-computed tomography

O.Caty, E.Rohmer, C.Lorrette, G.L.Vignoles, G.Couégnat, M.Charron

- University of Bordeaux -

Questions ??- Laboratoire des Composites ThermoStructuraux -

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Studying thermomechanical properties of thermostructural composites using X-ray microcomputed tomography