Determining the Shear Fracture Toughness, K IIc , for two grades of graphite
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Transcript of Determining the Shear Fracture Toughness, K IIc , for two grades of graphite
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
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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.
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Overview of Presentation
• Objectives of study
• Introduction
• Specimen geometries
• Experimental
• Results & Discussion (DEN Compression Specimens)
• Conclusions
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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
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Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Introduction
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D. K. Shetty, Trans ASME 109 (1987) 282-289
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
12
Ic
II
Ic
I
KC
K
K
K
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)
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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
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Defining the Biaxial Stress Quadrants
σ1 (Axial)
-σ1 (Axial)
σ2 (Hoop)-σ2 (Hoop)
INTERNAL PRESSURE PLUS COMPRESSIVE LOADING
EXTERNAL PRESSURE PLUS TENSILE LOADING
EXTERNAL PRESSURE PLUS COMPRESSIVE LOADING
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First and Fourth Stress Quadrant Biaxial Strength Data for NBG-18
EXPERIMENTAL RESULTS PREDICTION & MODEL FIT
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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?
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Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Mode II Testing Configurations
(a)Shear stress along a crack(b)Iosipescu specimen(c)Push-off specimen(d)Punch-through specimen(e)Four notch cylinder(f)Mixed – mode device according to Richard(g)Mixed – mode device according to Arcan(h)Mixed-mode disc loading (cracked chevron notched Brazilian disc)(i)Off center notched beam
Otto Graff Journal, Vol. 16, 2005
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Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Specimen Geometries
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Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Two promising specimen geometries were selected
I.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
ii.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.
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Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
100
30
1
DIMENSIONS IN mm
PCEA
Ext
rusi
on D
irecti
on (W
G)
MATERIALS: PCEA and NBG-18
NBG
-18
V. M
oldi
ng D
irecti
on (A
G)
CCNBD SpecimenThe 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.
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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
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Determining the Shear Fracture Toughness, KIIc, for two grades of
graphite
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Determining the Shear Fracture Toughness, KIIc, for two grades of
graphitePCEA
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 50 100 40 20 62.83 30 0.8 50 TRUE TRUE 130000050 100 50 100 50 100 30 15 47.12 35 0.8 37.5 TRUE TRUE 1000000
12.5 25 25 50 12.5 25 11 5.5 17.28 7 0.8 13.75 TRUE TRUE 312508 16 10 20 8 16 6 3 9.42 5 0.8 7.5 TRUE TRUE 5120
NBG-18 GraphiteHeight Width thickness ligament length notch depth RATIOS VOL.
h 2h w 2w t 2t 2a a πa c GSligament/
GS w>πa h>2a mm3
50 100 65 130 50 100 40 20 62.83 30 1.6 25 TRUE TRUE 130000050 100 50 100 50 100 30 15 47.12 35 1.6 18.75 TRUE TRUE 1000000
12.5 25 25 50 12.5 25 11 5.5 17.28 7 1.6 6.875 TRUE TRUE 312508 16 10 20 8 16 6 3 9.42 5 1.6 3.75 TRUE TRUE 5120
The specimen volume varies over two orders of magnitude!
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Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
KIIc
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. 21-78
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Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Experimental
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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 0.001
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
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Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
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Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
MATERAILS:
1.Nuclear grade NBG-18 graphite. Manufactured by SGL Carbon, vibrationally molded, filler particle size 1.6 mm (max)
2.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.
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Determining the Shear Fracture Toughness, KIIc, for two grades of
graphite
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Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Results & Discussion
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Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Type 1 specimens, 2w = 20 mm, compressive failure
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Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
Type 2 specimens, 2w = 50 mm, compressive failure
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Compression behavior of concrete, samples, showing load discontinuity or
critical shear load, i,e., load at which the shear failure occurs
BEHAVIOR OF CONCRETE
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Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
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Determining the Shear Fracture Toughness, KIIc, for two grades of
graphite
Type 3 specimen, 2w = 100 mm, shear failure
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Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
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Determining the Shear Fracture Toughness, KIIc, for two grades of
graphite
Type 3 specimen, 2w = 100 mm, shear failure
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Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
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Determining the Shear Fracture Toughness, KIIc, for two grades of
graphite
Type 3 specimen, 2w = 100 mm, shear failure
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Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
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Determining the Shear Fracture Toughness, KIIc, for two grades of
graphite
Type 3 specimen, 2w = 100 mm, shear failure
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Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
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Determining the Shear Fracture Toughness, KIIc, for two grades of
graphite
Type 3 specimen, 2w = 100 mm, shear failure
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Determining the Shear Fracture Toughness, KIIc, for two grades of
graphite
Type 3 specimen, 2w = 100 mm, partial shear failure
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Determining the Shear Fracture Toughness, KIIc, for two grades of
graphite
Type 4 specimen, 2w = 130 mm, compressive failure
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Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
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Determining the Shear Fracture Toughness, KIIc, for two grades of
graphite
Type 4 specimens, 2w = 130 mm, shear failure
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Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
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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
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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
KIIcWidth, wThickness
, t
Notch length,
2a σcrit
kip kN mm mm mm MPa MPa√m
PCEA Type 1-1 Compressive 10 16 6 PCEA Type 1-2 Compressive 10 16 6 PCEA Type 1-3 Compressive 10 16 6 PCEA Type 2-1 Compressive 25 25 11 PCEA Type 2-2 Compressive 25 25 11 PCEA Type 2-3 Compressive 25 25 11 PCEA Type 3-1 Shear 48.21 214.44 50 100 30 42.89 2.40PCEA Type 3-2 Compressive 50 100 30 PCEA Type 3-3 Shear 62.77 279.20 50 100 30 55.84 3.12PCEA Type 3-4 Shear 62.93 279.91 50 100 30 55.98 3.13
PCEA Type 3-5Compressive/Partial
Shear 50 100 30 PCEA Type 3-6 Compressive 50 100 30 PCEA Type 4-1 Compressive 65 100 40
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Determining the Shear Fracture Toughness, KIIc, for two grades of graphite
NBG-18 GRAPHITE
Specimen Failure ModeCritical Load,
Pc
Block nominal dimensions
Critical shear
fracture stress
KIIcWidth, wThickness
t
Notch length,
2a σcrit
kip kN mm mm mm MPa MPa√mNBG-18 Type 1-1 Compressive 10 16 6 NBG-18 Type 1-2 Compressive 10 16 6 NBG-18 Type 1-3 Compressive 10 16 6 NBG-18 Type 2-1 Compressive 25 25 11 NBG-18 Type 2-2 Compressive 25 25 11 NBG-18 Type 2-3 Compressive 25 25 11 NBG-18 Type 3-1 Shear 79.33 352.86 50 100 30 70.57 3.95NBG-18 Type 3-2 Shear 87.37 388.63 50 100 30 77.73 4.35NBG-18 Type 3-3 Compressive 50 100 30 NBG-18 Type 3-4 Compressive 50 100 30 NBG-18 Type 3-5 Compressive 50 100 30
NBG-18 Type 3-6Compressive/Partial Shear 50 100 30
NBG-18 Type 4-1 Shear 107.00 475.94 65 100 40 73.22 4.67
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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. 57-64, 19952. M.R.M. Aliha, R. Ashtari, M.R. Ayatollahi. Applied Mechanics and Materials, Vols. 5-6 (2006), pp. 181-188