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.
To calculate the increase in incubation time of the C-curve for reconstructive transformation, due to the presence of soluble boron.
Language: | FORTRAN |
Product form: | Source code |
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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DOUBLE PRECISION BTIME,FBOR1,FBOR2,GRAD,PPMBSL 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 CALL MAP_STEEL_BOR(BTIME,PPMBSL,FBOR1,FBOR2) WRITE (*,1) BTIME STOP 1 FORMAT(/'Increase in incubation time = ',F10.3,' seconds') END
Input concentration of soluble boron (ppm): 1.4 Input gradient of allotriomorphic ferrite/boron interaction: 3.4 Input limiting boron concentration (ppm): 3.0
Increase in incubation time = 4.760 seconds
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incubation time, boron, C curve
MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.
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