1. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Tim Burchell
Oak Ridge National Laboratory
ASTM Symposium on Graphite Testing for Nuclear Applications: The Significance of Test Specimen Volume and Geometry and the Statistical Significance of Test Specimen Population

2. Acknowledgments
This work is sponsored by the U.S. Department of Energy, Office of Nuclear Energy Science and Technology under contract DE-AC05- 00OR22725 with Oak Ridge National Laboratory, managed by UT- Battelle, LLC.

3. Overview of Presentation
Objectives of study
Introduction
Specimen geometries
Experimental
Results & Discussion (DEN Compression Specimens)
Conclusions

4. Objectives of Study
To model graphite biaxial failure data we need a failure criteria
The Shetty mixed mode fracture mechanics criteria when combined with a Microstructural fracture model can describe the biaxial data, but require knowledge of KIIc
Thus we need
to define KIIc for the graphite grades of interest
Preferably measure KIIc by two techniques (verification)
Determine if KIIc is subject to influence from texture and specimen volume

5. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Introduction

6. Shetty Mixed Mode Fracture Mechanics
Shetty mixed mode fracture criteria and Burchell fracture model for graphite are combined to predict bi-axial failure envelope and failure probabilities
KI is the mode I stress-intensity factor, KII is the mode II stress-intensity factor, and KIc is the mode I critical stress-intensity factor (or mode I fracture toughness) and C is an empirical constant (the Shetty shear-sensitivity coefficient)
D. K. Shetty, Trans ASME 109 (1987)

7. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Mode I or crack opening mode, KIc: Mode II, plane shear mode, KIIc: Mode III, Anti-plane shear, KIIIc

8. Biaxial Test Facility

9. Specimen and Grip Alignment

10. Defining the Biaxial Stress Quadrants
σ2 (Hoop)
-σ2 (Hoop)
INTERNAL PRESSURE PLUS COMPRESSIVE LOADING
EXTERNAL PRESSURE PLUS TENSILE LOADING
EXTERNAL PRESSURE PLUS COMPRESSIVE LOADING

11. First and Fourth Stress Quadrant Biaxial Strength Data for NBG-18
EXPERIMENTAL RESULTS
PREDICTION & MODEL FIT

12. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
What experimental methods and specimen geometries exist for the determination of critical shear stress intensity factor, KIIc, or shear fracture toughness?

13. Mode II Testing Configurations
Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Mode II Testing Configurations
Shear stress along a crack
Iosipescu specimen
Push-off specimen
Punch-through specimen
Four notch cylinder
Mixed – mode device according to Richard
Mixed – mode device according to Arcan
Mixed-mode disc loading (cracked chevron notched Brazilian disc)
Off center notched beam
Otto Graff Journal, Vol. 16, 2005

14. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Specimen Geometries

15. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Two promising specimen geometries were selected
Cracked Chevron Notched Brazilian Disc (CCNBD) Specimen
Similar to centrally slotted disc which has been used in the past for graphite, hence some literature data – central notch is cut from both sides with slitting saw to form chevron, thus difficult to vary specimen volume & geometry. Mixed mode thus can measure KIc or KIIc
Double Edge Notched Compression (DENC) Specimen
Relatively simple slotted rectangular geometry, thus easy to vary specimen volume & geometry. Has been used to test concrete, but NO graphite literature.

16. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
CCNBD Specimen
The notch is cut with a circular slitting saw from both sides of the specimen, thus the solid ligament has a “chevron”
shape on either end of the central slot.
Same geometry gives mixed fracture modes or pure KIc or KIIc depending on the test angle φ.

17. 96 specimens being machined
Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
96 specimens being machined
2 graphite grades
KIc and KIIC
4 notch variants, disc diameter 75 or 100 mm
6 replicates specimens
Testing to commence in Dec/Jan timeframe

18. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite

19. The specimen volume varies over two orders of magnitude!
Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
PCEA
Height
Width
thickness
ligament length
notch depth
RATIOS
VOL. h 2h w 2w t 2t 2a a πa c GS
Ligament/GS
w>πa
h>2a
mm3 50
100 65
130 40 20
62.83 30
0.8
TRUE 15
47.12 35
37.5
12.5 25 11
5.5
17.28 7
13.75
31250 8 16 10 6 3
9.42 5
7.5
5120
NBG-18 Graphite
Height
Width
thickness
ligament length
notch depth
RATIOS
VOL. h 2h w 2w t 2t 2a a πa c GS
ligament/GS
w>πa
h>2a
mm3 50
100 65
130 40 20
62.83 30
1.6 25
TRUE 15
47.12 35
18.75
12.5 11
5.5
17.28 7
6.875
31250 8 16 10 6 3
9.42 5
3.75
5120
The specimen volume varies over two orders of magnitude!

20. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
No of Geometries
No of specimens
No of graphite's
TOTAL 4 6 2 48
Xu, S and Reinhardt H.W., Otto-Graff Journal, Vol.16 (2005) pp

21. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Experimental

22. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
MTS servo-hydraulic 4-post 110 kip load frame
100 kip load cell
Crosshead speed in/sec or 25 μm/sec
Hemispherical compression platens
Upper platen “floats’ to self level
Specimen compressed between two square steel plates
Lab-view control software

23. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite

24. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
MATERAILS:
Nuclear grade NBG-18 graphite. Manufactured by SGL Carbon, vibrationally molded, filler particle size 1.6 mm (max)
Nuclear grade PCEA graphite. Manufactured by GrafTech International (GTI), extruded, filler particle size 0.8 mm (max). AREVA NGNP reference grade
SPECIMENS
Four DEN Compression specimen geometries, 2w=20, 50, 100 & 130 mm
48 specimens, 26 tested.

25. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite

26. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Results & Discussion

27. Type 1 specimens, 2w = 20 mm, compressive failure
Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Type 1 specimens, 2w = 20 mm, compressive failure

28. Type 2 specimens, 2w = 50 mm, compressive failure
Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Type 2 specimens, 2w = 50 mm, compressive failure

29. Compression behavior of concrete, samples, showing load discontinuity or critical shear load, i,e., load at which the shear failure occurs
BEHAVIOR OF CONCRETE

30. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite

31. Type 3 specimen, 2w = 100 mm, shear failure
Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Type 3 specimen, 2w = 100 mm, shear failure

32. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite

33. Type 3 specimen, 2w = 100 mm, shear failure
Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Type 3 specimen, 2w = 100 mm, shear failure

34. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite

35. Type 3 specimen, 2w = 100 mm, shear failure
Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Type 3 specimen, 2w = 100 mm, shear failure

36. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite

37. Type 3 specimen, 2w = 100 mm, shear failure
Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Type 3 specimen, 2w = 100 mm, shear failure

38. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite

39. Type 3 specimen, 2w = 100 mm, shear failure
Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Type 3 specimen, 2w = 100 mm, shear failure

40. Type 3 specimen, 2w = 100 mm, partial shear failure
Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Type 3 specimen, 2w = 100 mm, partial shear failure

41. Type 4 specimen, 2w = 130 mm, compressive failure
Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Type 4 specimen, 2w = 130 mm, compressive failure

42. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite

43. Type 4 specimens, 2w = 130 mm, shear failure
Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Type 4 specimens, 2w = 130 mm, shear failure

44. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite

45. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
From the concrete literature KIIc ≈ 2KIc (Xu & Reinhardt)
For nuclear graphite KIc ≈ 0.8 to 2.5 MPa√m
Hence KIIc ≈ 1.6 to 5.0 MPa√m

46. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
PCEA GRAPHITE
Specimen
Failure Mode
Critical Load, Pc
Block nominal dimensions
Critical shear fracture stress
KIIc
Width, w
Thickness, t
Notch length, 2a
σcrit
kip kN mm
MPa
MPa√m
PCEA Type 1-1
Compressive 10 16 6
PCEA Type 1-2
PCEA Type 1-3
PCEA Type 2-1 25 11
PCEA Type 2-2
PCEA Type 2-3
PCEA Type 3-1
Shear
48.21
214.44 50
100 30
42.89
2.40
PCEA Type 3-2
PCEA Type 3-3
62.77
279.20
55.84
3.12
PCEA Type 3-4
62.93
279.91
55.98
3.13
PCEA Type 3-5
Compressive/Partial Shear
PCEA Type 3-6
PCEA Type 4-1 65 40

47. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
NBG-18 GRAPHITE
Specimen
Failure Mode
Critical Load, Pc
Block nominal dimensions
Critical shear fracture stress
KIIc
Width, w
Thickness t
Notch length, 2a
σcrit
kip kN mm
MPa
MPa√m
NBG-18 Type 1-1
Compressive 10 16 6
NBG-18 Type 1-2
NBG-18 Type 1-3
NBG-18 Type 2-1 25 11
NBG-18 Type 2-2
NBG-18 Type 2-3
NBG-18 Type 3-1
Shear
79.33
352.86 50
100 30
70.57
3.95
NBG-18 Type 3-2
87.37
388.63
77.73
4.35
NBG-18 Type 3-3
NBG-18 Type 3-4
NBG-18 Type 3-5
NBG-18 Type 3-6
Compressive/Partial Shear
NBG-18 Type 4-1
107.00
475.94 65 40
73.22
4.67

48. Conclusions

49. Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
1: R.J. Fowell, Int Soc for Rock Mech, Commission on testing methods, CCNBD Specimens, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. Vol; 32, No. 1, pp , 1995
2. M.R.M. Aliha, R. Ashtari, M.R. Ayatollahi. Applied Mechanics and Materials, Vols. 5-6 (2006), pp