Skip to main content
SpringerLink
Log in

Phase-field simulation of multilayer microstructure of Cr-enriched phase induced by alternating strain

  • Published:
International Journal of Mechanics and Materials in Design Aims and scope Submit manuscript

Abstract

Strain-induced microstructures have special effects on the mechanical properties of alloys. Alternating tensile/compressive strains can produce multilayered strain distributions inside the alloys, the microstructure and elements of the nanoscale precipitates will be redistributed. It is the first attempt to reveal the effects of alternating strain on the morphology and composition evolution of the nanoscale phase by utilizing phase-field simulation. When the tensile/compressive strains are applied in the multilayer alloy with different magnitudes and orders, the solute atoms gather in a preferential model to the boundary which in relaxed strain state, forming the band shape morphology parallel to the boundary. Nanoscale lamellar structure of alternating precipitation/matrix is formed in the three dimensional space. When the layer width is small enough, the precipitation bands of boundary undergo coalescence into a lamellar by the diffusion of Cr atoms in the tensile strain regions, while the compressive strain regions become matrix layer. This study provides a better known of formation of nanoscale lamellar microstructure with the nanoscale phase evolution in iron-based alloys under alternating strain.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  • Andersson, J.O., Ågren, J.: Models for numerical treatment of multicomponent diffusion in simple phase. J. Appl. Phys. 72(4), 1350–1355 (1992)

    Article  Google Scholar 

  • Andersson, J.O., Sundman, B.: Thermodynamic properties of the Cr-Fe system. Calphad 11, 83–92 (1987)

    Article  Google Scholar 

  • Barkar, T., Höglund, L., Odqvist, J., Ågren, J.: Effect of concentration dependent gradient energy coefficient on spinodal decomposition in the Fe-Cr system. Comp. Mater. Sci. 143, 446–453 (2018)

    Article  Google Scholar 

  • Boussinot, G., Bouar, Y.L., Finel, A.: Phase-field simulations with inhomogeneous elasticity: Comparison with an atomic-scale method and application to superalloys. Acta. Mater. 58(12), 4170–4181 (2010)

    Article  Google Scholar 

  • Byun, T.S., Yang, Y., Overman, N.R., Busby, J.T.: Thermal aging phenomena in cast duplex stainless steels. JOM. 68(2), 507–516 (2016)

    Article  Google Scholar 

  • Cahn, J.W., Hilliard, J.E.: Free energy of a non-uniform system. I. Interfacial free energy. J. Chem. Phys. 28(2), 258–267 (1958)

    Article  MATH  Google Scholar 

  • Chen, L.Q.: Phase-field models for microstructure evolution. Annu. Rev. Mater. Res. 32, 113–140 (2002)

    Article  Google Scholar 

  • Chen, Y., Yang, B., Zhou, Y., Wu, Y., Zhu, H.: Evaluation of pitting corrosion in duplex stainless steel Fe20Cr9Ni for nuclear power application. Acta. Mater. 197, 172–183 (2020)

    Article  Google Scholar 

  • Danoix, F., Auger, P., Blavette, D.: Hardening of aged duplex stainless steels by spinodal separation. Micros. Microanal. 10, 349–354 (2004)

    Article  Google Scholar 

  • Danoix, F., Lacaze, J., Gibert, A., Mangelinck, D., Hoummada, K., Andrieu, E.: Effect of external stress on the Fe-Cr phase separation in 15–5 PH and Fe-15Cr-5Ni alloys. Ultramicroscopy 132, 193–198 (2013)

    Article  Google Scholar 

  • Gururajan, M.P., Abinandanan, T.A.: Phase-field study of precipitate rafting under a uniaxial stress. Acta. Mater. 55, 5015–5026 (2007)

    Article  Google Scholar 

  • Heesemann, A., Schmidtke, E., Faupel, F., Kolb-Telieps, A., Klöwer, J.: Aluminum and silicon diffusion in Fe-Cr-Al alloys. Scripta. Mater. 40(5), 517–522 (1999)

    Article  Google Scholar 

  • Hillert, M., Jarl, M.: A model for alloying in ferromagnetic metals. Calphad 2(3), 227–238 (1978)

    Article  Google Scholar 

  • Hu, S.Y., Chen, L.Q.: A phase-field model for evolving microstructures with strong elastic inhomogeneity. Acta. Mater. 49, 1879–1890 (2001)

    Article  Google Scholar 

  • Jacobs, M.H.G., Schmid-Fetzer, R., Markus, T., Motalov, V., Borchardt, G., Spitzer, K.H.: Thermodynamics and diffusion in ternary Fe-Al-Cr alloys, part I: thermodynamic modeling. Intermetallics 16(8), 995–1005 (2008)

