Chemo-elastic phase-field simulation of the cooperative growth of mutually-accommodating Widmanstätten plates

Amos, P.G. Kubendran; Schoof, Ephraim; Schneider, Daniel; Nestler, Britta

doi:10.1016/j.jallcom.2018.07.138

Cited by 28 publications

(13 citation statements)

References 57 publications

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“…These works are based on a grand-potential formulation, but evolution equations can also be derived starting from a free-energy functional [38]. This approach is compatible with elastic driving forces based on jump conditions [39,40] and has successfully been used for computation of first -order phase transformations [41]. The ability of this model formulation to account for spinodal phase separating behavior has recently been shown by Aagesen et al [42], though it had previously been considered impossible due to the requirement of convex free-energy functions [36].…”

Section: Introductionmentioning

confidence: 99%

Multiphase-field modeling of spinodal decomposition during intercalation in an Allen-Cahn framework

Daubner

Amos

Schoof

et al. 2021

Phys. Rev. Materials

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Owing to its unique thermodynamical description, phase separation has largely been modeled in the Cahn-Hilliard framework. In the present work, as a computationally efficient alternative, a multicomponent, multiphase-field model operating in Allen-Cahn framework is presented and subsequently employed to simulate spinodal decomposition. Stability analysis shows that the formulation can cover the effect of phase separation while simplifying the extension to multiple phases and incorporation of additional driving forces. Computational efficiency of the proposed approach is compared with the conventional technique by modeling intercalation in a representative one-dimensional domain. Moreover, intercalation within a multigrain system involving multiparticle interaction is studied. Our results suggest initiation of phase transformation at higher order junctions as well as a grain-by-grain intercalation behavior in a two-phase cathode material such as the well-studied LiFePO 4 .

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Section: Introductionmentioning

confidence: 99%

Multiphase-field modeling of spinodal decomposition during intercalation in an Allen-Cahn framework

Daubner

Amos

Schoof

et al. 2021

Phys. Rev. Materials

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“…The phase-field approach, based on the grand-potential formalism, has been employed extensively to model solidification [81][82][83][84] and solid-state transformation [85,86], including multicomponent systems [87,88]. Furthermore, this technique is also combined with an elastic model, in order to analyze chemoelastic transformations [89,90]. Much different from these conventional studies, this approach has recently been adopted to investigate energy-minimizing, curvaturedriven transformations, where the phase field behaves in a conserved fashion [91][92][93][94][95].…”

Section: A Grand-potential Modelmentioning

confidence: 99%

“…However, the efficiency of scalar and tensorial mobilities, in the context of coupled second-order conservative and nonconservative systems of equations, remains to be evaluated and is reserved for a future investigation. As the underlying grand-potential model was successfully extended to multiphysics (e.g., mechanics [89,90]), the current surface-diffusion model suits an easy amplification in future applications as well.…”

Section: A Freedom To Choose a Mobility Functionmentioning

confidence: 99%

Multiphase-field model for surface diffusion and attachment kinetics in the grand-potential framework

et al. 2021

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Grand-potential based multiphase-field model is extended to include surface diffusion. Diffusion is elevated in the interface through a scalar degenerate term. In contrast to the classical Cahn-Hilliard-based formulations, the present model circumvents the related difficulties in restricting diffusion solely to the interface by combining two second-order equations, an Allen-Cahn-type equation for the phase field supplemented with an obstacletype potential and a conservative diffusion equation for the chemical potential or composition evolution. The sharp interface limiting behavior of the model is deduced by means of asymptotic analysis. A combination of surface diffusion and finite attachment kinetics is retrieved as the governing law. Infinite attachment kinetics can be achieved through a minor modification of the model, and with a slight change in the interpretation, the same model handles the cases of pure substances and alloys. Relations between model parameters and physical properties are obtained which allow one to quantitatively interpret simulation results. An extensive study of thermal grooving is conducted to validate the model based on existing theories. The results show good agreement with the theoretical sharp-interface solutions. The obviation of fourth-order derivatives and the usage of the obstacle potential make the model computationally cost-effective.

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“…The phase field approach (PFA) as a bridge between atomistic simulations and continuum approaches has been broadly and efficiently used to study various phenomena at different scales such as nano and microscales. It deals with kinetics, thermodynamics and structure evolution [1–9]. At the nanoscale, it has been significantly used for modelling of various phase transformations (PTs) [10–17], slip systems and dislocations [18–22], fracture (cracks) [23–28], voids [29–31] and more.…”

Section: Introductionmentioning

confidence: 99%

Effect of a thermodynamically consistent interface stress on thermal-induced nanovoid evolution in NiAl

Ghaedi

Javanbakht

2021

Mathematics and Mechanics of Solids

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In the present work, the effect of a thermodynamically consistent inelastic interface stress on nanovoid evolution in NiAl is studied. Such interface stress is introduced for the solid–gas interface of nanovoids within the concept of the phase field approach. The Cahn–Hilliard (CH) equation using the Helmholtz free energy describes the evolution of nanovoid concentration. The interface stress changes the total stress distribution and affects the elastic stress field. Thus, due to the significant effect of the elastic energy on nanovoid dynamics, it can indirectly affect nanovoid nucleation and growth. The highly nonlinear coupled CH and elasticity equations are solved using the finite element method and the COMSOL code. The coupling appears due to the presence of the nonlinear nanovoid inelastic strain in the total strain, the presence of the nonlinear inelastic interface stress in the stress tensor and the presence of elastic energy in the Helmholtz free energy. Several examples of thermal-induced nanovoid evolutions are presented to investigate the effect of the solid–gas interface stress. The obtained results show the significant effect of the interface stress on the total stress distribution, and consequently a different distribution of thermodynamic driving force which can affect the nanostructure evolution and the deformation. Mainly, the interface stress represents a promotive effect on nanovoid growth which results in a faster nanovoid growth and a larger nanovoid concentration and region.

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Chemo-elastic phase-field simulation of the cooperative growth of mutually-accommodating Widmanstätten plates

Cited by 28 publications

References 57 publications

Multiphase-field modeling of spinodal decomposition during intercalation in an Allen-Cahn framework

Multiphase-field modeling of spinodal decomposition during intercalation in an Allen-Cahn framework

Multiphase-field model for surface diffusion and attachment kinetics in the grand-potential framework

Effect of a thermodynamically consistent interface stress on thermal-induced nanovoid evolution in NiAl

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