A mean field model of agglomeration as an extension to existing precipitation models
Source abstract
Abstract
Abstract This work presents an analytical mean field model of agglomeration (equivalent agglomeration model, EAM) by contact between growing precipitates. The principle of the EAM is to add a 2-steps task to existing precipitation models: at each time-step, (1) calculate the number of agglomerations per unit volume, then (2) use it to update the numbers and radii of classes in order to take agglomeration into account. The first step is validated by full-field simulations of growing spheres randomly placed in a cube. The EAM can be added as extension to existing precipitation models and be applied to the mean radius, multi-class Lagrangian and multi-class Eulerian representations of the precipitate population. The EAM is incorporated to a mean field precipitation model based on the classical nucleation theory and Zener’s law for size evolution, and catches the rarefaction of γ″ precipitates agglomerating as they grow during an isothermal annealing in a nickel-based superalloy.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Probabilistic and Robust Engineering Design · Wind and Air Flow Studies · Differential Equations and Numerical Methods
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (86)
Show source-provided references
1. Equations of state calculations by fast computing machines10.1063/1.1699114 ↗
2. Precipitate growth in concentrated binary alloys: a comparison between kinetic Monte Carlo simulations, cluster dynamics and the classical theory10.1080/14786435.2013.805275 ↗
3. Kinetics of precipitation: comparison between monte carlo simulations, cluster dynamics and the classical theories10.4028/www.scientific.net/DDF.237-240.671 ↗
4. Cluster free energy in the simple cubic ising model10.1103/PhysRevB.29.2689 ↗
5. Studies in molecular dynamics. i. general method10.1063/1.1730376 ↗
6. C. Becquart, M. Perez, Dynamique moléculaire appliquée aux matériaux, 2010, (http://michel.perez.net.free.fr/Becquart10.pdf).10.51257/a-v1-re136 ↗
7. Molecular dynamics simulation of defect formation and precipitation in heavily carbon doped silicon10.1016/j.mseb.2008.10.010 ↗
8. Coarse-grained molecular-dynamics simulations of nanoparticle diffusion in polymer nanocomposites10.1016/j.polymer.2018.04.058 ↗
9. Laé · 2007
10. Transient nucleation in condensed systems10.1063/1.445731 ↗
11. Modeling of copper precipitation in iron during thermal aging and irradiation10.1016/j.jnucmat.2003.08.035 ↗
12. Modeling of Nucleation Processes
13. Translation of J.D. van der Waals “the thermodynamic theory of capillarity under the hypothesis of a continuous variation of density”10.1007/BF01011513 ↗
14. Toward the superconductivity theory
15. Free energy of a nonuniform system. i. interfacial free energy10.1063/1.1744102 ↗
16. Phase-Field Modeling of θ′ Precipitation Kinetics in W319 Alloys
17. Phase-field simulation of the elastic effect on the transformation kinetics in precipitation10.2320/matertrans.MRA2007153 ↗
18. Computer simulation of phase transformation and plastic deformation in IN718 superalloy: microstructural evolution during precipitation10.1016/j.actamat.2013.10.069 ↗
19. Keimbildung in übersättigten gebilden10.1515/zpch-1926-11927 ↗
20. Kinetische behandlung der keimbildung in übersättigten dämpfen10.1002/andp.19354160806 ↗
21. Statistical theory of condensation phenomena10.1063/1.1750413 ↗
22. A general theory of heterophase fluctuations and pretransition phenomena10.1063/1.1750484 ↗
23. On the theory of a new phase formation: cavitation
24. K. Russell, Phase Transformations, American Society for Metals, pp. 219–268.
25. R. Kampmann, R. Wagner, Decomposition of Alloys: The Early Stages, Pergamon Press, pp. 91–103.
26. Theory of growth of spherical precipitates from solid solution10.1063/1.1698258 ↗
27. The kinetics of precipitation from supersaturated solid solutions10.1016/0022-3697(61)90054-3 ↗
28. Theorie der alterung von niederschlägen durch umlösen
29. Influence of predeformation and ageing of an Al–Zn–Mg alloy—II. modeling of precipitation kinetics and yield stress10.1016/S1359-6454(98)00296-1 ↗
30. R. Kampmann, R. Wagner, Materials Science and Technology: A Comprehensive Treatment, John Wiley & Sons Inc., pp. 213–302.
31. Modelling of non-isothermal transformations in alloys containing a particle distribution10.1016/S1359-6454(99)00435-8 ↗
32. Modelling of particle nucleation and growth in binary alloys under elastic deformation: an application to a Cu-0.95wt% Co alloy10.1016/j.commatsci.2011.02.044 ↗
33. Modelling precipitate nucleation and growth with multiple precipitate species under isothermal conditions: formulation and analysis10.1016/j.commatsci.2013.07.047 ↗
34. Modelling heterogeneous precipitation in 7xxx aluminium alloys during complex processing10.4028/www.scientific.net/MSF.519-521.1435 ↗
35. Characterization and modelling of precipitate evolution in an Al–Zn–Mg alloy during non-isothermal heat treatments10.1016/S1359-6454(03)00429-4 ↗
36. Kinetics of vanadium carbonitride precipitation in steel: a computer model10.1016/j.actamat.2005.03.036 ↗
37. Precipitation of niobium carbonitrides in ferrite: chemical composition measurements and thermodynamic modelling10.1080/09500830701427003 ↗
