Phase Field Simulation of Viscous Sintering

doi:10.11900/0412.1961.2022.00445

Acta Metall Sin

2024, Vol. 60

Issue (12): 1691-1700 DOI: 10.11900/0412.1961.2022.00445

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Phase Field Simulation of Viscous Sintering

GUO Songyuan¹, LIU Wenbo¹^,²(

), YANG Qingcheng³, QI Xiaoyong¹^,², YUN Di¹^,²

1 School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China
2 Shaanxi Key Laboratory of Advanced Nuclear Energy and Technology, Xi'an Jiaotong University, Xi'an 710049, China
3 Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China

Cite this article:

GUO Songyuan, LIU Wenbo, YANG Qingcheng, QI Xiaoyong, YUN Di. Phase Field Simulation of Viscous Sintering. Acta Metall Sin, 2024, 60(12): 1691-1700.

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Abstract

The presence of a liquid phase, which provides capillary force during viscous sintering, can accelerate the evolution of sintered particles. Due to the difficulty of coupling about the Navier-Stokes equations, however, it is quite challenging to obtain simulation results that meet the laws of physics. In the present study, a phase field model of the viscous sintering process is established, and the morphology, velocity field, and pressure field evolutions of the sintered particles are analyzed. First, the Cahn-Hilliard and Navier-Stokes equations are solved using the finite difference method and the predictor-corrector method. In the finite difference method, the upwind and central difference schemes are combined. The simulation results show that under the drive of surface tension, two circular particles gradually merge into one. The velocity field is divided into a pure straining region and a rigid body motion region inside the particle; the pressure difference between the inside and outside of the particles is proportional to the curvature of the particles. Then, the contact radius and shrinkage of the two circular particles are calculated, and then a curve over time is drawn. The results show that they vary drastically at the beginning stage of evolution and satisfy the law of viscoelastic contact. In the later stage of evolution, the change becomes slower when the contact radius and shrinkage of the two circular particles are close to the values of the equilibrium state. With the increase in mobility, the evolution rate accelerates, but the morphology of the stable state is almost unchanged. The evolution of multiparticles and pores is also simulated. The results show that the pores in the viscous sintering process are initially spheroidized and then slowly disappear, resulting in densification. Under the same simulation conditions, the smaller pores evolve faster.

Key words: phase field simulation viscoelastic contact viscous sintering pore evolution

Received: 09 September 2022

ZTFLH:

TG111.4

Fund: Joint Fund of National Natural Science Foundation of China and China Academy of Engineering Physics (NSAF Joint Fund)(U2130105);Key Research Project of Zhejiang Lab(2021PE0AC02);Innovative Scientific Program of China National Nuclear Corporation

Corresponding Authors: LIU Wenbo, associate professor, Tel: (029)82668948, E-mail: liuwenbo@xjtu.edu.cn

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	GUO Songyuan
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	YANG Qingcheng
	QI Xiaoyong
	YUN Di

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https://www.ams.org.cn/EN/10.11900/0412.1961.2022.00445 OR https://www.ams.org.cn/EN/Y2024/V60/I12/1691

Table 1 Physical parameters of nylon 12 (PA12) at 175^oC^[12,23]

Fig.1 Schematic illustration of staggered mesh (u is the velocity component in the x direction, and v is the velocity component in the y direction. The red points are used for the discrete format of u, and the blue points are used for the discrete format of v. The black points are used for the discrete format of scalars, including viscosity μ, density ρ and phase field c)

Fig.2 Microstructure evolutions of the two equal circle grains during sintering

Fig.3 Normalized contact radius growth curves under different mobilities ( $M ˜$ —mobility, T—time step)

Fig.4 Normalized shrinkage vs time step curves under different mobilities

Fig.5 Microstructure evolutions (a-c) and the corresponding horizontal velocity distributions (d-f) of the two equal circle grains (Blue represents negative values indicating the direction of velocity to the left; yellow is a positive value representing the right direction of velocity, ranging from -3.3 × 10^-3 m/s to 3.3 × 10^-3 m/s in the velocity cloud map) (a, d) 6 × 10⁵ step (b, e) 2 × 10⁶ step (c, f) 8 × 10⁶ step

Fig.6 Distributions of phase-field variable and velocity field along horizontal symmetry axis of the two circle grains

Fig.7 Pressure (P) distributions of two equal circle grains
(a) 2 × 10⁴ step (b) 1 × 10⁵ step (c) 2 × 10⁵ step (d) 1.2 × 10⁶ step (e) 1 × 10⁷ step (f) 4 × 10⁷ step

Fig.8 Microstructure evolutions of three particles with the initial contact angles 60°
(a) 0 step (b) 6 × 10⁴ step (c) 2 × 10⁵ step (d) 1 × 10⁶ step (e) 6 × 10⁶ step (f) 2 × 10⁷ step

Fig.9 Microstructure evolutions of multi-particles (The red circle shows the region of pore spheroidization, and the blue circle shows the region of pore disappearance)
(a) 0 step (b) 2 × 10⁴ step (c) 1 × 10⁵ step (d) 2 × 10⁶ step (e) 2.4 × 10⁶ step (f) 3 × 10⁶ step

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