    Article  Google Scholar 

  • Javanbakht, M., Levitas, V.I.: Phase-field simulations of plastic strain-induced phase transformations under high pressure and large shear. Phys. Rev. B. 94, 214104 (2016)

    Article  Google Scholar 

  • Khachaturyan, A.G.: Theory of structural transformations in solids. John Wiley and Sons, New York (1983)

    Google Scholar 

  • Kim, B., Sietsma, J., Santofimia, M.J.: Theoretical aspects of spinodal decomposition in Fe-C. Metall. Mater. Trans. a. 50, 1175–1184 (2019)

    Article  Google Scholar 

  • Kinoshita, N., Mura, T.: Elastic fields of inclusions in anisotropic media. Phys. Status. Solidi. a. 5, 759–768 (1971)

    Article  Google Scholar 

  • Lass, E.A., Johnson, W.C., Shiflet, G.J.: Correlation between CALPHAD data and the Cahn-Hilliard gradient energy coefficient and exploration into its composition dependence. Calphad 30(1), 42–52 (2006)

    Article  Google Scholar 

  • Levin, V.A., Levitas, V.I., Zingerman, K.M., Freiman, E.I.: Phase-field simulation of stress-induced martensitic phase transformations at large strains. Int. J. Solids. Struct. 50(19), 2914–2928 (2013)

    Article  Google Scholar 

  • Li, D., Meng, F.Y., Ma, X.Q., Qiao, L.J., Chu, W.Y.: Molecular dynamics simulation of porous layer-induced stress in Fe single crystal. Comp. Mater. Sci. 49, 641–644 (2010)

    Article  Google Scholar 

  • Li, Y.S., Yu, Y.Z., Cheng, X.L., Chen, G.: Phase field simulation of precipitates morphology with dislocations under applied stress. Mat. Sci. Eng. a. 528, 8628–8634 (2011)

    Article  Google Scholar 

  • Li, Y.S., Zhang, L., Zhu, H., Pang, Y.X.: Effects of applied strain on interface microstructure and interdiffusion in the diffusion couples. Metall. Mater. Trans. a. 44(7), 3060–3068 (2013)

    Article  Google Scholar 

  • Li, Y.S., Pang, Y.X., Wu, X.C., Liu, W.: Effects of temperature gradient and elastic strain on spinodal separation and microstructure evolution of binary alloys. Modelling. Simul. Mater. Sci. Eng. 22, 035009 (2014)

    Article  Google Scholar 

  • Liu, Y.C., Somme, F., Mittemeijer, E.J.: Austenite-ferrite transformation kinetics under uniaxial compressive stress in Fe-2.96at. % Ni alloy. Acta. Mater. 57, 2858–2868 (2009)

    Article  Google Scholar 

  • Mamivand, M., Zaeem, M.A., Kadiri, H.E.: A review on phase-field modeling of martensitic phase transformation. Comp. Mater. Sci. 77, 304–311 (2013)

    Article  Google Scholar 

  • Micheal, J.C., Moulinec, H., Suquet, P.: Effective properties of composite materials with periodic microstructure: a computational approach. Comput. Methods. Appl. Mech. Engrg. 172, 109–143 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  • Moelans, N.: A quantitative and thermodynamically consistent phase-field interpolation function for multi-phase systems. Acta. Mater. 59(3), 1077–1086 (2011)

    Article  Google Scholar 

  • Müller, F., Kubaschewski, O.: The thermodynamic properties and equilibrium diagram of the system Cr-Fe. High Temp-High Press. 1, 543–551 (1969)

    Google Scholar 

  • Prikhodko, S.V., Ardell, A.J.: Coarsening of γ′ in Ni-Al alloy aged under uniaxial compression: I. Early-Stage Kinetics. Acta. Mater. 51, 5001–5012 (2003a)

    Google Scholar 

  • Prikhodko, S.V., Ardell, A.J.: Coarsening of γ′ in Ni-Al alloy aged under uniaxial compression: III. Charact. Morphol. Acta. Mater. 51, 5021–5036 (2003b)

    Google Scholar 

  • Tong, X.W., Li, Y.S., Yan, Z.W., Wang, D., Shi, S.J.: Phase-field simulation of effects of normal strain on the morphology and kinetics evolution of nanoscale phase. J. Mater. Res. Technol. 9(2), 2063–2071 (2020)

    Article  Google Scholar 

  • Tsukada, Y., Koyama, T., Kubota, F., Murata, Y., Kondo, Y.: Phase-field simulation of rafting kinetics in a nickel-based single crystal superalloy. Intermetallics 85, 187–196 (2017)

