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A method for extracting phase change kinetics from dilatation for multistep transformations: Austenitization of a low carbon steel

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Abstract

This article describes the development of a method for determining phase change kinetics for multistep diffusion limited solid-state transformations from dilatation data. Since each step in a multistep reaction proceeds at a different rate, and the volume changes for the transformations are, in general, not equal, determination of the reaction kinetics from the dilatation data is not straightforward. Thus, a model is developed for the phase change process in which the transient dilatation is calculated based on the fractional extent of the various phases present. In this way, kinetic parameters are determined that allow the best match to the experimental data. However, both random and systematic experimental errors make reproduction of the experimental dilatation difficult. Therefore, a self-calibration process is developed that uses portions of the dilatation data to obtain the density variation of the various phases with temperature to help correct for experimental uncertainties. This procedure also enables the model to be used in situations where accurate property data are not available. The model and procedures are applied to the formation of austenite in a pearlite/ferrite low carbon steel where the pearlite and ferrite regions transform at different rates. A single kinetic parameter set allows reproduction of transformation transients of significantly different heating rates. These parameters can then be used to describe the austenitization for any time-temperature path. Excellent agreement between the model and experimental data is shown.

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Abbreviations

A e3 :

upper critical temperature

A :

fraction of pearlite transformed to austenite

B :

fraction of the ferrite region transformed to austenite

c̄ :

mean carbon content (wt pct)

c :

carbon content for a particular phase (wt pct)

d :

predicted dilatation

D(T) :

diffusion coefficient for carbon in austenite (cm2/s)

F :

volume fraction for a particular phase

K :

kinetic parameter

L :

sample length (m)

M :

mass fraction for a particular phase

m :

measured dilatation

n :

order of reaction

r :

radial location in assumed grain geometry (m)

R 1 :

initial pearlite colony radius (m)

R g :

prior austenite grain radius (m)

S(Π):

sensitivity fit to changes in parameter Π

t :

time (s)

T :

temperature (K)

V :

volume of unit mass (m3)

α :

kinetic free parameter

β :

kinetic free parameter

γ :

kinetic free parameter

ΔL :

sample length dilatation (m)

Δx :

change in distance (m)

Π:

input or fitting parameter

ρ :

density (g/cm3)

θ :

adjusted time (s)

ω :

density multiplier

c :

cementite

e :

eutectoid temperature

f :

ferrite

o :

standard temperature

p :

pearlite

p :

fraction within pearlite constituent

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Authors and Affiliations

  1. Thermal Sciences Department, Sandia National Laboratories, 87185, Albuquerque, NM

    R. C. Dykhuizen (Principal Member of the Technical Staff)

  2. Materials Joining Department, Sandia National Laboratories, 87185, Albuquerque, NM

    C. V. Robino (Principal Member of the Technical Staff) & G. A. Knorovsky (Senior Member of the Technical Staff)

Authors
  1. R. C. Dykhuizen
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  2. C. V. Robino
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  3. G. A. Knorovsky
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Dykhuizen, R.C., Robino, C.V. & Knorovsky, G.A. A method for extracting phase change kinetics from dilatation for multistep transformations: Austenitization of a low carbon steel. Metall Mater Trans B 30, 107–117 (1999). https://doi.org/10.1007/s11663-999-0011-z

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  • DOI: https://doi.org/10.1007/s11663-999-0011-z

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