Carbon Materials for Advanced Technologies Episode 14 ppt

500 The difference between the work input and the elastic stored energy is the crack growth resistance, R, As with the purely elastic case, the energy values associated with elastic-plastic fracture may be ascertained fiom the load versus load-point deflection diagram for a cracked body as shown in Fig. 5. U Fig. 5. Diagram of load versus load-point displacement for an elastic-plastic body experiencing stable crack extension [48]. For an increment of crack extension, AA is represented by a movement from B to D on the load versus deflection curve, the energy consumed may be represented by the area AnR. Hence the crack growth resistance may be expressed as and similarly and where cf+, = XJJdA is the plastic energy dissipation rate. The J value is defined as the elastic potential difference between the linear and nonlinear elastic bodies with the same geometric variables [52,53]. The elastic potential energy for a nonlinear elastic body is expressed by: The J integral can be written as -ax J=- aA For elastic-plastic deformation [54] 71: = ut - w = (u, + Up) -w or ax a C -w - J =-(-)= dA dA The graphical evaluation of J, is presented in the load versus load point displacement diagram of Fig. 6. 502 P U Fig. 6. Diagram of load versus load-point displacement illustrating a graphical determination of the J-integral[48]. Sakai et al. [48] investigated the fracture of an isotropic nuclear graphte, IG-11, using the chevron notched short bar specimen and found it to exhibit significant elastic-plastic behavior. Nonlinear fracture parameters y, R, J,, and @p were empirically determined from the load versus displacement diagrams. These nonlinear fracture parameters were found to be increasing functions of aP, and to converge to a constant value of G, as @p - 0. The value of K, calculated using the Irwin relation, Eq. 12, was only about one fourth the value measured using the ASTM E399 test method. This lfference was attributed to significant inelastic deformation which occurred during fracture. It was estimated that approximately 38% of the total fracture energy was consumed as plastic energy dissipation. Sakai et al. [48] further assessed the crack growth resistance @-curve) behavior of IG-11 using compact tension specimens and found crack growth resistance to increase with increasing crack extension for a range of dw values. This rising R- curve behavior was attributed to inelastic deformation and fiacture in the process zone and crack wake region. In the crack tip region, significant inelastic material response was identified with basal slip and extension of pre-existing microcracks. Grain bridging tractions having a chctexistic dimension of one filler coke grain, and compressive strains in the microcracking wake, contributed significantly to rising R-curve behavior. 503 5 Fracture Behavior of Small Flaws in Nuclear Graphites As noted in the above discussion on fracture mechanics characterization of graphites, EPFM has many advantages over LEFM in accounting for the nonlinear deformation and fracture behavior of graphite. This is particularly true for laboratory specimens containing a single macroscopic, artificial flaw for which the measurement of load-point displacements is rather straight forward. Without a knowledge of local displacements, the work and energy terms used to calculate nonlinear fracture parameters can only be estimated. The application of EPFM to graphite is further complicated by a number of factors. Multiple flaws may act in unison as the critical flaw at fracture. Furthermore, the critical flaw may have a size which approaches microstructural features with a location and orientation unknown. Hence, for most fracture mechanics assessments of graphite, many investigators have employed a LEFM failure criterion as a workable solution to quantifjmg graphite fracture. The authors have addressed critical issues in graphite fracture by exploring the lunits of LEFM while recognizing the nonlinear behavior of this unique material. Graphite is used as a moderator and a structural material in the core of the Gas Turbine - Modular Helium Reactor (GT-MHR). Although the design is based on a maximum principal stress failure criterion, the need for applying fracture mechanics to component strength assessment becomes obvious when one considers the possible presence of significant flaws in nuclear graphites. An investigation was undertaken to determine the flaw sizes relevant to the fracture of graphite and to assess the applicability of fracture mechanics to defiig an appropriate failure criterion for small macroscopic flaws in two grades of nuclear graphite, H-45 1 and IG-11. 