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Simulation of ductile fracture of zirconium alloys based on triaxiality dependent cohesive zone model. (English) Zbl 1475.74114

Summary: The growth and coalescence of microvoids nucleating in the second phase particles are the dominant mechanism of ductile fracture. The ductile fracture process is strongly influenced by the stress state. Based on a triaxiality dependent cohesive zone model, the ductile fracture process of zirconium alloys under different stress states is described in the present study. Under the condition of plane strain, a compact tension analysis configuration is established for hydrided zirconium alloys composed of matrix and hydrides. By comparing our prediction with the results based on the extended finite element method, we can calibrate model parameters and then verify the model. The results show that the presence of hydrides accelerates the crack propagation and decreases the post-peak load level. Moreover, we find that the fracture resistance of zirconium alloys is strongly affected by the length, arrangement, quantity, and spacing of the hydrides. Specifically, for hydrides with the length along the crack propagation path, the increase in their length enhances the peak load and reduces the corresponding boundary displacement. The increase in their quantity reduces the post-peak load level. Besides, the increase in their spacing enhances the boundary displacement corresponding to the sudden load drop. For the ductile fracture of zirconium alloys, these simulation results provide insights into their ability to resist crack propagation.

MSC:

74R20 Anelastic fracture and damage
74S05 Finite element methods applied to problems in solid mechanics

Software:

ABAQUS
Full Text: DOI

References:

