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The crack network is a typical cracking morphology caused by thermal fatigue loading. It was pointed out that the crack network appeared under relatively small temperature fluctuations and did not grow deeply. In this study, the mechanism of evolution of crack network and its influence on crack growth was examined by numerical calculation. First, the stress field near two interacting cracks was investigated. It was shown that there are stress-concentration and stress-shielding zones around interacting cracks, and that cracks can form a network under the bi-axial stress condition. Secondly, a Monte Carlo simulationwas developed in order to simulate the initiation and growth of cracks under thermal fatigue loading and the evolution of the crack network.
The local stress field formed by pre-existing cracks was evaluated by the body forcemethod and its role in the initiation and growth of crackswas considered. The simulation could simulate the evolution of the crack network and change in number of cracks observed in the experiments.
It was revealed that reduction in the stress intensity factor due to stress feature in the depth direction under high cycle thermal fatigue loading plays an important role in the evolution of the crack network and that mechanical interaction between cracks in the network affects initiation rather than growth of cracks. The crack network appears only when the crack growth in the depth direction is interrupted. It was concluded that the emergence of the crack network is preferable for the structural integrity of cracked components.
Introduction
Thermal fatigue is a critical issue in nuclear power plant components. The crack network is a typical cracking morphology caused by thermal fatigue loading and has been observed in plant components (Taheri, 2007) and experiments (Maillot et al., 2005). It was pointed out that the crack network appeared under relatively small temperature fluctuations and did not grow deeply inside components (Taheri, 2007), where it was shown through operational feed back that cracks were arrested at less than 2mm depth in components of pressurized water reactors (PWRs). Nearly the same resultswere obtained under experiments (Maillot et al., 2005). Not only experiments but also numerical studies were conducted in order to evaluate the crack growth in the network (Haddar and Fissolo, 2005; Haddar et al., 2005). The two main questions concerning the crack network are: why the network develops under thermal fatigue loading and how the crack network influences the growth of cracks. Neither of these two problems is fully understood yet. In particular, the latter problem is important for the structural integrity of components of nuclear power plants.
There are two characteristics thatwe should consider for evolution of the crack network under thermal fatigue loading. The first is peculiar distribution of stress in the depth direction. The magnitude of stress amplitude caused by temperature fluctuations is large near the surface and decreases with distance fromthe surface. This reduces the stress intensity factor (SIF) in the depth direction, and the degree of reduction is dependent on the magnitude and frequency of thermal fluctuations and thermal transfer coefficient (Kasahara et al., 2002; Hayashi and Hirano, 2003; Taheri, 2007). The other characteristic is the bi-axial stress field brought about by thermal loading. The bi-axial stress causes complex mechanical interaction between cracks in the network and produces a local stress field. The local stress affects the initiation of new cracks as well as growth of pre-existing cracks (Kamaya and Haruna,2007).
By taking into account these two characteristics, we conduct a numerical study of the evolution of the crack network. First, in order to evaluate the influence of interaction on the growth and initiation of cracks, the stress field near the interacting cracks is investigated under the bi-axial stress condition. It is discussed how the interaction and bi-axial stress contribute to the evolution of the crack network. Secondly, a Monte Carlo simulation is developed in order to simulate the initiation and growth of cracks under thermal fatigue loading and the evolution of the crack network. The target of the simulation is the experiment performed using the SPLASH experimental facility, in which thermal fatigue stress was caused by applying cool water periodically to the surface of the specimen (Maillot et al., 2005). Two-dimensional cracks are assumed to be initiated on the surface according to accumulated damage calculated from local stress, which is formed by pre-existing cracks and is calculated by using the body force method (BFM). The initiated cracks growfollowing the power lawof SIF. The crack growth in the depth direction is controlled by assuming a limitation of the crack length on the surface. Finally, based on the results of analyses, the influence of the crack network on the structural integrity of plant components is discussed.
