Materials Algorithms Project
Program Library

Program MAP_STEEL_MUCG73

1. Provenance of code.
2. Purpose of code.
3. Specification.
4. Description of program.
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

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

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Purpose

A powerful suite of software for modelling of the thermodynamics and kinetics of solid-state transformations in steels. Calculates Widmanstatten, Bainite and Martensite start temperatures.

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Specification

PROGRAM MAP_STEEL_MUCG73

DOUBLE PRECISION C(12),D(12),DDFTO(40),DIFFH(40),DT4(40)
DOUBLE PRECISION DXQ(40),SHEARH(40)

DOUBLE PRECISION A,AEQ,AFE,AFEH,AFEQ,AFE44,AH,AJ,AJH,AJ1,A1,A1H
DOUBLE PRECISION A44,BS,CONST,CORR,DAFE44,DA44,DFTO,DF441,DIFFT
DOUBLE PRECISION ETEQ,ETEQ2,F,FH,FPRO,FPROA,FSON,FTO,FTO400,F44
DOUBLE PRECISION GMAX,GMAXH,G9,G9400,H,H1,MS,MT,R,S,SHEART
DOUBLE PRECISION SLOPE,STRAIN,S1,T,TEQ,TEQ2,T10,T10H,T20
DOUBLE PRECISION T20H,T4,VOLF,V14,W,WH,WS,WS1,W1,X,XA
DOUBLE PRECISION XBAR,XBARH,XEQ,XEQ2,XH,XTO,XTO400,X1,X44

DOUBLE PRECISION MAP_STEEL_AFEG,MAP_STEEL_CG,MAP_STEEL_DAFEG
DOUBLE PRECISION MAP_STEEL_DCG,MAP_STEEL_ENERGY2,MAP_STEEL_FTO1
DOUBLE PRECISION MAP_STEEL_G91,MAP_STEEL_XALPH

INTEGER I,ID,J1,J2,J6,J5,J8,J9,J98,J99

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Description of Program

MAP_STEEL_MUCG73 is a very powerful program for the modelling of transformations in steels. Many people use it to calculate a TTT diagram, but there is in fact an enormous amount of phase diagram and kinetic and thermodynamic information generated each time the program is run and this is written to the output unit. This program is essentially for any of the solid state phase transformations from austenite to martensite, bainite, WidmanstŠtten ferrite, allotriomorphic ferrite etc. The program is based on MAP_STEEL_MUCG46 but has been extended to include four additional elements: cobalt, copper, aluminium and tungsten.

The TTT diagram consists of two C-curves for the initiation of transformation [1]. The higher temperature C-Curve is for reconstructive ("diffusional") reactions such as allotriomorphic ferrite. The lower C-curve is for displacive reactions such as WidmanstŠtten ferrite, bainite and acicular ferrite [2, pp. 175-185 & 124-134, Chapter 6].

• The output data contains the concentrations (C, Si, Mn, Ni, Mo, Cr, V, Co, Cu, Al and W) in wt.% and mole fraction (atomic % /100).
• FPRO is the driving force for allotriomorphic ferrite formation by a paraequilibrium mechanism. All driving forces are in units of J/mol and all calculations are for the paraequilibrium state.
• GMAX is the driving force for nucleation (Fig. 6.2b, Ref. 2).
• CTEMP is the temperature in centigrade.
• XNUCLEUS is the optimum nucleus carbon concentration in mole fraction.
• XEQ is the paraequilibrium carbon concentration of austenite in mole fraction.
• XEQ50 is the same as XEQ but allowing for 50 J/mol of strain energy in the ferrite in order to do calculations for Widmanstatten ferrite.
• FTO is the driving force for diffusionless transformation (Fig. 6.2c, Ref. 2).
• XTO is the T-zero carbon concentration in mole fraction (Fig. 1.4, Ref. 2).
• XTO400 is the same as XTO, but with 400 J/mol of stored energy in the ferrite, to allow calculations on bainite (Fig. 1.4, Ref. 2).
• SHEART and DIFFT are the times in seconds of the lower and upper C-curves of the TTT diagram (Ref. 1).

The program asks for compositions (in wt.%) of eleven constituents to be supplied. There are maximum and minimum limits imposed on each constituent as shown :-

The program will return an error message and ask for the data to be entered again if these limits are exceeded.

The maximum number of different alloys which can be analysed in a single run is set by the variable J1 (currently 20).

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References

1. H.K.D.H. Bhadeshia, A thermodynamic analysis of isothermal transformation diagrams, Metal Science, 16 (1982) 159-165.
2. H.K.D.H. Bhadeshia, Bainite in Steels, Institute of Materials, London (1992), 1-450.

