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Modeling of structural failure of Zircaloy claddings induced by multiple hydride cracks

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Abstract

Zirconium alloys have been serving as primary structural materials for nuclear fuel claddings. Structural failure analysis under extreme conditions is critical to the assessment of the performance and safety of nuclear fuel claddings. This work focuses on simulating structural failure of Zircaloy tubes with multiple hydride defects through modeling explicit crack propagation in ductile media. First, we developed an integrated cladding failure model by taking into account both crack initiation induced by hydride/matrix interface separation and ligament tearing-off between activated hydride cracks. Second, to accommodate the initiation, propagation, and coalescence of multiple cracks in finite plastic media we incorporated this structural failure model into a coupled continuous/discontinuous Galerkin (DG) based finite element code, a traditionally preferred implicit numerical framework. Third, to improve the adaptive placement of DG interface elements for crack propagation and to identify potential coalescence of cracks due to the interaction between adjacent hydride cracks, we defined a special failure index for the assessment of potential failure zones using both true plastic strain developed and predicted failure strain based on the Johnson–Cook material failure criterion. Finally, by calibrating the proposed material failure model using a cluster of Zircaloy material experimental tests, we successfully simulated a complete failure process of a fuel cladding tube with multiple hydride cracks.

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References

  • Adamson R, Coleman K, Mahmood T, Rudling P (2013) ZIRAT-18 special topics report. In: Mechanical testing of zirconium alloys, volume I. ANT International, Sweden, December, 2013

  • Allen T, Busby J, Meyer M, Petti D (2010) Materials challenges for nuclear systems. Mater Today 13:14–23

    Article  CAS  Google Scholar 

  • Argon AS, Im J, Safoglu R (1975) Cavity formation from inclusions in ductile fracture. Metall Trans A 6(4):825–837

    Article  Google Scholar 

  • Arias D, Palacios T, Turrillo C (1987) Composition of precipitates presente in zircaloy-2 and 4. J Nucl Mater 148:227–229

    Article  CAS  Google Scholar 

  • Bai Y, Wierzbicki T (2008) A new model of metal plasticity and fracture with pressure and Lode dependence. Int J Plast 24:1071–1096

    Article  CAS  Google Scholar 

  • Bai JB, Prioul C, Francois D (1994) Hydride embrittlement in Zircaloy-4 plate: Part I Influence of microstructure on the hydride embrittlement in ZIRCALOY-4 at 20 C and 350 C. Metall Mater Trans A 25:1185

    Article  Google Scholar 

  • Benzerga A, Leblond J-B, Needleman A, Tvergaard V (2016) Ductile failure modeling. Int J Fract 201:29–80

    Article  Google Scholar 

  • Beremin FM (1981) Cavity formation from inclusions in ductile fracture of A508 steel. Metall Trans A 12(5):723–731

    Article  CAS  Google Scholar 

  • Bertolino G, Meyer G, Ipina JP (2002) Degradation of the mechanical properties of Zircaloy-4 due to hydrogen embrittlement. J Alloys Compd 330:408–413

    Article  Google Scholar 

  • Bertolino G, Meyer G, Ipina JP (2002) Effects of hydrogen content and temperature on fracture toughness of Zircaloy-4. J Nucl Mater 320:272–279

    Article  Google Scholar 

  • Bertolino G, Meyer G, Ipina JP (2003) Effects of hydrogen content and temperature on fracture toughness of Zircaloy-4. J Nucl Mater 322:57–65

    Article  CAS  Google Scholar 

  • Bertsch J, Hoffelner W (2006) Crack resistance curves determination of tube cladding material. J Nucl Mater 352:116–125

    Article  CAS  Google Scholar 

  • Billone MC, Burtseva TA, Einziger R (2013) Ductile-to-brittle transition temperature for high burnup cladding alloys exposed to simulated drying-storage conditions. J Nucl Mater 433:431–448

    Article  CAS  Google Scholar 

  • Boyce BL (2014) The sandia fracture challenge: blind round robin predictions of ductile tearing. Int J Fract 186:5–68

    Article  Google Scholar 

  • Chan KS (1995) A fracture model for hydride-induced embrittlement. Acta Metall Mater 43:4325–4335

    Article  CAS  Google Scholar 

  • Chan KS (1996) A micromechanical model for predicting hydride embrittlement in nuclear fuel cladding material. J Nucl Mater 227:220–236

    Article  CAS  Google Scholar 

  • Choubey R, Puls MP (1994) Crack initiation at long radial hydrides in Zr-2.5nb pressure tube material at elevated temperatures. Met Trans 25A:993–1004

    Article  CAS  Google Scholar 

  • Cinbiz MN, Edmondson PD, Terrani K (2017) Hydride microstructure at the metal-oxide interface of a Zircaloy-4 fuel clad from the H. B. Robinson nuclear reactor. Trans Am Nucl Soc 116:354–356