[1] Mallipudi, V.; Valance, S.; Bertsch, J., Meso-scale analysis of the creep behavior of hydrogenated Zircaloy-4, Mech. Mater., 51, 15-28 (2012) · doi:10.1016/j.mechmat.2012.03.003
[2] Guo, DF; Li, M.; Shi, YD; Zhang, ZB; Zhang, HT; Liu, XM; Wei, BN; Zhang, XY, High strength and ductility in multimodal-structured Zr, Mater. Design, 34, 275-278 (2012) · doi:10.1016/j.matdes.2011.08.002
[3] Alam, T.; Khan, MK; Pathak, M.; Ravi, K.; Singh, R.; Gupta, SK, A review on the clad failure studies, Nucl. Eng. Des., 241, 9, 3658-3677 (2011) · doi:10.1016/j.nucengdes.2011.08.009
[4] Xiao, L.; Umakoshi, Y.; Sun, J., Biaxial low cycle fatigue properties and dislocation substructures of zircaloy-4 under in-phase and out-of-phase loading, Mater. Sci. Eng. A., 292, 40-48 (2000) · doi:10.1016/S0921-5093(00)01005-4
[5] Sundell, G.; Thuvander, M.; Andren, HO, Barrier oxide chemistry and hydrogen pick-up mechanisms in zirconium alloys, Corros. Sci., 102, 490-502 (2016) · doi:10.1016/j.corsci.2015.11.002
[6] Varias, AG; Massih, AR, Simulation of hydrogen embrittlement in zirconium alloys under stress and temperature gradients, J. Nucl. Mater., 279, 2-3, 273-285 (2000) · doi:10.1016/S0022-3115(99)00286-X
[7] Singh, RN; Mukherjee, S.; Gupta, A.; Banerjee, S., Terminal solid solubility of hydrogen in Zr-alloy pressure tube materials, J. Alloy. Compd., 389, 1-2, 102-112 (2005) · doi:10.1016/j.jallcom.2004.07.048
[8] Ghahremaninezhad, A.; Ravi-Chandar, K., Ductile failure behavior of polycrystalline Al 6061-T6, Int. J. Fracture, 174, 2, 177-202 (2012) · doi:10.1007/s10704-012-9689-z
[9] Pardoen, T.; Brechet, Y., Influence of microstructure-driven strain localization on the ductile fracture of metallic alloys, Philos. Mag., 84, 3-5, 269-297 (2004) · doi:10.1080/14786430310001610366
[10] Bao, Y.; Wierzbicki, T., On fracture locus in the equivalent strain and stress triaxiality space, Int. J. Mech. Sci., 46, 81-98 (2004) · doi:10.1016/j.ijmecsci.2004.02.006
[11] Nahshon, K.; Hutchinson, JW, Modification of the Gurson model for shear failure, Eur. J. Mech. A-Solid, 27, 1-17 (2008) · Zbl 1129.74041 · doi:10.1016/j.euromechsol.2007.08.002
[12] Li, Z.; Shi, J.; Tang, A., Investigation on fracture mechanisms of metals under various stress states, Acta Mech., 225, 7, 1867-1881 (2014) · doi:10.1007/s00707-013-1024-x
[13] Li, WC; Liao, FF; Zhou, TH; Askes, H., Ductile fracture of Q460 steel: effects of stress triaxiality and lode angle, J. Constr. Steel. Res., 123, 1-17 (2016) · doi:10.1016/j.jcsr.2016.04.018
[14] Wang, LN; Shi, YD; Zhang, YL; Bai, Y.; Lei, S., Ductile to brittle fracture of CP titanium with torsion deformation, Mater. Lett., 217, 263-266 (2018) · doi:10.1016/j.matlet.2018.01.110
[15] Gao, B.; Zhang, G.; Guo, TF; Jiang, C.; Guo, X.; Tang, S., Voiding and fracture in high-entropy alloy under multi-axis stress states, Mater. Lett., 237, 220-223 (2019) · doi:10.1016/j.matlet.2018.11.106
[16] Li, XC; Su, Y., A phase-field study of the martensitic detwinning in NiTi shape memory alloys under tension or compression, Acta Mech., 231, 4, 1539-1557 (2020) · Zbl 1440.74235 · doi:10.1007/s00707-020-02613-x
[17] Xi, SB; Su, Y., Phase field study of the microstructural dynamic evolution and mechanical response of NiTi shape memory alloy under mechanical loading, Materials, 14, 1, 183 (2021) · doi:10.3390/ma14010183
[18] Gurson, AL, Continuum theory of ductile rupture by void nucleation and growth, J. Eng. Mate-T. ASME, 99, 2, 2-15 (1977) · doi:10.1115/1.3443401
