Fracture Characterisation of Reactor Core Graphite under Biaxial Loading

1. Fracture Characterisation of Reactor Core Graphite under Biaxial Loading Dong Liu1,2, Mahmoud Mostafavi3 , Peter EJ Flewitt1,2, James Marrow3, David Smith4 1Interface Analysis Centre, School of Physics, University of Bristol, Bristol, BS8 1TL, UK 2 HH Wills Physics Laboratory, School of Physics, University of Bristol, Bristol, BS8 1TL, UK 3Department of Materials and Oxford Martin School, University of Oxford, Oxford OX1 3BD, UK 4Department of Mechanical Engineering, University of Bristol, Bristol, BS8 1TR, UK Contact: dong.liu@bristol.ac.uk 14th International Nuclear Graphite Specialists Meeting Seattle, USA

2. Content • Background • Materials • Finite Element Analysis • Experimental • Results • Concluding comments 14th International Nuclear Graphite Specialists Meeting Seattle, USA

3. Background • Quasi-brittle material • Heterogeneous • Polygranular • Aggregate • Porous 14th International Nuclear Graphite Specialists Meeting Seattle, USA

4. Background • Gilsocarbon graphite 12 mm Gilsocarbon Left: Optical image; Right: Electron image; 14th International Nuclear Graphite Specialists Meeting Seattle, USA

5. Background • Gilsocarbon graphite • The reactor core graphite is subject to (i) a range of loading conditions that develop over the service life and (ii) change of microstructure due to radiolytic oxidation. • It was established that the strain energy release rates of stable propagating shallow cracks (0.5 to 1 mm depth but up to tens of mm in surface length) are very different under uniaxial and equi-biaxial loadings. • The average initiation toughness is Jc = 176 ± 44 J/m2 under uniaxial and Jc = 779 ± 97 J/m2 under equi-biaxial stress. M. Mostafavi, S. A. McDonald, H. Çetinel, P. M. Mummery and T. J. Marrow: Carbon Vol. 59 (2013), p. 325. 14th International Nuclear Graphite Specialists Meeting Seattle, USA

6. Background • Gilsocarbon graphite • We wish to explore a range of biaxial loading conditions • Test based on a cruciform geometry specimen with four-point loading. Vary loading positions on the arms to change biaxiality. 14th International Nuclear Graphite Specialists Meeting Seattle, USA

7. (a) (b) Slot (~ 10 mm x 5 mm x 0.6 mm) 50 mm Material I • Cruciform virgin Gilsocarbon graphite • Pre-slot specimen with θ = 0 to 45° θ 25 mm 50 mm 14th International Nuclear Graphite Specialists Meeting Seattle, USA

8. Material I Clip gauges • Five-point loading • Clip gauges to measure crack mouth opening • Acoustic emission • Camera imaging Camera with LED lights Acoustic emission Roller supporter Loading jig Strain gauges 14th International Nuclear Graphite Specialists Meeting Seattle, USA

9. Material II • Cruciform virgin Gilsocarbon graphite • Plain specimen • Strain gauges • Acoustic emission • Camera imaging Strain gauges 14th International Nuclear Graphite Specialists Meeting Seattle, USA

10. Finite Element Analysis • FEA model showing the stress distribution and that the cracks initiate at the slot root (E=9.5GPa). 14th International Nuclear Graphite Specialists Meeting Seattle, USA

11. Finite Element Analysis • Stress intensity factor, K Distribution of K when a = 5 mm K change with a (5 to 10 mm) 14th International Nuclear Graphite Specialists Meeting Seattle, USA

12. Calibration using Perspex specimen • Change of the roller positions to change the loading biaxiality. These selected positions are from 1 to 3 (min, mid and max). • Pre-calibrated using Perspex specimens with four strain gauges. 3 2 2 3 3 3 3 3 14th International Nuclear Graphite Specialists Meeting Seattle, USA

13. Results σv • Specimen with pre-slots but different biaxiality σo σo σv σo:σv = 1:2 σo:σv = 1:1 σo:σv = 1:0 14th International Nuclear Graphite Specialists Meeting Seattle, USA

14. Results • Specimen with pre-slots but different biaxiality 14th International Nuclear Graphite Specialists Meeting Seattle, USA

15. Results • Specimen with pre-slots but different biaxiality • Fracture surface varies with loading condition. • The crack propagate at the crack tip then deflects due to the biaxiality. 14th International Nuclear Graphite Specialists Meeting Seattle, USA

16. Results • Plain specimen • Load-displacement curve under 3-3 equi-biaxial loading - - - 14th International Nuclear Graphite Specialists Meeting Seattle, USA

17. Results • Plain specimen • Load-displacement curve under 3-3 equi-biaxial loading - Acoustic emission graph Initial calibration 14th International Nuclear Graphite Specialists Meeting Seattle, USA

18. Results • Plain specimen • Load-displacement curve under 3-2 loading and acoustic emission graph 14th International Nuclear Graphite Specialists Meeting Seattle, USA

19. Concluding comments • The current experimental arrangement demonstrates that different degrees of biaxiality may be applied to a notched and plain cruciform specimen, and the load-displacement behaviour monitored. • Acoustic emission provides evidence that micro-scale cracking occurs within the specimen prior to the peak load. • Under multiple loading cycles, the curve follows the gradient of the previous cycle. • The crack geometry will be verified by examination of interrupted tests in the non-linear range of the load-displacement curve. In addition the specimens will be wedged open and observed by X-ray tomography and high spatial resolution serial sectioning. The effect of notch orientation relative to the cruciform specimen axes will also be studied to verify the stress states that are developed in this specimen. 14th International Nuclear Graphite Specialists Meeting Seattle, USA

20. Acknowledgement We acknowledge the financial support from EPSRC funded project – QUBE (QUasi-Brittle fracture: a 3D Experimentally-validated approach). Grant number: EP/J019801/1. The Materials Research Laboratory at the Culham Centre for Fusion Energy was used for the nano-indentation on Gilsocarbon graphite. 14th International Nuclear Graphite Specialists Meeting Seattle, USA

21. Rhossili bay, Gower 14th International Nuclear Graphite Specialists Meeting Seattle, USA