DataVXInternational Journal of FracturePaper
journal article·2025-05-15

The role of β-phase on crack nucleation and propagation in dual phase zirconium polycrystals: a crystal plasticity finite element modeling

Saiedeh Marashi, Hamidreza Abdolvand

International Journal of Fracture· Volume 249· Issue 2
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OpenAlex topics: Nuclear Materials and Properties · Titanium Alloys Microstructure and Properties · Advanced materials and composites

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References (83)

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1. Abdolvand H (2022) Development of microstructure-sensitive damage models for zirconium polycrystals. Int J Plast 149:103156. https://doi.org/10.1016/J.IJPLAS.2021.10315610.1016/J.IJPLAS.2021.103156 ↗
2. Abdolvand H, Wilkinson AJ (2016) On the effects of reorientation and shear transfer during twin formation: comparison between high resolution electron backscatter diffraction experiments and a crystal plasticity finite element model. Int J Plast 84:160–182. https://doi.org/10.1016/j.ijplas.2016.05.00610.1016/j.ijplas.2016.05.006 ↗
3. Abdolvand H, Wright JP, Wilkinson AJ (2018) On the state of deformation in a polycrystalline material in three-dimension: elastic strains, lattice rotations, and deformation mechanisms. Int J Plast 106:145–163. https://doi.org/10.1016/J.IJPLAS.2018.03.00610.1016/J.IJPLAS.2018.03.006 ↗
4. Asaro RJ (1983) Crystal plasticity. J Appl Mech 50(4b):921–93410.1115/1.3167205 ↗
5. Briffod F et al (2019) Effect of crystallographic orientation and geometrical compatibility on fatigue crack initiation and propagation in rolled Ti-6Al-4V alloy. Acta Mater 177:56–67. https://doi.org/10.1016/j.actamat.2019.07.02510.1016/j.actamat.2019.07.025 ↗
6. Burgers WG (1934) On the process of transition of the cubic-body-centered modification into the hexagonal-close-packed modification of zirconium. Physica 1(7–12):561–58610.1016/S0031-8914(34)80244-3 ↗
7. Cai S et al (2009a) Elastic and plastic properties of βZr at room temperature. J Nucl Mater 393(1):67–76. https://doi.org/10.1016/j.jnucmat.2009.05.00710.1016/j.jnucmat.2009.05.007 ↗
8. Cai S, Daymond MR, Holt RA (2009b) Modeling the room temperature deformation of a two-phase zirconium alloy. Acta Mater 57(2):407–419. https://doi.org/10.1016/j.actamat.2008.09.02010.1016/j.actamat.2008.09.020 ↗
9. Cai S, Daymond MR, Holt RA (2012) Deformation of high β-phase fraction Zr–Nb alloys at room temperature. Acta Mater 60(8):3355–3369. https://doi.org/10.1016/j.actamat.2012.02.04010.1016/j.actamat.2012.02.040 ↗
10. Cho D, et al (2016) Development of evaluation procedures for crack initiation from in-service flaws in CANDU Zr–2.5Nb pressure tubes with hydrogen. In: Pressure vessels and piping conference, p V01AT01A05310.1115/PVP2016-64009 ↗
11. Clayton JD, Knap J (2015) Phase field modeling of directional fracture in anisotropic polycrystals. Comput Mater Sci 98:158–169. https://doi.org/10.1016/j.commatsci.2014.11.00910.1016/j.commatsci.2014.11.009 ↗
12. Cui J, Shek GK, Wang Z (2009) Overload fracture of hydrided region at simulated blunt flaws in Zr–2.5Nb pressure tube material. J Press Vessel Technol Trans ASME. https://doi.org/10.1115/1.314774310.1115/1.3147743 ↗
