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Avrami analysis

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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 More
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...