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monte carlo model
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in Modeling and Simulation of Texture Evolution during the Thermomechanical Processing of Titanium Alloys
> Fundamentals of Modeling for Metals Processing
Published: 01 December 2009
Fig. 5 Monte Carlo model simulation of texture-controlled grain growth for a material with two texture components. (a) Comparison of predicted grain-growth kinetics (solid line) and normal grain-growth kinetics (broken line). MU, model lattice units; MCS, Monte Carlo steps. (b) Simulated (100
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in Modeling and Simulation of Texture Evolution during the Thermomechanical Processing of Titanium Alloys
> Fundamentals of Modeling for Metals Processing
Published: 01 December 2009
Fig. 6 Monte Carlo model predictions of the grain-size distributions after 15 Monte Carlo steps for the simulation of texture-controlled grain growth in a material with two texture components. (a) For the entire material. (b) For the grains belonging to texture component “A.” MU, model lattice
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Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005428
EISBN: 978-1-62708-196-2
... Abstract The misorientation of a boundary of a growing grain is defined not only by its crystallography but also by the crystallography of the grain into which it is growing. This article focuses on the Monte Carlo Potts model that is typically used to model grain growth, Zener-Smith pinning...
Abstract
The misorientation of a boundary of a growing grain is defined not only by its crystallography but also by the crystallography of the grain into which it is growing. This article focuses on the Monte Carlo Potts model that is typically used to model grain growth, Zener-Smith pinning, abnormal grain growth, and recrystallization. It introduces the basics of the model, providing details of the dynamics, simulation variables, boundary energy, boundary mobility, pinning systems, and stored energy. The article explains how to incorporate experimental parameters and how to validate the model by comparing the observed behavior quantitatively with theory. The industrial applications of the model are also discussed. The article also provides a wide selection of the algorithms for implementing the Potts model, such as boundary-site models, n -fold way models, and parallel models, which are needed to simulate large-scale industrial applications.
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.
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Published: 01 January 2005
Fig. 5 Monte Carlo (three-dimensional) model predictions of (a, b, and c) grain structure (two-dimensional) sections after 1000 Monte-Carlo Steps and (d) grain-growth behavior for materials with various starting textures and assumed grain-boundary properties. (a) Case A, isotropic starting
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Image
Published: 01 January 2005
Fig. 12 Monte Carlo (3D) model predictions of (a, b, c) grain structure (2D sections after 1000 MC steps) and (d) grain-growth behavior for materials with various starting textures and assumed grain-boundary properties. (a) Case A, isotropic starting texture and isotropic boundary properties
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Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005401
EISBN: 978-1-62708-196-2
... with a strong initial texture showing periods of rapid and slow growth. Source: Ref 22 Texture-controlled grain growth during beta annealing of titanium alloys has been simulated using both the Monte Carlo (Potts) and phase-field modeling approaches. In the work of Ivasishin et al. ( Ref 24 , 25...
Abstract
The modeling and simulation of texture evolution for titanium alloys is often tightly coupled to microstructure evolution. This article focuses on a number of problems for titanium alloys in which such coupling is critical in the development of quantitative models. It discusses the phase equilibria, crystallography, and deformation behavior of titanium and titanium alloys. The article describes the modeling and simulation of recrystallization and grain growth of single-phase beta and single-phase alpha titanium. The deformation- and transformation-texture evolution of two-phase (alpha/beta) titanium alloys are also discussed.
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003514
EISBN: 978-1-62708-180-1
... element. Examples of the use of probabilistic analysis are presented. The article concludes with an overview of some of the commercially available software programs for performing probabilistic analysis. advanced mean value method failure model first-second-order reliability methods Monte Carlo...
Abstract
This article describes the historical background, uncertainties in structural parameters, classifications, and application areas of probabilistic analysis. It provides a discussion on the basic definition of random variables, some common distribution functions used in engineering, selection of a probability distribution, the failure model definition, and a definition of the probability of failure. The article also explains the solution techniques for special cases and general solution techniques, such as first-second-order reliability methods, the advanced mean value method, the response surface method, and Monte Carlo sampling. A brief introduction to importance sampling, time-variant reliability, system reliability, and risk analysis and target reliabilities is also provided. The article examines the various application problems for which probabilistic analysis is an essential element. Examples of the use of probabilistic analysis are presented. The article concludes with an overview of some of the commercially available software programs for performing probabilistic analysis.
