[MAP Logo]

Materials Algorithms Project
Program Library



Function MAP_STEEL_WNSOLVE

  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.

Top | Next

Purpose

Calculates the effective nucleation rate which, in a given time, results in a specified Widmanstätten ferrite or bainite volume fraction.

Top | Next | Prev

Specification

Language:FORTRAN
Product form:Source code

DOUBLE PRECISION FUNCTION MAP_STEEL_WNSOLVE(GBN, V, G, RADIUS, VM,
& SV, TIME)

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

Top | Next | Prev

Description

The function uses the previously calculated value for the nucleation rate (GBN) as a starting point. It sets bounds for the nucleation rate required to form volume fraction V in time TIME, and then solves for it. The solution method is bisection [2].

If there is no previously calculated value for the nucleation rate, GBN may be set to 1.0.

Top | Next | Prev

References

  1. H.K.D.H. Bhadeshia, Metal Science, 16, (1982), 156-165.
  2. W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, Numerical Recipes, Cambridge University Press, Cambridge, U.K., (1986).

Top | Next | Prev

Parameters

Input parameters

GBN - real
GBN is the previously calculated value of MAP_STEEL_WNSOLVE. If the function is being called for the first time, the value of GBN is set to 1.0.

V - real
V is the volume fraction assumed to have formed by time TIME.

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 temperature concerned.

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

TIME - real
TIME is the incubation period at the given temperature [1] (in seconds).

Output parameters

MAP_STEEL_WNSOLVE - real
MAP_STEEL_WNSOLVE is the nucleation rate (in ms-1).

Top | Next | Prev

Error Indicators

None.

Top | Next | Prev

Accuracy

The successful solution gives a nucleation rate for which the predicted volume fraction matches the target value V with a maximum error of |Delta| so that:

|(Delta V/V)| < 0.015

Top | Next | Prev

Further Comments

None.

Top | Next | Prev

Example

1. Program text

       DOUBLE PRECISION GBN, V, G, RADIUS, VM, SV, TIME
       DOUBLE PRECISION MAP_STEEL_WNSOLVE, NRATE
       READ (5,*) GBN, V, G, RADIUS
       READ (5,*) VM, SV, TIME
       NRATE = MAP_STEEL_WNSOLVE(GBN, V, G, RADIUS, VM, SV, TIME)
       WRITE (6,10) NRATE
10     FORMAT ('Nucleation rate = ', D13.5,' m/s')
       STOP
       END

2. Program data

0.40294D-01   0.10000D-01   0.10447D-04   0.19331D-08   0.18303D+00   0.20000D+05   0.12204D+02


3. Program results

Nucleation rate = 0.47849D-01 m/s

Top | Next | Prev

Auxiliary Routines

MAP_STEEL_WKINETIC

Top | Next | Prev

Keywords

nucleation rate, Widmanstatten, bainite, volume fraction

Top | Next | Prev

Download

Download source code

Top | Prev


MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.

MAP Website administration / map@msm.cam.ac.uk

Top | Index | MAP Homepage Valid HTML 3.2!