Conclusion
The mechanism of evolution of the crack network and its influence on crack growth was examined based on numerical calculations. Firstly, the stress field near two interacting cracks was investigated under the bi-axial stress condition. Secondly, a Monte Carlo simulation was developed in order to simulate the initiation and growth of cracks under thermal fatigue loading and the evolution of the crack network. Then, the influence of the crack network on the structural integrity of plant components was discussed. The following conclusions were obtained:
(1) There are stress-concentration and stress-shielding zones aroundinteracting cracks, and cracks can cross eachother under the bi-axial stress condition.
(2) The Monte Carlo simulation developed can simulate the evolution of the crack network and change in number of cracks which were observed in the experiments.
(3) The reduction in crack growth rate due to small SIF in the depth direction plays an important role in the evolution of the crack network.
(4) Mechanical interaction between cracks in the network affects the initiation rather than growth of cracks.
(5) Cracks cannot penetrate thewall thickness when the crack network appears. Namely, the emergence of a crack network is preferable for the structural integrity of cracked components.
References
Erdogan, F., Sih, G.C., 1963. On the crack extension in plates under plane loading and transverse shear. J. Basic Eng., 519–527.
Haddar, N., Fissolo, A., 2005. 2D simulation of the initiation and propagation of crack array under thermal fatigue. Nucl. Eng. Des. 235, 945–964.
Haddar, N., Fissolo, A.,Maillot, V., 2005. Thermal fatigue crack networks: an computational study. Int. J. Solid Struct. 42, 771–788.
Hayashi, M., Hirano, A., 2003. High cycle thermal fatigue crack initiation and growth behavior in simulated BWR environment. Trans. Jpn. Soc. Mech. Eng. A 69, 1353–1359.
Jaske, C.E., O’Donnell, W.J., 1977. Fatigue design criteria for pressure vessel alloys. Trans. ASME, J. Press. Vess. Technol. 99, 584–592.
Kamaya, M., 2008. Growth evaluation of multiple interacting surface cracks. Part I. Experiments and simulation of coalesced crack. Eng. Fracture Mech. 75, 1336–1349.
Kamaya, M., 2005. Influence of the interaction on stress intensity factor of semielliptical surface cracks. In: Proceedings of the 2005 ASME Pressure Vessels and Piping Division Conference, Denver, PVP, p. 71352.
Kamaya, M., Haruna, T., 2006. Crack initiation model for sensitized 304 stainless steel in high temperature water. Corros. Sci. 48, 2442–
2456.
Kamaya, M., Haruna, T., 2007. Influence of local stress on initiation behavior of stress corrosion cracking for sensitized 304 stainless steel. Corros. Sci. 49, 3303–3324.
Kamaya, M., Totsuka, N., 2002. Influence of interaction between multiple cracks on stress corrosion crack propagation. Corros. Sci. 44, 2333–2352.
Kasahara, N., Nagata, T., Iwata, K., Negishi, H., 1995. Advanced creep-fatigue evaluation rule for fast breeder reactor components: generalization of elastic follow-up model. Nucl. Eng. Des. 155, 499–518.
Kasahara, N., Takasho, H., Yscumpai, A., 2002. Structural response function approach for evaluation of thermal striping phenomena. Nucl. Eng. Des. 212, 281–292.
Maillot, V., Fissolo, A., Degallaix, G., Degallaix, S., 2005. Thermal fatigue crack networks parameters and stability: an experimental study. Int. J. Solids Struct. 42, 759–769.
Molinie, E., Monteil, N., Delatouche, S., Roux, S., Robert, N., Pages, C., 2002. Caracterisation des troncons RRA 900–1300MWe deposes: synthese des enseignements acquis. Porc. Fontevroud 5, 883–895.
Murakami, Y., Nishitani, H., 1981. Trans. Jpn. Soc. Mech. Eng. A 47, 295–303.
Murakami, Y., Nemat-Nasser, S., 1982. Interacting dissimilar semi-elliptical surface flaws under tension and bending. Eng. Fracture Mech. 16, 373–386.
