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H.K.D.H. Bhadeshia,

Phase Transformations Group,

Department of Materials Science and Metallurgy,

University of Cambridge,

Cambridge, U.K.

Added to MAP: August 1999.

For a steel weld it calculates (a) the distribution of oxygen among the constituent elements Si, Al, Ti and Mn, (b) the amount of Ti tied up by N and (c) the amount of B in solution and the amount tied up by N.

Language: | FORTRAN |

Product form: | Source code |

SUBROUTINE MAP_STEEL_PARTIC( ALTOT,ALSOL,OXYWT,OXYMIN,TITOT, & PEROAL,PEROTI,PEROMN,PEROSI,PERTIN,PERTIO,PERBSL, & PERBN,IFAIL,NITWT,NITSOL,BWT,STATE,FBORT ) DOUBLE PRECISION ALTOT,ALSOL,OXYWT,OXYMIN,TITOT,PEROAL,PEROTI DOUBLE PRECISION PEROMN,PEROSI,PERTIN,PERTIO,PERBSL,PERBN,NITWT DOUBLE PRECISION NITSOL,BWT,STATE,FBORT INTEGER IFAIL

The subroutine divides up any oxygen and nitrogen present in the weld between the elements Al, Ti, B, Mn and Si in the following way:

- All of the Al present reacts with oxygen to form Al
_{2}O_{3}. - Any remaining oxygen reacts with Ti to form either TiO, Ti
_{2}O_{3}or TiO_{2}. (The oxidation state of the Ti oxide to be formed must be supplied as an input parameter to the subroutine.) - If there is insufficient oxygen to tie up all of the Ti in this way, then the remaining Ti reacts to form TiN.
- Any remaining N reacts with B to form BN:

If there are more atoms of B than N, then all of the N is assumed to react with the boron and the remaining B goes into solution. If there are more atoms of N than B, the amount of B staying in solution is calculated from the equation

log([%B][%N]) = 5.24 - 13970/T

(See equations 9 and 10 in reference 2); the rest of the B forms BN. - Any remaining N goes into solution.
- Any remaining O is divided up between Mn and Si, using the result obtained by Evans [3] that SiO
_{2}and MnO form in the ratio of 1.64:1 by weight.

The oxidation state of the titanium oxide formed must be specified through the input parameter, STATE, as follows:

` STATE = 2.0 ` if the oxide of titanium is assumed to be TiO_{2}.

` STATE = 1.5 ` if the oxide of titanium is assumed to be Ti_{2}O_{3}.

` STATE = 1.0 ` if the oxide of titanium is assumed to be TiO.

- T.W. Lau, M.M. Sadowski, T.H. North, G.C. Weatherly, 1988,
*Mat. Sci. & Tech*,**4**, 52-61. - W. Fountain and J. Chapman,
*Trans. Met. Soc. AIME*, 1962,**224**, 599-606. - G.M. Evans, 1991,
*Welding Journal*,**70**, 32-39.

**ALTOT**- real- ALTOT is the total aluminium concentration (wt.%).
**ALSOL**- real- ALSOL is the dissolved aluminium concentration (wt.%).
**OXYWT**- real- OXYWT is the total oxygen concentration (wt.%).
**TITOT**- real- TITOT is the total titanium concentration (wt.%).
**NITWT**- real- NITWT is the total nitrogen concentration (wt.%).
**BWT**- real- BWT is the total boron concentration (wt.%).
**STATE**- real- Set STATE to 1, 1.5 or 2 for the formation of TiO, Ti
_{2}O_{3}, or TiO_{2}respectively. **FBORT**- real- FBORT is the temperature (Kelvin) at which the boron solubility product is to be evaluated.

