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  • 1.
    Loginova, I.
    et al.
    KTH.
    Amberg, Gustav
    KTH.
    Ågren, John
    KTH.
    Phase-field simulations of non-isothermal binary alloy solidification2001In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 49, no 4, p. 573-581Article in journal (Refereed)
    Abstract [en]

    A phase-field method for two-dimensional simulations of binary alloy solidification is studied. Phase-field equations that involve both temperature and solute redistribution are formulated. The equations are solved using the finite element method with triangular elements on unstructured meshes, which are adapted to the solution. Dendritic growth into a supersaturated melt is simulated for two temperature regimes: (a) the temperature is prescribed on the boundary of the computational domain; and (b) the heat is extracted through the domain boundary at a constant rate. In the former regime the solute redistribution is compared with the one given by an isothermal model. In the latter case the influence of the size of the computational domain and of the heat extraction rate on dendritic structure is investigated. It is shown that at high cooling rates the supersaturation is replaced by thermal undercooling as the driving force for growth.

  • 2.
    Loginova, I.
    et al.
    KTH.
    Odqvist, J.
    KTH.
    Amberg, Gustav
    KTH.
    Ågren, John
    KTH.
    The phase-field approach and solute drag modeling of the transition to massive gamma ->alpha transformation in binary Fe-C alloys2003In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 51, no 5, p. 1327-1339Article in journal (Refereed)
    Abstract [en]

    The transition between diffusion controlled and massive transformation gamma --> alpha in Fe-C alloys is investigated by means of phase-field simulations and thermodynamic functions assessed by the Calphad technique as well as diffusional mobilities available in the literature. A gradual variation in properties over an incoherent interface, having a thickness around 1 nm, is assumed. The phase-field simulations are compared with a newly developed technique to model solute drag during phase transformations. Both approaches show qualitatively the same behavior and predict a transition to a massive transformation at a critical temperature below the T-0 line and close to the alpha/alpha + gamma phase boundary. It is concluded that the quantitative difference between the two predictions stems from different assumptions on how the properties vary across the phase interface yielding a lower dissipation of Gibbs energy by diffusion in the phase-field simulations. The need for more detailed information about the actual variation in interfacial properties is emphasized.

  • 3.
    Loginova, I.
    et al.
    KTH.
    Ågren, J.
    KTH.
    Amberg, Gustav
    KTH.
    On the formation of Widmanstätten ferrite in binary Fe-C - Phase-field approach2004In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 52, no 13, p. 4055-4063Article in journal (Refereed)
    Abstract [en]

    A phase-field method, based on a Gibbs energy functional, is formulated for γ→α transformation in Fe-C. The derived phase-field model reproduces the following important types of phase transitions: from C diffusion controlled growth through Widmanstätten microstructures to massive growth without partitioning of C. Applying thermodynamic functions assessed by the Calphad technique and diffusional mobilities available in the literature, we study two-dimensional growth of ferrite side plates emanating from an austenite grain boundary. The morphology of the ferrite precipitates is defined by a highly anisotropic interfacial energy. As large values of anisotropy lead to an ill-posed phase-field equation we present a regularization method capable of circumvent non-differentiable domains of interfacial energy.

  • 4.
    Malik, Amer
    et al.
    KTH.
    Amberg, Gustav
    KTH.
    Borgenstam, Annika
    KTH.
    Ågren, John
    KTH.
    Effect of external loading on the martensitic transformation - A phase field study2013In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 61, no 20, p. 7868-7880Article in journal (Refereed)
    Abstract [en]

    In this work, the effect of external loading on the martensitic transformation is analyzed using an elasto-plastic phase field model. The phase field microelasticity theory, incorporating a non-linear strain tensor and the effect of grain boundaries, is used to study the impact of applied stresses on an Fe-0.3%C polycrystalline alloy, both in two and three dimensions. The evolution of plasticity is computed using a time-dependent equation that solves for the minimization of the shear strain energy. Crystallographic orientation of the grains in the polycrystal is chosen randomly and it is verified that the said assumption does not have a significant effect on the final volume fraction of martensite. Two-dimensional (2-D) and three-dimensional (3-D) simulations are performed at a temperature significantly higher than the martensitic start temperature of the alloy with uniaxial tensile, compressive and shear loading, along with hydrostatic stresses. It is found that the 3-D simulations are necessary to investigate the effect of external loading on the martensitic transformation using the phase field method since the 2-D numerical simulations produce results that are physically incorrect, while the results obtained from the 3-D simulations are in good agreement with the empirical observations found in the literature. Finally, it is concluded that the given model can be used to predict the volume fraction of martensite in a material with any kind of external loading.