13. Daniel CS et al (2019) A detailed study of texture changes during alpha–beta processing of a zirconium alloy. J Alloys Compd 804:65–83. https://doi.org/10.1016/j.jallcom.2019.06.33810.1016/j.jallcom.2019.06.338 ↗
14. Daniel CS et al (2021) Co-deformation and dynamic annealing effects on the texture development during alpha–beta processing of a model Zr–Nb alloy. Acta Mater. https://doi.org/10.1016/j.actamat.2020.11653810.1016/j.actamat.2020.116538 ↗
15. Levine ED (1966) Deformation mechanisms in titanium at low temperatures. AIME Met Soc Trans 236(11):1558–1565
16. Fearnehough GD, Watkins B (1968) Application of the crack opening displacement approach to the prediction of pressurized tube failure. Int J Fract Mech 4(3):233–24310.1007/BF00185259 ↗
17. Feng ZH et al (2021) Evolution of β phase and mechanical mechanisms in an α-type Zr alloy processed by rolling at different temperatures. Mater Charact. https://doi.org/10.1016/j.matchar.2021.11087310.1016/j.matchar.2021.110873 ↗
18. Fong RWL et al (2012) Crystallographic texture and volume fraction of α and β phases in Zr–2.5Nb pressure tube material during heating and cooling. Metall Mater Trans a: Phys Metall Mater Sci 43(3):806–821. https://doi.org/10.1007/s11661-011-0914-610.1007/s11661-011-0914-6 ↗
19. Fu B et al (2015) The effects of Nb content on microstructure and fracture behavior of near α titanium alloys. Mater des (1980–2015) 66(1):267–273. https://doi.org/10.1016/J.MATDES.2014.10.06910.1016/J.MATDES.2014.10.069 ↗
20. Gopalan A et al (2022) Effect of manufacturing route on thermal creep behaviour of Zr–2.5Nb pressure tube alloy used in Indian PHWR. J Nucl Mater. https://doi.org/10.1016/j.jnucmat.2022.15390310.1016/j.jnucmat.2022.153903 ↗
21. He D et al (2014) Effect of retained beta layer on slip transmission in Ti–6Al–2Zr–1Mo–1V near alpha titanium alloy during tensile deformation at room temperature. Mater des 56:937–942. https://doi.org/10.1016/j.matdes.2013.12.01810.1016/j.matdes.2013.12.018 ↗
22. Hémery S, Stinville JC (2022) Microstructural and load hold effects on small fatigue crack growth in α+β dual phase Ti alloys. Int J Fatigue. https://doi.org/10.1016/j.ijfatigue.2021.10669910.1016/j.ijfatigue.2021.106699 ↗
23. Holt RA, Bickel GA, Christodoulou N (2008) Effect of fast neutron fluence on the creep anisotropy of Zr–2.5Nb tubes. J Nucl Mater 373(1–3):130–136. https://doi.org/10.1016/j.jnucmat.2007.05.03310.1016/j.jnucmat.2007.05.033 ↗
24. Kim YS, Cheong YM (2008) Anisotropic delayed hydride cracking velocity of CANDU Zr–2.5Nb pressure tubes’. J Nucl Mater 373(1–3):179–185. https://doi.org/10.1016/J.JNUCMAT.2007.05.04710.1016/J.JNUCMAT.2007.05.047 ↗
25. Kuhn C, Schlüter A, Müller R (2015) On degradation functions in phase field fracture models. Comput Mater Sci 108:374–384. https://doi.org/10.1016/j.commatsci.2015.05.03410.1016/j.commatsci.2015.05.034 ↗
26. Li J et al (2019) Effect of hydride precipitation on the fatigue cracking behavior in a zirconium alloy cladding tube. Int J Fatigue. https://doi.org/10.1016/j.ijfatigue.2019.10523010.1016/j.ijfatigue.2019.105230 ↗
27. Liao Z et al (2023) Improving strength-ductility synergy in a TRIP metastable β-Zr alloy containing heterogeneous α precipitates. J Mater Res Technol 24:5956–5970. https://doi.org/10.1016/j.jmrt.2023.04.21010.1016/j.jmrt.2023.04.210 ↗