    Google Scholar 

  • Cockburn B, Shu C (1998) The local discontinuous Galerkin finite element method for convection-diffusion systems. SIAM J Numer Anal 35:2440–2463

    Article  Google Scholar 

  • Cockeram BV, Chan KS (2009) Modeling the tension-compression asymmetric yield behavior of beta-treated Zircaloy-4. J Nucl Mater 393:387–408

    Article  CAS  Google Scholar 

  • Cockeram BV, Chan KS (2013) In situ studies and modeling of the deformation and fracture mechanism for wrought Zircaloy-4 and Zircaloy-2 as a function of stress-state. J Nucl Mater 434:97–123

    Article  CAS  Google Scholar 

  • Cockeram BV, Hollenbeck JL (2015) The role of stress-state on the deformation and fracture mechanism of hydrided and non-hydrided Zircaloy-4. J Nucl Mater 467:9–31

    Article  CAS  Google Scholar 

  • Coleman CE (2012) Comprehensive nuclear materials, Chap 6.03. In: Cracking of hydride-forming metals and alloys. Elsevier, Amsterdam

    Chapter  Google Scholar 

  • Fitoussi J, Guo G, Baptiste D (1996) Determination of a tridimensional failure criterion at the fibre/matrix interface of an organic-matrix/discontinuous-reinforcement composite. Compos Sci Technol 56:755–760

    Article  CAS  Google Scholar 

  • Gao X, Kim J (2006) Modeling of ductile fracture: significance of void coalescence. Int J Solids Struct 43:6277–6293

    Article  Google Scholar 

  • Grange M, Besson J (2000) Anisotropic behavior and rupture of hydrided Zircaloy-4 sheets. Metall Mater Trans 31A:679–690

    Article  CAS  Google Scholar 

  • Gross AJ, Ravi-Chandar K (2014) Prediction of ductile failure using a local strain-to-failure criterion. Int J Fract 186:69–91

    Article  Google Scholar 

  • Gross AJ, Ravi-Chandar K (2016) Prediction of ductile failure in Ti–6Al–4V using a local strain-to-failure criterion. Int J Fract 198(2016):221–245

    Article  CAS  Google Scholar 

  • Hansbo P, Larson MG (2002) Discontinuous Galerkin method for incompressible and nearly incompressible elasticity by Nitche’s methods. Comput Methods Appl Mech Eng 191:1895–1908

    Article  Google Scholar 

  • Huang FH (1993) Brittle-fracture potential of irradiated Zircaloy-2 pressure tubes. J Nucl Mater 207:103–115

    Article  CAS  Google Scholar 

  • Johnson GR, Cook WH (1985) Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng Fract Mech 21:31–48

    Article  Google Scholar 

  • Kerr M, Daymond MR, Holt RA, Almer JD (2008) Strain evolution of zirconium hydride embedded in a Zircaloy-2 matrix. J Nucl Mater 380:70–75

    Article  CAS  Google Scholar 

  • Kikuchi M, Wada Y, Suga K, Ohdama C (2011) Numerical simulation of coalescence behavior of multiple surface cracks. In: American society of mechanical engineers, pressure vessels and piping division

  • Le Saux M, Besson J, Carassou S, Poussard C, Averty X (2010) Behavior and failure of uniformly hydrided Zircaloy-4 fuel claddings under various stress states, including RIA loading conditions. Eng Fail Anal 17:683–700

    Article  Google Scholar 

  • Lee BJ, Mear M (1999) Stress concentration induced by an elastic spheroidal particle in a plastically deforming solid. J Mech Phys Solids 47:1301–1336

    Article  Google Scholar 

  • Lew A, Neff P, Sulsky D, Ortiz M (2004) Optimal BV estimates for a discontinuous Galerkin method for linear elasticity. Appl Math Res Express 3:73–106

    Article  Google Scholar 

  • Liu R, Wheeler MF, Yotov I (2012) On the spatial formulation of discontinuous Galerkin methods for finite elastoplasticity. Comput Methods Appl Mech Eng 253:219–236

    Article  Google Scholar 

  • Liu Z, Moore JA, Liu WK (2016) An extended micromechanics method for probing interphase properties in polymer nanocomposites. J Mech Phys Solids 95:663–680

    Article  CAS  Google Scholar 

  • Liu R, Liu Z (2018) An implicit discontinuous Galerkin finite element framework for modeling fracture failure of ductile materials undergoing finite plastic deformation. Int J Numer Methods Eng 115:1383–1409

    Article  Google Scholar 

  • Martin Rengel MA (2012) A micromechanical model for predicting hydride embrittlement in nuclear fuel cladding material. J Nucl Mater 429:276–283

    Article  CAS  Google Scholar 

  • Nilsson K-F, Jaksil N, Vokal V (2010) An elastic–plastic fracture mechanics based model assessment of hydride embrittlement in zircaloy cladding tubes. J Nucl Mater 396:71–85

