mucg73.f

MUCG73 is a program available from map, which is written in FORTRAN. The program was originally written by HKDH (Harry) Bhadeshia and using the methods described in the 1982 paper, “Thermodynamic analysis of Isothermal transformation diagrams”. PDF available here: Thermodynamics analysis of isothermal transformation diagrams from phase transformations group.

I’ve been making some changes to the program since I at first wanted to increase the range of the calculation to lower temperatures, and also wanted to decrease the temperature step size from 20 degrees to 1 degree. This was to allow me to calculate the kinetics below 200 degrees Celcius which is the temperature range I am interested in for the ‘low temperature’ bainite. Calculating with a temperature step of 1 degree allows me to more easily calculate a CCT diagram using Scheil’s Additive law, otherwise it is necessary to interpolate between each 20 degrees step.

The most useful change I made so far was to replace the regression routine used for calculating the intersection of the free energy and the stored energy for bainite and for martensite. This was necessary after changing either the range or the step size used in the calculation because the regression previously was calculated by using the energy calculated for each temperature except the last 10 points. This corresponds to the range, range 200-480, which you can see in the figure graph of T vs FTO below contains a change in gradient. Finding the intersection can be made more robust/general by replacing this with a comparison of the free energy at each temperature, when the energy reaches the level for bainite or martensite I then interpolate to find the critical temperature. Since the energy in the program varies almost linearly with temperature this means the solution no longer depends upon the temperature step, it should always work find the same answer as long as the lines intersect within the temperature range calculated.

Criterion for calculation of martensite and bainite start temperatures.
[Download gnuplot script to reproduce this graph here: gnuplot gallery.

Professor Bhadeshia recommended replacing the ENERGY subroutine with the original routine from MUCG46 for the time being, since the constants determined in the rest of the program where calculated using the original version of this function, therefore any fitting was to these values. The ENERGY2 routine written by Suresh Babu should be more correct, but to use it various parameters need to be recalculated to reproduce the TTT diagram. The next step in this project is to compare these two functions, and also I also to take a look at the calculation of the Widmanstatten start temperature, which does also change slightly with the step size. I think the functions should be extended to work below 0 degrees Celcius if possible to allow calculation of the martensite start temperature in steels with higher alloy contents.

hmmm… also I have to work out a way to avoid getting NaN for a result at low temperatures.

Here are some snipets of FORTRAN code.

The changes in the main part of the program (it’s also necessary to declare the existance of subroutines).

C CALL MAP_UTIL_ANALY(J8,10,CONST,SLOPE,CORR,DT4,DDFTO)
C
C BS=(-400.0-CONST)/SLOPE
C MS=(-1120.0D+00-10568.0D+00*X1+94.1D+00-CONST)/SLOPE
BS=MAT_BS(J8,DT4,DDFTO)
MS=MAT_MS(J8,DT4,DDFTO,X1)
C

The subroutine for calculating the martensite start temperature.

C***************************************************************************
C MATHEW JAMES PEET, 21 APRIL 2006
C UNIVERSITY OF CAMBRIDGE
C
DOUBLE PRECISION FUNCTION MAT_MS(IMAX,T,G,X1)
IMPLICIT NONE
INTEGER I,IMAX,IMS
DOUBLE PRECISION T(1000),G(1000)
DOUBLE PRECISION MCOND
DOUBLE PRECISION X1
MCOND=-1120.0D+00-10568.0D+00*X1+94.1D+00
C
C WRITE(*,*) "MCOND, X1"
C WRITE(*,*) MCOND,X1
C
DO 1 I=1,IMAX
IF(G(I) .LT. MCOND) THEN
MAT_MS = T(I)
IMS = I
C WRITE (*,*) MAT_MS,I
C
ENDIF
C
1 CONTINUE
C WRITE (*,*) MAT_MS
C MAT_MS = 0.5*(T(IMS)+T(IMS-1))
MAT_MS = T(IMS-1)+(T(IMS)-T(IMS-1))*
& ((G(IMS-1)-MCOND)/(G(IMS-1)-G(IMS)))
RETURN
END
C******************************************************************

It would be nice to get hold of the data used to train the models. A similar problem exists in calculating TTT diagrams with the MAP program MTTTDATA, which uses MTDATA, which as far as I understand is also incomplete for calculating TTT diagrams.

