Growth behavior of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mrow><mml:mi>γ</mml:mi><mml:mo>'</mml:mo><mml:mo>/</mml:mo><mml:mi>γ</mml:mi><mml:mo>'</mml:mo><mml:mo>'</mml:mo></mml:mrow></mml:math> coprecipitates in Ni-Base superalloys

Shi, Rongpei; McAllister, Donald; Zhou, Ning; Detor, Andrew J.; DiDomizio, Richard; Mills, Michael J.; Wang, Yunzhi

doi:10.1016/j.actamat.2018.10.028

Cited by 59 publications

(27 citation statements)

References 27 publications

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“…In Table II also a stiffness contrast C γ ij /C γ ij is given. In the case of anisotropic elasticity, we apply the mixture rule in Equation (7) to compare the respective tensors of elasticity. We report a mean value as the different elastic constants show different stiffness contrasts.…”

Section: Elastic Constantsmentioning

confidence: 99%

“…Values of a mean stiffness contrast C γ ij /C γ ij are provided. Data is generated via: 1 resonance ultrasound spectroscopy 2 first-principles calculations [50,51] and Equation (3) 3 Equation (4) 4 Equation (7) All evaluations of the elastic moduli of the phases based Equation (4) are dependent on the volume fraction V α . In this work, we assume a γ volume fraction of 12 % which is in accordance with previously reported values [56,57] and higher than it was calculated using the Thermo-Calc software with the TCNi8 database.…”

Section: Elastic Constantsmentioning

confidence: 99%

“…Table I shows the nominal composition of IN718 and a derivative IN718M without γ forming elements. Recent studies aim at deliberate co-precipitation of γ and γ to exploit ripening inhibiting effects [6,7] and a dual lattice microstructure [8,9]. IN718 powders also gain importance for additive manufacturing in the industrial environment [10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

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Phase-field modeling of γ/γ″ microstructure formation in Ni-based superalloys with high γ″ volume fraction

et al. 2020

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The excellent mechanical properties of the Ni-based superalloy IN718 mainly result from coherent γ precipitates. Due to a strongly anisotropic lattice misfit between the matrix and the precipitate phase, the particles exhibit pronounced plate-shaped morphologies. Using a phase-field model, we investigate various influencing factors that determine the equilibrium shapes of γ precipitates, minimizing the sum of the total elastic and interfacial energy. Upon increasing precipitate phase fractions, the model predicts increasingly stronger particle-particle interactions, leading to shapes with significantly increased aspect ratios. Matching the a priori unknown interfacial energy density to fit experimental γ shapes is sensitive to the phase content imposed in the underlying model. Considering vanishing phase content leads to 30 % lower estimates of the interfacial energy density, as compared to estimates based on realistic phase fractions of 12 %. We consider the periodic arrangement of precipitates in different hexagonal and rectangular superstructures, which result from distinct choices of point-symmetric and periodic boundary conditions. Further, non-volume conserving boundary conditions are implemented to compensate for strains due to an anisotropic lattice mismatch between the γ matrix and the γ precipitate. As compared to conventional boundary conditions, this specifically tailored simulation configuration does not conflict with the systems periodicity and provides substantially more realistic total elastic energies at high precipitate volume fractions. The energetically most favorable superstructure is found to be a hexagonal precipitate arrangement.c 2020. The manuscript is made available under the license CC-BY-NC-ND 4.0

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Section: Elastic Constantsmentioning

confidence: 99%

Section: Elastic Constantsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Phase-field modeling of γ/γ″ microstructure formation in Ni-based superalloys with high γ″ volume fraction

et al. 2020

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“…Although there are extensive studies of microstructural evolution during phase separation in binary alloy systems with coherent elastic misfit [16,17,18,19,20], there are very few studies focusing on the effects of elastic stress when more than two phases are present in the microstructure [21,22]. De Fontaine [23] and Morral and Cahn [24] analyzed the compositional stability, fluctuations and early stage kinetics of ternary SD and derived Cahn-Morral equations to describe phase separation.…”

Section: Introductionmentioning

confidence: 99%

A phase-field study of elastic stress effects on phase separation in ternary alloys

Sugathan

Bhattacharyya

2020

Computational Materials Science

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Most of the commercially important alloys are multicomponent, producing multiphase microstructures as a result of processing. When the coexisting phases are elastically coherent, the elastic interactions between these phases play a major role in the development of microstructures. To elucidate the key effects of elastic stress on microstructural evolution when more than two misfitting phases are present in the microstructure, we have developed a microelastic phase-field model in two dimensions to study phase separation in ternary alloy system. Numerical solutions of a set of coupled Cahn-Hilliard equations for the composition fields govern the spatiotemporal evolution of the three-phase microstructure. The model incorporates coherency strain interactions between the phases using Khachaturyan's microelasticity theory.We systematically vary the misfit strains (magnitude and sign) between the phases along with the bulk alloy composition to study their effects on the morphological development of the phases and the resulting phase separation * Corresponding author Email addresses: ms14resch01001@iith.ac.in (Sandeep Sugathan), saswata@iith.ac.in (Saswata Bhattacharya) 1 arXiv:1904.07401v1 [cond-mat.mtrl-sci] 16 Apr 2019 ( βγ = αβ − αγ ).

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“…Here a cubic ðL1 2 Þ(c) matrix yields tetragonal variants of the precipitates (body-centered tetragonal) (c 00 ). Several other examples include sandwich and compact structures involving the c 0 and c 00 precipitates which have been observed in the IN718 superalloy and its variants, [26][27][28][29][30][31] that have also been modeled using phase-field simulations. [29,31] The existence of such multivariant clusters in different alloy systems is attributed to the elastic interaction between the precipitates which leads to a reduced energy of the system.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium Multi-precipitate Configurations

Bhadak

Singh

Choudhury

2020

Metall Mater Trans A

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In this paper, we formulate a phase-field model for the computation of equilibrium configurations of multiple phases that arise out of a solid-state precipitate reaction, in the presence of coherency stresses. Here, we utilize the phase-field framework to minimize the sum of the elastic and the interfacial energies for a given volume of the precipitates using an extension of the volume-preserved Allen-Cahn algorithm (

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Growth behavior of γ'/γ'' coprecipitates in Ni-Base superalloys

Cited by 59 publications

References 27 publications

Phase-field modeling of γ/γ″ microstructure formation in Ni-based superalloys with high γ″ volume fraction

Phase-field modeling of γ/γ″ microstructure formation in Ni-based superalloys with high γ″ volume fraction

A phase-field study of elastic stress effects on phase separation in ternary alloys

Equilibrium Multi-precipitate Configurations

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