[19] Needleman, A.; Tvergaard, V., An analysis of ductile rupture modes at a crack tip, J. Mech. Phy. Solids, 35, 151-183 (1987) · Zbl 0601.73106 · doi:10.1016/0022-5096(87)90034-2
[20] Reboul, J.; Vadillo, G., Homogenized Gurson-type behavior equations for strain rate sensitive materials, Acta Mech., 229, 1-20 (2018) · Zbl 1396.74050 · doi:10.1007/s00707-018-2189-0
[21] Suman, S.; Khan, MK; Pathak, M.; Singh, RN, 3D simulation of hydride-assisted crack propagation in zircaloy-4 using XFEM, Int. J. Hydrogen Energ., 42, 29, 18668-18673 (2017) · doi:10.1016/j.ijhydene.2017.04.163
[22] Hughes, T.; Cottrell, JA; Bazilevs, Y., Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Method. Appl. M., 194, 39-41, 4135-4195 (2005) · Zbl 1151.74419 · doi:10.1016/j.cma.2004.10.008
[23] Nguyen, VO; Anitescu, C.; Bordas, SPA; Rabczuk, T., Isogeometric analysis: An overview and computer implementation aspects, Math. Comput. Simulat., 117, 89-116 (2015) · Zbl 1540.65492 · doi:10.1016/j.matcom.2015.05.008
[24] Song, JH; Wang, HW; Belytschko, T., A comparative study on finite element methods for dynamic fracture, Comput. Mech., 42, 239-250 (2008) · Zbl 1160.74048 · doi:10.1007/s00466-007-0210-x
[25] Dugdale, DS, Yielding of steel sheets containing slits, J. Mech. Phy. Solids, 8, 2, 100-104 (1960) · doi:10.1016/0022-5096(60)90013-2
[26] Barenblatt, GI, The mechanical theory of equilibrium cracks in brittle fracture, Adv. App. Mech., 7, 55-129 (1962) · doi:10.1016/S0065-2156(08)70121-2
[27] Needleman, A., A continuum model for void nucleation by inclusion debonding, J. Appl. Mech., 54, 525-531 (1987) · Zbl 0626.73010 · doi:10.1115/1.3173064
[28] Guo, X.; Yang, G.; Weng, GJ; Lu, J., Interface effects on the strength and ductility of bimodal nanostructured metals, Acta Mech., 229, 8, 3475-3487 (2018) · doi:10.1007/s00707-018-2181-8
[29] Xu, XP; Needleman, A., Void nucleation by inclusion debonding in a crystal matrix, Model. Simul. Mater. Sc., 1, 2, 111-132 (1993) · doi:10.1088/0965-0393/1/2/001
[30] Tvergaard, V.; Hutchinson, JW, The relation between crack growth resistance and fracture process parameters in elastic-plastic solids, J. Mech. Phy. Solids, 40, 6, 1377-1397 (1992) · Zbl 0775.73218 · doi:10.1016/0022-5096(92)90020-3
[31] Scheider, I.; Brocks, W., The effect of the traction separation law on the results of cohesive zone crack propagation analyses, Key. Eng. Mater., 251, 313-318 (2003) · doi:10.4028/www.scientific.net/KEM.251-252.313
[32] Shen, N.; Peng, MY; Gu, ST; Hu, YG, Effects of the progressive damage interphase on the effective bulk behavior of spherical particulate composites, Acta Mech., 232, 2, 1-15 (2021) · Zbl 1458.74010 · doi:10.1007/s00707-020-02836-y
[33] Siegmund, T.; Brocks, W., Prediction of the work of separation and implications to modeling, Int. J. Fracture, 99, 1-2, 97-116 (1999) · doi:10.1023/A:1018300226682
[34] Siegmund, T.; Brocks, W., A numerical study on the correlation between the work of separation and the dissipation rate in ductile fracture, Eng. Fract. Mech., 67, 139-154 (2000) · doi:10.1016/S0013-7944(00)00054-0
[35] Anvari, M.; Scheider, I.; Thaulow, C., Simulation of dynamic ductile growth using strain-rate and triaxiality dependent cohesive elements, Eng. Fract. Mech., 73, 2210-2228 (2006) · doi:10.1016/j.engfracmech.2006.03.016
[36] Banerjee, A.; Manivasagam, R., Triaxiality dependent cohesive zone model, Eng. Fract. Mech., 76, 1761-1770 (2009) · doi:10.1016/j.engfracmech.2009.03.009
[37] Rashid, FM; Banerjee, A., Implementation and validation of a triaxiality dependent cohesive model: experiments and simulations, Int. J. Fracture, 181, 2, 227-239 (2013) · doi:10.1007/s10704-013-9837-0
