Abstract
The purpose of the present article is to develop a multi-scale brittle fracture modelling for irradiated RPV materials. For this development, applicability of local brittle fracture criteria for radiation embrittlement modelling is analysed through comparison of the predicted and test results on radiation embrittlement of RPV steels in terms of ductile-to-brittle transition temperature and fracture toughness. The influence of radiation-induced defects on the processes of cleavage microcrack nucleation and propagation is clarified. The physical-and-mechanical models of the effect of irradiation-induced defects on cleavage microcrack nucleation are developed on the basis of dislocation and brittle fracture theories. Stress-and-strain controlled fracture criterion is developed that allows the adequate prediction of radiation embrittlement by various mechanisms. The differences and commonalities are revealed in the nature of material embrittlement due to cold work and neutron irradiation. The mechanism is explained of significant recovery of fracture resistance properties with simultaneous increase of fraction of intercrystalline fracture after post-irradiation annealing. Engineering approach for prediction of the temperature dependence of fracture toughness as a function of neutron fluence is justified.
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Abbreviations
- σ 1 :
-
The maximumprincipal stress
- σ eq :
-
The equivalent stress
- \({{\ae}=\int {{d}\varepsilon_{\rm eq}^{\rm p}}}\) :
-
The accumulated plastic strain
- \({{d}\varepsilon_{{\rm eq}}^{\rm p}}\) :
-
The equivalent plastic strain increment
- σ Y :
-
The yield stress
- S C :
-
The critical stress for microcrack propagation (the critical brittle fracture stress)
- σ d :
-
The critical stress for microcrack nucleation
- \({\tilde{\sigma}_{\rm d} ,\quad \sigma_{{\rm d0}}}\) and \({\eta}\) :
-
The Weibull parameters for the probability of microcrack nucleation in unit cell
- \({\widetilde{{S}}_{\rm C}}\) and\({\xi}\) :
-
The Weibull parameters for the probability of microcrack propagation in unit cell
- KJC :
-
Fracture toughness
- Ttr :
-
The ductile-to-brittle transition temperature
- \({\Omega}\) :
-
The parameter controlling KJC(T) in the Unified Curve method
- T:
-
Temperature
- F:
-
Neutron fluence
References
Alekseenko NN, Amaev AD, Gorynin IV, Nikolaev VA (1997) Radiation damage of nuclear power plant pressure vessel steels. La Grange Park, Illinois
Allen NP (1959) Mechanism for brittle fracture of metals. In: Averbach BL (ed) Fracture: proceedings of an international conference on the atomic mechanisms of fracture held in Swampscott, Massachusetts. The Technology Press of Massachusetts Institute of Technology, Wiley, New York, 12–16 April 1959
Ashby MF (1970) About the Orovan stress. In: Argon A (ed) Physics of strength and plasticity. The M.I.T. Press, Cambridge
Beremin FM (1983) A local criterion for cleavage fracture of a nuclear pressure vessel steel. Metall Trans 14A: 2277–2287
Bordet SR, Karstensen AD, Knowles DM, Wiesner CS (2005) A new statistical local criterion for cleavage fracture in steel. Eng Fract Mech 72: 435–474
Chen JH, Yan C, Sun J (1994) Further study on the mechanism of cleavage fracture at low temperatures. Acta Metall Mater 42: 251–261
Davidenkov NN (1936) Dynamic testing of materials. ONTI, Moscow (in Russian)
Debarberis L, Acosta B, Sevini F, Kryukov A, Gillemot F, Valo M, Nikolaev V, Brumovsky M (2005) Role of nickel in a semi-mechanistic analytical model for radiation embrittlement of model alloys. J Nucl Mater 336: 210–216
Diard O (2005) A multi-scale approach for prediction of irradiation effect on RPV steel toughness. In: Proceeding of 2005 ASME pressure vessels and piping conference, PVP 2005-71710
Erak D, Gurovich B, Shtrombakh Ya, Zhurko D (2010) Degradation and recovery of mechanical properties of VVER-1000 pressure vessel materials. Fontevraud, vol 7, 26–30 Sept 2010, Ref. n. A096-T01
Fortner E, Katz L, Evanchan NL (1976) Proceedings of 2nd international conference mechanical behavior of materials, Boston, pp 1264–1275
Fridman YB (1952) Mechanical properties of metals. Oborongiz, Moscow (in Russian)