5. I Material In our fracture mechanics studies and fracture model development we have utilized several grades of graphite. Three of the graphites examined are shown in Fig. 7. Grade H-451 graphite is an extruded, medium-grained, near isotropic, nuclear graphite which has been selected for use as the moderator and core structural material in the GT-MHR. Grade H-45 1 was manufactured by Sigri-Great Lakes Carbon Company in the USA. In addition to macroscopic pores and cracks, H-45 i contains arrays of associated pores with trace lengths in the 1 to 5-mm range which are clearly visible on a machined surface of H-451 graphite. Individual spherical pores with diameters as large as 3 mm are common. Grade IG- 110 graphite is an isostatically molded, fine-grained, isotropic, nuclear graphite which is used as the moderator and core structural material for the High Temperature Test Reactor (HTTR) which is currently under construction by the Japan Atomic Energy Research Institute. Grade IG-110 graphite is manufactured by Toyo-Tanso in 504 Japan and is a purified version of IG-11. Grade AXF-5Q is an isostatically molded, ultrafine-grained, isotropic, high strength graphite. Grade AXF-5Q is used for a variety of applications such as throats, nozzles, etc., in the aerospace industry, boats, crucibles and fumace parts in the semi-conductor industry and for other applications such as electrode discharge machining tools. Grade AXF-5Q is manufactured in the USA by the POCO Graphite Company. Grade AGX, (not shown in Fig. 7) is manufactured by UCAR Carbon Company, and is used for the production of arc-furnace electrodes for the steel industry. The widely different textures of three of the graphites initially studied here are clearly shown in the photomicrographs in Fig. 7. Grade H-45 1 [Fig. 7(a)] contains relatively large filler coke particles, [F] in Fig 7(a), and pores, [PI in Fig 7(a). The microsiructure shown in Fig. 7(a) reveals the presence of a large crack, [C] in Fig. 7(a), that has propagated between pores in the graphite. Microstmctural evidence such as this supports the graphite fracture mechanism adopted in the Burchell fracture model (section 6). In contrast to H-451, grade IG-110 pig. 7@)] contains much smaller filler coke particles, [F] in Fig. 7(b). The particles are typically 10- 150 pm in length compared to the 0.5-1.5 mm filler particles found in H-451. Moreover, pores in IG-110, [PI in Fig. 7(b), are considerably smaller than in H- 451, being in the range 10-250 pm. Grade Am-5Q graphite [Fig. 7(c)] has an extremely fine texture. The filler particles are difficult to resolve in the photomicrograph. Typical pore sizes are <10 pm and particle sizes appear to be C5 pm. 5.2 Test procedure Four-point bend specimens of square cross-section measuring 25 mm x 25 mm and 50 nun x 50 rnm were used in this investigation. Specimen comers were chamferred to minimize failure initiation there. A single artificial flaw was machmed in the center of the tensile surface of most specimens. The flaw geometry perpen&cular to the tensile axis was a circular section with a slot thickness of 0.25 mm and notch root angle of 45". Crack depth ranged from a = 0.025 to 10 mm and the surface length ranged from 2c = 0.55 to 22 mm. The surface flaw geometry is shown in Fig. 8. A number of specimens contained no artificial flaw, i.e., contained only intrinsic flaws. Six specimens not containing artificial flaws were infiitrated under vacuum with a polyurethane bearing fluorescent dye to delineate surface connected porosity. Four-point bend tests were conducted in strict accordance with ASTM standard C651-91 [55 1. All specimens were loaded in four-point bendmg to failure under displacement control. The peak load was measured and the fracture origin was noted as being at the artificial flaw or away from the flaw. Subsequent to testing, the flaw depth, a, and surface length, 2c, were precisely measured in the fracture plane using an optical comparator. 505 Fig. 7. Microstructures of the three primary graphites used in this work: (a) H-45 1, (b) IG-11, and (c) AXF-5Q. [F]-filler particles, [PI-pores and [C] cracks. 506 Specimen Dimensions B = W 25.4 mm or 50.8 mm a = 0.025 mm to 10 mm 2c 0.5 mm to 22 mm crack tip geometry Fig. 8. Schematic of circular section flaws introduced in the tensile surface of IG-11 and H-45 1 graphites. 