28. Lin B, Zhao LG, Tong J (2011) A crystal plasticity study of cyclic constitutive behaviour, crack-tip deformation and crack-growth path for a polycrystalline nickel-based superalloy. Eng Fract Mech 78(10):2174–2192. https://doi.org/10.1016/J.ENGFRACMECH.2011.04.00610.1016/J.ENGFRACMECH.2011.04.006 ↗
29. Long F et al (2016) Effect of neutron irradiation on deformation mechanisms operating during tensile testing of Zr–2.5Nb. Acta Mater 102:352–363. https://doi.org/10.1016/J.ACTAMAT.2015.09.03210.1016/J.ACTAMAT.2015.09.032 ↗
30. Louca K et al (2024) The asymmetric evolution of grain-scale stresses in notched specimens under cyclic loads. Acta Mater. https://doi.org/10.1016/j.actamat.2023.11956710.1016/j.actamat.2023.119567 ↗
31. Marashi S et al (2023) Resolving local microstructure variations in Zr–2.5Nb CANDU pressure tubes using high spatial resolution electron backscatter diffraction and imaging. J Nucl Mater 577:154321. https://doi.org/10.1016/j.jnucmat.2023.15432110.1016/j.jnucmat.2023.154321 ↗
32. Marashi S, Abdolvand H (2024a) The interactions of deformation twins, zirconium hydrides, and microcracks. Int J Plast. https://doi.org/10.1016/j.ijplas.2024.10414910.1016/j.ijplas.2024.104149 ↗
33. Marashi S, Abdolvand H (2024b) The micromechanics of fracture of zirconium hydrides. Acta Mater. https://doi.org/10.1016/j.actamat.2024.12014310.1016/j.actamat.2024.120143 ↗
34. Marashi S, Abdolvand H (2025) Deformation, mechanical properties, and fracture of titanium hydrides. J Alloys Compds. https://doi.org/10.1016/j.jallcom.2025.17933310.1016/j.jallcom.2025.179333 ↗
35. Mozafari A et al (2024) Residual stress measurement of laser powder bed fusion additively manufactured hastelloy-X through crystal plasticity simulations and neutron diffraction experiments. Metall Mater Trans a: Phys Metall Mater Sci 55(9):3388–3406. https://doi.org/10.1007/s11661-024-07474-w10.1007/s11661-024-07474-w ↗
36. Muránsky O et al (2013) Load partitioning and evidence of deformation twinning in dual-phase fine-grained Zr–2.5%Nb alloy. Mater Sci Eng: A 564:548–558. https://doi.org/10.1016/J.MSEA.2012.11.07510.1016/J.MSEA.2012.11.075 ↗
37. Needleman A et al (1985) Finite element analysis of crystalline solids. Comput Methods Appl Mech Eng 52(1–3):689–708. https://doi.org/10.1016/0045-7825(85)90014-310.1016/0045-7825(85)90014-3 ↗
38. Nigro CF, Bjerkén C, Mellbin Y (2021) Phase-field modelling: effect of an interface crack on precipitation kinetics in a multi-phase microstructure. Int J Fract 227(2):219–241. https://doi.org/10.1007/s10704-020-00510-x10.1007/s10704-020-00510-x ↗
39. Peace R, Miller RE (2005) Experimental observations of void growth in the Zr–2.5Nb pressure tube alloy. J Nucl Mater 341(2–3):231–234. https://doi.org/10.1016/J.JNUCMAT.2005.03.00110.1016/J.JNUCMAT.2005.03.001 ↗
40. Proudhon H, et al (2016) 3D simulation of short fatigue crack propagation by finite element crystal plasticity and remeshing. In: International journal of fatigue. Elsevier, pp 238–246. https://doi.org/10.1016/j.ijfatigue.2015.05.02210.1016/j.ijfatigue.2015.05.022 ↗
