Effects of internal stresses and intermediate phases on the coarsening of coherent precipitates: A phase-field study

M. Asle Zaeem, H. El Kadiri, M. F. Horstemeyer, M. Khafizov, Z. Utegulov

    Research output: Contribution to journalArticle

    14 Citations (Scopus)

    Abstract

    Phase stability, topology and size evolution of precipitates are important factors in determining the mechanical properties of crystalline materials. In this article, the Cahn-Hilliard type of phase-field model was coupled to elasticity equations within a mixed-order Galerkin finite element framework to study the coarsening morphology of coherent precipitates. The effects of capillarity, particle size and fraction, compositional strain, and inhomogeneous elasticity on the kinetics and kinematics of coherent precipitates in a binary dual phase crystal admitting a third intermediate stable/meta-stable phase were investigated. The results demonstrated the ability of the model to simulate coarsening under the concomitant action of Ostwald ripening and mismatch elastic strain mechanisms. Using a phenomenological coarsening power law, coarsening rates were determined to depend on precipitate size and volume fraction, compositional strain, and strain mismatch between precipitates and the matrix. Results also showed that the necking incubation time between two neighboring precipitates depends inversely on the precipitate's initial sizes; however, under fixed volume fraction of precipitates, any increase in the initial sizes of the precipitates mitigates the coarsening. Meanwhile, the compositional strain and the growth of the intermediate stable/meta-stable phase leads to substantial enhancements of precipitate coarsening.

    Original languageEnglish
    Pages (from-to)570-580
    Number of pages11
    JournalCurrent Applied Physics
    Volume12
    Issue number2
    DOIs
    Publication statusPublished - Mar 2012

    Fingerprint

    Coarsening
    residual stress
    Precipitates
    precipitates
    Residual stresses
    Metastable phases
    Elasticity
    Volume fraction
    elastic properties
    Ostwald ripening
    Phase stability
    Capillarity
    Kinematics
    kinematics
    topology
    Particle size
    Topology
    mechanical properties
    Crystalline materials
    Mechanical properties

    Keywords

    • Cahn-Hilliard phase-field model
    • Coarsening
    • Coherent precipitates
    • Compositional strain
    • Finite element
    • Intermediate phase

    ASJC Scopus subject areas

    • Materials Science(all)
    • Physics and Astronomy(all)

    Cite this

    Effects of internal stresses and intermediate phases on the coarsening of coherent precipitates : A phase-field study. / Asle Zaeem, M.; El Kadiri, H.; Horstemeyer, M. F.; Khafizov, M.; Utegulov, Z.

    In: Current Applied Physics, Vol. 12, No. 2, 03.2012, p. 570-580.

    Research output: Contribution to journalArticle

    Asle Zaeem, M. ; El Kadiri, H. ; Horstemeyer, M. F. ; Khafizov, M. ; Utegulov, Z. / Effects of internal stresses and intermediate phases on the coarsening of coherent precipitates : A phase-field study. In: Current Applied Physics. 2012 ; Vol. 12, No. 2. pp. 570-580.
    @article{55490191d81f46c6a3b8be99f75e6607,
    title = "Effects of internal stresses and intermediate phases on the coarsening of coherent precipitates: A phase-field study",
    abstract = "Phase stability, topology and size evolution of precipitates are important factors in determining the mechanical properties of crystalline materials. In this article, the Cahn-Hilliard type of phase-field model was coupled to elasticity equations within a mixed-order Galerkin finite element framework to study the coarsening morphology of coherent precipitates. The effects of capillarity, particle size and fraction, compositional strain, and inhomogeneous elasticity on the kinetics and kinematics of coherent precipitates in a binary dual phase crystal admitting a third intermediate stable/meta-stable phase were investigated. The results demonstrated the ability of the model to simulate coarsening under the concomitant action of Ostwald ripening and mismatch elastic strain mechanisms. Using a phenomenological coarsening power law, coarsening rates were determined to depend on precipitate size and volume fraction, compositional strain, and strain mismatch between precipitates and the matrix. Results also showed that the necking incubation time between two neighboring precipitates depends inversely on the precipitate's initial sizes; however, under fixed volume fraction of precipitates, any increase in the initial sizes of the precipitates mitigates the coarsening. Meanwhile, the compositional strain and the growth of the intermediate stable/meta-stable phase leads to substantial enhancements of precipitate coarsening.",
    keywords = "Cahn-Hilliard phase-field model, Coarsening, Coherent precipitates, Compositional strain, Finite element, Intermediate phase",
    author = "{Asle Zaeem}, M. and {El Kadiri}, H. and Horstemeyer, {M. F.} and M. Khafizov and Z. Utegulov",
    year = "2012",
    month = "3",
    doi = "10.1016/j.cap.2011.09.004",
    language = "English",
    volume = "12",
    pages = "570--580",
    journal = "Current Applied Physics",
    issn = "1567-1739",
    publisher = "Elsevier",
    number = "2",