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Parameters

Input parameters

C - real array of dimension 12

C holds the composition of each alloy:-

C(1) is the Carbon concentration (in weight percent).

C(2) is the Silicon concentration (in weight percent).

C(3) is the Manganese concentration (in weight percent).

C(4) is the Nickel concentration (in weight percent).

C(5) is the Molybdenum concentration (in weight percent).

C(6) is the Chromium concentration (in weight percent).

C(7) is the Vanadium concentration (in weight percent).

C(8) is the Cobalt concentration (in weight percent).

C(9) is the Copper concentration (in weight percent).

C(10) is the Aluminium concentration (in weight percent).

C(11) is the Tungsten concentration (in weight percent).

C(12) is the Ferrite concentration (not entered).

J6 - integer

J6 is the identifying number of each alloy to be examined.

Output parameters

None

All output is to the screen.

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Error Indicators

Allowable composition ranges limited - see Description.

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Accuracy

No information supplied.

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Further Comments

None.

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Example

1. Program text

       N/A - complete program

2. Program data

1
0.39  2.05  0.001  4.08  0.001  0.001  0.001 0.5 0.5 0.01 0.01

3. Program Results

------------------------------------------------------------------------------------------------------------------------------- 
   
 *******  NUMBER    1  *********
    C=  0.3900   Si=  2.0500   Mn=  0.0010   Ni=  4.0800   Mo=  0.0010   Cr=  0.0010
    V=  0.0010   Co=  0.5000   Cu=  0.5000   Al=  0.0100    W=  0.0100
    
    C=  0.0176   Si=  0.0395   Mn=  0.0000   Ni=  0.0376   Mo=  0.0000   Cr=  0.0000
    V=  0.0000   Co=  0.0046   Cu=  0.0043   Al=  0.0002    W=  0.0000
    
