smirt23-presentation652

18-04-23

Challenge the future

DelftUniversity ofTechnology

Experimentally informed multi-scale modelling of size effect and fracture in porous graphiteB. Šavija, G.E. Smith, D. Liu, E. Schlangen, P.E.J. Flewitt

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:

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)

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

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:

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)

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:

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

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

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

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

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:

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

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

15Experimentally informed multi-scale modelling of size effect and fracture in porous graphite

ResultsSize effect

There is a decrease in bending strength with increasing specimen size. Furthermore, the scatter

also decreases.

16Experimentally informed multi-scale modelling of size effect and fracture in porous graphite

ResultsSize effect

Flexural modulus and fracture energy also show a decrease with increasing specimen size.

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:

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

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