Gorynin IV, Nesterova EV, Nikolaev VA, Rybin VV (1996) Microstructure and mechanical properties of WWER-440 reactor vessel metal after service life expiration and recovery anneal. In: Gelles D, Nanstad R, Kumar A, Little E (eds) Effect of radiation on materials: 17 international symposium, ASTM STP 1270, ASTM, pp 248–259
Gurovich BA, Kuleshova EA, Lavrenchuk OV (1996) Comparative study of fracture in pressure vessel steels A533B and A508. J Nucl Mater 228: 330–337
Gurovich BA, Kuleshova EA, Nikolaev YA, Shtrombakh YI (1997) Assessment of relative contributions from different mechanisms to radiation embrittlement of reactor pressure vessel steels. J Nucl Mater 246: 91–120
Gurovich BA, Kuleshova EA, Shtrombakh YI et al (2000) Intergranular and intragranular phosphorus segregation in Russian pressure vessel steels due to neutron irradiation. J Nucl Mater 279: 259–272
Gurovich B, Kuleshova E, Prikhodko K, Fedotova S (2010) Assessment of the recovery annealing efficiency for VVER-1000 materials structure reset and lifetime extension. Fontevraud, vol 7, 26–30 Sept 2010, Ref. n. A009-T01
Hawthorne JR (1983) Radiation embrittlement. In: Briant C, Banerji S (eds) Embrittlement of engineering alloys. Academic Press, New York
Knott JF (1973) Fundamentals of fracture mechanics. Butterworths, London
Kurdyumov GV, Utevsky LM, Entin RI (1983) Transformation of austenite under cooling and tempering of quenched steel. In: Berstein ML, Rakhshtadt AG (eds) Metal science and thermal treatment of steel, vol 2. Metallurgia, Moscow, pp 111–177 (in Russian)
Lidbury D, Bugat S, Diard O, Keim E, Marini B, Viehrig H-W, Wallin K (2006) PERFECT: progress with multi-scale modelling in RPV mechanics sub-project. In: Besson J, Moinerau D, Steglich D (eds) EUROMECH-MECAMAT 2006: local approach to fracture. Mines, pp 459–464
Margolin BZ, Shvetsova VA (1992) Brittle fracture criterion: physical and mechanical approach. Probl Prochnosti (Probl Strength) N2:3–16 (in Russian)
Margolin BZ, Shvetsova VA (1996) Local criterion for cleavage fracture: structural and mechanical approach. J Phys IV 6: C6-225–C6-234
Margolin BZ, Shvetsova VA, Varovin AY (1996) Preliminary compression of a material as a factor of change in brittle fracture mechanism for BCC metals. Probl Prochnosti (Probl Strength) N4:5–18 (in Russian)
Margolin BZ, Shvetsova VA, Karzov GP (1997a) Brittle fracture of nuclear pressure vessel steels. Part I. Local criterion for cleavage fracture. Int J Press Vessel Pip 72: 73–87
Margolin BZ, Karzov GP, Shvetsova VA (1997b) Brittle fracture of nuclear pressure vessel steels. Part II. Prediction of fracture toughness. Int J Press Vessel Pip 72: 89–96
Margolin BZ, Gulenko AG, Shvetsova VA (1998a) Probabilistic model for fracture toughness prediction based on the new local fracture criteria. Int J Press Vessel Pip 75: 307–320
Margolin BZ, Gulenko AG, Shvetsova VA (1998b) Improved probabilistic model for fracture toughness prediction for nuclear pressure vessel steels. Int J Press Vessel Pip 75: 843–855
Margolin BZ, Shvetsova VA, Gulenko AG (1999) Radiation embrittlement modelling for reactor pressure vessel steels: I. Brittle fracture toughness prediction. Int J Press Vessel Pip 76: 715–729
Margolin BZ, Shvetsova VA, Gulenko AG et al (2002) Fracture toughness prediction for a reactor pressure vessel steel in the initial and highly embrittled states with the Master Curve approach and a probabilistic model. Int J Press Vessel Pip 79: 219–231
Margolin BZ, Gulenko AG, Nikolaev VA, Ryadkov LN (2003) A new engineering method for prediction of the fracture toughness temperature dependence for RPV steels. Int J Press Vessel Pip 80: 817–829
Margolin BZ, Gulenko AG, Nikolaev VA, Ryadkov LN (2005) Prediction of the dependence KJC(T) on neutron fluence for RPV steels on the basis of the Unified Curve concept. Int J Press Vessel Pip 82: 679–689
Margolin BZ, Shvetsova VA, Gulenko AG, Kostylev VI (2006) Application of a new cleavage fracture criterion for fracture toughness prediction for RPV steels. Fatigue Fract Eng Mater Struct 29(9): 697–713
Margolin BZ, Shvetsova VA, Gulenko AG, Kostylev VI (2007) Development of Prometey local approach and analysis of physical and mechanical aspects of brittle fracture of RPV steels. Int J Press Vessel Pip 84(5): 320–336
Margolin BZ, Shvetsova VA, Gulenko AG, Kostylev VI (2008a) Prometey local approach to brittle fracture: development and application. Eng Fract Mech 75: 3483–3498
