Determining the Shear Fracture Toughness, K IIc, for two grades of graphite Tim Burchell Oak Ridge National Laboratory ASTM Symposium on Graphite Testing

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 Managed by UT-Battellefor the U.S. Department of Energy

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.


Overview of Presentation

• Objectives of study

• Introduction

• Specimen geometries

• Experimental

• Results & Discussion (DEN Compression Specimens)

• Conclusions


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



Introduction


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)



Mode I or crack opening mode, KIc: Mode II, plane shear mode, KIIc: Mode III, Anti-plane shear, KIIIc


Biaxial Test Facility


Specimen and Grip Alignment


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


First and Fourth Stress Quadrant Biaxial Strength Data for NBG-18

EXPERIMENTAL RESULTS PREDICTION & MODEL FIT



What experimental methods and specimen geometries exist for the determination of critical shear stress intensity factor,

KIIc, or shear fracture toughness?



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



Specimen Geometries



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.



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.



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


Determining the Shear Fracture Toughness, KIIc, for two grades of

graphite



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!



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



Experimental



• 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





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.



graphite



Results & Discussion



Type 1 specimens, 2w = 20 mm, compressive failure



Type 2 specimens, 2w = 50 mm, compressive failure


Compression behavior of concrete, samples, showing load discontinuity or

critical shear load, i,e., load at which the shear failure occurs

BEHAVIOR OF CONCRETE





graphite

Type 3 specimen, 2w = 100 mm, shear failure





graphite






graphite






graphite






graphite




graphite

Type 3 specimen, 2w = 100 mm, partial shear failure



graphite

Type 4 specimen, 2w = 130 mm, compressive failure





graphite

Type 4 specimens, 2w = 130 mm, shear failure





• 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



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



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


Conclusions



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

Documents

Determining the Shear Fracture Toughness, K IIc, for two grades of graphite Tim Burchell Oak Ridge National Laboratory ASTM Symposium on Graphite Testing