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Simulation of M23C6 precipitation mechanism during solidification of Ni40A coated on phosphorus removal roll by phase field method

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Abstract

The inseparability of material macroscopic properties and microstructure has prompted scholars to continuously delve into microstructural studies. The phase-field method has become an important basis for modern microstructure simulation techniques. The difficulty of the phase-field method lies in the modeling and parameter input. In this paper, the evolution mechanism of carbide precipitation in the process of plasma cladding of nickel-based alloy on phosphorus removal roll is investigated by the method of phase-field modeling and finite-element coupling. A Ni–Cr–C ternary phase-field precipitation model is developed, and the Ni40A macroscopic solidification process is simulated by ProCAST software, and then the boundary conditions are input into the phase-field model to simulate the carbide precipitation process in the solidification of nickel-based alloy. The simulated atomic diagram shows that the carbide is a core–shell structure, consisting of a Cr-rich core and a C-rich shell, and the carbide morphology changes significantly after coupling the elastic energy. The simulation results are in good agreement with the experimental results, which verifies the feasibility and accuracy of the phase-field method.

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Data availability

Data supporting the findings of this study are available in Thermodynamic evaluation of the Cr-Ni-C system. These data were derived from the following resources available in the public domain: https://link.springer.com/article/10.1007/BF02646072. Kajihara M, Hillert M. Thermodynamic evaluation of the Cr-Ni-C system [J]. Metallurgical Transactions A, 1990, 21(10):2777–2787.

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Funding

This research was supported by the National Key Research and Development Program (No. 2021YFB3702003).

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, University of Science and Technology Liaoning, Anshan, 114051, China

    Jiahui Ji, Ming Chen & Zhiwen Xie

  2. School of Materials and Metallurgy, University of Science and Technology Liaoning, Anshan, 114051, China

    Chunlin Zhang & Shengli Li

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Contributions

Conceptualization: M.C. and S.L.; methodology: J.J. and M.C.; validation: J.J. and C.Z.; formal Analysis: J.J. and C.Z.; experiment: C.Z.; resources: M.C.; Supervision: M.C.; writing—original draft preparation: J.J.; funding acquisition: Z.X.

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Correspondence to Ming Chen.

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Appendix

Appendix

In this paper, in constructing the phase-specific molar free energy of the ternary system through the sub-point solvation model, a thermodynamic evaluation of the ternary alloy system is required, and its corresponding Gibbs free energy and interaction coefficients are queried through the literature [45,46,47], and its specific thermodynamic and kinetic parameters are shown as follows:

Liquid phase

$${G}_{C}^{liq}={G}_{C}^{gra}+117369-24.63T$$

BCC phase

$${G}_{Cr}^{hbcc}={H}^{SER}-8851.93+157.48T-26.908TlnT+0.00189435{T}^{2}-1.47721\times {10}^{-6}{T}^{3}+139250\times {T}^{-1}$$

FCC phase

$${G}_{Cr:v}^{fcc}={G}_{Cr}^{hbcc}+7284+0.163T$$
$${G}_{Cr:C}^{fcc}={G}_{Cr}^{hbcc}+{G}_{C}^{gra}+25000$$
$${G}_{Ni:C}^{fcc}={H}_{Ni}^{SER}+{H}_{C}^{SER}+62000-7.6T+GHSERNI+GHSERCC$$
$${G}_{Ni:v}^{fcc}={H}_{Ni}^{SER}+GHSERNI$$
$${G}_{Ni:C}^{fcc}={H}_{Ni}^{SER}+{H}_{C}^{SER}+62000-7.6T+GHSERNI+GHSERCC$$
$${G}_{Ni}^{hfcc}={H}^{SER}-5179.159+117.854T-22.096TlnT-0.0048407{T}^{2}$$
$${L}_{Cr:C,v}^{fcc}=-29686-18T$$
$${L}_{Cr,Ni:v}^{0fcc}=8347-12.1038T$$
$${L}_{Cr,Ni:v}^{1fcc}=29895-16.3838T$$
$${L}_{Cr,Ni:C}^{fcc}=-81265+81.8T$$

Graphite

$${G}_{C}^{gra}-{H}^{SER}=-17369+170.73T-24.3TlnT-4.723\times {10}^{-4}{T}^{2}+2562600{T}^{-1}-2.643\times {10}^{8}{T}^{-2}+1.2\times {10}^{10}{T}^{-3}$$

M23C6 phase

$${G}_{Cr:Cr:C}^{m23c6}={H}^{SER}-462844+3200T-550TlnT-0.204{T}^{2}$$
$${G}_{Ni:Ni:C}^{m23c6}=212988+23{G}_{Ni}^{hfcc}+6{G}_{C}^{gra}$$
$${L}_{Ni:Cr:C}^{m23c6}=10434-14281T$$

SYMBOLS

$$\mathrm{GHSERCC}=-17368.441+170.73\mathrm{T}-24.3\mathrm{TlnT}-4.723\times {10}^{-4}{T}^{2}+2562600{T}^{-1}-2.643\times {10}^{8}{T}^{-2}+1.2\times {10}^{10}{T}^{-3}$$
$$\mathrm{GHSERNI}=-5179.159+117.854\mathrm{T}-22.096\mathrm{TlnT}-4.8407\times {10}^{3}{T}^{2}$$

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Ji, J., Zhang, C., Li, S. et al. Simulation of M23C6 precipitation mechanism during solidification of Ni40A coated on phosphorus removal roll by phase field method. Appl. Phys. A 129, 618 (2023). https://doi.org/10.1007/s00339-023-06872-y

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