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cellular automaton model
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Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005432
EISBN: 978-1-62708-196-2
..., distributing nuclei of recrystallized grains, growing the recrystallized grains, and updating the dislocation density. The article concludes with information on the developments in CA simulations. cellular automaton model static recrystallization dynamic recrystallization microstructure dislocation...
Abstract
This article examines how cellular automaton (CA) can be applied to the simulation of static and dynamic recrystallization. It describes the steps involved in the CA simulation of recrystallization. These include defining the CA framework, generating the initial microstructure, distributing nuclei of recrystallized grains, growing the recrystallized grains, and updating the dislocation density. The article concludes with information on the developments in CA simulations.
Image
Published: 01 November 2010
Fig. 10 Cellular automaton model produces realistic dendrite growth. (a) Predicted dendritic structure density. (b) Solutal adjusted undercooling distribution under thermal conditions of 45° inclined isotherms with respect to the growth direction moving at a constant velocity of 150 μm/s
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Series: ASM Handbook
Volume: 9
Publisher: ASM International
Published: 01 December 2004
DOI: 10.31399/asm.hb.v09.a0003729
EISBN: 978-1-62708-177-1
... of the general capabilities of the various models that can generate microstructure maps and thus transform the computer into a dynamic microscope. These include standard transport models, phase-field models, Monte Carlo models, and cellular automaton models. cellular automaton models computer modeling...
Abstract
Computational modeling assists in addressing the issues of solid/liquid interface dynamics at the microlevel. It also helps to visualize the grain length scale, fraction of phases, or even microstructure transitions through microstructure maps. This article provides a detailed account of the general capabilities of the various models that can generate microstructure maps and thus transform the computer into a dynamic microscope. These include standard transport models, phase-field models, Monte Carlo models, and cellular automaton models.
Image
Published: 01 December 2008
Fig. 9 Predictions from the cellular automaton finite element model. (a) Final grain structure. (b) Segregation map of tin with its composition scale. (c) Composition profiles for a Pb-48wt%Sn alloy. Equiaxed grains nucleated in the undercooled melt are free to move due to sedimentation
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Image
Published: 01 December 2009
Fig. 4 The cellular automaton finite-element (CAFÉ) model of hot rolling of steel. (a) Slab exiting the rolling gap after it has been rolled at 30% reduction in thickness. (b) Initial cellular automaton microstructure with equiaxed grains. (c) Microstructure near the slab surface within box “O
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in Modeling of Microstructure Evolution during Solidification Processing[1]
> Fundamentals of Modeling for Metals Processing
Published: 01 December 2009
Fig. 9 Predictions from the cellular automaton finite element model. (a) Final grain structure. (b) Segregation map of tin with its composition scale. (c) Composition profiles for a Pb-48wt%Sn alloy. Equiaxed grains nucleated in the undercooled melt are free to move due to sedimentation
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in Thermophysical Properties of Liquids and Solidification Microstructure Characteristics—Benchmark Data Generated in Microgravity
> Metals Process Simulation
Published: 01 November 2010
). (b) Map of indium concentration (wt%) predicted by the cellular automaton finite-element model (thick black line: growth front deduced from the cellular automaton model) ( Ref 12 )
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Image
Published: 01 January 2005
Fig. 10 Microstructural evolution during recrystallization simulated using a hybrid Monte Carlo-Potts cellular automaton model; the white grains are recrystallized. Source: Ref 23
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Series: ASM Handbook
Volume: 1A
Publisher: ASM International
Published: 31 August 2017
DOI: 10.31399/asm.hb.v01a.a0006314
EISBN: 978-1-62708-179-5
... include the dendrite growth models and the cooperative eutectic growth models. The article provides some solutions using numerical models to simulate the kinetics of microstructure formation in cast iron. It concludes with a discussion on cellular automaton (CA) technique that can handle complex topology...
Abstract
The microstructure that develops during the solidification stage of cast iron largely influences the subsequent solid-state transformations and mechanical properties of the cast components. This article provides a brief introduction of methods that can be used for simulating the solidification microstructure of cast iron. Analytical as well as numerical models describing solidification phenomena at both macroscopic and microscopic scales are presented. The article introduces macroscopic transport equations and presents analytical microscopic models for solidification. These models include the dendrite growth models and the cooperative eutectic growth models. The article provides some solutions using numerical models to simulate the kinetics of microstructure formation in cast iron. It concludes with a discussion on cellular automaton (CA) technique that can handle complex topology changes and reproduce most of the solidification microstructure features observed experimentally.
Image
Published: 01 December 2009
Fig. 5 Recrystallization modeling. (a) Original undeformed cellular automaton (CA) grain structure in gray and the recrystallized grains in black. (b) Ratio of the recrystallization nuclei cells to the total number of cells within a CA attached to one Gauss point. Source: Ref 20
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Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005236
EISBN: 978-1-62708-187-0
... and applications of the phase field method and the cellular automaton method for modeling the direct evolution of structure at the intermediate length scales, where transport phenomena govern the spatial and temporal evolution of the structure that involves nucleation and growth. casting cellular automaton...