**OXYMIN**- real- OXYMIN is the minimum amount of oxygen (wt.%) that is required to oxidise all of the aluminium and titanium.
**PEROAL**- real- PEROAL is the percentage of oxygen (% moles) tied up with aluminium.
**PEROTI**- real- PEROTI is the percentage of oxygen (% moles) tied up with titanium.
**PEROMN**- real- PEROMN is the percentage of oxygen (% moles) tied up with manganese.
**PEROSI**- real- PEROSI is the percentage of oxygen (% moles) tied up with silicon.
**PERTIN**- real- PERTIN is the percentage of titanium (% moles) tied up with nitrogen.
**PERTIO**- real- PERTIO is the percentage of titanium (% moles) tied up with oxygen.
**PERBSL**- real- PERBSL is the percentage of boron (% moles) which is in solution.
**PERBN**- real- PERBN is the percentage of boron (% moles) tied up with nitrogen.
**IFAIL**- integer- IFAIL=1 if the amount of oxygen present is insufficient to tie up aluminium.
**NITSOL**- real- NITSOL is the amount of nitrogen in solution (ppm by weight).

`IFAIL` = 1 if the amount of oxygen present is insufficient to tie up aluminium,

`IFAIL` = 0 otherwise.

No information supplied.

None.

DOUBLE PRECISION ALTOT,ALSOL,TITOT,PEROAL,PEROTI,PEROMN, & PEROSI,PERTIN,PERTIO,PERBSL,PERBN,NITWT,NITSOL,BWT,STATE, & FBORT,OXYWT,OXYMIN INTEGER IFAIL C STATE = 1.5 WRITE(*,*) WRITE(*,*) 'Input total and dissolved Al concentrations (wt%):' READ (*,*) ALTOT,ALSOL WRITE(*,*) 'Input total O and total Ti concentrations (wt%):' READ (*,*) OXYWT,TITOT WRITE(*,*) 'Input total N and total B concentrations (wt%):' READ (*,*) NITWT,BWT WRITE(*,*) 'Input temperature for evaluating B solubility (K):' READ (*,*) FBORT CALL MAP_STEEL_PARTIC(ALTOT,ALSOL,OXYWT,OXYMIN,TITOT,PEROAL, & PEROTI,PEROMN,PEROSI,PERTIN,PERTIO,PERBSL,PERBN, & IFAIL,NITWT,NITSOL,BWT,STATE,FBORT) IF (IFAIL.NE.0) & WRITE (*,*) 'Insufficient oxygen to oxidise the Al.' WRITE (*,1) OXYMIN WRITE (*,2) WRITE (*,3) 'Aluminium',PEROAL WRITE (*,3) 'Titanium ',PEROTI WRITE (*,3) 'Manganese',PEROMN WRITE (*,3) 'Silicon ',PEROSI WRITE (*,4) PERTIN WRITE (*,5) PERTIO WRITE (*,6) PERBSL WRITE (*,7) PERBN WRITE (*,8) NITSOL STOP 1 FORMAT (//'Minimum oxygen content required to oxidise ' & 'Al & Ti completely =',F8.4,' wt%') 2 FORMAT ( / 1H ,9H Element ,5X,15H% of the oxygen ) 3 FORMAT ( 4(1H ,A9,10X,F6.2) ) 4 FORMAT (/' Percentage of Ti tied up with N = ', F6.2) 5 FORMAT ( ' Percentage of Ti tied up with O = ', F6.2) 6 FORMAT (/' Percentage of B in solution = ', F6.2) 7 FORMAT ( ' Percentage of B as BN = ', F6.2) 8 FORMAT (/' Amount of nitrogen in solution =',F7.2,' ppmw'/) END

Input total and dissolved Al concentrations (wt%): 0.02 0.005 Input total O and total Ti concentrations (wt%): 0.03 0.02 Input total N and total B concentrations (wt%): 0.01 0.002 Input temperature for evaluating B solubility (K): 940

Minimum oxygen content required to oxidise Al & Ti completely = 0.0234 wt% Element % of the oxygen Aluminium 44.47 Titanium 33.40 Manganese 4.54 Silicon 17.58 Percentage of Ti tied up with N = 0.00 Percentage of Ti tied up with O = 100.00 Percentage of B in solution = 3.53 Percentage of B as BN = 96.47 Amount of nitrogen in solution = 75.00 ppmw

None.

weld, oxide, nitride, solubility, inclusions

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