This document describes a multi-scale modeling study of the influence of porosity on the mechanical properties and fracture of Gilsocarbon graphite. The study used micro-cantilever tests to determine material properties at the microscale and developed a multi-scale model to predict properties at larger scales. The model accounted for the graphite's microstructure of matrix, filler particles, and pores. Simulation results showed decreasing mechanical properties with increasing porosity and that pore size distribution and particle-matrix interface strength significantly affect properties and crack propagation.

1. 17-09-15
Challenge the future
Delft
University of
Technology
Influence of porosity on mechanical properties
and fracture of Gilsocarbon graphite: a multi-
scale modelling study
B. Šavija, G.E. Smith, D. Liu, K.R. Hallam, E. Schlangen, P.E.J. Flewitt

2. 2Influence of porosity on mechanical properties and fracture of Gilsocarbon graphite: a multi-scale modelling study
• Introduction
• Experimental data
• Multi-scale modelling procedure
• Results
• Conclusions and perspectives
Outline:

3. 3Influence of porosity on mechanical properties and fracture of Gilsocarbon graphite: a multi-scale modelling study
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. 4Influence of porosity on mechanical properties and fracture of Gilsocarbon graphite: a multi-scale modelling study
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. 5Influence of porosity on mechanical properties and fracture of Gilsocarbon graphite: a multi-scale modelling study
• Introduction
• Experimental data
• Multi-scale modelling procedure
• Results
• Conclusions and perspectives
Outline:

6. 6Influence of porosity on mechanical properties and fracture of Gilsocarbon graphite: a multi-scale modelling study
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. 7Influence of porosity on mechanical properties and fracture of Gilsocarbon graphite: a multi-scale modelling study
• Introduction
• Experimental data
• Multi-scale modelling procedure
• Results
• Conclusions and perspectives
Outline:

8. 8Influence of porosity on mechanical properties and fracture of Gilsocarbon graphite: a multi-scale modelling study
Multi-scale modelling procedure
• In this work, Gilsocarbon graphite is considered
• Microstructure comprising matrix, filler particles, and porosity
• Pores modelled as spheres which were allowed to grow and coalesce
until desired porosity was reached
Microstructural modelling

9. 9Influence of porosity on mechanical properties and fracture of Gilsocarbon graphite: a multi-scale modelling study
Multi-scale modelling procedure
• Microstructures of 5x5x5 mm were generated and divided into
1x1x1mm3
cubes for the multi-scale fracture analysis
Microstructural modelling

10. 10Influence of porosity on mechanical properties and fracture of Gilsocarbon graphite: a multi-scale modelling study
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. 11Influence of porosity on mechanical properties and fracture of Gilsocarbon graphite: a multi-scale modelling study
Multi-scale modelling procedure
• Information from the fine scale is passed on to the large scale specimen
Multi-scale model

12. 12Influence of porosity on mechanical properties and fracture of Gilsocarbon graphite: a multi-scale modelling study
• Introduction
• Experimental data
• Multi-scale modelling procedure
• Results
• Conclusions and perspectives
Outline:

13. 13Influence of porosity on mechanical properties and fracture of Gilsocarbon graphite: a multi-scale modelling study
Results
• Matrix, particles, and the particle/matrix interface assumed to have the
same properties
Test case 1

14. 14Influence of porosity on mechanical properties and fracture of Gilsocarbon graphite: a multi-scale modelling study
Results
• Particle/matrix interface assumed to be the “weak” zone
Test case 2

15. 15Influence of porosity on mechanical properties and fracture of Gilsocarbon graphite: a multi-scale modelling study
Results
• Bi-modal porosity distribution (20% “large” pores, while the increase in
porosity comes from “small” pores)
Test case 3 (part 1)

16. 16Influence of porosity on mechanical properties and fracture of Gilsocarbon graphite: a multi-scale modelling study
Results
• Bi-modal porosity distribution
Test case 3 (part 2)

17. 17Influence of porosity on mechanical properties and fracture of Gilsocarbon graphite: a multi-scale modelling study
Results
Influence of porosity on simulated mechanical
properties
• There is a trend of decreasing mechanical properties
with increasing porosity (i.e. mass loss)
• Note that virgin Gilsocarbon (~20% porosity) has
ft~20MPa -> strength overestimated by a factor of 4-5

18. 18Influence of porosity on mechanical properties and fracture of Gilsocarbon graphite: a multi-scale modelling study
• Introduction
• Experimental data
• Multi-scale modelling procedure
• Results
• Conclusions and perspectives
Outline:

19. 19Influence of porosity on mechanical properties and fracture of Gilsocarbon graphite: a multi-scale modelling study
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
• As expected, mechanical properties (E modulus, tensile strength) decrease with
increasing porosity
• Particle/matrix interface strength has a significant effect on mechanical
properties and crack propagation
• Pore size distribution is also important
• Tensile strength is in the right order of magnitude, but overestimated. This is
probably due to simplifications in the generated microstructure (spherical pore
shape)
Conclusions

20. 20Influence of porosity on mechanical properties and fracture of Gilsocarbon graphite: a multi-scale modelling study
Conclusions and perspectives
The developed methodology will be used in the future for:
•Modelling the influence of irradiation hardening and radiolytic
oxidation on long-term mechanical properties
•Inclusion of microstructural defects, such as onion ring flaws
or weak planes in the filler particles
•Upscaling to size of full-scale graphite bricks
Perspectives