Of course most of this wont be necessary when we can solve the Shrodinger Equation.

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Some effects of Alloying elements in Steel

Alloying additions are commonly added to steels to;

  • increase hardenability,
  • improve strength,
  • improve mechanical properties (at operating temperature),
  • improve toughness for a given strength or hardness,
  • increase wear resitance,
  • improve magnetic properties.

Increasing the hardenability means that pearlite transformation will be delayed to longer times. This means it is easier to obtain martensite or bainite on cooling, or by isothermal holding after cooling past the pearlite start temperature.

Classification of alloying elements by Bain in The Alloying Elements in Steel

Dissolved in Ferrite

Ni, Si, Al, Zr, Mn, Cr, W, Mo, V, Ti, P, S (?) Cu.

Nickel, silicon, aluminium, zirconia, manganese, chromium, tungsten, molybdenum, vanadium, titanium, phoshorous, sulphur and copper.

Combined in Carbide

Mn, Cr, W, Mo, Nb, V, Ti.

Manganese, chromium, tungsten, molybdenum, niobium, vanadium, titanium.

B

Boron can be present in borocarbides, or as borides.

In Nonmetallic Inclusions

SiO2, MxOy, Al202, etc

ZrO, MnS, MnFeO, MnO, SiO2, CrxOy

VxOy, TixOy, MnFeS, ZrS

Special Intermetallic Compounds

Ni-Si Compound (?), AlxNy, ZrxNy

VxNy, TixNyC2, TixNy

Elemental state

Cu above 0.8%

Pb (?)

The effects of common alloying elements in steel was summarised as follows (data from ‘Metals Handbook’ 1948, American Society for Metals, Metals Park, Ohio.

Al – Aluminium

Solid Solubility

In Gamma Iron (austenite)

1.1 % (increased by C)

In Alpha Iron (ferrite)

36 %

Influence on ferrite

Hardens considerably by solid solution.

Influence on austenite (hardenability)

Increases hardenability mildly, if dissolved in austenite.

Influence exerted through carbide

Carbide forming tendency

Negative (graphitizes).

Action during tempering

Principal functions

  • Dexodises efficiently.
  • Restricts grain growth (by forming dispersed oxides or nitrides).
  • Alloying element in nitriding steel.

Cr – Chromium

Solid Solubility

In Gamma Iron (austenite)

12.8 % (20 % with 0.5 C)

In Alpha Iron (ferrite)

Unlimited

Influence on ferrite

Hardens slightly; increases corrosion resistance.

Influence on austenite (hardenability)

Increases hardenability moderately.

Influence exerted through carbide

Carbide forming tendency

Greater than Mn; less than W.

Action during tempering

Mildly resists softening.

Principal functions

  • Increases resistance to corrosion and oxidation.
  • Increases hardenability.
  • Adds some strength at high temperatures.
  • Resists abrasion and wear (with high carbon).

Co – Cobalt

Solid Solubility

In Gamma Iron (austenite)

Unlimited

In Alpha Iron (ferrite)

75 %

Influence on ferrite

Hardens considerably by solid solution.

Influence on austenite (hardenability)

Decreases hardenability as dissolved.

Influence exerted through carbide

Carbide forming tendency

Similar to Fe.

Action during tempering

Sustains hardness by solid solution.

Principal functions

  • Contributed to red-hardness by hardening the ferrite.

Mn – Manganese

Solid Solubility

In Gamma Iron (austenite)

Unlimited

In Alpha Iron (ferrite)

3 %

Influence on ferrite

Hardens markedly; reduces plasticity somewhat.

Influence on austenite (hardenability)

Increases hardenability moderately.

Influence exerted through carbide

Carbide forming tendency

Greater than Fe; less than Cr.

Action during tempering

Very little in usual quantities.

