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Unified Model for Plate and Lath Martensite with Athermal Kinetics

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Abstract

A unified formalism was developed to describe the transformation curve of athermal martensite with plate and lath/packet morphologies, which exhibit unique spatial aspects. Plates tend to partition grains and spread the reaction into a next grain, whereas laths generally do not exhibit grain partitioning and are contained within the packets. Using extended space concepts, it was possible to factor out the spatial aspects of martensite and to derive a unified model for the transformation curves. This model showed very good agreement with experimental data regarding carbon steels (lath) and nickel-carbon alloys (plate) martensite transformations that exhibit practical and scientific interest.

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Abbreviations

superscriptX :

extended space quantity

T :

temperature

T* :

highest temperature at which martensite nucleation sites are available

k:

Boltzmann constant

ΔG :

driving force; negative of the change in Gibbs free energy

ΔG 0 :

value of ΔG at T = T*

ΔS :

change in entropy austenite/martensite

wt pct:

weight percent

M B :

burst temperature

V V :

volume fraction of martensite

N V :

number of martensite units per unit volume

n V :

volume density of martensite nucleation sites

\( n_{V}^{0} \) :

value of n V at T = T*

n S :

area density of martensite nucleation sites

\( n_{S}^{0} \) :

value of n S at T = T*

S V,mγ :

area per unit volume of martensite-austenite interface

S Vγ :

area per unit volume of austenite grain boundaries

q :

mean grain volume

\( \bar{v}_{{}}^{X} \) :

mean volume of martensite units in extended space

\( \bar{v}_{0}^{X} \) and \( \bar{v}_{1}^{X} \):

initial and final values of \( \bar{v}_{{}}^{X} \)

R 2 :

correlation coefficient

α, m, ς P , ς L , ζ, ζ L :

proportionality factors

z :

asymmetry factor

Γ, Ψ1, and Ψ2 :

lump factors

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Acknowledgments

One of the authors (PRR) is grateful to Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq, and to Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro, FAPERJ, for financial support. PRR also thanks the Humboldt Foundation for the Humboldt Research Award and Professor Günter Gottstein for his hospitality during the author’s stay at the Institut für Metallkunde and Metallphysik of RWTH–Aachen, where this work has been done.

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Authors and Affiliations

  1. Universidade Federal Fluminense, Escola de Engenharia Industrial Metalúrgica de Volta Redonda, Volta Redonda, RJ, 27255-125, Brasil

    J. R. C. Guimarães (Researcher) & P. R. Rios (Professor)

  2. Mal. Moura 338H/22C, São Paulo, SP, 05641-000, Brasil

    J. R. C. Guimarães (Researcher)

  3. Institut für Metallkunde und Metallphysik, RWTH Aachen University, D-52056, Aachen, Germany

    P. R. Rios (Professor)

Authors
  1. J. R. C. Guimarães
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  2. P. R. Rios
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Correspondence to P. R. Rios.

Additional information

Manuscript submitted January 10, 2010.

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Guimarães, J.R.C., Rios, P.R. Unified Model for Plate and Lath Martensite with Athermal Kinetics. Metall Mater Trans A 41, 1928–1935 (2010). https://doi.org/10.1007/s11661-010-0239-x

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