  CARBON CONTENT=   0.01757  T10=  0.420581  T20= -0.305922   WGAMMA=  8702.
  MELTING TEMPERATURE OF DELTA FERRITE =    1793. KELVIN
    C=  0.0176   Si=  0.0281   Mn=  0.0000   Ni=  0.0171   Mo=  0.0000   Cr=  0.0000
    V=  0.0000   Co= 99.9371   Cu=  0.0000   Al=  0.0000    W=  0.0000
-------------------------------------------------------------------------------------------------------------------------------
   FPRO  FPROA   GMAX  CTEMP  X NUCLEUS  FSON      XEQ    XEQ50   FTO      XTO     VOLF    X44      XTO400       SHEART     DIFFT   
  -2464. -2697. -2957.  200.  0.24D-07  -2928.   0.1926   0.1913 -2077.  0.0709   0.9117 0.508D-01  0.0596  3   0.23D+05   0.30D+24
  -2321. -2548. -2804.  220.  0.54D-07  -2779.   0.1867   0.1854 -1946.  0.0700   0.9088 0.481D-01  0.0565  5   0.57D+04   0.17D+22
  -2190. -2411. -2668.  240.  0.12D-06  -2642.   0.1811   0.1797 -1843.  0.0684   0.9059 0.460D-01  0.0537  5   0.16D+04   0.15D+20
  -2069. -2286. -2545.  260.  0.23D-06  -2516.   0.1757   0.1742 -1739.  0.0662   0.9029 0.442D-01  0.0512  5   0.51D+03   0.19D+18
  -1953. -2164. -2423.  280.  0.44D-06  -2395.   0.1703   0.1688 -1639.  0.0634   0.8998 0.427D-01  0.0488  5   0.19D+03   0.36D+16
  -1831. -2038. -2294.  300.  0.80D-06  -2267.   0.1646   0.1630 -1533.  0.0605   0.8964 0.408D-01  0.0461  5   0.80D+02   0.93D+14
  -1691. -1891. -2143.  320.  0.14D-05  -2118.   0.1580   0.1564 -1405.  0.0567   0.8922 0.382D-01  0.0429  5   0.40D+02   0.34D+13
  -1546. -1738. -1985.  340.  0.24D-05  -1961.   0.1510   0.1492 -1270.  0.0527   0.8872 0.353D-01  0.0393  5   0.23D+02   0.16D+12
  -1425. -1611. -1854.  360.  0.39D-05  -1831.   0.1447   0.1429 -1161.  0.0497   0.8825 0.333D-01  0.0365  5   0.13D+02   0.98D+10
  -1308. -1487. -1727.  380.  0.62D-05  -1703.   0.1383   0.1364 -1055.  0.0467   0.8771 0.316D-01  0.0337  5   0.86D+01   0.72D+09
  -1194. -1367. -1602.  400.  0.95D-05  -1578.   0.1319   0.1298  -951.  0.0438   0.8712 0.298D-01  0.0312  4   0.61D+01   0.66D+08
  -1083. -1249. -1485.  420.  0.14D-04  -1455.   0.1253   0.1231  -850.  0.0409   0.8646 0.282D-01  0.0284  5   0.45D+01   0.71D+07
   -981. -1141. -1364.  440.  0.21D-04  -1343.   0.1189   0.1166  -758.  0.0382   0.8575 0.270D-01  0.0260  4   0.38D+01   0.94D+06
   -881. -1035. -1251.  460.  0.30D-04  -1231.   0.1124   0.1100  -667.  0.0356   0.8494 0.258D-01  0.0244  3   0.33D+01   0.14D+06
   -772.  -919. -1126.  480.  0.42D-04  -1106.   0.1050   0.1025  -563.  0.0326   0.8389 0.241D-01  0.0220  4   0.33D+01   0.27D+05
   -662.  -800. -1000.  500.  0.59D-04   -978.   0.0971   0.0944  -456.  0.0294   0.8259 0.222D-01  0.0193  4   0.37D+01   0.61D+04
   -556.  -684.  -872.  520.  0.80D-04   -852.   0.0890   0.0861  -351.  0.0270   0.8100 0.205D-01  0.0165  4   0.47D+01   0.16D+04
   -458.  -578.  -751.  540.  0.11D-03   -734.   0.0809   0.0778  -253.  0.0249   0.7910 0.190D-01  0.0137  4   0.66D+01   0.52D+03
   -374.  -485.  -646.  560.  0.14D-03   -629.   0.0733   0.0700  -168.  0.0227   0.7691 0.183D-01  0.0110  5   0.96D+01   0.18D+03
   -306.  -410.  -567.  580.  0.18D-03   -544.   0.0667   0.0632  -103.  0.0209   0.7460 0.187D-01  0.0090  4   0.13D+02   0.63D+02
   -244.  -339.  -475.  600.  0.23D-03   -461.   0.0601   0.0564   -40.  0.0191   0.7176 0.195D-01  0.0068  4   0.23D+02   0.29D+02
   -175.  -259.  -378.  620.  0.30D-03   -365.   0.0521   0.0482    37.  0.0166   0.6740 0.182D-01  0.0040  5   0.53D+02   0.18D+02
   -119.  -191.  -296.  640.  0.37D-03   -280.   0.0448   0.0406     0.  0.0144   0.6193 0.200D-01  0.0014  5   0.14D+03   0.12D+02
    -76.  -136.  -220.  660.  0.46D-03   -209.   0.0383   0.0339     0.  0.0126   0.5533 0.259D-01  0.0000  2   0.47D+03   0.11D+02
    -42.   -90.  -156.  680.  0.57D-03   -146.   0.0323   0.0277     0.  0.0108   0.4675 0.100D+12  0.0000  1   0.21D+04   0.14D+02
    -18.   -51.   -97.  700.  0.69D-03    -87.   0.0265   0.0217     0.  0.0091   0.3491 0.100D+12  0.0000  1   0.18D+05   0.28D+02
     -3.   -18.   -45.  720.  0.83D-03    -33.   0.0210   0.0160     0.  0.0075   0.1726 0.100D+12  0.0000  1   0.65D+06   0.20D+03
    
    ***** FTO VERSUS TEMPERATURE ****   
 WIDMANSTATTEN START TEMP RANGE=     0. C TO    720. C
 NUCLEATION LIMITED BAINITE START TEMP    =   507. C
 MARTENSITE START TEMPERATURE             =   356. C
-------------------------------------------------------------------------------------------------------------------------------
-------------------------------------------------------------------------------------------------------------------------------

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Auxiliary Routines

Steel Subroutines

MAP_STEEL_GALGA
MAP_STEEL_GMAAX
MAP_STEEL_HETRO
MAP_STEEL_OMEGA2

Steel Functions

MAP_STEEL_AFEG
MAP_STEEL_CG
MAP_STEEL_DAFEG
MAP_STEEL_DCG
MAP_STEEL_ENERGY2
MAP_STEEL_FTO1
MAP_STEEL_G91
MAP_STEEL_XALPH

Utility Subroutines

MAP_UTIL_ANALY
MAP_UTIL_REED
MAP_UTIL_REEDI

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Keywords

Widmanstatten, bainite, martensite, start temperature

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Download

Download source code

Download compiled executable for Windows

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