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Function MAP_STEEL_WKINETIC

  1. Provenance of code.
  2. Purpose of code.
  3. Specification.
  4. Description of subroutine's operation.
  5. References.
  6. Parameter descriptions.
  7. Error indicators.
  8. Accuracy estimate.
  9. Any additional information.
  10. Example of code
  11. Auxiliary subroutines required.
  12. Keywords.
  13. Download source code.
  14. Links.

Provenance of Source Code

G.I. Rees,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.

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Purpose

Calculates the volume fraction of Widmanstätten ferrite or bainite formed after a specified time, given the nucleation rate and the growth rate.

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Specification

Language:FORTRAN
Product form:Source code

DOUBLE PRECISION FUNCTION MAP_STEEL_WKINETIC(NUC, T, G, RADIUS,
& VM, SV)

DOUBLE PRECISION NUC, T, G, RADIUS, VM, SV

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Description

For a given nucleation rate I, growth rate G, and plate tip radius rhoc, the volume fraction of Widmanstätten ferrite or bainite, denoted by Vp, is determined as follows [1,2]:

If tc is the time required for a plate to grow across an austenite grain of mean linear intercept L, then the expression for volume fraction of the precipitated phase falls into two domains [2] according to the reaction time.

(a) if t < tc

Equation

where:
Equation

where Vmax is the maximum extent to which transformation to bainite or Widmanstätten ferrite is possible.

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References

  1. M. Umemoto, A. Hiramatsu, A. Moriya, T. Watanabe, S. Nanba, N. Nakajima, G. Anan, and Y. Higo, I.S.I.J. Int., 32, (1992), 306-315.
  2. G.I. Rees, H.K.D.H. Bhadeshia, and T. Maurickx, Progress Report for SOLLAC, August 1995.

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Parameters

Input parameters

NUC - real
NUC is the nucleation rate I per unit area of austenite grain boundary surface (in m-2s-1).

T - real
T is the time t if reaction (in s-1).

G - real
G is the growth rate of a plate under carbon diffusion control (in ms-1).

RADIUS - real
RADIUS is the critical radius of curvature rhoc of a ferrite plate tip which gives zero growth rate (in metres).

VM - real
VM is the maximum allowable volume fraction Vmax of either bainite or Widmanstätten ferrite that can form at the given temperature.

SV - real
SV is Sv, the surface area of austenite grain boundary per unit volume (in m-1).

Output parameters

MAP_STEEL_WKINETIC - real
MAP_STEEL_WKINETIC is the volume fraction of Widmanstätten ferrite or bainite formed.

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Error Indicators

None.

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Accuracy

The numerical integration is performed using the trapezium rule, with the range of integration divided into 51 steps.

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Further Comments

Used by the functions MAP_STEEL_CCTSOLVE and MAP_STEEL_WNSOLVE, and the routine MAP_STEEL_MICRO.

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Example

1. Program text

       DOUBLE PRECISION NUC, T, G, RADIUS, VM, SV
       DOUBLE PRECISION VP, MAP_STEEL_WKINETIC
       READ (5,*) NUC, T, G, RADIUS
       READ (5,*) VM, SV
       VP = MAP_STEEL_WKINETIC(NUC, T, G, RADIUS, VM, SV)
       WRITE (6,10) VP
10     FORMAT ('Volume fraction = ', D13.5)
       STOP
       END

2. Program data

0.56916D-01   0.27125D+02   0.10447D-04   0.19331D-08   0.18303D+00    0.20000D+05

3. Program results

Volume fraction = 0.35815D-01

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Auxiliary Routines

MAP_STEEL_YB
MAP_STEEL_YBB

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Keywords

Widmanstätten ferrite, bainite, nucleation rate

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Download

Download source code

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