5.4 Results and discussion Fracture at artificial flaws occurred by extending the plane of the flaw perpendicular to the tensile axis of the specimen. A typical fracture surface for specimens that failed at artificial flaws is shown in Fig. 9. Failure away from artificial flaws, i.e., at intrinsic flaws, always occurred between the loading points in the region of constant tensile stress. Typical fracture surfaces for failure at intrinsic flaws are shown in Fig. 10 for an H-451 graphite specimen which had been infiltrated with fluorescent dye before testing. Near surface flaws with maximum dimensions around 1 rnm appear to be the origins of failure. Origins of failure at intrinsic flaws in IG-11 graphite could not be identified on fracture surfaces even for specimens treated with fluorescent dye. Test results for IG- 1 1 graphite are given in Fig. 1 1 as a plot of fracture stress versus crack depth for specimens with and without artificial flaws. At longer crack lengths, the fracture stress is proportional to the square root of crack depth. The slope of fracture stress versus crack depth is approximately - % on the logarithmic scale. As the artificial flaw size is reduced, failure occurs at higher stress levels until the fracture strength is equivalent to the unflawed specimens, i. e., the mean flexural strength. At the transition crack depth, half of the specimens failed at the artificial flaw and half failed at intrinsic flaws. The transition crack depth is 0.050 mm for IG- 1 1 graphite. It is notable that this value is comparable to the mean filler coke particle sue for this graphite. 507 Test results for H-451 graphite are given in Fig. 12 as a plot of fracture stress versus crack depth for specimens with and without artificial flaws. The transition from artificial flaws controlling fracture strength to intrinsic flaws controlling strength occurs at 1 mm for this graphite. Although the mean filler coke particle size is around 0.5 111111, filler coke particles as large as 1 mm are common. Here again, at the transition crack depth, half of the specimens failed at the artificial flaw and half failed at intrinsic flaws. The fracture stress for H-45 1 graphite exhibited greater variability than for IG- 1 1 graphite in all tests, regardless of whether failure occurred at or away from artificial flaws. This greater variability may be attributed to a coarser microstructure for H- 45 1 graphite. In the absence of artificial flaws, H-45 1 graphite presents a broader distribution of intrinsic flaw sizes from which failure may initiate. When artificial flaws are large enough to control strength, the microstructure along the front of an incipient crack was more variable for H-451 graphite, thus offering more varied resistance to crack extension. 4 ,5 mm, TENSILE SURFACE big. 9. Photosraph of fracture surface of H-451 graphite bend specimen illustrating fulurc at artificial flaw. 508 ,5 mm, TENSILE SURFACE Fig. 10. Photograph of fracture surface of H-451 graphite bend specimen illustrating failure originating at natural flaws at the tensile surface. ED AT INTRINSIC FLA CRACK DEPTH (mm) Fig. 11. Fracture stress versus crack depth for small flaw fracture tests in IG-11 graphite. 509 A I I I I Ill1 I I I I I IIII I I I I1 Ill 0.1 1 10 CRACK DEPTH (mm) Fig. 12. Fracture stress versus crack depth for small flaw fracture tests in H-45 1 graphite. Fracture mechanics analysis requires the determination of the mode I stress intensity factor for a surface crack having a circular section profile. Here the circular section flaw will be approximated by a semi-elliptical flaw. Irwin [23] developed an expression for the mode I stress intensity factor around an elliptical crack embedded in an infinite elastic solid subjected to uniform tension. The most general formulation is given by: @ a’ K = o __ [sin% + - COS^^]^'^ cp C2 where @ is an elliptical integral of the second kind and is given by d8 (25) c2 - a’ cp = 1”” [1 - ___ 0 a’ and the geometric variables a, c, and 8 are defmed in Fig. 8. Newman [56] has developed expressions for calculating the mode I stress intensity factor for a semi- elliptical surface flaw subject to umform bending that incorporates correction [...]