    }

    TY - JOUR

    T1 - Effects of internal stresses and intermediate phases on the coarsening of coherent precipitates

    T2 - A phase-field study

    AU - Asle Zaeem, M.

    AU - El Kadiri, H.

    AU - Horstemeyer, M. F.

    AU - Khafizov, M.

    AU - Utegulov, Z.

    PY - 2012/3

    Y1 - 2012/3

    N2 - Phase stability, topology and size evolution of precipitates are important factors in determining the mechanical properties of crystalline materials. In this article, the Cahn-Hilliard type of phase-field model was coupled to elasticity equations within a mixed-order Galerkin finite element framework to study the coarsening morphology of coherent precipitates. The effects of capillarity, particle size and fraction, compositional strain, and inhomogeneous elasticity on the kinetics and kinematics of coherent precipitates in a binary dual phase crystal admitting a third intermediate stable/meta-stable phase were investigated. The results demonstrated the ability of the model to simulate coarsening under the concomitant action of Ostwald ripening and mismatch elastic strain mechanisms. Using a phenomenological coarsening power law, coarsening rates were determined to depend on precipitate size and volume fraction, compositional strain, and strain mismatch between precipitates and the matrix. Results also showed that the necking incubation time between two neighboring precipitates depends inversely on the precipitate's initial sizes; however, under fixed volume fraction of precipitates, any increase in the initial sizes of the precipitates mitigates the coarsening. Meanwhile, the compositional strain and the growth of the intermediate stable/meta-stable phase leads to substantial enhancements of precipitate coarsening.

    AB - Phase stability, topology and size evolution of precipitates are important factors in determining the mechanical properties of crystalline materials. In this article, the Cahn-Hilliard type of phase-field model was coupled to elasticity equations within a mixed-order Galerkin finite element framework to study the coarsening morphology of coherent precipitates. The effects of capillarity, particle size and fraction, compositional strain, and inhomogeneous elasticity on the kinetics and kinematics of coherent precipitates in a binary dual phase crystal admitting a third intermediate stable/meta-stable phase were investigated. The results demonstrated the ability of the model to simulate coarsening under the concomitant action of Ostwald ripening and mismatch elastic strain mechanisms. Using a phenomenological coarsening power law, coarsening rates were determined to depend on precipitate size and volume fraction, compositional strain, and strain mismatch between precipitates and the matrix. Results also showed that the necking incubation time between two neighboring precipitates depends inversely on the precipitate's initial sizes; however, under fixed volume fraction of precipitates, any increase in the initial sizes of the precipitates mitigates the coarsening. Meanwhile, the compositional strain and the growth of the intermediate stable/meta-stable phase leads to substantial enhancements of precipitate coarsening.

    KW - Cahn-Hilliard phase-field model

    KW - Coarsening

    KW - Coherent precipitates

    KW - Compositional strain

    KW - Finite element

    KW - Intermediate phase

    UR - http://www.scopus.com/inward/record.url?scp=81155139635&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=81155139635&partnerID=8YFLogxK

    U2 - 10.1016/j.cap.2011.09.004

    DO - 10.1016/j.cap.2011.09.004

    M3 - Article

    AN - SCOPUS:81155139635

    VL - 12

    SP - 570

    EP - 580

    JO - Current Applied Physics

    JF - Current Applied Physics

    SN - 1567-1739

    IS - 2

    ER -