Phase field simulation of stress evolution during solidification

Uehara, Takuya; Tsujino, Takahiro

doi:10.1016/j.jcrysgro.2004.11.056

Cited by 14 publications

(11 citation statements)

References 13 publications

(16 reference statements)

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“…Doherty [50] subdivided dendrite bending into mechanical bending and morphological bending. He attributed mechanical bending to mechanical forces arising from thermal [45], shrinkage [51,52] or convective stresses [54][55][56]72,73]. These stress driven processes result in crystal lattice rotations.…”

Section: Discussionmentioning

confidence: 99%

“…A detailed overview of dendrite deformation phenomena has been published by Doherty [50]. In several publications, thermal and shrinkage stresses were invoked to explain the deformation of dendrites [38,[50][51][52][53]. Other explanations, such as convective forces [54][55][56], precipitation-related phenomena [45], interactions with the mold wall [47][48][49], gravity [49] and asymmetric distributions of the solute around dendrite stems [46] have also been put forward.…”

Section: Introductionmentioning

confidence: 99%

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On Crystal Mosaicity in Single Crystal Ni-Based Superalloys

et al. 2019

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In the present work, we investigate the evolution of mosaicity during seeded Bridgman processing of technical Ni-based single crystal superalloys (SXs). For this purpose, we combine solidification experiments performed at different withdrawal rates between 45 and 720 mm/h with advanced optical microscopy and quantitative image analysis. The results obtained in the present work suggest that crystal mosaicity represents an inherent feature of SXs, which is related to elementary stochastic processes which govern dendritic solidification. In SXs, mosaicity is related to two factors: inherited mosaicity of the seed crystal and dendrite deformation. Individual SXs have unique mosaicity fingerprints. Most crystals differ in this respect, even when they were produced using identical processing conditions. Small differences in the orientation spread of the seed crystals and small stochastic orientation deviations continuously accumulate during dendritic solidification. Direct evidence for dendrite bending in a seeded Bridgman growth process is provided. It was observed that continuous or sudden bending affects the growth directions of dendrites. We provide evidence which shows that some dendrites continuously bend by 1.7° over a solidification distance of 25 mm.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Crystal Mosaicity in Single Crystal Ni-Based Superalloys

et al. 2019

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“…Since the fundamental equations are derived in a thermodynamically consistent way [9], including the anisotropic detail [10], this model is recognized as a physically proper model. For application to the mechanical behavior, Uehara et al calculated elastic stresses of solid during solidification process by a one-dimensional model [11]. In order to estimate more precise stresses, they formulated the coupling effects among phase, temperature and stress/strain including plastic stress [12,13], and executed numerical simulations on the stress evolution during an in-solid phase transformation [13,14].…”

Section: Introductionmentioning

confidence: 99%

Phase field simulations of stress distributions in solidification structures

Uehara

Fukui

Ohno

2008

Journal of Crystal Growth

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“…Morphologies arising during solidification in a narrow channel were studied in [97,300,301]. An interesting phase field model of stress evolution during solidification of a thin rod was presented in [302]. Other examples of the phase field applications include modeling of crack propagation [303][304][305][306][307][308], electrochemistry [309][310][311], shape memory polycrystals [312], electrically and magnetically active materials [313] and wave propagation in anatomical models of the heart [314].…”

Section: Other Applicationsmentioning

confidence: 99%

The phase field technique for modeling multiphase materials

2008

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This paper reviews methods and applications of the phase field technique, one of the fastest growing areas in computational materials science. The phase field method is used as a theory and computational tool for predictions of the evolution of arbitrarily shaped morphologies and complex microstructures in materials. In this method, the interface between two phases (e.g. solid and liquid) is treated as a region of finite width having a gradual variation of different physical quantities, i.e. it is a diffuse interface model. An auxiliary variable, the phase field or order parameter φ( x), is introduced, which distinguishes one phase from the other. Interfaces are identified by the variation of the phase field. We begin with presenting the physical background of the phase field method and give a detailed thermodynamical derivation of the phase field equations. We demonstrate how equilibrium and non-equilibrium physical phenomena at the phase interface are incorporated into the phase field methods. Then we address in detail dendritic and directional solidification of pure and multicomponent alloys, effects of natural convection and forced flow, grain growth, nucleation, solid-solid phase transformation and highlight other applications of the phase field methods. In particular, we review the novel phase field crystal model, which combines atomistic length scales with diffusive time scales. We also discuss aspects of quantitative phase field modeling such as thin interface asymptotic analysis and coupling to thermodynamic databases. The phase field methods result in a set of partial differential equations, whose solutions require time-consuming large-scale computations and often limit the applicability of the method. Subsequently, we review numerical approaches to solve the phase field equations and present a finite difference discretization of the anisotropic Laplacian operator.

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Phase field simulation of stress evolution during solidification

Cited by 14 publications

References 13 publications

On Crystal Mosaicity in Single Crystal Ni-Based Superalloys

On Crystal Mosaicity in Single Crystal Ni-Based Superalloys

Phase field simulations of stress distributions in solidification structures

The phase field technique for modeling multiphase materials

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