smirt23-presentation652
TRANSCRIPT
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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
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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:
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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)
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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
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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:
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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)
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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:
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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
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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
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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
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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
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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:
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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
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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
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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.
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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.
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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:
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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
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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