38. Implementation of classical nucleation and growth theories for precipitation10.1016/j.actamat.2007.12.050 ↗
39. Statistical theory of crystallization of metals
40. Reaction kinetics in processes of nucleation and growth
41. A commentary on: “reaction kinetics in processes of nucleation and growth”10.1007/s11661-010-0421-1 ↗
42. Kinetics of phase change. i. general theory10.1063/1.1750380 ↗
43. Kinetics of phase change. II transformation-time relations for random distribution of nuclei10.1063/1.1750631 ↗
44. Kinetics of phase change. III. granulation, phase change, and microstructure10.1063/1.1750872 ↗
45. Kinetics of nucleation in near-critical fluids10.1103/PhysRevA.21.948 ↗
46. R. Kampmann, R. Wagner, Decomposition of Alloys: the Early Stages, Pergamon Press, pp. 91–103.
47. Corrigendum to -Implementation of classical nucleation and growth theories for precipitation-[Acta Materialia 56 (2008) 2119–2132]10.1016/j.actamat.2008.11.020 ↗
48. Drei vorträge über diffusion, brownsche molekularbewegung und koagulation von kolloidteilchen
49. Coarsening of liquid Al–Pb dispersions under reduced gravity conditions10.1016/0921-5093(95)09854-2 ↗
50. Studien über die bildung und umwandlung fester körper10.1515/zpch-1897-2233 ↗
51. Coarsening and dissolution of γ′ precipitates during solution treatment of AD730TM Ni-based superalloy: mechanisms and kinetics models10.1016/j.jallcom.2015.11.002 ↗
52. Durcissement par précipitation d’un alliage Fe - 30 % Ni - 9% ta10.1016/0036-9748(69)90234-8 ↗
53. The influence of iron and aluminum on the precipitation of metastable Ni3Nb phases in the Ni3–Nb system10.1007/BF02662742 ↗
54. The metallurgy of alloy 625
55. Influence of the co/ni ratio on the γ′ and γ″ precipitation in fe–ni–co–ta alloys10.1007/BF02644030 ↗
56. H. Eiselstein, J. Gadbut, Matrix-stiffened alloy, US patent number 3160500, 1964.
57. Effects of long-time exposure in alloy 625 at 1200∘ F, 1400∘ F and 1600∘ F
58. Some aspects of the heterogeneous precipitation of the metastable γ″ phase in alloy 625
59. Microstructure and mechanical properties of Inconel® 625 superalloy10.1016/S0022-3115(00)00723-6 ↗
60. A comparison of the precipitation kinetics of γ″ particles in virgin and re-solutioned alloy 625
61. Impact of microstructural evolutions during thermal aging of alloy 625 on its monotonic mechanical properties
62. Gamma double prime precipitation kinetic in alloy 71810.1016/j.msea.2007.08.046 ↗
63. On the equilibrium of heterogeneous substances
64. On the equilibrium of heterogeneous substances
65. Theoretical considerations on the effect of pressure in lowering the freezing point of water10.1017/S0080456800022493 ↗
66. On crystallization and liquefaction, as influenced by stresses tending to changes of form of crystals
67. On the equilibrium at vapor at a curved surface of a liquid10.1080/14786447108640606 ↗
68. Approche multi-échelle de la précipitation
69. AD730TM - a new nickel-based superalloy for high temperature engine rotative parts
70. Kinetics and mechanisms of γ′ reprecipitation in a Ni-based superalloy10.1038/srep28650 ↗
71. Multimodal size distributions of γ′ precipitates during continuous cooling of UDIMET 720Li10.1016/j.actamat.2009.08.002 ↗
72. Influence of cooling rate on the development of multiple generations of γ′ precipitates in a commercial nickel base superalloy10.1016/j.matchar.2011.06.002 ↗
73. Mechanisms related to different generations of γ′ precipitation during continuous cooling of a nickel base superalloy10.1016/j.actamat.2012.09.058 ↗
74. Influence of tertiary gamma prime (γ′) size evolution on dwell fatigue crack growth behavior in CG RR100010.1007/s11661-018-4779-9 ↗
75. The effect of cooling rate on high-temperature precipitation in a powder-metallurgy, gamma/gamma-prime nickel-base superalloy10.1007/s11661-018-4896-5 ↗
76. The determination of the size distribution of particles in an opaque material from a measurement of the size distribution of their sections
77. On optimal and data-based histograms10.1093/biomet/66.3.605 ↗
78. Precipitation of an intermetallic phase with Pt2Mo-type structure in alloy 62510.1007/s11661-999-0194-6 ↗
79. Microstructural evolutions during thermal aging of alloy 625: impact of temperature and forming process10.1007/s11661-014-2256-7 ↗
80. Lattice misfit measurement in Inconel® 625 by X-Ray diffraction technique10.1142/S0217979208048772 ↗
81. Elasticity of ni-based L12-type intermetallic compounds10.1016/0956-7151(92)90312-3 ↗
82. Optimization of metal forming processes for improving final mechanical strength
83. On the coupling between recrystallization and precipitation following hot deformation in a γ-γ′ nickel-based superalloy10.1007/s11661-018-4707-z ↗
84. Seret · 2019
85. The role of strain energy during precipitation of copper and gold from alpha iron10.1016/0001-6160(62)90197-9 ↗
86. Nucleation on dislocations10.1016/0001-6160(57)90021-4 ↗