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Subroutine MAP_STEEL_TTT_TO_CCT

  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

S.J. Jones* and H.K.D.H. Bhadeshia,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.

*Dr S.J. Jones is now with Ford Motor Co. (UK) Ltd.

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Purpose

To convert an input TTT (time-temperature-transformation) curve into a CCT (continuous-cooling-transformation) curve using Scheil's additive reaction rule.

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Specification

Language:FORTRAN
Product form:Source code 

 SUBROUTINE MAP_STEEL_TTT_TO_CCT(IINFORM,IPAIRS,THEQU,PAE3,
& MS,ISWITCH,TITTT,TMTTT,ITTTPT,TTIME,TTEMP,ICCTPT,TICCT,
& TMCCT)

 IMPLICIT NONE

 DOUBLE PRECISION TITTT(1000),TMTTT(1000),
& TMCCT(300),TICCT(300),TTEMP(1000),TTIME(1000)

 DOUBLE PRECISION THEQU,PAE3,MS,TITTT,TMTTT,TTIME,
& TTEMP,TICCT,TMCCT,TEMP,PRETEMP
 DOUBLE PRECISION ANUM,BNUM,CONS,AVAL,BVAL,DELTA,
& C1,C2,A2,A3,AFAC,BFAC,STARTEFFHT,NEW1EFFHT,PRE2EFFHT,
& NEW2EFFHT,EFFHT,SUM,PREEFFHT,TINTV,FRAC,PRESUM,
& RTEMP,CONA,CONB,REAST
 INTEGER IINFORM,IPAIRS,ISWITCH,ITTTPT,ICCTPT,
& IBEGIN,IELOOP,IENDL,IPLONE,I35
 INTEGER J5,J7,J10,J20,J30,J40,J60,J70,J80

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Description

An input TTT curve is converted into a CCT curve using Scheil's additive reaction rule. The calculated natural cooling curve is divided into a series of small isothermal steps.

If tau(T) is the incubation time at the temperature T as given by the TTT curve then transformation is considered initiated when :-

[Eqn 1]

where :-

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References

  1. J.W. Christian, "The Theory of Phase Transformations in Metals and Alloys", Part 1, 2nd ed., Permagon, Oxford, (1965).
  2. H.K.D.H. Bhadeshia, B. Gretoft and L.-E. Svensson, "An Analysis of Cooling Curves From the Fusion Zone of Steel Weld Deposits", Scandinavian Journal Of Metallurgy, 15, 97-103 (1986a).

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Parameters

Input parameters

IINFORM - integer
IINFORM specifies the format of the input TTT curve.

IPAIRS - integer
IPAIRS specifies the number of points in the input TTT curve.

THEQU - real
THEQU is the temperature above which the product phase cannot form (°C).

PAE3 - real
PAE3 is the Ae3' temperature above which the ferrite cannot form under paraequilibrium conditions. At this temperature the time is set to zero (°C).

MS - real
MS is the martensite start temperature (°C).

ISWITCH - integer
ISWITCH is a flag which if set to unity causes all the arrays in the subroutine to be initialised. This is needed if the subroutine is called more than once.

TITTT - real
TITTT is an array used to store the transformation start times for the input TTT curve (s).

TMTTT - real
TMTTT is an array used to store the temperature for the input TTT curve (°C).

Output parameters

ITTTPT - integer
ITTTPT is the number of points in the output TTT curve.

TTIME - real
TTIME is an array used to store the transformation start times for the output TTT curve (s).

TTEMP - real
TTEMP is an array used to store the temperature for the output TTT curve (°C).

ICCTPT - integer
ICCTPT is the number of points in the output CCT curve.

TICCT - real
TICCT is an array used to store the transformation start times for the output CCT curve (s).

TMCCT - real
TMCCT is an array used to store the temperature for the output CCT curve (°C).

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Error Indicators

  1. If ISWITCH has been incorrectly set then an error is reported and the program execution is stopped.
  2. If the arrays used to store the CCT curve are too small then an error is reported and the program execution is stopped.

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Accuracy

No information supplied.

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Further Comments

The subroutine could be easily modified to generate a CCT curve using linear cooling curves instead of natural cooling curves. However, tests indicate that this makes very little difference.

