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Avrami analysis
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in Modeling of Microstructure Evolution during the Thermomechanical Processing of Nickel-Base Superalloys
> Fundamentals of Modeling for Metals Processing
Published: 01 December 2009
Fig. 20 Avrami analysis of the recrystallized-fraction curves in Fig. 19 . X denotes the recrystallized fraction; the slope of the curves is the Avrami exponent n . Source: Ref 42
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Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005403
EISBN: 978-1-62708-196-2
... dynamic recrystallization (DDRX). The article discusses the assumptions and simplifications for the Avrami analysis. It describes the effects of nucleation and growth rates on recrystallization kinetics and recrystallized grain size based on the Johnson-Mehl-Avrami-Kolmogorov model for static...
Abstract
Recrystallization is to a large extent responsible for their final mechanical properties. This article commences with a discussion on static recrystallization (SRX) and dynamic recrystallization (DRX). The DRX includes continuous dynamic recrystallization (CDRX) and discontinuous dynamic recrystallization (DDRX). The article discusses the assumptions and simplifications for the Avrami analysis. It describes the effects of nucleation and growth rates on recrystallization kinetics and recrystallized grain size based on the Johnson-Mehl-Avrami-Kolmogorov model for static recrystallization. The article reviews the kinetics of DRX with the aid of the Avrami relations. It considers the basic framework of the mesoscale approach for DDRX, including the three basic equations for grain size changes, strain hardening and dynamic recovery, and nucleation. The article explains the mesoscale approach for CDRX to predict microstructural evolutions occurring during hot deformation, along with an illustration of the main features of the CDRX mesoscale model.
Series: ASM Handbook
Volume: 4B
Publisher: ASM International
Published: 30 September 2014
DOI: 10.31399/asm.hb.v04b.a0005934
EISBN: 978-1-62708-166-5
... or additivity rule. Scheil first proposed the additivity rule to describe incubation or nucleation during phase transformation ( Ref 15 ). Avrami continued this analysis and showed that, when the nucleation rate is proportional to the growth rate, the additivity rule is applicable ( Ref 16 , 17 ). Avrami...
Abstract
Successful hardening depends on the hardenability of steel composition, the geometry of parts, the quenching system, and on the heat treating process used. This article provides a brief overview of the computation and use of quench factor analysis (QFA) to quantify as-quenched hardness for carbon and low-alloy steels. As a single-value parameter alternative to Grossmann H-values, QFA is a potential method to qualify a quenching medium or process or to effectively monitor variation of quench severity due to either the quenchant or the system. The article describes the procedures for experimentally determining the quench factors by using a type 304 austenitic stainless steel probe. Typical examples of the utilization of QFA for quenchant characterization are provided. The article also describes the methods for experimentally generating time-temperature-property curves.
Book Chapter
Series: ASM Handbook
Volume: 4E
Publisher: ASM International
Published: 01 June 2016
DOI: 10.31399/asm.hb.v04e.a0006272
EISBN: 978-1-62708-169-6
... precipitates ( Ref 36 ). This is shown in Table 3 ( Ref 36 ). Staley ( Ref 20 ) agreed that n can vary with the nucleation rate and morphology of the precipitate; however, no changes were made to the basic quench factor analysis model. Values of <italic>n</italic> in the Avrami kinetic law Table 3...
Abstract
This article discusses the various methods for evaluating the quench sensitivity of aluminum alloys, namely, time-temperature-property diagrams, the quench factor analysis, the Jominy end-quench method, and continuous-cooling precipitation diagrams. It briefly describes the procedures, applications, advantages, and limitations of these 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
... methodologies. These include JMAK (Avrami) models, topological models, and mesoscale physics-based models. microstructure evolution thermomechanical processing nickel-base superalloys avrami model topological model mesoscale physics-based model THE MODELING OF MICROSTRUCTURE EVOLUTION during...
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.
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
... but decreases substantially at long times; this behavior is accentuated in Avrami plots of the recrystallization kinetics ( Fig. 9b ). The mobility of special boundaries can have a pronounced effect on microstructure/texture evolution and recrystallization kinetics, as illustrated in Fig. 10...
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
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0009002
EISBN: 978-1-62708-185-6
...) constants; and ε c and ε 0.5 denote the critical strain for the onset of DDRX (≈ 5ε p /6) and the strain for 50% recrystallization, respectively. Equation 10 is a classical Avrami-type relation ( Ref 1 , Ref 20 ) for the nucleation-and-growth type processes that characterize DDRX. The Avrami exponent...
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: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005425
EISBN: 978-1-62708-196-2
... of: Deformation and strain hardening, such as Schmid's law and the Hollomon equation Kinetics of recrystallization (such as the Avrami equation), grain growth (such as the Beck equation), and precipitation/phase transformation Ductility for solid-state processes Similarly, phenomenological models...