Nishitani, H., Murakami, Y., 1974. Stress intensity factors of an elliptical crack or a semi-elliptical crack subject to tension. Int. J. Fracture 10, 353–368.
Taheri, T., 2007. Some advances on understanding of high cycle thermal fatigue crazing. ASME J. Press. Technol. 129, 400–410.
It was revealed that reduction in the stress intensity factor due to stress feature in the depth direction under high cycle thermal fatigue loading plays an important role in the evolution of the crack network and that mechanical interaction between cracks in the network affects initiation rather than growth of cracks. The crack network appears only when the crack growth in the depth direction is interrupted. It was concluded that the emergence of the crack network is preferable for the structural integrity of cracked components.
Introduction
Thermal fatigue is a critical issue in nuclear power plant components. The crack network is a typical cracking morphology caused by thermal fatigue loading and has been observed in plant components (Taheri, 2007) and experiments (Maillot et al., 2005). It was pointed out that the crack network appeared under relatively small temperature fluctuations and did not grow deeply inside components (Taheri, 2007), where it was shown through operational feed back that cracks were arrested at less than 2mm depth in components of pressurized water reactors (PWRs). Nearly the same resultswere obtained under experiments (Maillot et al., 2005). Not only experiments but also numerical studies were conducted in order to evaluate the crack growth in the network (Haddar and Fissolo, 2005; Haddar et al., 2005). The two main questions concerning the crack network are: why the network develops under thermal fatigue loading and how the crack network influences the growth of cracks. Neither of these two problems is fully understood yet. In particular, the latter problem is important for the structural integrity of components of nuclear power plants.
There are two characteristics thatwe should consider for evolution of the crack network under thermal fatigue loading. The first is peculiar distribution of stress in the depth direction. The magnitude of stress amplitude caused by temperature fluctuations is large near the surface and decreases with distance fromthe surface. This reduces the stress intensity factor (SIF) in the depth direction, and the degree of reduction is dependent on the magnitude and frequency of thermal fluctuations and thermal transfer coefficient (Kasahara et al., 2002; Hayashi and Hirano, 2003; Taheri, 2007). The other characteristic is the bi-axial stress field brought about by thermal loading. The bi-axial stress causes complex mechanical interaction between cracks in the network and produces a local stress field. The local stress affects the initiation of new cracks as well as growth of pre-existing cracks (Kamaya and Haruna,2007).
By taking into account these two characteristics, we conduct a numerical study of the evolution of the crack network. First, in order to evaluate the influence of interaction on the growth and initiation of cracks, the stress field near the interacting cracks is investigated under the bi-axial stress condition. It is discussed how the interaction and bi-axial stress contribute to the evolution of the crack network. Secondly, a Monte Carlo simulation is developed in order to simulate the initiation and growth of cracks under thermal fatigue loading and the evolution of the crack network. The target of the simulation is the experiment performed using the SPLASH experimental facility, in which thermal fatigue stress was caused by applying cool water periodically to the surface of the specimen (Maillot et al., 2005). Two-dimensional cracks are assumed to be initiated on the surface according to accumulated damage calculated from local stress, which is formed by pre-existing cracks and is calculated by using the body force method (BFM). The initiated cracks growfollowing the power lawof SIF. The crack growth in the depth direction is controlled by assuming a limitation of the crack length on the surface. Finally, based on the results of analyses, the influence of the crack network on the structural integrity of plant components is discussed.
Conclusion
The mechanism of evolution of the crack network and its influence on crack growth was examined based on numerical calculations. Firstly, the stress field near two interacting cracks was investigated under the bi-axial stress condition. Secondly, a Monte Carlo simulation was developed in order to simulate the initiation and growth of cracks under thermal fatigue loading and the evolution of the crack network. Then, the influence of the crack network on the structural integrity of plant components was discussed. The following conclusions were obtained:
(1) There are stress-concentration and stress-shielding zones aroundinteracting cracks, and cracks can cross eachother under the bi-axial stress condition.