    Article  CAS  Google Scholar 

  • Nitsche J (1970) Über ein Variationsprinzip zur Lösung von Dirichlet bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh Math Univ Hamburg 36:9–15

    Article  Google Scholar 

  • Noels L, Radovitzky R (2006) A general discontinuous Galerkin method for finite hyperelasticity. Formulation and numerical applications. Int J Numer Methods Eng 68:64–97

    Article  Google Scholar 

  • Northwood DO, Kosasih U (1983) Hydrides and delayed hydrogen cracking in zirconium and its alloys. Int Met Rev 28:92–121

    Article  CAS  Google Scholar 

  • Pardoen T, Hutchinson JW (2000) An extended model for void growth and coalescence. J Mech Phys Solids 48:2467–2512

    Article  Google Scholar 

  • Pardoen T, Hutchinson JW (2003) Micromechanics-based model for trends in toughness of ductile metals. Acta Mater 51:133–148

    Article  CAS  Google Scholar 

  • Puls MP (1988) The influence of hydride size and matrix strength on fracture initiation at hydrides in zirconium alloys. Metall Trans A 19(1988):1507–1522

    Article  Google Scholar 

  • Puls MP (1991) Fracture initiation at hydrides in zirconium. Metall Trans A 22:2327–2337

    Article  Google Scholar 

  • Puls MP (2012) The effect of hydrogen and hydrides on the integrity of zirconium alloy components: delayed hydride cracking engineering materials, vol 13. Springer, Berlin, pp 978–1447

    Book  Google Scholar 

  • Qin W, Szpunar JA, Kiran Kumar NAP, Kozinsk J (2014) Microstructural criteria for abrupt ductile-to-brittle transition induced by hydrides in zirconium alloys. Acta Meter 81:219–229

    Article  CAS  Google Scholar 

  • Riviere B, Shaw S, Wheeler MF, Whiteman JR (2003) Discontinuous Galerkin finite element methods for linear elasticity and quasistatic linear viscoelasticity. Numer Math 95:347–376

    Article  Google Scholar 

  • Roux E, Shakoor M, Bernacki M, Bouchard P-O (2014) A new finite element approach for modelling ductile damage void nucleation and growth—analysis of loading path effect on damage mechanisms. Model Simul Mater Sci Eng 22:075001

    Article  Google Scholar 

  • Sakamoto K, Nakatsuka M (2006) Stress reorientation of hydrides in recrystallized Zircaloy-2 sheet. J Nucl Sci Technol 43:1136–1141

    Article  CAS  Google Scholar 

  • Thomason PF (1985) Three-dimensional models for the plastic limit-loads at incipient failure of the intervoid matrix in ductile porous solids. Acta Metall 33:1079–1085

    Article  CAS  Google Scholar 

  • Truster TJ, Masud A (2013) A discontinuous/continuous Galerkin method for modeling of interphase damage in fibrous composite systems. Comput Mech 52:499–514

    Article  Google Scholar 

  • Tvergaard V, Hutchinson JW (2002) Two mechanisms of ductile fracture: void by void growth versus multiple void interaction. Int J Solids Struct 39:3581–3597

    Article  Google Scholar 

  • Walker TJ, Kass JN (1974) Zirconium in the nuclear applications. In: ASTM STP 551. American Society for Testing and Materials, pp 328–354

  • WARP3D (2016) WARP3D-release 17.7.0. 3-D dynamic nonlinear fracture analysis of solids using parallel computers and workstations. In: University of Illinois report UILU-ENG-95-2012. University of Illinois at Urbana-Champaign, Urbana, Illinois

  • Wells GN, Garikipati K, Molari L (2004) A discontinuous Galerkin formulation for a strain gradient-dependent damage model. Comput Methods Appl Mech Eng 193:3633–3645

    Article  Google Scholar 

  • Xue L (2008) Constitutive modeling of void shearing effect in ductile fracture of porous materials and pressures. Eng Fract Mech 75:3343–3366

    Article  Google Scholar 

  • Zhai J, Gao X, Sobotka JC, Webler BA, Cockeram BV (2014) Modeling the tension-compression asymmetric yield behavior of beta-treated Zircaloy-4. J Nucl Mater 451:292–299

    Article  CAS  Google Scholar 

  • Zhou J, Gao X, Sobotka JC, Webler BA, Cockeram BV (2014) On the extension of the Gurson-type porous plasticity models for prediction of ductile fracture under shear-dominated conditions. J Solid Struct 51:3273–3291

    Article  Google Scholar 

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Acknowledgements

This research was supported by the new faculty startup fund at The University of Texas at San Antonio. Advice from and discussion with Dr. K. Ravi-Chandar are appreciated.

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Correspondence to Ruijie Liu.

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Liu, R., Mostafa, A. & Liu, Z. Modeling of structural failure of Zircaloy claddings induced by multiple hydride cracks. Int J Fract 213, 171–191 (2018). https://doi.org/10.1007/s10704-018-0312-9

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