Abstract
Modeling of structure formation in casting of alloys involves several length scales, ranging from the atomic level to macroscopic scale. Intermediate length scales are used to define the microstructure of the growing phases and the grain structure. This article discusses the principles and applications of the phase field method and the cellular automaton method for modeling the direct evolution of structure at the intermediate length scales, where transport phenomena govern the spatial and temporal evolution of the structure that involves nucleation and growth.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005406
EISBN: 978-1-62708-196-2
... Abstract This article focuses on the intermediate length scales, where transport phenomena govern the spatial and temporal evolution of a structure. It presents the cellular automaton (CA) and phase field (PF) methods that represent the state of the art for modeling macrostructure...
Abstract
This article focuses on the intermediate length scales, where transport phenomena govern the spatial and temporal evolution of a structure. It presents the cellular automaton (CA) and phase field (PF) methods that represent the state of the art for modeling macrostructure and microstructure. The article describes the principles of the PF method and provides information on the applications of the PF method. The CA model is introduced as a computationally efficient method to predict grain structures in castings using the mesoscopic scale of individual grains. The article discusses the coupling of the CA to macroscopic calculation of heat, flow, and mass transfers in castings and applications to realistic casting conditions.
Image
Published: 01 December 2008
Fig. 2 Schematic of a single grain ( Ref 8 ) growing in a uniform temperature field is shown in (a). The square highlighted in (a) shows a typical length scale for representative elementary volumes (REV) used by the cellular automaton (CA) method. The two small squares in (b) show the typical
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in Modeling of Microstructure Evolution during Solidification Processing[1]
> Fundamentals of Modeling for Metals Processing
Published: 01 December 2009
Fig. 2 Schematic of a single grain ( Ref 8 ) growing in a uniform temperature field is shown in (a). The square highlighted in (a) shows a typical length scale for representative elementary volumes (REV) used by the cellular automaton (CA) method. The two small squares in (b) show the typical
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Image
in Formation of Microstructures, Grain Textures, and Defects during Solidification
> Metals Process Simulation
Published: 01 November 2010
Fig. 13 (a) Image of a cellular automaton simulation of solidification in a Zn-0.2wt%Al galvanized coating. The 5 by 3 mm domain is cooled at –12 K/s with a positive temperature gradient from left to right. (b) Experimental and calculated number densities of grains as a function of the cooling
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Image
Published: 01 November 2010
Fig. 7 Direct modeling of solidification of a single equiaxed grain using the cellular automaton (CA) method coupled with the finite-element (FE) method is a refinement of the indirect modeling approach ( Fig. 5 ). Integration over time on the geometrical CA grid of kinetics laws
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in Thermophysical Properties of Liquids and Solidification Microstructure Characteristics—Benchmark Data Generated in Microgravity
> Metals Process Simulation
Published: 01 November 2010
. Herlach et al., German Space Agency (DLR)-Köln. Corresponding numerical simulation using a three-dimensional cellular automaton finite-element model shows (b) the envelope of the growing grain and (c) the active (darker or red) chevron-shaped region through the midsection of the sphere and deactivated
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Image
Published: 01 November 2010
Fig. 6 Schematic two-dimensional geometric description of a dendritic grain using direct modeling the grain structure by means of the cellular automaton (CA) method coupled with the finite-element (FE) method ( Fig. 1b ). A representation is given of (a) a unit triangular mesh used by the FE
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Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005522
EISBN: 978-1-62708-197-9
... stratifies in the liquid ahead of the growth front ( Ref 10 , 11 ). The indium concentration stratifications and the growth front predicted by the cellular automaton finite-element (CAFE) model are illustrated in Fig. 3(b) ( Ref 12 ). Solutal convection during directional solidification is shown in Fig...
Abstract
For a wide range of new or better products, solidification processing of metallic materials from the melt is a step of uppermost importance in the industrial production chain. This article discusses the casting and solidification of molten metallic alloy along with the application of low-gravity platforms and facilities for solidification processing. It provides a description of dendritic growth studies and electromagnetic levitation. The article concludes with information on the in situ and real-time monitoring of solidification processing.
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005511
EISBN: 978-1-62708-197-9
... couple. Finally, in example 8, thermodynamic modeling is integrated with a microscopic and cellular automaton model to simulate the microstructure and microsegregation of aluminum alloys during solidification. Example 5: Prediction of Liquation Cracking of Aluminum Welds In this example...
Abstract
This article focuses on the industrial applications of phase diagrams. It presents examples to illustrate how a multicomponent phase diagram calculation can be readily useful for industrial applications. The article demonstrates how the integration of a phase diagram calculation with kinetic and microstructural evolution models greatly enhances the power of the CALPHAD approach in materials design and processing development. It also discusses the limitations of the CALPHAD approach.
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