Phase-Field Simulations of Phase Transformation and Crack Evolution in Zirconium Alloy Oxide Film

doi:10.11900/0412.1961.2023.00240

Acta Metall Sin

2025, Vol. 61

Issue (7): 1082-1092 DOI: 10.11900/0412.1961.2023.00240

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Phase-Field Simulations of Phase Transformation and Crack Evolution in Zirconium Alloy Oxide Film

WANG Xiaoqi¹^,², ZHANG Jinhu¹^,²(

), GUO Hui¹^,², LI Xuexiong¹, XU Haisheng¹^,², BAI Chunguang¹^,², XU Dongsheng¹^,²(

), YANG Rui¹^,²

1 Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
2 School of Materials Science and Engineering, University of Science and Technology of China, Shenyang 110016, China

Cite this article:

WANG Xiaoqi, ZHANG Jinhu, GUO Hui, LI Xuexiong, XU Haisheng, BAI Chunguang, XU Dongsheng, YANG Rui. Phase-Field Simulations of Phase Transformation and Crack Evolution in Zirconium Alloy Oxide Film. Acta Metall Sin, 2025, 61(7): 1082-1092.

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Abstract

Zirconium alloys are considered as important nuclear reactor structural materials owing to their low thermal neutron absorption cross-section, good corrosion resistance, and good mechanical properties in high-temperature and high-pressure water. However, under high temperature and corrosion conditions, an oxide film forms on the surface of zirconium alloys, and its growth rate increases rapidly when the thickness is 2-3 μm, leading to a transition in corrosion kinetics, which limits its service life in the reactor. In this study, the transformation of zirconia from tetragonal (t-ZrO₂) to monoclinic (m-ZrO₂) and the crack propagation behavior in the oxidation layer on zirconium alloys have been investigated using phase-field simulation. During the transformation of t-ZrO₂ to m-ZrO₂ in the oxide film, the t-ZrO₂ matrix undergoes compressive and tensile stresses along the long and short axes of the m-ZrO₂ precipitate, respectively, whereas the m-ZrO₂ precipitate primarily undergoes compressive stress during the transformation. Moreover, the stresses increase with the growth of the m-ZrO₂ grains. The simulations of crack evolution reveal that the cracks in the oxidation layer parallel to the oxide-metal interface expand under applied tensile stress perpendicular to the interface. Such cracks may connect with other isolated cracks and defects forming a defect layer. Upon extending to the oxide-metal interface, surface cracks perpendicular to the interface bifurcate in the oxide rather than penetrate into the metal matrix, which facilitates the peeling off of the oxidation layer from the substrate.

Key words: zircaloy phase-field method phase transformation crack

Received: 05 June 2023

ZTFLH:

TG146.4

Fund: National Key Research and Development Program of China(2021YFB3702604);Informatization Program of Chinese Academy of Sciences(CAS-WX2021PY-0103)

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	WANG Xiaoqi
	ZHANG Jinhu
	GUO Hui
	LI Xuexiong
	XU Haisheng
	BAI Chunguang
	XU Dongsheng
	YANG Rui

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https://www.ams.org.cn/EN/10.11900/0412.1961.2023.00240 OR https://www.ams.org.cn/EN/Y2025/V61/I7/1082

Parameter	Symbol	Value
Chemical driving force	$Δ G$	36.8 × 10⁶ J·m^-3
Gradient energy coefficient	$k η$	1 × 10^-8 J·m^-1
Energy density coefficient	$a$	0.14
Energy density coefficient	$b$	12.42
Energy density coefficient	$c$	12.28
Kinetic coefficient	$L$	2 m³·J^-1·s^-1

Table 1 Parameters employed in the simulation^[24]

Parameters	Symbol	Value
Young's modulus of t-ZrO₂	$E t$	212 GPa
Young's modulus of m-ZrO₂	$E m$	241 GPa
Poisson's ratio of t-ZrO₂	$ν t$	0.33
Poisson's ratio of m-ZrO₂	$ν m$	0.29
Eigenstrain of t-ZrO₂	$ε i j 0$ (t-ZrO₂)	$0.0049 0.0761 0.0761 0.0180$
Eigenstrain of m-ZrO₂	$ε i j 0$ (m-ZrO₂)	$0.0049 - 0.0761 - 0.0761 0.0180$
Eigenstrain of t-ZrO₂ (after 90° rotation about Y axis)	$ε i j 0'$ (t-ZrO₂)	$0 0.0761 0 0.0180$
Eigenstrain of m-ZrO₂ (after 90° rotation about Y axis)	$ε i j 0'$ (m-ZrO₂)	$0 - 0.0761 0 0.0180$

Table 2 Parameters employed in elastic energy calculation^[24]

Fig.1 Schematic of single crystal phase-field model with an m-ZrO₂ nucleus

Fig.2 Grain growth process and evolution of the morphology of m-ZrO₂ ( $η$ —non-conserved order parameter, t—time)
(a) t = 1.0 × 10^-12 s (b) t = 6.0 × 10^-8 s (c) t = 1.0 × 10^-7 s (d) t = 3.0 × 10^-7 s

Fig.3 Evolution of stress distribution during the growth of m-ZrO₂ at t = 1.0 × 10^-12 s (a1-c1), t = 6.0 × 10^-8 s (a2-c2), t = 1.0 × 10^-7 s (a3-c3), and t = 3.0 × 10^-7 s (a4-c4)
(a1-a4) principal stress S₁₁ (b1-b4) principal stress S₂₂ (c1-c4) shear stress S₁₂

Fig.4 Grain growth of m-ZrO₂ after 90° rotation about Y axis
(a) t = 1.0 × 10^-12 s (b) t = 6.0 × 10^-8 s (c) t = 1.0 × 10^-7 s (d) t = 3.0 × 10^-7 s

Fig.5 Evolution of stress distribution during grain growth after rotation of 90° about Y axis at t = 1.0 × 10^-12 s (a1-c1), t = 6.0 × 10^-8 s (a2-c2), t = 1.0 × 10^-7 s (a3-c3), and t = 3.0 × 10^-7 s (a4-c4)
(a1-a4) S₁₁ (b1-b4) S₂₂ (c1-c4) S₁₂

Fig.6 Schematic of crack parallel to the oxide-metal interface (unit: mm. σ—tensile stress)

Fig.7 Phase-field simulations of stress distribution (a, c) and phase-field variable (b, d) of crack parallel to the oxide-metal interface
(a, b) prior to propagation (step = 470) (c, d) after the propagation (step = 475)

Fig.8 Force-displacement curve for crack parallel to the oxide-metal interface by simulation

Fig.9 Schematic of crack perpendicular to the oxide-metal interface (unit: mm)

Fig.10 Phase-field simulation of crack perpendicular to the oxide-metal interface (ϕ—phase-field order parameter)
(a) initial crack (b) crack reaches interface
(c) crack propagates parallel to interface (d) force-displacement curve

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