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Function MAP_STEEL_YBB

  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

Called by the function MAP_STEEL_WKINETIC in the calculation of the volume fraction of Widmanstätten ferrite or bainite formed, when the nucleation rate and growth rate are known.

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Specification

Language:FORTRAN
Product form:Source code

DOUBLE PRECISION FUNCTION MAP_STEEL_YBB(S, T, TC, X)

DOUBLE PRECISION S, T, TC, X, MAP_STEEL_YBB

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Description

The trapezium rule is used in the function MAP_STEEL_WKINETIC to calculate the volume fraction of Widmanstätten ferrite or bainite formed.

MAP_STEEL_YBB is used to calculate an element in the numerical integration for the case t < tc, where:

Equations

where Vmax is the maximum extent to which transformation to bainite or Widmanstätten ferrite is possible, G is the growth rate, rho is the plate tip radius, I is the nucleation rate, and Sv is the surface area of austenite grain boundary per unit volume.

Equations

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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

S - real
S = 2sqrt2I(G*rho)0.5Sv (see above).

T - real
T is the time of reaction (in seconds).

TC - real
TC is the time to grow across a grain (in seconds).

X - real
X is a measure of the position in the integration, e.g. n/N , where N is the total number of steps, and n the the number of the given step.

Output parameters

MAP_STEEL_YBB - real function.
MAP_STEEL_YBB = {1 - exp {{2/3}S(T(1 - X))1.5}}

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Error Indicators

None.

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Accuracy

If the exponent in the expression for Yb (see above) is less than -173 then Yb is taken to be 1.

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Further Comments

None.

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Example

1. Program text

       DOUBLE PRECISION S, T, TC, X, YBBX, MAP_STEEL_YBB
       READ (5,*) S, T, TC, X
       YBBX = MAP_STEEL_YBB(S, T, TC, X)
       WRITE (6,10) YBBX
10     FORMAT ('YBB = ', D13.5)
       STOP
       END

2. Program data

0.45754D-03   0.27125D+02   0.95721D+01   0.39216D-01

3. Program results

YBB = 0.39769D-01

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Auxiliary Routines

None.

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Keywords

trapezium rule

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Download

Download source code

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