... Standard Test Method for Flexural Strength of Manufactured Carbon And Graphite Articles Using Four-Point Loading at Room Temperature, American Society for Testing and Materials, 1991 56 J C Newman, Jr “A Review and Assessment of the Stress Intensity Factors for Surface Cracks,“ Part-Through Crack Fatigue Life Prediction, ASTM STP 687, J.B Chang, Ed, American Society for Testing and Materials, 1979, pp... Meeting on The Status of Graphite Development for Gas Cooled Reactors Tokai-mura, Japan, 1991 58 ASTM C 749-92, ”Standard Test Method for Tensile Stress-Strain of Carbon and Graphite” ASTM Standards Vol 15.01, pp 196 207, Pub American Society for Testing of Materials, Philadelphia, USA (1994) 535 Index A Adsorbents 280,287 see also activated carbon, active carbon fibers fractional pore volumes 289 methane... between carbon atoms 1 Buckminsterfullerene see fullerenes Bulk modulus 11 Burchell fracture model 5 15 performance 524 Butane working capacity 244, 252-253 C Carbon application in fission reactors 429,473 coal derived see coal derived carbons films 14 hard 15 sofi 15 graphitic, in Li batteries 353 graphitizing 23 hard 344 see also carbon, non-graphitizing hydrogen containing 358 insulation materials. .. the fracture mechanics formulations developed for metals, ceramics and other brittle materials The principles of linear elastic fracture mechanics and elastic plastic fracture mechanics have been reviewed, and the former applied to describe the fracture behavior of small flaws in two grades of nuclear graphite For both of the graphites studied a decreasing K,, value was noted for decreasing crack sizes... and J P Strizak Modelling the Tensile Strength of H-451 Nuclear Graphite In Proc 2 P Biennial Con$ on Carbon, Buffalo N Y , USA Pub American Carbon Society, 1993, pp 687 688 T D Burchell and J P Strizak The Performance of a Fracture Model for Graphites In Proc Carbon 94, Granada, Spain Published Spanish Carbon Society, 1994, pp 128 129 J Kaiser Untersuchungen uber das Auftreton von gerauschen beim zugversuch... Metallic Materials , ASTM STP 410, American Society for Testing and Materials, Philadelphia, 1966, pp 75 76 34 R A.Smith, “On the Short Crack Limitations of Fracture Mechanics”, International Journal OfFracture, Vol 13, 1977, pp 717 720 35 W F Brown and J E Strawley, “Plane Strain Crack Toughness Testing of High Strength Metallic Materials , ASTM STP 410, American Society for Testing and Materials, ... 13 and 14 for small flaw tests on IG-I1 graphite and H-451 graphite, respectively Two regimes of behavior are observed for both graphites Fracture behavior at longer crack lengths, greater than 1 111111,is characterized by a nearly constant value of stress intensity factor at failure The measured fracture toughness in this regime is approximately 1 O M P a 6 for IG-11 graphite and 1 2 M P a 6 for H-451... i i n g the Effective Inherent Defect Size of Graphite for Fracture Mechanics Applicabons, Extended Abstracts and Program-16”Biennial Conference on Carbon, Pub American Carbon Society, 1983, pp 404405 40 E I? Kennedy, Fracture Mechanics Analysis of Extruded Graphite, Extended Abstracts and Program-16” Biennial Conference on Carbon, Pub American Carbon Society, 1985, pp 287 288 534 41 C R Kenedy, Fracture... (standard deviation) on the predicted tensile failure probability distribution for grade H-451 graphite 529 10 f2 14 i6 10 20 22 24 STRESS (MPa) Fig 27 The effect of density on the predicted tensile failure probability distribution for grade H-45 1 graphite Microstructural input data for the "SIFTING"code are reported in Table 1 for four graphites, AGX, H-451, IG-110 and AXF-5Q The spread of texture represented... emission fiom graphite In Proc I @ Cbnz on Carbon, University of California, San Diego, CA USA, 1983, pp 406 407 I Ioka, S Yoda and T Konishi Behavior of acoustic emission caused by microfracture in polycrystalline graphites, Carbon 1990,28(6), 879 885 T D Burchell, M 0 Tucker and B McEnaney Qualitative and Quantitative Studies of Fracture in Nuclear Graphites, Materialsfor nuclear reactor core applications . accounting for the nonlinear deformation and fracture behavior of graphite. This is particularly true for laboratory specimens containing a single macroscopic, artificial flaw for which the. expressions for calculating the mode I stress intensity factor for a semi- elliptical surface flaw subject to umform bending that incorporates correction 510 factors to account for: the free. diagram for a cracked body as shown in Fig. 5. U Fig. 5. Diagram of load versus load-point displacement for an elastic-plastic body experiencing stable crack extension [48]. For