Margolin B, Gulenko A, Shvetsova V, Nikolaev V, Lidbury D, Keim E (2008b) Physical and mechanical aspects of radiation embrittlement of RPV steels. In: Proceeding of 2008 ASME pressure vessels and piping conference, PVP 2008-61133
Margolin BZ, Shvetsova VA, Gulenko AG, Nesterova EV (2010) Local criterion of brittle fracture and radiation embrittlement of RPV steels. Probl Prochnosti (Strength Mater) N5:31–61 (in Russian)
Merkle JG, Wallin K, McCabe DE (1999) Technical basis for an ASTM standard on determining the reference temperature, T0 for ferritic steels in the transition range. NUREG/CR-5504, ORNL/TM-13631
Mudry F (1987) A local approach to cleavage fracture. Nucl Eng Des 105: 65–76
Nikolaev VA, Rybin VV (1996) Mechanisms controlling the composition influence on radiation hardening and embrittlement of iron-base alloys. In: Effect of radiation on materials, 17th international symposium, ASTM STP 1270, 1996, pp 3–24
Okamoto PR, Rehn LE (1979) Radiation-induced segregation in binary and ternary alloys. J Nucl Mater 83: 2–23
Ortner SR (2006) The ductile-to-brittle transition in steels controlled by particle cracking. Fatigue Fract Eng Mater Struct 29(9): 752–769
Parrot A, Dahl A, Forget P, Marini B (2006) Evaluation of fracture toughness from instrumented Charpy impact tests for a reactor pressure vessel steel using local approach to fracture. In: Besson J, Moinerau D, Steglich D (eds) EUROMECH-MECAMAT 2006: local approach to fracture. Mines, pp 291–296
Pisarenko GS, Krasowsky AJ (1972) Analysis of kinetics of quasibrittle fracture of crystalline materials. Mechanical Behaviour of Materials. In: Procedings of international conference mechanical behaviour of materials, vol 1. Kyoto 1971, pp 421–432
Qiao Y, Argon AS (2003) Cleavage crack-growth-resistance of grain boundaries in polycrystalline Fe-2% Si alloy: experiments and modeling. Mech Mater 35: 129–154
Rellick JR, McMahon CJ (1974) Intergranular embrittlement of iron-carbon alloys by impurities. Metall Trans 5: 2439–2450
Ritchie RO, Knott JF, Rice JR (1973) On the relation between critical tensile stress and fracture toughness in mild steel. J Mech Phys Solids 21: 395–410
Seah MP (1977) Grain boundary segregation and the T-t dependence of temper brittleness. Acta Metall 25: 345–357
Tikhonchev MY, Svetukhin VV (2011) Computational determination of threshold displacement energies and study of atom displacement cascade evolution near extended Zr-Nb interface: molecular dynamics simulation. Voprosy Mater (Mater Sci Probl) N4(68):140–152 (in Russian)
Tanguy B, Bouchet C, Bugat S, Besson J (2006) Local approach to fracture based prediction of the ΔT56J and ΔTIc,100 shifts due to irradiation for an A508 pressure vessel steel. Eng Fract Mech 73: 191–206
Thomson R (1983) Physics of fracture. In: Latanision R, Pickens J (eds) Atomistic of fracture. Plenum Press, New York, pp 167–204
Troschenko VT, Pokrovsky VV, Yasny PV et al (1989) The effect of pre-strain on brittle fracture resistance. Fisiko-Chim Mech Mater (Phys Chem Mech Mater) 6:3–12 (in Russian)
Tyson WR (1978) Kinetics of temper embrittlement. Acta Metall 26: 1471–1478
Wallin K (1984) The scatter in KIC results. Eng Fract Mech 19: 1085–1093
Wallin K (1985) The size effect in KIC results. Eng Fract Mech 22: 149–163
Williams TJ, Ellis D, English CA, Hyde J (2002) A model of irradiation damage in high nickel submerged arc welds. Int J Press Vessel Pip 79: 649–660
Yasny PV (1998) Plastically deformed materials: plasticity and fracture toughness. Svet, L’vov (in Ukrainian)
Yoffe AF, Kirpicheva MV, Levitskay MA (1924) Deformation and strength of crystals. Zhurnal Russ Phys Chim Obzchestva (J Russ Phys Chem Soc) 56:489–504 (in Russian)
Zelensky VF, Necludov IM, Ozhigov LC et al (1979) Some problems of the radiation damage physics. Kiev, Naukova Dumkas (in Russian)
Zerilli FJ, Armstrong RW (1987) Dislocation-mechanics-based constitutive relations for material dynamics calculations. J Appl Phys 61(5): 1816–1825
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Margolin, B., Shvetsova, V. & Gulenko, A. Radiation embrittlement modelling in multi-scale approach to brittle fracture of RPV steels. Int J Fract 179, 87–108 (2013). https://doi.org/10.1007/s10704-012-9775-2
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DOI: https://doi.org/10.1007/s10704-012-9775-2