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Subroutine MAP_STEEL_BOR

  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

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

Added to MAP: June 1999.

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To calculate the increase in incubation time of the C-curve for reconstructive transformation, due to the presence of soluble boron.

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Product form:Source code



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Boron, present in solution in steels, retards the heterogeneous nucleation of allotriomorphic ferrite by segregating to austenite grain boundaries [1]. This reduces their interface energy per unit area and hence increases the activation energy for heterogeneous nucleation. A boron addition of ~0.002 wt% is sufficient for typical commercial steels. Too large an addition, however, is detrimental as it leads to the formation of borides at the austenite grain boundaries, which can enhance the nucleation of ferrite.

This routine calculates the effect of boron on the C-curve for reconstructive transformation to ferrite or pearlite. The increase in the incubation time (delta_t) before reconstructive transformation begins has been investigated by Pickering [2] as a function of the concentration of boron in solution. There is a proportional increase in the incubation period up to a concentration of about 20ppm, beyond which it becomes insensitive to any further increase in the the boron concentration. This limiting value can vary and is thought to be dependent on the size of the austenite grains.

MAP_STEEL_BOR calculates the additional incubation time using the equations:

       delta_t = x . F / 20               for x<x_max
delta_t = x_max . F / 20 for x>x_max

where x is the concentration of the soluble boron, in parts per million by weight, and x_max is the limiting boron concentration. F/20 is the slope of the allotriomorphic ferrite/boron interaction, i.e. it is the slope of the graph of increase in incubation time against soluble boron concentration. See reference 3 for further details.

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  1. H.K.D.H. Bhadeshia, 1992, Bainite in Steels, The Institute of Materials No. 504, Cambridge University Press, pp183.
  2. F.B. Pickering, 1978, Physical Metallurgy and the Design of Steels, App. Sci., UK.
  3. H.K.D.H. Bhadeshia and L.-E. Svensson, 1993, Modeling and Control of Joining Processes, ed. T. Zacharia, American Welding Society, pp153-160.

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Input parameters

PPMBSL - real
PPMBSL is the soluble boron concentration (ppm by wt.).

FBOR1 - real
FBOR1/20 is the slope of the graph of increase in incubation time against soluble boron concentration. If a linear increase in incubation time occurred up to a soluble boron concentration of 20ppm, then FBOR1 is the increase in incubation time (seconds) at this boron concentration. Pickering's data [2] gives a value for FBOR1 of 68.

FBOR2 - real
FBOR2 is the limiting boron concentration of the interaction (ppm by wt.), beyond which any further increase in soluble boron has little effect.

Output parameters

BTIME - real
BTIME is the increase in incubation time (seconds), for the diffusional C-curve, caused by the presence of soluble boron.

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Error Indicators


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Not specified.

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Further Comments


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1. Program text

      WRITE(*,*) 'Input concentration of soluble boron (ppm):'
      READ (*,*) PPMBSL
      WRITE(*,*) 'Input gradient of allotriomorphic ferrite/boron',
     &           ' interaction:'
      READ (*,*) GRAD
      WRITE(*,*) 'Input limiting boron concentration (ppm):'
      READ (*,*) FBOR2
      FBOR1 = GRAD*20D0
      WRITE (*,1) BTIME
    1 FORMAT(/'Increase in incubation time = ',F10.3,' seconds')

2. Program data

 Input concentration of soluble boron (ppm):
 Input gradient of allotriomorphic ferrite/boron interaction:
 Input limiting boron concentration (ppm):

3. Program results

Increase in incubation time =      4.760 seconds

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Auxiliary Routines


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incubation time, boron, C curve

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Download source code

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