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in Monte Carlo Models for Grain Growth and Recrystallization
> Fundamentals of Modeling for Metals Processing
Published: 01 December 2009
Fig. 5 Relationship between boundary energy and node angle. (a) Continuum system. (b) Monte Carlo Potts model. Each grain orientation is represented by a different gray scale; the boundaries are sharp, being implicitly defined between sites of different orientations. (c) Implementation
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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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Published: 01 December 2009
proposed for SiO 2 CVD, combining a macroscale finite-element model (FEM) and a ballistic transport and reaction model at the feature scale. A third FEM mesoscale model is used to link both scales. Source: Ref 186 . (c) Monte Carlo simulation of sputtered-aluminum deposition on a 0.025 mm trench. Source
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Published: 01 December 2009
Fig. 19 Main simulation models used in materials science and related length and time scales. DFT, density functional theory; MD, molecular dynamics; MC, Monte Carlo. Source: Ref 177
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Published: 01 January 2005
Fig. 8 A series of snapshots during a two-dimensional grain-growth simulation using the Monte Carlo-Potts model. The system size is 400 by 400 with periodic boundary conditions and isotropic boundary energies and mobilities. Source: Ref 20
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in Modeling and Simulation of Texture Evolution during the Thermomechanical Processing of Titanium Alloys
> Fundamentals of Modeling for Metals Processing
Published: 01 December 2009
Fig. 8 Baseline dependences. (a) Normalized grain-boundary energy and mobility (m a = 1) dependence on misorientation. (b) Normalized stored energy dependence on location used in Monte Carlo simulations of recrystallization and grain growth. “A,” “B,” and “C” are energy-level distributions
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Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005425
EISBN: 978-1-62708-196-2
... of mechanism-based models, such as those designed to predict phase equilibria (e.g., Calphad), recrystallization and grain growth (Monte Carlo and cellular-automaton techniques), and precipitation and solidification problems (e.g., phase-field methods). The successful implementation of these newer techniques...
Abstract
This article provides a brief historical perspective, a classification of metallurgical processes, basic model development efforts, and an overview of the potential future directions for the modeling of metals processing. It describes the classification of material behavior models, which can be grouped broadly into three classes: statistical, phenomenological, and mechanistic models. The article also presents an overview of the potential directions for the modeling of metals processing.
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004027
EISBN: 978-1-62708-185-6
... steel (observations shown in points). Source: Ref 11 Fig. 8 A series of snapshots during a two-dimensional grain-growth simulation using the Monte Carlo-Potts model. The system size is 400 by 400 with periodic boundary conditions and isotropic boundary energies and mobilities. Source: Ref...
Abstract
The systematic study of microstructural evolution during deformation under hot working conditions is important in controlling processing variables to achieve dimensional accuracy. This article explains the microstructural features that need to be modeled and provides an outline of the principles and achievements of each of the various microstructural models, including black-box modeling, gray-box modeling, white-box modeling, and hybrid modeling.
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006803
EISBN: 978-1-62708-329-4
... of the Monte Carlo simulation method and work performed at the Los Alamos National Laboratories at the end of World War II ( Ref 12 ). The limitation of the original method is the large sample size required for convergence, which can become a problem when the individual “deterministic” model evaluation...
Abstract
This article provides an outline of the issues to consider in performing a probabilistic life assessment. It begins with an historical background and introduces the most common methods. The article then describes those methods covering subjects such as the required random variable definitions, how uncertainty is quantified, and input for the associated random variables, as well as the characterization of the response uncertainty. Next, it focuses on specific and generic uncertainty propagation techniques: first- and second-order reliability methods, the response surface method, and the most frequently used simulation methods, standard Monte Carlo sampling, Latin hypercube sampling, and discrete probability distribution sampling. Further, the article discusses methods developed to analyze the results of probabilistic methods and covers the use of epistemic and aleatory sampling as well as several statistical techniques. Finally, it illustrates some of the techniques with application problems for which probabilistic analysis is an essential element.
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0009002
EISBN: 978-1-62708-185-6
... of microstructure evolution. cellular automata dynamic recovery grain growth hot working microstructure evolution microstructure evolution modeling Monte-Carlo techniques plastic flow recrystallization static recovery texture evolution models thermomechanical processing IN PROCESS DESIGN...
Abstract
This article reviews the general aspects of microstructure evolution during thermomechanical processing. The effect of thermomechanical processing on microstructure evolution is summarized to provide insight into the aspect of process design. The article provides information on hot working and key processes that control microstructure evolution: dynamic recovery, static recovery, recrystallization, and grain growth. Some of the key phenomenological descriptions of plastic flow and microstructure evolution are also summarized. The article concludes with a discussion on the modeling of microstructure evolution.
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005534
EISBN: 978-1-62708-197-9
... effects—of each variable and therefore determining those that can be ignored ( Ref 8 ). For these calculations, the variances are usually determined by Monte Carlo simulations using a crude model that is usually assumed to be adequate for this purpose but not for an accurate description of system behavior...
Abstract
This article presents an approach to manage the uncertainty present in materials design. It describes inductive and deductive approaches to deal with uncertainty. The article focuses on providing an understanding of the opportunities for managing uncertainty and the decisions that influence the accuracy of the results. A design of experiments (DOE) represents a sequence of experiments to be performed, expressed in terms of factors set at specified levels. The article discusses the two types of DOEs: the full factorial design and the fractional factorial design. It explains the factors to be considered when selecting a procedure for propagating uncertainty. The article lists the categories of the popular types of uncertainty propagation methods, including simulation-based methods, local expansion methods, and numerical integration-based methods.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005459
EISBN: 978-1-62708-196-2
...,” “Monte Carlo Models for Grain Growth and Recrystallization,” and “Network and Vertex Models for Grain Growth” in this Volume. Overview of Microstructure Evolution in Nickel-Base Superalloys during Hot Working Experimental observations of the various features and mechanisms of microstructure...
Abstract
This article summarizes the general features of microstructure evolution during the thermomechanical processing (TMP) of nickel-base superalloys and the challenges posed by the modeling of such phenomena. It describes the fundamentals and implementations of various modeling methodologies. These include JMAK (Avrami) models, topological models, and mesoscale physics-based models.
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