Filler particles

Filler-coke particles with good basal plane alignment were highly susceptible to microcracking along basal planes at low stresses. This cleavage was facilitated by the needle-like cracks that lay parallel to the basal planes and which were formed by anisotropic contraction of the filler-coke particles during the calcination process. Frequently, when a crack propa­gating through the binder phase encountered a well — aligned filler particle, it took advantage of the easy cleavage path and propagated through the particle. However, in contrast to the mechanism suggested by Ioka eta/.,36 the reverse process, that is, propagation of a crack initiated in the filler particle into the binder phase, was much less commonly observed.

While some of the direct observations discussed above are not in total agreement with the mechanism postulated from AE data, there are a number of similarities. Both AE and the microstructural study showed that failure was preceded by the propagation and coalescence of microcracks to yield a critical defect. However, based on the foregoing discussion of graphite-fracture processes, it is evident that the microstructure plays a dominant role in controlling the fracture behavior of the material. Therefore, any new fracture model should attempt to capture the essence of the microstructural processes influen­cing fracture. Particularly, a fracture model should embody the following: (1) the distribution of pore sizes, (2) the initiation of fracture cracks from stress raising pores, and (3) the propagation of cracks to a critical length prior to catastrophic failure of the graphite (i. e., subcritical growth). The Burchell frac­ture model27,43-45 recognizes these aspects of graph­ite fracture and applies a fracture mechanics criterion to describe steps (2) and (3). The model was first postulated27 to describe the fracture behavior of AGR fuel sleeve pitch-coke graphite and was suc­cessfully applied to describe the tensile failure statis­tics. Moreover, the model was shown to predict more closely the AE response of graphite than its forerun­ner, the Rose and Tucker model. Subsequently, the model was extended and applied to two additional nuclear graphites.45 Again, the model performed well and was demonstrated to be capable of predicting the tensile failure probabilities of the two graphites (grades H-451 and IG-110). In an attempt to further strengthen the model,45 quantitative image analysis was used to determine the statistical distribution of pore sizes for grade H-451 graphite. Moreover, a calibration exercise was performed to determine a single value of particle critical stress-intensity factor for the Burchell model.28, Most recently, the model was successfully validated against experimental ten­sile strength data for three graphites of widely differ-

28,45,46

ent texture.

The model and code were successfully bench — marked28,46 against H-451 tensile strength data and

Подпись: Figure 24 A comparison of experimental and predicted tensile failure probabilities for graphite with widely different textures: AGX, H-451, IG-110, and AXF-5Q. Reproduced from Burchell, T. D. Carbon 1996, 34, 297-316. validated against tensile strength data for grades IG-110 and AXF-5Q. Two levels of verification were adopted. Initially, the model’s predictions for the growth of a subcritical defect in H-451 as a function of applied stress was evaluated and found to be qualitatively correct.28,46 Both the initial and final defect length was found to decrease with increasing applied stress. Moreover, the subcritical crack growth required prior to fracture was predicted to be substantially less at higher applied stresses. Both of these observations are qualitatively correct and are readily explained in terms of linear elastic fracture mechanics. The probability that a particular defect exists and will propagate through the material to cause failure was also predicted to increase with increasing applied stress. Quantitative validation was achieved by successfully testing the model against an experimentally determined tensile strength dis­tribution for grade H-451. Moreover, the model appeared to qualitatively predict the effect of textural changes on the strength of graphite. This was subse­quently investigated and the model further validated by testing against two additional graphites, namely grade IG-110 and AXF-5Q For each grade of graphite, the model accurately predicted the mean tensile strength.

In an appendant study, the Burchell28,46 fracture model was applied to a coarse-textured electrode graphite. The microstructural input data obtained during the study was extremely limited and can only be considered to give a tentative indication ofthe real pore-size distribution. Despite this limitation, how­ever, the performance of the model was very good, extending the range of graphite grades successfully modeled from a 4-p. m particle size, fine-textured graphite to a 6.35-mm particle size, coarse-textured graphite. The versatility and excellent performance of the Burchell28,46 fracture model is attributed to its sound physical basis, which recognizes the dominant role of porosity in the graphite-fracture process (Figure 24).

Kelly12 has reviewed multiaxial failure the­ories for synthetic graphite. The fracture theory of Burchell28,46 has recently been extended to multiaxial stress failure conditions.47 The model’s predictions in the first and fourth quadrants are reported and compared with the experimental data in Figure 25. The performance was satisfactory, demonstrating the sound physical basis of the model and its versatility. The model in combination with the Principal of Independent Action describes the experimental data in the first quadrant well. The failure envelope

Stress (MPa)

image347

Figure 25 A summary of the Burchell model’s predicted failure surface in the first (PIA) and fourth (effective stress) quadrants and the experimental data. Reproduced from Burchell, T.; Yahr, T.; Battiste, R. Carbon2007,45, 2570-2583.

predicted by the fracture model for the first quadrant is a better fit to the experimental data than that of the maximum principal stress theory, which would be represented by two perpendicular lines through the

Подпись:Подпись: DПодпись: [14]Подпись: Dthmean values of the uniaxial tensile and hoop strengths. The failure surface predicted by the fracture model offers more conservatism at high combined stresses than the maximum principal stress criterion. In the fourth quadrant, the fracture model predicts the failure envelope well (and conservatively) when the effective (net) stress is applied with the fracture model. Again, as in the first quadrant, the maximum princi­pal stress criteria would be extremely unconservative, especially at higher stress ratios. Overall, the model’s predictions were satisfactory and reflect the sound physical basis of the fracture model.47

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