41. Qin W, Szpunar JA, Kozinski J (2015) Hydride-induced degradation of zirconium alloys: a criterion for complete ductile-to-brittle transition and its dependence on microstructure. In: Proceedings of the royal society a: mathematical, physical and engineering sciences. Royal Society of London. https://doi.org/10.1098/rspa.2015.019210.1098/rspa.2015.0192 ↗
42. Sahoo SK et al (2010) Deformed microstructures of two-phase Zr–2.5Nb alloy: Effects of the second phase hardnesss. J Nucl Mater 404(3):222–230. https://doi.org/10.1016/j.jnucmat.2010.07.02810.1016/j.jnucmat.2010.07.028 ↗
43. Sanyal G, Samal MK (2012) Fracture behavior of thin-walled Zircaloy fuel clad tubes of Indian pressurized heavy water reactor. Int J Fract 173(2):175–188. https://doi.org/10.1007/s10704-012-9678-210.1007/s10704-012-9678-2 ↗
44. Sedaghat O, Abdolvand H (2021) A non-local crystal plasticity constitutive model for hexagonal close-packed polycrystals. Int J Plast 136:102883. https://doi.org/10.1016/J.IJPLAS.2020.10288310.1016/J.IJPLAS.2020.102883 ↗
45. Shahba A, Ghosh S (2019) Coupled phase field finite element model for crack propagation in elastic polycrystalline microstructures. Int J Fract 219(1):31–64. https://doi.org/10.1007/s10704-019-00378-610.1007/s10704-019-00378-6 ↗
46. Shan D et al (2019) Fracture behavior of notched TC21 alloy observed by In-situ SEM. Results Phys. https://doi.org/10.1016/j.rinp.2019.10260410.1016/j.rinp.2019.102604 ↗
47. Shen J et al (2022) Developing parametrically upscaled constitutive and crack nucleation models for the α/β Ti64 alloy. Int J Plast. https://doi.org/10.1016/j.ijplas.2021.10318210.1016/j.ijplas.2021.103182 ↗
48. Shi R et al (2018) Correlation between dislocation-density-based strain hardening and microstructural evolution in dual phase TC6 titanium alloy. Mater Sci Eng A 715:101–107. https://doi.org/10.1016/j.msea.2017.12.09810.1016/j.msea.2017.12.098 ↗
49. Shi S et al (2022) Microstructure stability and damage mechanisms in an α/β Ti–6Al–4V–055Fe alloy during low cycle dwell-fatigue at room temperature. Int J Fatigue. https://doi.org/10.1016/j.ijfatigue.2021.10658510.1016/j.ijfatigue.2021.106585 ↗
50. Shukla S et al (2021) Investigation of hydrogen diffusivity in Zr–2.5%Nb alloy pressure tube material using Metallography and Neutron Radiography. J Nucl Mater. https://doi.org/10.1016/j.jnucmat.2020.15267910.1016/j.jnucmat.2020.152679 ↗
51. Shukla S et al (2023) Anisotropy study of hydrogen diffusion along different directions of Zr-2.5%Nb alloy pressure tube using neutron imaging. J Nucl Mater. https://doi.org/10.1016/j.jnucmat.2023.15441410.1016/j.jnucmat.2023.154414 ↗
52. Siddharth S et al (2024) Coupled crystal plasticity and damage model for micro crack propagation in polycrystalline microstructures. Int J Fract [preprint]. https://doi.org/10.1007/s10704-024-00772-910.1007/s10704-024-00772-9 ↗
53. Simpson LA (1981) Criteria for fracture initiation at hydrides in zirconium-2.5 Pct niobium alloy. Metall Trans A 12:2113–212410.1007/BF02644181 ↗
54. Singh D et al (2019) Atomistic simulations to study crack tip behaviour in single crystal of bcc niobium and hcp zirconium. Curr Appl Phys 19(1):37–43. https://doi.org/10.1016/j.cap.2018.11.00210.1016/j.cap.2018.11.002 ↗
