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Function MAP_STEEL_CCTSOLVE

  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

To calculate the time required to form a given volume fraction of Widmanstätten ferrite or bainite.

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Specification

Language:FORTRAN
Product form:Source code

DOUBLE PRECISION FUNCTION CCTSOLVE(GBN, V, G, RADIUS,
& VM, SV, TPREV)

DOUBLE PRECISION GBN, V, G, RADIUS, VM, SV, TPREV

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Description

The time taken to achieve the given volume fraction V (as calculated by the function MAP_STEEL_WKINETIC) is calculated using a bisection method [1] for the given growth rate and nucleation rate.

Bainite and Widmanstätten ferrite are assumed to grow as plates under carbon diffusion control. The input parameters include the plate growth rate G, the critical plate tip radius rhoc, and the austenite grain surface area per unit volume Sv.

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References

  1. W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, Numerical Recipes, Cambridge University Press, Cambridge, U.K., (1986).

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Parameters

Input parameters

GBN - real
GBN is the effective nucleation rate I of bainite or Widmanstätten ferrite per unit area of austenite grain boundary (in m-2s-1).

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

TC - real
TC is the temperature (in centigrade).

G - real
G is the growth rate of a plate under carbon diffusion control (in m s-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 the surface area of austenite grain boundary per unit volume Sv (in m-1).

TPREV - real
TPREV is the previous value of MAP_STEEL_CCTSOLVE (i.e. the value of MAP_STEEL_CCTSOLVE when it was called at the previous temperature in the cooling history). If the function is being called for the first time, TPREV should be set to 1.0. The units of TPREV are seconds.

Output parameters

MAP_STEEL_CCTSOLVE - real
MAP_STEEL_CCTSOLVE is the time to formation of a given volume fraction of bainite or Widmanstätten ferrite (in seconds).

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Error Indicators

None.

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Accuracy

The function finds a solution for V for which the error Delta V satisfies:

(Delta V/V) < 0.05 ~~~~~ if 0.05 < V < 0.65

or

(Delta V/V) < 0.015 ~~~~ if V < 0.05 ~~~or~~~ V > 0.65

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Further Comments

None.

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Example

1. Program text

       DOUBLE PRECISION GBN, V, G, RADIUS, VM, SV, TPREV
       DOUBLE PRECISION MAP_STEEL_CCTSOLVE, SOLX
       READ (5,*) GBN, V, G, RADIUS
       READ (5,*) VM, SV, TPREV
       SOLX = MAP_STEEL_CCTSOLVE(GBN, V, G, RADIUS, VM, SV, TPREV)
       WRITE (6,10) SOLX
10     FORMAT ('Time = ',D13.5,' seconds')
       STOP
       END

2. Program data

0.10275D-01   0.13810D-01   0.11406D-04   0.29716D-08
0.27369D+00   0.20000D+05   0.10000D+01

3. Program results

Time = 0.38163D+02 seconds

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Auxiliary Routines

MAP_STEEL_WKINETIC

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Keywords

nucleation rate, bainite, Widmanstatten ferrite

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Download

Download source code

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