    Article  Google Scholar 

  • Wang, J.C., Osaw, M., Yokokawa, T., Harada, H., Enomoto, M.: Modeling the microstructural evolution of Ni-base superalloys by phase-field method combined with CALPHAD and CVM. Comp. Mater. Sci. 39, 871–879 (2007)

    Article  Google Scholar 

  • Wang, D., Li, Y.S., Shi, S.J., Tong, X.W., Yan, Z.W.: Phase-field simulation of γ′ precipitates rafting and creep property of Co-base superalloys. Mater. Design. 196, 109077 (2020)

    Article  Google Scholar 

  • Xiao, Q., Jang, C., Kim, C., Kim, H., Chen, J., Lee, H.B.: Corrosion behavior of stainless steels in simulated PWR primary water: The effect of composition and matrix phases. Corro. Sci. 177, 108991 (2020)

    Article  Google Scholar 

  • Xiong, W., Selleby, M., Chen, Q., Odqvist, J., Du, Y.: Phase equilibria and thermodynamic properties in the Fe-Cr system. Crtic. Rev. Solid. State. 35, 125–152 (2010)

    Article  Google Scholar 

  • Yang, M., Zhang, J., Wei, H., Zhao, Y., Gui, W.M., Su, H.J., Jin, T., Liu, L.: Study of γ’ rafting under different stress states-A phase-field simulation considering viscoplasticity. J. Alloy. Compd. 769, 453–462 (2018)

    Article  Google Scholar 

  • Zeng, X., Yang, X.P., Liu, L.: The directional coarsening of the aging precipitates in Ni75Al11.5V13.5 alloy under an externally applied stress. Mater. Sci. Tech-lond. 23(2), 58–62 (2015)

    Google Scholar 

  • Zhang, X.D., Godfrey, A., Huang, X.X., Hansen, N., Liu, Q.: Microstrucure and strengthening mechanisms in cold-drawn pearlitic steel wire. Acta. Mater. 59(9), 3422–3430 (2011)

    Article  Google Scholar 

  • Zhu, J., Chen, L.Q., Shen, J., Tikare, V.: Coarsening kinetics from a variable-mobility Cahn-Hilliard equation: application of a semi-implicit Fourier spectral method. Phys. Rev. e. 60(4), 3564 (1999)

    Article  Google Scholar 

  • Zhu, L.H., Li, Y.S., Liu, C.W., Chen, S., Shi, S.J., Jin, S.S.: Effect of applied strain on phase separation of Fe–28 at.% Cr alloy: 3D phase-field simulation. Modell. Simul. Mater. Sci. Eng. 26, 035015 (2018)

    Article  Google Scholar 

  • Zhu, L.H., Li, Y.S., Shi, S.J., Yan, Z.W., Chen, J.: Morphology and kinetics evolution of nanoscale phase in Fe-Cr alloys under external strain. Nanomatrerials. 9, 294 (2019)

    Article  Google Scholar 

  • Zhu, J.M., Wang, D., Gao, Y.P., Zhang, T.Y., Wang, Y.Z.: Linear-superelastic metals by controlled strain release via nanoscale concentration-gradient engineering. Mater. Today. 33, 17–23 (2020)

    Article  Google Scholar 

  • Zuo, P., Zhao, Y.P.: A phase field model coupling lithium diffusion and stress evolution with crack propagation and application in lithium ion batteries. Phys. Chem. Chem. Phys. 17, 287–297 (2015)

    Article  Google Scholar 

Download references

Funding

This work was supported by the National Natural Science Foundation of China (No. 51571122) and the Fundamental Research Funds for the Central Universities (No. 30921013107).

Author information

Authors and Affiliations

  1. School of Materials Science and Engineering, Nanjing University of Science andTechnology, Nanjing, 210094, China

    Xinwen Tong, Yongsheng Li, Zhengwei Yan, Dong Wang & Shujing Shi

  2. MIITKey Laboratory of Advanced Metallic and Intermetallic Materials Technology, Nanjing, 210094, China

    Xinwen Tong, Yongsheng Li, Zhengwei Yan, Dong Wang & Shujing Shi

Authors
  1. Xinwen Tong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yongsheng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhengwei Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shujing Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Xinwen Tong, Zhengwei Yan, Shujing Shi and Dong Wang. The first draft of the manuscript was written by Xinwen Tong. Yongsheng Li contributed to Writing- review and editing. All authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Yongsheng Li.

Ethics declarations

Conflicts of interest

The authors declare no conflicts of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tong, X., Li, Y., Yan, Z. et al. Phase-field simulation of multilayer microstructure of Cr-enriched phase induced by alternating strain. Int J Mech Mater Des 18, 185–197 (2022). https://doi.org/10.1007/s10999-021-09572-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10999-021-09572-8

Keyword

Search

Navigation