55. Sung SJ et al (2019) Effects of curvature on ductile fracture initiation in curved compact tension specimens of hydrided irradiated Zr–2.5Nb materials with split circumferential hydrides. Eng Fract Mech 211:180–197. https://doi.org/10.1016/J.ENGFRACMECH.2019.02.01910.1016/J.ENGFRACMECH.2019.02.019 ↗
56. Sunil S et al (2016) Effect of orientation and presence of hydride on the fatigue crack growth behavior of Zr–2.5 wt% Nb. Int J Fatigue 85:49–56. https://doi.org/10.1016/J.IJFATIGUE.2015.12.00510.1016/J.IJFATIGUE.2015.12.005 ↗
57. Sunil S et al (2020) Effect of radial hydride on delayed hydride cracking behaviour of Zr–2.5Nb pressure tube material. J Nucl Mater. https://doi.org/10.1016/j.jnucmat.2020.15245710.1016/j.jnucmat.2020.152457 ↗
58. Taherijam M et al (2023) On the effects of transformation strain induced by hydride precipitation. Acta Mater. https://doi.org/10.1016/j.actamat.2023.11935610.1016/j.actamat.2023.119356 ↗
59. Taherijam M, Abdolvand H (2025) Hydrogen and Hydride Induced Stress Localization in Single Phase HCP and Dual Phase HCP-BCC Alloys. Int J Plast. https://doi.org/10.1016/j.ijplas.2025.10432510.1016/j.ijplas.2025.104325 ↗
60. Tan C, Sun Q, Zhang G (2021) Role of microstructure in plastic deformation and crack propagation behaviour of an α/β titanium alloy. Vacuum. https://doi.org/10.1016/j.vacuum.2020.10984810.1016/j.vacuum.2020.109848 ↗
61. Tome C et al (1984) The relation between macroscopic and microscopic strain hardening in F.C.C. polycrystals. Acta Metall 32(10):1637–1653. https://doi.org/10.1016/0001-6160(84)90222-010.1016/0001-6160(84)90222-0 ↗
62. Tondro A, Abdolvand H (2022) On the effects of texture and microstructure on hydrogen transport towards notch tips: a CPFE study. Int J Plast 152:103234. https://doi.org/10.1016/J.IJPLAS.2022.10323410.1016/J.IJPLAS.2022.103234 ↗
63. Tondro A, Taherijam M, Abdolvand H (2023) Diffusion and redistribution of hydrogen atoms in the vicinity of localized deformation zones. Mech Mater 177:104544. https://doi.org/10.1016/J.MECHMAT.2022.10454410.1016/J.MECHMAT.2022.104544 ↗
64. Waheed S et al (2019) Microstructural effects on strain rate and dwell sensitivity in dual-phase titanium alloys. Acta Mater 162:136–148. https://doi.org/10.1016/J.ACTAMAT.2018.09.03510.1016/J.ACTAMAT.2018.09.035 ↗
65. Wang J et al (2021) In-situ study on tensile deformation and damage evolution of metastable β titanium alloy with lamellar microstructure. Mater Sci Eng A. https://doi.org/10.1016/j.msea.2021.14179010.1016/j.msea.2021.141790 ↗
66. Wang J et al (2022) Comparison on impact toughness of high-strength metastable β titanium alloy with bimodal and lamellar microstructures. Metals. https://doi.org/10.3390/met1202027110.3390/met12020271 ↗
67. Wang Z et al (2020) Crack propagation path selection and plastic deformation at a crack tip in zirconium. Mater Sci Eng A. https://doi.org/10.1016/j.msea.2020.13914310.1016/j.msea.2020.139143 ↗
68. Wang Z et al (2022) In-situ dwell-fatigue fracture experiment and CPFE simulation of SLM AlSi10Mg alloy at high temperature. Int J Fract 235(1):159–178. https://doi.org/10.1007/s10704-022-00647-x10.1007/s10704-022-00647-x ↗
69. Werwer M et al (2007) Fracture in lamellar TiAl simulated with the cohesive model. Eng Fract Mech 74(16):2615–2638. https://doi.org/10.1016/J.ENGFRACMECH.2006.09.02210.1016/J.ENGFRACMECH.2006.09.022 ↗
