An elastoplastic phase-field model for the evolution of hydride precipitation in zirconium. Part II: Specimen with flaws

Guo, Xueshi; Shi, San-Qiang; Zhang, Q.M.; Ma, Xingqiao

doi:10.1016/j.jnucmat.2008.05.006

Cited by 31 publications

(12 citation statements)

References 10 publications

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“…36,37 The system's total energy can be expressed as The inclusion of elastic and/or plastic deformation in the model is completely feasible because it has been done in other systems. [38][39][40] It can be even necessary to include the strain energy term if a volumetric non-compatible passive film develops during corrosion. Because the formation of a passive film will not be considered in the first stage of this work, for simplicity, the elastic strain energy is not considered here.…”

Section: Resultsmentioning

confidence: 99%

Phase-field model of pitting corrosion kinetics in metallic materials

Ansari

Xiao

et al. 2018

npj Comput Mater

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Pitting corrosion is one of the most destructive forms of corrosion that can lead to catastrophic failure of structures. This study presents a thermodynamically consistent phase field model for the quantitative prediction of the pitting corrosion kinetics in metallic materials. An order parameter is introduced to represent the local physical state of the metal within a metal-electrolyte system. The free energy of the system is described in terms of its metal ion concentration and the order parameter. Both the ion transport in the electrolyte and the electrochemical reactions at the electrolyte/metal interface are explicitly taken into consideration. The temporal evolution of ion concentration profile and the order parameter field is driven by the reduction in the total free energy of the system and is obtained by numerically solving the governing equations. A calibration study is performed to couple the kinetic interface parameter with the corrosion current density to obtain a direct relationship between overpotential and the kinetic interface parameter. The phase field model is validated against the experimental results, and several examples are presented for applications of the phase-field model to understand the corrosion behavior of closely located pits, stressed material, ceramic particles-reinforced steel, and their crystallographic orientation dependence. INTRODUCTIONCorrosion is the gradual destruction of materials (usually metallic materials) via chemical and/or electrochemical reaction with their environment. It costs about 3.1% of the gross domestic product (GDP) in the United States, which is much more than the cost of all natural disasters combined. Localized corrosion, such as pitting corrosion, is one of the most destructive forms of corrosion; it leads to the catastrophic failure of structures and raises both human safety and financial concerns. 1-3 Pitting corrosion of stainless steel usually occurs in two different stages: (1) pit initiation from passive film breakage 4-6 and (2) pit growth. 2,3,[7][8][9][10][11][12] In this study, we focused on the development of a phase-field modeling capability to study pit growth by considering both anodic and cathodic reactions.In the past few decades, great efforts have been made to develop numerical models for pitting corrosion. The moving interface and the electrical double layer at the metal/electrolyte interface are the two challenging problems faced by most of these numerical models. These numerical models can be divided according to the method in which a moving interface is incorporated in their models. Several steady state 9,10,13-18 and transient state 19-28 models have been developed over the years that did not allow for changes in the shape and dimensions of the pits/crevices as corrosion proceeds.Recent advances in numerical techniques, such as the finite element method, the finite volume method, the arbitrary Lagrangian-Eulerian method, the mesh-free method, and the level set method have encouraged researchers to model the evolving morphology...

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Section: Resultsmentioning

confidence: 99%

Phase-field model of pitting corrosion kinetics in metallic materials

Ansari

Xiao

et al. 2018

npj Comput Mater

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“…Some other dimensionless phase field modeling studies using a similar free energy have also been done for bicrystalline Zr [92], for non-uniform applied loads [93], and for a specimen with flaws such as a crack [94,95]. Modeling of cracks was accomplished through adding plasticity to previous models driven by a reduction in distortion strain energy using a variation on the classic Prandtl Reuss theory [109].…”

Section: Phase Field Modeling Of Hydride Precipitatesmentioning

confidence: 99%

A review on hydride precipitation in zirconium alloys

Bair

Zaeem

Tonks

2015

Journal of Nuclear Materials

131

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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%

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

121

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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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An elastoplastic phase-field model for the evolution of hydride precipitation in zirconium. Part II: Specimen with flaws

Cited by 31 publications

References 10 publications

Phase-field model of pitting corrosion kinetics in metallic materials

Phase-field model of pitting corrosion kinetics in metallic materials

A review on hydride precipitation in zirconium alloys

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

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