Principal functions

  • Counteracts brittleness from sulphur [by forming MnS sulphides).
  • Increases hardenability inexpensively.

Mo – Molybdenum

Solid Solubility

In Gamma Iron (austenite)

~3% (8% with 0.3% C)

In Alpha Iron (ferrite)

37.5% (less with lowered temperature)

Influence on ferrite

Provides age hardening system in high Mo-Fe alloys.

Influence on austenite (hardenability)

Increases hardenability strongly (Mo > Cr).

Influence exerted through carbide

Carbide forming tendency

Strong; greater than Cr.

Action during tempering

Opposes softening, by secondary hardening.

Principal functions

  • Raises grain-coarsening temperature of austenite.
  • Deepens hardening.
  • Counteracts tendency toward temper brittleness.
  • Raises hot and creep strength, red-hardness.
  • Enhances corrosion resistance in stainless steel.
  • Forms abrasion resisting particles.

Ni – Nickel

Solid Solubility

In Gamma Iron (austenite)

Unlimited

In Alpha Iron (ferrite)

10% (irrespective of carbon content)

Influence on ferrite

Strengthens and toughens by solid solution.

Influence on austenite (hardenability)

Increases hardenability mildly, but tends to retain austenite at higher carbon contents.

Influence exerted through carbide

Carbide forming tendency

Negative (graphitizes).

Action during tempering

Very little in small percentages.

Principal functions

  • Strengthens unquenched or annealed steels.
  • Toughens pearlitic-ferritic steels (especially at low temperature).
  • Renders high-chromium iron alloys austenitic.

P – Phosphorus

Solid Solubility

In Gamma Iron (austenite)

0.5%

In Alpha Iron (ferrite)

2.8% (irrespective of carbon content)

Influence on ferrite

Hardens strongly by solid solution.

Influence on austenite (hardenability)

Increases hardenability.

Influence exerted through carbide

Carbide forming tendency

.

Nil

Action during tempering

Principal functions

  • Strengthens low-carbon steel.
  • Increases resistance to corrosion.
  • Improves machinability in free-cutting steels.

Si – Silicon

Solid Solubility

In Gamma Iron (austenite)

~2% (9% with 0.35% C)

In Alpha Iron (ferrite)

18.5% (not much changed by carbon).

Influence on ferrite

Hardens with loss in plasticity (Mn Influence on austenite (hardenability)
Increases hardenability moderately.

Influence exerted through carbide

Carbide forming tendency

Negative (graphitizes).

Action during tempering

Sustains hardness by solid solution.

Principal functions

  • Used as a general purpose deoxidiser.
  • Alloying element for electrical and magnetic sheet.
  • Improve oxidation resistance.
  • Increase hardenability of steels carrying non-graphitising elements.
  • Strengthens low-alloy steels.

Ti – Titanium

Solid Solubility

In Gamma Iron (austenite)

0.75% (1% with 0.2 % C)

In Alpha Iron (ferrite)

~6% (less with lowered temperature)

Influence on ferrite

Provides age hardening system in high Ti-Fe alloys.

Influence on austenite (hardenability)

Probably increases hardenability very strongly as dissolved, the carbide effects reduce hardenability.

Influence exerted through carbide

Carbide forming tendency

Greatest known (2% Ti renders 0.5% carbon steel unhardenable).

Action during tempering

Persistent carbides probably unaffected. Some secondary hardening.

Principal functions

  • Fixes carbon in inert particles;
  • reduces martensitic hardness and hardenability in medium Cr steels.
  • prevents formation of austenite in high Cr steels.
  • prevents localised depletion of chromium in stainless steel during long heating.

W – Tungsten

Solid Solubility

In Gamma Iron (austenite)

6% (11% with 0.25C)

In Alpha Iron (ferrite)

33% (less with lowered temperature)

Influence on ferrite

Provides age hardening system in high W-Fe alloys.

Influence on austenite (hardenability)

Increases hardenability strongly in small amounts.

Influence exerted through carbide

Carbide forming tendency

Strong.

Action during tempering

Opposes softening by secondary hardening.

Principal functions

.