70. Wilson D, Dunne FPE (2019) A mechanistic modelling methodology for microstructure-sensitive fatigue crack growth. J Mech Phys Solids 124:827–848. https://doi.org/10.1016/j.jmps.2018.11.02310.1016/j.jmps.2018.11.023 ↗
71. Wilson D, Wan W, Dunne FPE (2019) ‘Microstructurally-sensitive fatigue crack growth in HCP, BCC and FCC polycrystals. J Mech Phys Solids 126:204–225. https://doi.org/10.1016/j.jmps.2019.02.01210.1016/j.jmps.2019.02.012 ↗
72. Wilson D, Zheng Z, Dunne FPE (2018) A microstructure-sensitive driving force for crack growth. J Mech Phys Solids 121:147–174. https://doi.org/10.1016/j.jmps.2018.07.00510.1016/j.jmps.2018.07.005 ↗
73. Wu Z et al (2021) Microstructural influences on the high cycle fatigue life dispersion and damage mechanism in a metastable β titanium alloy. J Mater Sci Technol 70:12–23. https://doi.org/10.1016/j.jmst.2020.07.01810.1016/j.jmst.2020.07.018 ↗
74. Xu Y, Wan W, Dunne FPE (2021) Microstructural fracture mechanics: Stored energy density at fatigue cracks. J Mech Phys Solids. https://doi.org/10.1016/j.jmps.2020.10420910.1016/j.jmps.2020.104209 ↗
75. Yeratapally SR et al (2017) Investigation of fatigue crack incubation and growth in cast MAR-M247 subjected to low cycle fatigue at room temperature. Int J Fract 208(1–2):79–96. https://doi.org/10.1007/s10704-017-0213-310.1007/s10704-017-0213-3 ↗
76. Zeng X et al (2022) Quantitative characterization of short fatigue crack and grain boundary interaction behavior in zirconium. Int J Fatigue. https://doi.org/10.1016/j.ijfatigue.2022.10689410.1016/j.ijfatigue.2022.106894 ↗
77. Zhang JW et al (2020) Twin hopping in nanolayered Zr–2.5Nb. Mater Res Lett 8(8):307–313. https://doi.org/10.1080/21663831.2020.175590210.1080/21663831.2020.1755902 ↗
78. Zhang JW et al (2022) Texture evolution and temperature-dependent deformation modes in ambient- and cryogenic-rolled nanolayered Zr–2.5Nb. Acta Mater. https://doi.org/10.1016/j.actamat.2022.11802310.1016/j.actamat.2022.118023 ↗
79. Zhang P, et al (2021) A framework of modelling slip-controlled crack growth in polycrystals using crystal plasticity and XFEM. In: Journal of physics: conference series. IOP Publishing Ltd. https://doi.org/10.1088/1742-6596/1885/4/04201410.1088/1742-6596/1885/4/042014 ↗
80. Zhang S et al (2022) Investigation of α phase evolution and tensile fracture behavior of Ti5Al2Sn2Zr4Mo4Cr alloy fabricated by directed energy deposition. J Alloys Compds. https://doi.org/10.1016/j.jallcom.2021.16349710.1016/j.jallcom.2021.163497 ↗
81. Zhang Z et al (2016) Determination of Ti-6242 α and β slip properties using micro-pillar test and computational crystal plasticity. J Mech Phys Solids 95:393–410. https://doi.org/10.1016/j.jmps.2016.06.00710.1016/j.jmps.2016.06.007 ↗
82. Zhang Z, Dunne FPE (2018) Phase morphology, variants and crystallography of alloy microstructures in cold dwell fatigue. Int J Fatigue 113:324–334. https://doi.org/10.1016/j.ijfatigue.2018.03.03010.1016/j.ijfatigue.2018.03.030 ↗
83. Zheng Z et al (2018) Slip transfer across phase boundaries in dual phase titanium alloys and the effect on strain rate sensitivity. Int J Plast 104:23–38. https://doi.org/10.1016/j.ijplas.2018.01.01110.1016/j.ijplas.2018.01.011 ↗