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Coupled diffusional/displacive transformations: Part II. Solute trapping

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Abstract

An earlier theory for the nonequilibrium transformation of austenite in Fe-C alloys to partially supersaturated plates of ferrite is extended to include a recent solute trapping model by Aziz. The previous model yielded a relationship between interface velocity and supersaturation for a specified transformation temperature. However, a unique growth velocity was determined from a velocity maximization criterion that could not be justified. By including the Aziz solute trapping function as a third interface response function (in addition to functions describing the diffusion field velocity and interface mobility), it has been possible to obtain a more physically based unique solution to the growth velocity for a specified temperature. The new calculations on an Fe-C alloy indicate a smoothly increasing supersaturation during both nucleation and growth, as the transformation temperature is reduced. Both the nucleation and growth processes tend to become completely diffusionless only below the martensite start temperature.

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Abbreviations

D :

diffusivity of carbon in austenite

−D :

weighted average diffusivity of carbon in austenite

ΔG :

magnitude of Gibbs free energy change per unit volume

Qo :

activation free energy necessary to overcome the resistance to interfacial motion in the absence of an interfacial driving force

Q* :

activation free energy for interfacial motion

Gdd :

Gibbs free energy per unit volume, dissipated in the diffusion of solute ahead of the transformation interface

Gid :

Gibbs free energy per unit volume, dissipated in the process of interfacial motior

Gel :

stored free energy per unit volume due to elastic strains

G surf :

stored free energy per unit volume, due to interface

k:

Boltzmann constant

ke :

equilibrium partition coefficient

kp :

actual partition coefficient

p :

Peclet number

p :

plate tip radius

T :

absolute temperature

V :

velocity for the continuous motion of a planar interface

Vd :

velocity as calculated using the diffusion field velocity law

Vk :

velocity as calculated using the Aziz solute trapping law

Vi :

velocity as calculated using the interfacial mobility law

Vo :

preexponential velocity factor for thermally activated interface motion

x :

carbon concentration, mole fraction

−x :

average carbon concentration in alloy, mole fraction

xl :

carbon concentration in γ at the α/γ interface

xα :

carbon concentration in α at the α/γ interface

x αγ :

equilibrium carbon concentration in ferrite

x γα :

equilibrium carbon concentration in austenite

α :

ferrite

γ :

austenite

μ :

shear modulus of austenite

Gid′ :

maximum glide resistance presented by obstacles to dislocation motion

Ω:

volume per atom

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Authors and Affiliations

  1. Department of Materials Science and Engineering, Northwestern University, 60208, Evanston, IL

    G. B. Olson (Professor)

  2. Department of Materials Science and Metallurgy, University of Cambridge, CB2 3QZ, Cambridge, UK

    H. K. D. H. Bhadeshia (Lecturer)

  3. Department of Materials Science and Engineering, Massachusetts Institute of Technology, 02139, Cambridge, MA

    M. Cohen (Institute Professor Emeritus)

Authors
  1. G. B. Olson
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  2. H. K. D. H. Bhadeshia
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  3. M. Cohen
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Additional information

This paper is based on a presentation made in the symposium “International Conference on Bainite” presented at the 1988 World Materials Congress in Chicago, IL, on September 26 and 27, 1988, under the auspices of the ASM INTERNATIONAL Phase Transformations Committee and the TMS Ferrous Metallurgy Committee.

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Olson, G.B., Bhadeshia, H.K.D.H. & Cohen, M. Coupled diffusional/displacive transformations: Part II. Solute trapping. Metall Trans A 21, 805–809 (1990). https://doi.org/10.1007/BF02656563

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