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

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

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

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) 282-289

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

Biaxial Test Facility

Specimen and Grip Alignment

Defining the Biaxial Stress Quadrants 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

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?

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

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

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.

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.

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

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

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 1300000 15 47.12 35 37.5 1000000 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 1300000 15 47.12 35 18.75 1000000 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!

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. 21-78

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Conclusions  

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, 1995 2. M.R.M. Aliha, R. Ashtari, M.R. Ayatollahi. Applied Mechanics and Materials, Vols. 5-6 (2006), pp. 181-188