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Johnson-Mehl-Avrami-Kolmogorov model

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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...
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Published: 30 June 2023
Fig. 7 Numerical models for microstructure prediction. JMAK, Johnson-Mehl-Avrami-Kolmogorov; HAZ, heat-affected zone. Adapted from Ref 42 . Courtesy of TWI More
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
... The basis of the formulation developed by Johnson, Mehl, Avrami, and Kolmogorov ( Ref 15 , Ref 16 , Ref 17 , Ref 18 , Ref 19 ) lies in the definition of an extended volume, denoted X ext , as that of the total volume occupied by recrystallized grains should their growth not be constrained...
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
... component. Expressions similar to Eq 30 have also been proposed by Johnson and Mehl ( Ref 3 ) and Avrami ( Ref 55 ); therefore; the modification brought to Eq 28 is known in the literature as the Kolmogorov-Johnson-Mehl-Avrami model. Consequently, the volumetric evolution rate of the solid phase...
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.a0005401
EISBN: 978-1-62708-196-2
...; see text for details. JMAK, Johnson-Mehl-Avrami-Kolmogorov; GB, grain boundary; MCS, Monte Carlo steps. Source: Ref 42 During recrystallization, the cold rolling texture diminishes in intensity, and a recrystallization-texture component (φ 1 = 15°, Φ = 35°, φ 2 = 35°) appears...
Series: ASM Handbook
Volume: 4A
Publisher: ASM International
Published: 01 August 2013
DOI: 10.31399/asm.hb.v04a.a0005786
EISBN: 978-1-62708-165-8
... formation from eutectoid pearlite has been shown to follow the well-known Johnson-Mehl-Avrami-Kolmogorov model ( Ref 8 , 9 ) that applies to many diffusional processes. Austenite formation in Fig. 3 occurs at shorter times with increasing temperature (i.e., the reaction rate increases monotonically...
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: 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: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005408
EISBN: 978-1-62708-196-2
... that U RV = 200 kJ/mol. The recrystallization model is an extension of the classical Johnson-Mehl-Avrami-Kolmogorov approach, treating recrystallization as a nucleation and growth process: (Eq 7) X ˙ = ( 1 − X ( t ) ) ⋅ N ( t ) ⋅ 4 π ⋅ r ( t ) 2 ⋅ G ( t...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005410
EISBN: 978-1-62708-196-2
... steady-state nucleation rate incubation time homogeneous phase cluster condensation evaporation rate cluster dynamics nucleation modeling precipitate size distribution NUCLEATION is the onset of a first-order phase transition by which a metastable phase transforms into a more stable one...
Series: ASM Handbook
Volume: 4A
Publisher: ASM International
Published: 01 August 2013
DOI: 10.31399/asm.hb.v04a.a0005818
EISBN: 978-1-62708-165-8
Series: ASM Handbook
Volume: 4A
Publisher: ASM International
Published: 01 August 2013
DOI: 10.31399/asm.hb.v04a.a0005787
EISBN: 978-1-62708-165-8
... interactions of governing phase-transformation kinetics in an industrial scenario can be effectively captured through mathematical modeling of the annealing operation, resulting in significant improvement in quality and furnace productivity ( Ref 16 , Ref 17 , 18 ). Annealing of Steel Sheet and Strip...
Series: ASM Handbook
Volume: 4A
Publisher: ASM International
Published: 01 August 2013
DOI: 10.31399/asm.hb.v04a.9781627081658
EISBN: 978-1-62708-165-8