  • 5.
    Tahir, Abdul Malik
    et al.
    KTH.
    Amberg, Gustav
    KTH.
    Do-Quang, Minh
    KTH.
    Initial rapid wetting in metallic systems2013In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 61, no 14, p. 5375-5386Article in journal (Refereed)
    Abstract [en]

    The initial rapid wetting of a solid surface by a liquid phase is an important step in many industrial processes. Liquid-phase sintering of powder metallurgical steels is one such industrial process, where metallic powders of micrometer size are used. Investigating the dynamic wetting of a high-temperature metallic drop of micrometer size experimentally is very challenging. Here, a phase-field-based numerical model is first implemented and verified by accurately capturing the initial dynamic wetting of millimeter-sized metal drops and then the model is extended to predict the dynamic wetting of a micrometer-sized metal drop. We found, in accordance with recent observations, that contact line friction is required for accurate simulation of dynamic wetting. Our results predict the wetting time for a micrometer-sized metal drop and also indicate that the dynamic wetting patterns at the micro- and millimeter length scales are qualitatively similar. We also found that the wetting process is much faster for a micrometer-sized metal drop compared to a millimeter-sized metal drop.

  • 6.
    Villanueva, Walter
    et al.
    Institute of Standards & Technology (NIST), Gaithersburg, USA.
    Boettinger, W. J.
    National Institute of Standards & Technology (NIST), Gaithersburg, USA.
    Warren, J. A.
    Institute of Standards & Technology (NIST), Gaithersburg, USA.
    Amberg, Gustav
    KTH.
    Effect of phase change and solute diffusion on spreading on a dissolving substrate2009In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 57, no 20, p. 6022-6036Article in journal (Refereed)
    Abstract [en]

    Dissolutive wetting is investigated numerically using a diffuse-interface model that incorporates fluid flow, solute diffusion and phase change. A range of materials parameters are investigated: (1) permitting recovery of the hydrodynamic limit by suppressing the dissolution of the substrate and (2) evaluating the role of diffusion. The time history of droplet size, droplet concentration and angles between the interfaces are given. For cases in which convection dominates, the dynamics of spreading agrees with a known hydrodynamic model for spreading of inert fluids. A phase change increases wetting speed, due to a condensation that takes place near the triple junction. There is also a strong dependence of the wetting kinetics on the solute diffusivities. Details of composition changes during spreading are also discussed, such as the composition path of the bulk liquid probed at different locations in the drop. Published by Elsevier Ltd on behalf of Acta Materialia Inc.

  • 7.
    Yeddu, Hemantha Kumar
    et al.
    KTH.
    Malik, Amer
    KTH.
    Ågren, John
    KTH.
    Amberg, Gustav
    KTH.
    Borgenstam, Annika
    KTH.
    Three-dimensional phase-field modeling of martensitic microstructure evolution in steels2012In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 60, no 4, p. 1538-1547Article in journal (Refereed)
    Abstract [en]

    In the present work a 3-D elastoplastic phase-field (PF) model is developed, based on the PF microelasticity theory proposed by A.G.Khachaturyan and by including plastic deformation as well as anisotropic elastic properties, for modeling the martensitic transformation (MT) by using the finite-element method. PF simulations in 3D are performed by considering different cases of MT occurring in an elastic material, with and without dilatation, and in an elastic perfectly plastic material with dilatation having isotropic as well as anisotropic elastic properties. As input data for the simulations the thermodynamic parameters corresponding to anFe–0.3%C alloy as well as the physical parameters corresponding to steels acquired from experimental results are considered. The simulation results clearly show auto-catalysis and morphological mirror image formation, which are some of the typical characteristics of a martensitic microstructure. The results indicate that elastic strain energy, anisotropic elastic properties, plasticity and the external clamping conditions affect MT as well as the microstructure.

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