Phase-Field Simulation of the Interaction Between Pore and Grain Boundary

doi:10.11900/0412.1961.2020.00120

Acta Metall Sin

2020, Vol. 56

Issue (12): 1643-1653 DOI: 10.11900/0412.1961.2020.00120

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Phase-Field Simulation of the Interaction Between Pore and Grain Boundary

SUN Zhengyang¹^,², WANG Yutian³, LIU Wenbo¹^,²(

)

1 School of Nuclear Science and Technology, Xi'an Jiaotong University, Xi'an 710049, China
2 Shaanxi Key Laboratory of Advanced Nuclear Energy and Technology, Shaanxi Engineering Research Center of Advanced Nuclear Energy, Xi'an Jiaotong University, Xi'an 710049, China
3 School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049, China

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SUN Zhengyang, WANG Yutian, LIU Wenbo. Phase-Field Simulation of the Interaction Between Pore and Grain Boundary. Acta Metall Sin, 2020, 56(12): 1643-1653.

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Abstract

The grain boundary (GB) and average grain size considerably affect the properties of materials, such as the fracture strength, dielectric constant, and thermal conductivity. For instance, when subjected to irradiation at 1750 ℃, the swelling of the UO₂ pellets and the release of fission gas from them decrease significantly with the increasing average grain size. However, several second-phase particles, such as pores, are inevitably introduced into a material during the solid-phase sintering or neutron radiation processes. Therefore, studying the interaction between the pores and GBs is considerably important. In this study, a phase-field model of the interaction between the pores and GBs is developed. Subsequently, the free-energy density function was modified, where the diffusion coefficient was incorporated in the tensor form. In addition, the selection of the phenomenological parameters, such as the coefficient in the free-energy density function of the phase-field model, was analyzed, and the influencing factors of interface energy and interface width were discussed. The phase-field model simulation results of the interaction between the pores and GBs show that the curvature of GB was the major driving force associated with the movement of GB and that pores resisted the movement of GB. Accordingly, the pores moved together with the GBs when the maximum pinning force exerted by the pores was larger than the driving force produced by the curvature of GB; however, the pores and GBs separated in the opposite case, during which the GB moved much faster than pores. The results of the phase-field simulation of the grain growth of the pore-containing UO₂ show that the grain growth speed decreases with the increasing porosity. The average grain size of UO₂ is a power function of time, the exponent of which increases with the increasing porosity.

Key words: phase field simulation pore grain boundary grain growth diffusion

Received: 16 April 2020

ZTFLH:

TG148

Fund: NSAF Joint Fund(U1830124);National Natural Science Foundation of China(11705137);China Postdoctoral Science Foundation(2019M663738);State Key Laboratory of New Ceramic and Fine Processing Tsinghua University(KF201713)

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	Zhengyang SUN
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https://www.ams.org.cn/EN/10.11900/0412.1961.2020.00120 OR https://www.ams.org.cn/EN/Y2020/V56/I12/1643

Fig.1 Schematic of phase field model (C—concentration field variable; C_α—concentration in grain; C_β—concentration in pore; η $1 α$ , η $2 α$ —orientation field variable of grains 1, 2, respectively; η^β—orientation field variable of pore )

Table 1 Dimensionless parameters in simulation

Fig.2 Equilibrium profiles for phase field variables at different κ_α(a) orientation field variables η $1 α$ , η $2 α$ (b) concentration field variable C

Fig.3 Linear fitting curves of energy density and width of grain boundary vsκ $α 1 / 2$ (l—width of grain boundary, σ_gb—energy density of grain boundary)

Fig.4 Equilibrium profiles for phase field variables at different κ_c(a) orientation field variables η $1 α$ , η^β(b) concentration field variable C

Fig.5 Linear fitting curves of energy density of phase boundary σ_intvsκ $α 1 / 2$ , κ $β 1 / 2$ or κ $c 1 / 2$

Fig.6 Phase-field simulation results of the microstructure evolution of two grain system

Fig.7 Dynamic curves of grain boundary velocity and central grain size vs dimensionlesstimescale t_d

Fig.8 Phase-field simulation results of the microstructure evolution of one pore system

Fig.9 Phase-field simulation results of the microstructure evolution of two pore system

Fig.10 Phase-field simulation results of the microstructure evolution of four pore system

Fig.11 Phase-field simulation results of microstructure evolution of multi-grains UO₂ at porosity f_p=2% (The pores in the red elliptical areas hinder the movement of grain boundaries)

Fig.12 Grain growth curves at different f_p

Table 2 Grain growth exponents at different f_p

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