(2) The Monte Carlo simulation developed can simulate the evolution of the crack network and change in number of cracks which were observed in the experiments.
(3) The reduction in crack growth rate due to small SIF in the depth direction plays an important role in the evolution of the crack network.
(4) Mechanical interaction between cracks in the network affects the initiation rather than growth of cracks.
(5) Cracks cannot penetrate thewall thickness when the crack network appears. Namely, the emergence of a crack network is preferable for the structural integrity of cracked components.
References
Erdogan, F., Sih, G.C., 1963. On the crack extension in plates under plane loading and transverse shear. J. Basic Eng., 519–527.
Haddar, N., Fissolo, A., 2005. 2D simulation of the initiation and propagation of crack array under thermal fatigue. Nucl. Eng. Des. 235, 945–964.
Haddar, N., Fissolo, A.,Maillot, V., 2005. Thermal fatigue crack networks: an computational study. Int. J. Solid Struct. 42, 771–788.
Hayashi, M., Hirano, A., 2003. High cycle thermal fatigue crack initiation and growth behavior in simulated BWR environment. Trans. Jpn. Soc. Mech. Eng. A 69, 1353–1359.
Jaske, C.E., O’Donnell, W.J., 1977. Fatigue design criteria for pressure vessel alloys. Trans. ASME, J. Press. Vess. Technol. 99, 584–592.
Kamaya, M., 2008. Growth evaluation of multiple interacting surface cracks. Part I. Experiments and simulation of coalesced crack. Eng. Fracture Mech. 75, 1336–1349.
Kamaya, M., 2005. Influence of the interaction on stress intensity factor of semielliptical surface cracks. In: Proceedings of the 2005 ASME Pressure Vessels and Piping Division Conference, Denver, PVP, p. 71352.
Kamaya, M., Haruna, T., 2006. Crack initiation model for sensitized 304 stainless steel in high temperature water. Corros. Sci. 48, 2442–
2456.
Kamaya, M., Haruna, T., 2007. Influence of local stress on initiation behavior of stress corrosion cracking for sensitized 304 stainless steel. Corros. Sci. 49, 3303–3324.
Kamaya, M., Totsuka, N., 2002. Influence of interaction between multiple cracks on stress corrosion crack propagation. Corros. Sci. 44, 2333–2352.
Kasahara, N., Nagata, T., Iwata, K., Negishi, H., 1995. Advanced creep-fatigue evaluation rule for fast breeder reactor components: generalization of elastic follow-up model. Nucl. Eng. Des. 155, 499–518.
Kasahara, N., Takasho, H., Yscumpai, A., 2002. Structural response function approach for evaluation of thermal striping phenomena. Nucl. Eng. Des. 212, 281–292.
Maillot, V., Fissolo, A., Degallaix, G., Degallaix, S., 2005. Thermal fatigue crack networks parameters and stability: an experimental study. Int. J. Solids Struct. 42, 759–769.
Molinie, E., Monteil, N., Delatouche, S., Roux, S., Robert, N., Pages, C., 2002. Caracterisation des troncons RRA 900–1300MWe deposes: synthese des enseignements acquis. Porc. Fontevroud 5, 883–895.
Murakami, Y., Nishitani, H., 1981. Trans. Jpn. Soc. Mech. Eng. A 47, 295–303.
Murakami, Y., Nemat-Nasser, S., 1982. Interacting dissimilar semi-elliptical surface flaws under tension and bending. Eng. Fracture Mech. 16, 373–386.
Nishitani, H., Murakami, Y., 1974. Stress intensity factors of an elliptical crack or a semi-elliptical crack subject to tension. Int. J. Fracture 10, 353–368.
Taheri, T., 2007. Some advances on understanding of high cycle thermal fatigue crazing. ASME J. Press. Technol. 129, 400–410.
By : Masayuki Kamaya, Said Taheri
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