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: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005409
EISBN: 978-1-62708-196-2
... f α volume fraction of alpha G growth rate during phase transformation G s shear modulus J mass flux K strength coefficient k rate constant in Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation ( Eq 23 ) k B Boltzmann's constant k LSW Lifshitz, Slyosov...
Abstract
This article focuses on the modeling of microstructure evolution during thermomechanical processing in the two-phase field for alpha/beta and beta titanium alloys. It also discusses the mechanisms of spheroidization, the coarsening, particle growth, and phase decomposition in titanium alloys, with their corresponding equations.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005414
EISBN: 978-1-62708-196-2
... models for recrystallization kinetics have been developed based on the well-known Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation: (Eq 6) X = 1 − exp ( − 0.693 ( t t 0.5 ) n ) where X is the fraction recrystallized at time t , t 0.5 is the time for 50...
Abstract
Computer simulation of microstructural evolution during hot rolling of steels is a major topic of research and development in academia and industry. This article describes the methodology and procedures commonly employed to develop microstructural evolution models to simulate microstructural evolution in steels. It presents an example of the integration of finite element modeling and microstructural evolution models for the simulation of metal flow and microstructural evolution in a hot rolling process.
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0003989
EISBN: 978-1-62708-185-6
...-dynamically recrystallized grain size may be reduced by increasing the total strain or strain rate. Increasing the temperature or hold time tends to increase the meta-dynamic or statically recrystallized grain size. The following is a description of a model of classical Mehl-Johnson-Avrami basis...
Abstract
This article describes the presses, transportation equipment, and manufacturing processes associated with cogging. It discusses the practical and metallurgical issues encountered during the conversion of ingot to billet. The article explains the use of numerical modeling as part of the continuing efforts to reduce the cost and time associated with developing new cogging sequences, increase the yield, make the processes more robust, and increase the quality of the produced product.
Book Chapter
Book: Alloy Phase Diagrams
Series: ASM Handbook
Volume: 3
Publisher: ASM International
Published: 27 April 2016
DOI: 10.31399/asm.hb.v03.a0006222
EISBN: 978-1-62708-163-4
... behavior for most solid-state reactions. For solid-state transformations displaying the kinetic behavior in Fig. 17 , the fraction of transformation, y , is a function of time, t , and follows the Avrami equation: (Eq 16) y = 1 − e − k t n where k and n are time-independent...
Abstract
This article begins with the one-component, or unary, diagram for magnesium. The diagram shows what phases are present as a function of the temperature and pressure. When two metals are mixed in the liquid state to produce a solution, the resulting alloy is called a binary alloy. The article describes the various types of solid solutions such as interstitial solid solutions and substitutional solid solutions. Free energy is important because it determines whether or not a phase transformation is thermodynamically possible. The article discusses the thermodynamics of phase transformations and free energy, as well as kinetics of phase transformations. It concludes with a description of solid-state phase transformations that occur when one or more parent phases, usually on cooling, produces a phase or phases.
Series: ASM Handbook
Volume: 6A
Publisher: ASM International
Published: 31 October 2011
DOI: 10.31399/asm.hb.v06a.a0005604
EISBN: 978-1-62708-174-0
... make valuable contributions to assist them; some industrial application examples are given in Ref 1 . For trouble-free communication with the customers, a defined and generally applicable guideline for execution, analysis, and postprocessing is imperative to assure reliability and relevance...
Abstract
This article focuses on the necessary basics for thermomechanical fusion welding simulations and provides an overview of the specific aspects to be considered for a simulation project. These aspects include the required material properties, experimental data needed for validation of the simulation results, simplifications and assumptions as a prerequisite for modeling, and thermomechanical simulation. The article concludes with information on the sensitivity of the material properties data with respect to the simulation results. It also provides hints on the central challenge of having the right material properties at hand for a specific simulation task.
Series: ASM Handbook
Volume: 1A
Publisher: ASM International
Published: 31 August 2017
DOI: 10.31399/asm.hb.v01a.a0006307
EISBN: 978-1-62708-179-5
... for the eutectoid transformation was developed where both ferrite and pearlite growth were assumed to be described by Avrami’s equation, with rate constants originally developed for steel alloys. The rate constants were modified to fit the experimental cooling curves. The researchers considered that the stable...
Abstract
This article describes a method to predict mechanical properties of cast iron materials and illustrates how to use the predictions in computer-aided tools for the analysis of castings subjected to load. It outlines some ways to predict the hardness and elastic modulus of cast iron without going into dislocation theory. The article discusses modeling of hardness in cast iron based on a regular solution equation in which the properties of each phase depend on chemical composition and coarseness. It describes the evaluation of material parameters from the tensile stress-strain curve. The article concludes with an illustration of a finite-element method (FEM) model containing heterogeneous mechanical properties using local material definitions.
