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

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Presentation on theme: "Determining the Shear Fracture Toughness, K IIc, for two grades of graphite Tim Burchell Oak Ridge National Laboratory ASTM Symposium on Graphite Testing."— Presentation transcript:

1 Determining the Shear Fracture Toughness, K IIc, 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 2Managed by UT-Battelle for 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.

3 3Managed by UT-Battelle for the U.S. Department of Energy Overview of Presentation Objectives of study Introduction Specimen geometries Experimental Results & Discussion (DEN Compression Specimens) Conclusions

4 4Managed by UT-Battelle for the U.S. Department of Energy 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 K IIc Thus we need – to define K IIc for the graphite grades of interest – Preferably measure K IIc by two techniques (verification) – Determine if K IIc is subject to influence from texture and specimen volume

5 5Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite Introduction

6 6Managed by UT-Battelle for the U.S. Department of Energy D. K. Shetty, Trans ASME 109 (1987) 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 K I is the mode I stress-intensity factor, K II is the mode II stress- intensity factor, and K Ic is the mode I critical stress-intensity factor (or mode I fracture toughness) and C is an empirical constant (the Shetty shear-sensitivity coefficient)

7 7Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite Mode I or crack opening mode, K Ic : Mode II, plane shear mode, K IIc : Mode III, Anti-plane shear, K IIIc

8 8Managed by UT-Battelle for the U.S. Department of Energy Biaxial Test Facility

9 9Managed by UT-Battelle for the U.S. Department of Energy Specimen and Grip Alignment

10 10Managed by UT-Battelle for the U.S. Department of Energy Defining the Biaxial Stress Quadrants σ 1 (Axial) -σ 1 (Axial) σ 2 (Hoop)-σ 2 (Hoop) INTERNAL PRESSURE PLUS COMPRESSIVE LOADING EXTERNAL PRESSURE PLUS TENSILE LOADING EXTERNAL PRESSURE PLUS COMPRESSIVE LOADING

11 11Managed by UT-Battelle for the U.S. Department of Energy First and Fourth Stress Quadrant Biaxial Strength Data for NBG-18 EXPERIMENTAL RESULTS PREDICTION & MODEL FIT

12 12Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite What experimental methods and specimen geometries exist for the determination of critical shear stress intensity factor, K IIc, or shear fracture toughness?

13 13Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, 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

14 14Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite Specimen Geometries

15 15Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, 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 K Ic or K IIc 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.

16 16Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, 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 17Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite 96 specimens being machined 2 graphite grades K Ic and K IIC 4 notch variants, disc diameter 75 or 100 mm 6 replicates specimens Testing to commence in Dec/Jan timeframe

18 18Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite

19 19Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite PCEA HeightWidththicknessligament lengthnotch depthRATIOSVOL. h2hw2wt2t2aaπaπacGSLigament/GSw>πah>2amm TRUE TRUE TRUE TRUE 5120 NBG-18 Graphite HeightWidththicknessligament lengthnotch depthRATIOSVOL. h2hw2wt2t2aaπaπacGS ligament/ GSw>πah>2amm TRUE TRUE TRUE TRUE 5120 The specimen volume varies over two orders of magnitude!

20 20Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite KIIc No of GeometriesNo of specimensNo of graphite'sTOTAL Xu, S and Reinhardt H.W., Otto-Graff Journal, Vol.16 (2005) pp

21 21Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite Experimental

22 22Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, 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 23Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite

24 24Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, 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.

25 25Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite

26 26Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite Results & Discussion

27 27Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite Type 1 specimens, 2w = 20 mm, compressive failure

28 28Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite Type 2 specimens, 2w = 50 mm, compressive failure

29 29Managed by UT-Battelle for the U.S. Department of Energy 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 30Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite

31 31Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite Type 3 specimen, 2w = 100 mm, shear failure

32 32Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite

33 33Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite Type 3 specimen, 2w = 100 mm, shear failure

34 34Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite

35 35Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite Type 3 specimen, 2w = 100 mm, shear failure

36 36Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite

37 37Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite Type 3 specimen, 2w = 100 mm, shear failure

38 38Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite

39 39Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite Type 3 specimen, 2w = 100 mm, shear failure

40 40Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite Type 3 specimen, 2w = 100 mm, partial shear failure

41 41Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite Type 4 specimen, 2w = 130 mm, compressive failure

42 42Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite

43 43Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite Type 4 specimens, 2w = 130 mm, shear failure

44 44Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite

45 45Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite From the concrete literature K IIc ≈ 2K Ic (Xu & Reinhardt) For nuclear graphite K Ic ≈ 0.8 to 2.5 MPa√m Hence K IIc ≈ 1.6 to 5.0 MPa√m

46 46Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite PCEA GRAPHITE SpecimenFailure ModeCritical Load, P c Block nominal dimensions Critical shear fracture stress K IIc Width, w Thickness, t Notch length, 2aσ crit kipkNmm MPaMPa√m PCEA Type 1-1Compressive PCEA Type 1-2Compressive PCEA Type 1-3Compressive PCEA Type 2-1Compressive PCEA Type 2-2Compressive PCEA Type 2-3Compressive PCEA Type 3-1Shear PCEA Type 3-2Compressive PCEA Type 3-3Shear PCEA Type 3-4Shear PCEA Type 3-5 Compressive/Partial Shear PCEA Type 3-6Compressive PCEA Type 4-1Compressive

47 47Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, for two grades of graphite NBG-18 GRAPHITE SpecimenFailure Mode Critical Load, P c Block nominal dimensions Critical shear fracture stress K IIc Width, w Thickness t Notch length, 2aσ crit kipkNmm MPaMPa√m NBG-18 Type 1-1Compressive NBG-18 Type 1-2Compressive NBG-18 Type 1-3Compressive NBG-18 Type 2-1Compressive NBG-18 Type 2-2Compressive NBG-18 Type 2-3Compressive NBG-18 Type 3-1Shear NBG-18 Type 3-2Shear NBG-18 Type 3-3Compressive NBG-18 Type 3-4Compressive NBG-18 Type 3-5Compressive NBG-18 Type 3-6 Compressive/Par tial Shear NBG-18 Type 4-1Shear

48 48Managed by UT-Battelle for the U.S. Department of Energy Conclusions

49 49Managed by UT-Battelle for the U.S. Department of Energy Determining the Shear Fracture Toughness, K IIc, 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 , M.R.M. Aliha, R. Ashtari, M.R. Ayatollahi. Applied Mechanics and Materials, Vols. 5-6 (2006), pp


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