[38] Rashid, FM; Banerjee, A., Simulation of fracture in a low ductility aluminum alloy using a triaxiality dependent cohesive model, Eng. Fract. Mech., 179, 1-12 (2017) · doi:10.1016/j.engfracmech.2017.04.028
[39] Scheider, I.; Rajendran, M.; Banerjee, A., Comparison of different stress-state dependent cohesive zone models applied to thin-walled structures, Eng. Fract. Mech., 78, 3, 534-543 (2011) · doi:10.1016/j.engfracmech.2010.05.003
[40] Liong, RT; Proppe, C., Application of the cohesive zone model for the evaluation of stiffness losses in a rotor with a transverse breathing crack, J. Sound Vib., 332, 8, 2098-2110 (2013) · doi:10.1016/j.jsv.2012.11.032
[41] Pineau, A.; Benzerga, AA; Pardoen, T., Failure of metals I: Brittle and ductile fracture, Acta Mater., 107, 424-483 (2016) · doi:10.1016/j.actamat.2015.12.034
[42] Rahnama, H.; Salehi, D.; Taheri-Behrooz, F., Centrosymmetric equilibrium of nested spherical inhomogeneities in first strain gradient elasticity, Acta Mech., 231, 4, 1377-1402 (2020) · Zbl 1440.74061 · doi:10.1007/s00707-019-02570-0
[43] Pshenichnikov, A.; Stuckert, J.; Walter, M., Microstructure and mechanical properties of Zircaloy-4 cladding hydrogenated at temperatures typical for loss-of-coolant accident (LOCA) conditions, Nucl. Eng. Des., 283, 33-39 (2015) · doi:10.1016/j.nucengdes.2014.06.022
[44] Kim, JS; Kim, TH; Kook, DH; Kim, YS, Effects of hydride morphology on the embrittlement of Zircaloy-4 cladding, J. Nucl. Mater., 456, 235-245 (2015) · doi:10.1016/j.jnucmat.2014.09.025
[45] Chen, W.; Kou, H.; Chen, L.; Wang, F.; Zeng, XG, Theory model combined with XFEM of threshold stress intensity factor and critical hydride length for delay hydride cracking, Int. J. Hydrogen Energ., 44, 54, 29047-29056 (2019) · doi:10.1016/j.ijhydene.2019.08.157
[46] Tseng, CC; Sun, MH; Chao, CK, Hydride effect on crack instability of Zircaloy cladding, Nucl. Eng. Des., 270, 427-435 (2014) · doi:10.1016/j.nucengdes.2014.01.013
[47] Cheng, H.; Chen, G.; Zhang, Z.; Chen, X., Uniaxial ratcheting behaviors of Zircaloy-4 tubes at 400 °C, J. Nucl. Mater., 458, 129-137 (2015) · doi:10.1016/j.jnucmat.2014.12.028
[48] ABAQUS User’s Manual. USA: ABAQUS User’s manual, version 6.11; 2011.
[49] Brocks, W.; Scheider, I.; Schödel, M., Simulation of crack extension in shell structures and prediction of residual strength, Arch. Appl. Mech., 76, 11-12, 655-665 (2006) · Zbl 1161.74468 · doi:10.1007/s00419-006-0041-9
[50] Xu, J.; Shi, SQ, Investigation of mechanical properties of ε-zirconium hydride using micro- and nano-indentation techniques, J. Nucl. Mater., 327, 2, 165-170 (2004) · doi:10.1016/j.jnucmat.2004.02.004
[51] Wen, MJ; Li, H.; Yu, DJ; Chen, G.; Chen, X., Uniaxial ratcheting behavior of Zircaloy-4 tubes at room temperature, Mater. Design, 46, 426-434 (2013) · doi:10.1016/j.matdes.2012.10.049
[52] Zhang, JY; Zhu, JC; Ding, SR; Chen, L.; Li, WJ; Pang, H., Theoretical models of threshold stress intensity factor and critical hydride length for delayed hydride cracking considering thermal stresses, Nucl. Eng. Technol., 50, 7, 1138-1147 (2018) · doi:10.1016/j.net.2018.07.001
[53] Daum, RS; Majumdar, S.; Liu, YY; Billone, MC, Radial-hydride embrittlement of high-burnup Zircaloy-4 fuel cladding, J. Nucl. Sci. Technol., 43, 9, 1054-1067 (2006) · doi:10.1080/18811248.2006.9711195
[54] Hsu, HH; Tsay, LW, Effect of hydride orientation on fracture toughness of Zircaloy-4 cladding, J. Nucl. Mater., 408, 1, 67-72 (2011) · doi:10.1016/j.jnucmat.2010.10.068
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