Simulation of γ-hydride precipitation in bi-crystalline zirconium under uniformly applied load

Ma, Xingqiao; Shi, San-Qiang; Woo, C.H.; Chen, Lei

doi:10.1016/s0921-5093(01)01770-1

Cited by 26 publications

(6 citation statements)

References 24 publications

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“…The PF method was used to simulate the morphological evolution of hydride precipitation and growth in a zirconium bulk material with and without flaws by considering elastic deformation and elastic-plastic deformation, respectively. [81][82][83][84][85][86][87] In the PF models of hydride precipitation [81][82][83][84][85][86] a nonconservative order parameter vector, η = {η 1 (x,t),η 2 (x,t),···,η N (x,t)}, was used to describe the crystal orientations of hydride precipitates, and a conserved field variable, c 1 (x,t) = c H (x,t), was used to describe the concentration of hydrogen in precipitates and matrix. The chemical free energy density was a summation of the forms of Model 1 for the concentration of hydrogen and Model 2 for different orientated hydride precipitates plus their interaction terms.…”

Section: Simulations Of Different Phenomena In Radiation-induced Micrmentioning

confidence: 99%

“…Applications of the PF method in predicting microstructure evolution in solidification and solid state phase transition have been reviewed in several articles. [46][47][48][49][50][51][52][53] During the past decade, the PF approach has been applied to study microstructure evolutions in irradiated nuclear materials such as gas bubble evolution in nuclear fuels, [54][55][56][57][58][59][60][61][62] void formation and evolution, [63][64][65][66][67][68][69][70][71][72][73] void and gas bubble lattice formation, 62,74 void migration under temperature gradient, [75][76][77] SIA loop growth kinetics, [78][79][80] precipitation, [81][82][83][84][85][86][87][88][89][90] grain growth and recrystallization. [91]…”

Section: Introductionmentioning

confidence: 99%

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A review: applications of the phase field method in predicting microstructure and property evolution of irradiated nuclear materials

Sun

et al. 2017

npj Comput Mater

122

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Complex microstructure changes occur in nuclear fuel and structural materials due to the extreme environments of intense irradiation and high temperature. This paper evaluates the role of the phase field method in predicting the microstructure evolution of irradiated nuclear materials and the impact on their mechanical, thermal, and magnetic properties. The paper starts with an overview of the important physical mechanisms of defect evolution and the significant gaps in simulating microstructure evolution in irradiated nuclear materials. Then, the phase field method is introduced as a powerful and predictive tool and its applications to microstructure and property evolution in irradiated nuclear materials are reviewed. The review shows that (1) Phase field models can correctly describe important phenomena such as spatial-dependent generation, migration, and recombination of defects, radiation-induced dissolution, the Soret effect, strong interfacial energy anisotropy, and elastic interaction; (2) The phase field method can qualitatively and quantitatively simulate two-dimensional and three-dimensional microstructure evolution, including radiation-induced segregation, second phase nucleation, void migration, void and gas bubble superlattice formation, interstitial loop evolution, hydrate formation, and grain growth, and (3) The Phase field method correctly predicts the relationships between microstructures and properties. The final section is dedicated to a discussion of the strengths and limitations of the phase field method, as applied to irradiation effects in nuclear materials. npj Computational Materials (2017) 3:16 ; doi:10.1038/s41524-017-0018-y INTRODUCTIONHigh energy particle (such as neutron, ion, and electron) radiation can create major changes in the shape and thermo-mechanical properties of nuclear fuels and structural components of nuclear reactors. These changes are caused by radiation-induced evolution of compositions and microstructures. The main effects of radiation on reactor materials are: (1) dimensional change associated with gas bubble swelling, void swelling, grain growth, and creep; 1-5 (2) loss of ductility and increase in ductile-brittle transition temperature (DBTT) due to the formation of secondphase precipitates, self-interstitial atomic (SIA) loops, and dislocation networks; 6, 7 (3) oxidation and corrosion accelerated by high temperature, fission products, and radiation damage; 8-10 and (4) local and bulk changes in chemical composition, including irradiation-enhanced segregation of alloy components and phase separation.11-17 Figure 1 shows typical microstructures observed in irradiated materials.9, 18-21 The radiation-induced heterogeneity of the microstructures depends on the initial phase and defect structure of the fresh (non-irradiated) materials and on the type and severity of the radiation environment. Fundamental understanding of heterogeneous three-dimensional microstructure evolution is crucial to the development of advanced radiation tolerant materials that can significa...

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Section: Simulations Of Different Phenomena In Radiation-induced Micrmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A review: applications of the phase field method in predicting microstructure and property evolution of irradiated nuclear materials

Sun

et al. 2017

npj Comput Mater

122

View full text Add to dashboard Cite

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“…The phase field method has also been applied to investigate proper and improper martensitic transformations in single and polycrystals [326][327][328][329][330][331], cubic-to-tetragonal transformations [332][333][334], hexagonalto-orthorhombic transformations [335][336][337][338], ferroelectric transformations [339,340], phase transformations under applied stress [327,330,[341][342][343] and in the presence of strain [344][345][346]. Attempts to describe the dynamics of nanovoids and nanobubbles in solids [347], particle splitting [348], dynamics of dislocations [349][350][351][352] and formation of dislocation networks [353,354], development of zirconium hydride precipitation [355][356][357] and microstructural evolution in the presence of structural defects [352,358] have been performed.…”

Section: Solid-state Transformationsmentioning

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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“…Most of them were created for the ζ -hydride [26][27][28] and the γ-hydride. [29][30][31][32][33][34] In recent years, many researchers have focused on the δ -hydrides and started to develop corresponding PF models to study the characteristics of δ -hydride morphology. Jokisaari et al [35] developed a δ -hydride PF model to study the growth kinetics of the δ -hydride by modifying the free energies based on the CALPHAD (CALculation of PHAse Diagrams).…”

Section: Introductionmentioning

confidence: 99%

Phase-field simulations of the effect of temperature and interface for zirconium δ-hydrides

Chen 陈,

Sheng 盛,

Liu 刘

et al. 2024

Chinese Phys. B

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Hydride precipitation in zirconium cladding materials can damage their integrity and durability. Service temperature and material defects have a significant effect on the dynamic growth of hydrides. In this study, we have developed a phase-field model based on the assumption of elastic behaviour within a specific temperature range (613 - 653 K). This model allows us to study the influence of temperature and interfacial effects on the morphology, stress, and average growth rate of zirconium hydride. The results suggest that changes in temperature and interfacial energy influence the length-to-thickness ratio and average growth rate of the hydride morphology. The ultimate determinant of hydride orientation is the loss of interfacial coherency, primarily induced by interfacial dislocation defects and quantifiable by the mismatch degree q. An escalation in interfacial coherency loss leads to a transition of hydride growth from horizontal to vertical, accompanied by the onset of redirection behaviour. Interestingly, redirection occurs at a critical mismatch level, denoted q c , and remains unaffected by variations in temperature and interfacial energy. However, this redirection leads to an increase in the maximum stress, which may influence the direction of hydride crack propagation. This research highlights the importance of interfacial coherency and provides valuable insights into the morphology and growth kinetics of hydrides in zirconium alloys.

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Simulation of γ-hydride precipitation in bi-crystalline zirconium under uniformly applied load

Cited by 26 publications

References 24 publications

A review: applications of the phase field method in predicting microstructure and property evolution of irradiated nuclear materials

A review: applications of the phase field method in predicting microstructure and property evolution of irradiated nuclear materials

The phase field technique for modeling multiphase materials

Phase-field simulations of the effect of temperature and interface for zirconium δ-hydrides

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