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Example

1. Program text

        PROGRAM MAP_STEEL_TTT_CCT_EX
        IMPLICIT NONE
C
        DOUBLE PRECISION TITTT(1000),TMTTT(1000),
     &  TMCCT(300),TICCT(300),TTEMP(1000),TTIME(1000)
        DOUBLE PRECISION THEQU,PAE3,MS,TITTT,TMTTT,TTIME,
     &  TTEMP,TICCT,TMCCT
        INTEGER IINFORM,IPAIRS,ISWITCH,ITTTPT,ICCTPT,
     &  I10,I20
C
        READ(*,*) IINFORM,IPAIRS,THEQU,PAE3,MS,ISWITCH
        DO 10 I10=1,IPAIRS,1
         READ(*,*) TMTTT(I10),TITTT(I10)
10      CONTINUE
        CALL MAP_STEEL_TTT_TO_CCT(IINFORM,IPAIRS,THEQU,PAE3,MS,
     &  ISWITCH,TITTT,TMTTT,ITTTPT,TTIME,TTEMP,ICCTPT,TICCT,TMCCT)
        DO 20 I20=1,30,1
         WRITE(*,30) TMCCT(I20),TICCT(I20)
20      CONTINUE
30      FORMAT(E10.4,1X,E10.4)
        STOP
        END

2. Program data

	1 29 0.8139E3 0.8139E3 0.4746E3 0
	0.7600E+03 0.1675E+12
	0.7400E+03 0.2112E+06
	0.7200E+03 0.7462E+03
	0.7000E+03 0.6394E+02
	0.6800E+03 0.2026E+02
	0.6600E+03 0.9643E+01
	0.6400E+03 0.6796E+01
	0.6200E+03 0.8430E+01
	0.6000E+03 0.3299E+02
	0.5800E+03 0.4692E+02
	0.5600E+03 0.9134E+02
	0.5400E+03 0.2300E+03
	0.5200E+03 0.7192E+03
	0.5000E+03 0.2730E+04
	0.4800E+03 0.1234E+05
	0.4600E+03 0.6583E+05
	0.4400E+03 0.4225E+06
	0.4200E+03 0.3220E+07
	0.4000E+03 0.2945E+08
	0.3800E+03 0.3262E+09
	0.3600E+03 0.4437E+10
	0.3400E+03 0.7165E+11
	0.3200E+03 0.1487E+13
	0.3000E+03 0.4106E+14
	0.2800E+03 0.1507E+16
	0.2600E+03 0.7929E+17
	0.2400E+03 0.5942E+19
	0.2200E+03 0.6672E+21
	0.2000E+03 0.1192E+24

3. Program results

	0.6971E+03 0.7343E+03
	0.6965E+03 0.6773E+03
	0.6958E+03 0.6249E+03
	0.6951E+03 0.5768E+03
	0.6944E+03 0.5326E+03
	0.6936E+03 0.4920E+03
	0.6927E+03 0.4547E+03
	0.6919E+03 0.4203E+03
	0.6909E+03 0.3887E+03
	0.6900E+03 0.3595E+03
	0.6890E+03 0.3327E+03
	0.6880E+03 0.3079E+03
	0.6870E+03 0.2850E+03
	0.6860E+03 0.2638E+03
	0.6849E+03 0.2442E+03
	0.6839E+03 0.2261E+03
	0.6828E+03 0.2093E+03
	0.6818E+03 0.1938E+03
	0.6807E+03 0.1793E+03
	0.6797E+03 0.1659E+03
	0.6786E+03 0.1536E+03
	0.6774E+03 0.1423E+03
	0.6762E+03 0.1319E+03
	0.6750E+03 0.1223E+03
	0.6737E+03 0.1134E+03
	0.6723E+03 0.1052E+03
	0.6709E+03 0.9770E+02
	0.6694E+03 0.9073E+02
	0.6679E+03 0.8427E+02
	0.6664E+03 0.7830E+02

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Auxiliary Routines

None.

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Keywords

TTT, CCT, conversion, Scheil, incubation, weld, time, temperature, transformation, continuous, cooling

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Download

Download source code

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