![[MAP Logo]](../../maplogo1.gif)
A.A.B. Sugden and H.K.D.H. Bhadeshia,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.
Program added: May 1999
To calculate the Ae3 temperature of low alloy steels containing Mn, Si, Ni, Cr, Mo, Cu, V, Nb, W, Co and C as a function of the carbon concentration between 0 and 0.5wt%.
| Language: | FORTRAN |
| Product form: | Source code. |
Established thermodynamic procedures have been used to estimate the liquidus, solidus and Ae3 transformation temperatures for multi-component steels [1]. The program calculates the temperature deviation of the phase boundaries in the steel from that of the Fe-C system by using the analysis of Kirkaldy and Bagnis [2], which is based on equating the chemical potentials of the two phases at the equilibrium temperature. This analysis calculates the temperature deviation which results from the addition of each alloying component separately to the Fe-C system. The temperature changes in a multi-component alloy is then equal to the sum of the changes due to individual alloy additions, provided the solute-solute interactions are negligible. The resulting expression for the temperature deviation is:
The program calculates the Ae3 temperature for a range of values of carbon content between 0 and 0.5 wt%. As the equations being evaluated are a function of temperature, the calculations are iterated, with To as the initial value, until a change in temperature of less than 0.1K between successive iterations is obtained.
Steel content: wt% of Mn, Si, Ni, Cr, Mo, Cu, V, Nb, W and Co in that order. The total solute content should be < 6wt% and the Si content < 1wt%.
The Ae3 temperature is calculated for a range of carbon concentrations between 0 and 0.5 wt%. For each value of the carbon wt% the program outputs the following parameters:
None.
The calculations assume that the solute-solute interaction is negligible. This assumption has been found to be valid for a total alloying element content of less than about 6 wt%, provided the silicon content is < 1wt% [2]. Comparison of calculated results and experimental results give a standard error of ± 10 ° C.
None.
Complete program.
Input Mn Si Ni Cr Mo Cu V Nb W Co wt%:
2.0 0.1 0 0 0 0 0 0 0 0
--------------------------------------------------------------
A e 3 P R O G R A M
--------------------------------------------------------------
The steel contains:
2.00 wt% manganese
0.10 wt% silicon
+---------------------------+----------------------------+
Wt%C T/degreesC Partition coefficients
+---------------------------+----------------------------+
0.00 875.2 A(c) : 0.063
A(2) : 0.718
A(3) : 1.167
0.01 869.6 A(c) : 0.061
A(2) : 0.705
A(3) : 1.165
0.02 864.6 A(c) : 0.060
A(2) : 0.693
A(3) : 1.164
0.03 860.2 A(c) : 0.058
A(2) : 0.684
A(3) : 1.162
0.04 860.7 A(c) : 0.065
A(2) : 0.746
A(3) : 1.175
0.05 855.6 A(c) : 0.057
A(2) : 0.672
A(3) : 1.160
0.06 853.1 A(c) : 0.056
A(2) : 0.666
A(3) : 1.158
0.07 850.6 A(c) : 0.056
A(2) : 0.661
A(3) : 1.157
0.08 848.2 A(c) : 0.055
A(2) : 0.655
A(3) : 1.156
0.09 845.9 A(c) : 0.054
A(2) : 0.650
A(3) : 1.155
0.10 843.6 A(c) : 0.054
A(2) : 0.644
A(3) : 1.153
0.11 841.4 A(c) : 0.053
A(2) : 0.638
A(3) : 1.152
0.12 839.2 A(c) : 0.052
A(2) : 0.634
A(3) : 1.151
0.13 837.1 A(c) : 0.052
A(2) : 0.629
A(3) : 1.149
0.14 835.0 A(c) : 0.051
A(2) : 0.624
A(3) : 1.148
0.15 832.9 A(c) : 0.051
A(2) : 0.619
A(3) : 1.147
0.16 830.9 A(c) : 0.050
A(2) : 0.615
A(3) : 1.146
0.17 828.9 A(c) : 0.050
A(2) : 0.610
A(3) : 1.144
0.18 827.0 A(c) : 0.049
A(2) : 0.606
A(3) : 1.143
0.19 825.1 A(c) : 0.049
A(2) : 0.601
A(3) : 1.142
0.20 823.3 A(c) : 0.048
A(2) : 0.597
A(3) : 1.141
0.21 821.4 A(c) : 0.048
A(2) : 0.593
A(3) : 1.139
0.22 819.6 A(c) : 0.047
A(2) : 0.589
A(3) : 1.138
0.23 817.9 A(c) : 0.047
A(2) : 0.584
A(3) : 1.137
0.24 816.1 A(c) : 0.046
A(2) : 0.580
A(3) : 1.136
0.25 814.4 A(c) : 0.046
A(2) : 0.576
A(3) : 1.134
0.26 812.8 A(c) : 0.045
A(2) : 0.572
A(3) : 1.133
0.27 811.2 A(c) : 0.045
A(2) : 0.568
A(3) : 1.131
0.28 809.6 A(c) : 0.045
A(2) : 0.564
A(3) : 1.130
0.29 808.0 A(c) : 0.044
A(2) : 0.560
A(3) : 1.129
0.30 806.4 A(c) : 0.044
A(2) : 0.557
A(3) : 1.127
0.31 804.9 A(c) : 0.043
A(2) : 0.553
A(3) : 1.126
0.32 803.4 A(c) : 0.043
A(2) : 0.549
A(3) : 1.125
0.33 801.9 A(c) : 0.043
A(2) : 0.546
A(3) : 1.124
0.34 800.4 A(c) : 0.042
A(2) : 0.542
A(3) : 1.122
0.35 798.9 A(c) : 0.042
A(2) : 0.539
A(3) : 1.121
0.36 797.5 A(c) : 0.042
A(2) : 0.536
A(3) : 1.120
0.37 796.1 A(c) : 0.041
A(2) : 0.532
A(3) : 1.118
0.38 794.7 A(c) : 0.041
A(2) : 0.529
A(3) : 1.117
0.39 793.4 A(c) : 0.041
A(2) : 0.526
A(3) : 1.116
0.40 792.0 A(c) : 0.041
A(2) : 0.523
A(3) : 1.114
0.41 790.7 A(c) : 0.040
A(2) : 0.520
A(3) : 1.113
0.42 789.4 A(c) : 0.040
A(2) : 0.517
A(3) : 1.112
0.43 788.1 A(c) : 0.040
A(2) : 0.514
A(3) : 1.111
0.44 786.8 A(c) : 0.039
A(2) : 0.511
A(3) : 1.109
0.45 785.5 A(c) : 0.039
A(2) : 0.508
A(3) : 1.108
0.46 784.3 A(c) : 0.039
A(2) : 0.505
A(3) : 1.107
0.47 783.0 A(c) : 0.039
A(2) : 0.503
A(3) : 1.106
0.48 781.8 A(c) : 0.038
A(2) : 0.500
A(3) : 1.104
0.49 780.6 A(c) : 0.038
A(2) : 0.497
A(3) : 1.103
0.50 779.4 A(c) : 0.038
A(2) : 0.494
A(3) : 1.102
NAG library routine E02BBF. This routine is not included with this program. It is used to evaluate a cubic spline from the spline coefficients for delta oHo from Kaufman et al.[4].
Ae3 temperature, low alloy steel, partition coefficient
MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.
MAP Website administration / map@msm.cam.ac.uk