1) The document describes an experimentally informed multi-scale model for predicting size effects and fracture in porous graphite. 2) Micro-cantilever tests were used to determine elastic properties at the microscale and inform the multi-scale model. 3) The model successfully predicted the bending strength, flexural modulus, fracture energy, and crack patterns of graphite beams at various sizes. It also captured the decrease in properties and scatter with increasing beam size.

1. 16-08-15
Challenge the future
Delft
University of
Technology
Experimentally informed multi-scale
modelling of size effect and fracture in porous
graphite
B. Šavija, G.E. Smith, D. Liu, E. Schlangen, P.E.J. Flewitt

2. 2Experimentally informed multi-scale modelling of size effect and fracture in porous graphite
• Introduction
• Experimental data
• Multi-scale modelling procedure
• Results
• Conclusions and perspectives
Outline:

3. 3Experimentally informed multi-scale modelling of size effect and fracture in porous graphite
Introduction
• AGR gas-cooled reactors in the UK, cores
consist of interlocking graphite bricks
surrounding the fuel rods, acting as neutron
moderators
• Cooled by CO2 gas
• Deteriorate over time due to irradiation and
radiolytic oxidation
• Porosity increase and mass loss result
• Need to be able to predict long-term
mechanical performance
• Microstructure based modelling can be of use
Problem statement
Smith et al. (2013)

4. 4Experimentally informed multi-scale modelling of size effect and fracture in porous graphite
Introduction
• Minimal experimental data
• No inverse modelling
• Good description of the microstructure
• Validation using experiments
• (Reliable) use of the model for areas where no experimental
data exists (e.g. high mass loss, high irradiation damage)
• Use in decision making
Modelling needs

5. 5Experimentally informed multi-scale modelling of size effect and fracture in porous graphite
• Introduction
• Experimental data
• Multi-scale modelling procedure
• Results
• Conclusions and perspectives
Outline:

6. 6Experimentally informed multi-scale modelling of size effect and fracture in porous graphite
Experimental data
• Graphite specimens commonly tested in
mm/cm size range
• To obtain true material properties,
measurements need to be performed at the
appropriate length-scale
• For models used in this work, this is the
micrometre-scale
• Pure material (excluding porosity) should be
tested, and porosity included in the
microstructural model
• Micro-cantilever tests used to determine elastic
modulus and fracture strength
Problem statement and approach
Liu et al. (2014)

7. 7Experimentally informed multi-scale modelling of size effect and fracture in porous graphite
• Introduction
• Experimental data
• Multi-scale modelling procedure
• Results
• Conclusions and perspectives
Outline:

8. 8Experimentally informed multi-scale modelling of size effect and fracture in porous graphite
Multi-scale modelling procedure
• In this work, PG25 (Filter graphite) is considered
• “Simpler” microstructure compared to e.g. Gilsocarbon graphite,
comprising only matrix and porosity (no filler particles)
• Pores modelled as spheres which were allowed to grow and coalesce
until desired porosity was reached
Microstructural modelling

9. 9Experimentally informed multi-scale modelling of size effect and fracture in porous graphite
Multi-scale modelling procedure
• Microstructure of 6x6x18 mm was generated and divided into 1x1x1mm3
cubes for the multi-scale fracture analysis
Microstructural modelling

10. 10Experimentally informed multi-scale modelling of size effect and fracture in porous graphite
Multi-scale modelling procedure
• Lattice model is used as a basis (Schlangen and van Mier, 1992)
Multi-scale model
Input from micro-
cantilever tests

11. 11Experimentally informed multi-scale modelling of size effect and fracture in porous graphite
Multi-scale modelling procedure
• Information from the fine scale is passed on to the large scale specimen
Multi-scale model

12. 12Experimentally informed multi-scale modelling of size effect and fracture in porous graphite
• Introduction
• Experimental data
• Multi-scale modelling procedure
• Results
• Conclusions and perspectives
Outline:

13. 13Experimentally informed multi-scale modelling of size effect and fracture in porous graphite
Results
• The beam was simulated four times by rotating the microstructure along
the longitudinal axis to check the variability in the results
Beam properties
Bending strength of the right order of
magnitude, overestimated by a factor ~4
Crack pattern correctly predicted

14. 14Experimentally informed multi-scale modelling of size effect and fracture in porous graphite
Results
• Smaller-sized beams were “sampled” from the microstructure to check
the influence of “specimen” size on simulated mechanical properties
• Five beam sizes were tested:
1. 0.3mm x 0.3mm x 0.9 mm (6 x 6 x 18 voxels)
2. 0.6mm x 0.6 mm x 1.8 mm (12 x 12 x 36 voxels)
3. 1.2mm x 1.2 mm x 3.6mm (24 x 12 x 72 voxels)
4. 3 mm x 3 mm x 9 mm (60 x 60 x 180 voxels)
5. 6 mm x 6 mm x 18 mm, (120 x 120 x 360 voxels) the full-sized beam
• Multiple specimens of each size were tested to check the scatter
Size effect

15. 15Experimentally informed multi-scale modelling of size effect and fracture in porous graphite
Results
Size effect
There is a decrease in bending strength with increasing
specimen size. Furthermore, the scatter also decreases.

16. 16Experimentally informed multi-scale modelling of size effect and fracture in porous graphite
Results
Size effect
Flexural modulus and fracture energy also show a decrease
with increasing specimen size.

17. 17Experimentally informed multi-scale modelling of size effect and fracture in porous graphite
• Introduction
• Experimental data
• Multi-scale modelling procedure
• Results
• Conclusions and perspectives
Outline:

18. 18Experimentally informed multi-scale modelling of size effect and fracture in porous graphite
Conclusions and perspectives
• The proposed modelling scheme is innovative in a sense that it uses micro-
scale experimental results (i.e. mechanical properties) as input, while the larger
scale experiments can be used for validation. No assumptions are made on
“real” mechanical properties of the solid phase. This is an important
improvement compared to models used in the literature
• There is a significant scale effect of mechanical and fracture properties. This is
in line with experimental data.
• The scatter for both flexural modulus and strength decreases as the specimen
size increases. This is also in line with available experimental data.
• The model can predict realistic crack patterns for a filter graphite eg PG25.
Conclusions

19. 19Experimentally informed multi-scale modelling of size effect and fracture in porous graphite
Conclusions and perspectives
The developed methodology will be used in the future for:
•Modelling of more complex graphite types, such as
Gilsocarbon
•Modelling the influence of irradiation hardening and radiolytic
oxidation on long-term mechanical properties
•Upscaling to size of full-scale graphite bricks
Perspectives