Series: ASM Handbook
Volume: 4E
Publisher: ASM International
Published: 01 June 2016
DOI: 10.31399/asm.hb.v04e.a0006260
EISBN: 978-1-62708-169-6
... rate. It describes the quench sensitivity and severity of alloys, quench mechanisms and the different types of quenchants used in immersion, spray, and fog quenching. The article provides a detailed description of the quench-factor analysis that mainly includes residual stress and distortion, which can...
Abstract
Quenching refers to the rapid cooling of metal from the solution treating temperature, typically between 465 and 565 deg C (870 and 1050 deg F) for aluminum alloys. This article provides an overview on the appropriate quenching process and factors used to determine suitable cooling rate. It describes the quench sensitivity and severity of alloys, quench mechanisms and the different types of quenchants used in immersion, spray, and fog quenching. The article provides a detailed description of the quench-factor analysis that mainly includes residual stress and distortion, which can be controlled by proper racking. It concludes with information on agitation and the quench tank system used in the quenching of aluminum alloys.
Book Chapter
Book: Alloy Phase Diagrams
Series: ASM Handbook
Volume: 3
Publisher: ASM International
Published: 27 April 2016
DOI: 10.31399/asm.hb.v03.a0006228
EISBN: 978-1-62708-163-4
... of pearlite is best represented by the Johnson-Mehl-Avrami equation: (Eq 7) f = 1 − exp ( − k t n ) where f is fraction transformed, k accounts for the growth and nucleation rates, t is time, and n is the Avrami exponent. The exponent n varies from 1 to 4, where 1 represents...
Abstract
Eutectoid and peritectoid transformations are classified as solid-state invariant transformations. This article focuses primarily on the structures from eutectoid transformations with emphasis on the classic iron-carbon system of steel. It reviews peritectoid phase equilibria that are very common in several binary systems. The addition of substitutional alloying elements causes the eutectoid composition and temperature to shift in the iron-carbon system. The article graphically illustrates the effect of various substitutional alloying elements on the eutectoid transformation temperature and effective carbon content. The partitioning effect of substitutional alloying elements, such as chromium, manganese, and silicon, in pearlitic steel is also illustrated.
Series: ASM Handbook
Volume: 24A
Publisher: ASM International
Published: 30 June 2023
DOI: 10.31399/asm.hb.v24A.a0006950
EISBN: 978-1-62708-439-0
... to the process parameters, several numerical models have been developed. Phenomenological methods (Johnson-Mehl-Avrami-Kolmogorov, or JMAK), kinetic Monte Carlo, cellular automata, and phase field ( Fig. 7 ) are examples of the most-used models ( Ref 41 ). Those methods are primarily based on the previous...
Abstract
Additive manufacturing (AM) provides exceptional design flexibility, enabling the manufacture of parts with shapes and functions not viable with traditional manufacturing processes. The two paradigms aiming to leverage computational methods to design AM parts imbuing the design-for-additive-manufacturing (DFAM) principles are design optimization (DO) and simulation-driven design (SDD). In line with the adoption of AM processes by industry and extensive research efforts in the research community, this article focuses on powder-bed fusion for metal AM and material extrusion for polymer AM. It includes detailed sections on SDD and DO as well as three case studies on the adoption of SDD, DO, and artificial-intelligence-based DFAM in real-life engineering applications, highlighting the benefits of these methods for the wider adoption of AM in the manufacturing industry.
Series: ASM Handbook
Volume: 4A
Publisher: ASM International
Published: 01 August 2013
DOI: 10.31399/asm.hb.v04a.a0005814
EISBN: 978-1-62708-165-8
... mathematically—considering an isothermal event—using the Johnson-Mehl-Avrami-Kolomgorov equation ( Ref 34 , 35 ): (Eq 11) f k = 1 − exp [ − b t n ] where f k is the volume fraction ( k ≡ ferrite, pearlite, or bainite), and b and n are parameters to be determined...
Abstract
This article describes the mechanisms and characteristics of heat transfer in the quenching of steel. This article describes the characterization of boiling heat transfer, including pool boiling, forced convective boiling, and rewetting, which plays a key role in defining the heat-extraction characteristics of a liquid quenchant. It provides information on heat generated microstructural field evolution and information on the analysis and characterization of heat transfer boundary conditions.
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
...-Science+Business Media , B.V., 1992 , p 188 – 192 (English translation by G. Lindquist) 55. Avrami M. , Kinetics of Phase Change, Part II: Transformation-Time Relations for Random Distribution of Nuclei , J. Chem. Phys. , Vol 8, 212 , 1940 , p 212 – 224 56. Kapturkiewicz W...
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.
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
... microstructural evolution, from which the Avrami equation for recrystallization kinetics is “rediscovered.” An important point is that the philosophy underlying the CA approach mimics our apprehension of the physical world. Bird “A” does not know what trajectory bird “B” is taking several meters away...
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.
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