  • Forms hard, abrasion resistant particles in tool steels.
  • Promotes hardness and strength at elevated temperature.

V – Vanadium

1 (4% with 0.2% C)

Solid Solubility

In Gamma Iron (austenite)

Unlimited.

In Alpha Iron (ferrite)

Hardens moderately by solid solution.

Influence on ferrite

Unlimited.

Influence on austenite (hardenability)

Increases hardenability very strongly as dissolved.

Influence exerted through carbide

Carbide forming tendency

Very strong

Action during tempering

Maximum for secondary hardening.

Principal functions

  • Elevates coarsening temperature of austenite (promotes fine grain).
  • Increases hardenability (when dissolved).
  • Resists tempering and causes marked secondary hardening.

Carbon in steels – near equilibrium structures.

Alloying of iron with carbon can produce a wide variety of properties. In general steels become stronger and less ductile with increasing carbon content. However a wide variety of combinations of properties can be obtained by altering the both the composition along with thermal and mechanical processing. Steel containing containing 0.4 per cent (by mass) of carbon is twice as strong as pure iron. Steels with 1 per cent carbon are nearly 3 times as strong. Iron-carbon alloys are classified by carbon content in the table below.

Classifcation Carbon content (mass or weight percent)
Intersitial free steel ?
Extra low carbon steel ?
Mild steel 0.1-0.25
Medium carbon steel 0.25-0.45
High carbon steel 0.45-1.50
Rarely used 1.50-2.5
Cast Iron 2.5-4.0

Examples of different carbon contents in different applications are shown in this figure.
Applications of steels with different carbon contents (weight or mass percent)

Slowly cooling from the high temperature crystal structure (austenite) in carbon steels will develop microstructures as shown in this figure. At room temperature less than 0.01 per cent carbon exists in equilibrium in solid solution in the low temperature crystal structure of iron (ferrite). Carbon is instead found to exist in an intermetallic compound, iron carbide, of three iron atoms and one carbon atom. Greater proportions of this compound form at higher carbon contents. b = 0.3, c = 0.6, d = 0.8 in the figure below. The cementite forms as an intimate mixture with lamalae of ferrite and cementite. Above the eutectic composition of 0.8 per cent the carbide forms first at the previously existing austenite grain boundaries as shown in case d (1.1 per cent carbon) below.
Microstructure on slow cooling from austenite
Eutectic area of equilibrium phase diagram.

Faster cooling will produce structures further away from the equilibrium structure. Fast cooling can produce ferrite supersaturated with carbon, which has a tetragonal closed packed structure called martensite. Intermediate cooling rates or isothermal transformation can form bainite.

Links
Key to steel explaination

What is Bainite?

Bainite is a structure which can form in steels, named after Edgar Bain (photo below) who discovered (with E. C. Davenport) the structure around 1930. This microstructure generally forms as an aggregate of ferrite (the stable crystal structure of pure iron at room temperature) and cementite/ carbides (stoichmetric combinations of iron, other metallic elements and carbon).

Edgar Bain

The components in the final microstructure can be similar to those forming at higher temperature in the transformation to pearlite, or upon tempering martensitic steels. The bainite transformation has different kinetics and transformation mechanism than pearlite or martensite, although all the details of the transformation are yet to be revealed and agreed upon. Bain reported that the microstructure appeared as martensite which had been subsequently heated to precipitate carbides, later work has confirmed that the transformation mechanism is martensitic (although most aspects are refuted by somebody).

Some bainitic steels are alloyed in such a way that the transformation occurs without the formation of any carbides. It is these steels which have been the topic of my own research.

Read about the naming of Bainite.

Vimto Disappointment

Imagine my disappointment on returning to buy the newly discovered and most excellent Vimto Chew Sweets, only to be told they had sold out. I was distraut. However all was not lost, because these new (to me) Vimto Bonbons were available…

Vimto Chewy Bonbons

… not as good as the real thing. These sweets are morish but fail to satisfy in the way a single Vimto Chew can. If the newsagents doesn’t improve I may have to scout around for a new retailer, things are getting desperate already.