Empirical Rant

In metallurgy we often term very simple models to be `empirical models’ in contrast to `physical models’. I really wish there was a better name for the `empirical models` – since physical models are more empirical, and `empirical models’ are actually less empirical. Use of such equations can be very useful because they do provide a summary of observations with-in some range of observed behaviour. Even when a physical model exists these simple models are often still preferred because of the ease with which they can be used.

The source of my confusion is the now contradictory uses of the word empirical…

Physical models incorporate more physical understanding, are based on a theoretical understanding. Any theory can only be based on, and validated against, observations. (Edit: i.e. empirical observations)

A better description for our `empirical models’ would be Ad-hoc, make-do, summary or arbitrary.

Comparison of empirical and physical models
This is best described by an example. The martensite start temperature (MS) is often described by an equation of the form; MS = A*XC + B*XMn + C*XCr…

MS(C) = 521 – 353.C – 225.Si – 24.3.Mn – 27.4.Ni 0 17.7.Cr – 25.8.Mo

Another example is the use of various ‘carbon equivilant’s.
Carbon Equivilant = CE = C + Mn/5 + Mo / 5 + Cr/10 + Ni/50

Thomas Sourmail and Carlos Garcia-Mateo have written a paper on prediciton of M_S by various methods,
(Critical assessment of models for predicting the Ms temperature of steels, T. Sourmail and C. Garcia-Mateo Comp. Mater. Sci., 2005:34, p323-334) it is available on Thomas’s webpage;Predicting the martensite start temperature (Ms) of steels.

Ms/ K, all compositions in wt%
[8] 772-316.7C-33.3Mn-11.1Si-27.8Cr-16.7Ni-11.1Mo-11.1W
[9] 811-361C-38.9Mn-38.9Cr-19.4Ni-27.8Mo
[10] 772-300C-33.3Mn-11.1Si-22.2Cr-16.7Ni-11.1Mo
[11] 834.2-473.9C-33Mn-16.7Cr-16.7Ni-21.2Mo
[12] 812-423C-30.4Mn-12.1Cr-17.7Ni-7.5Mo
[12] 785-453C-16.9Ni-15Cr-9.5Mo+217(C)2-71.5(C)(Mn)-67.6(C)(Cr)

Potency of Elements on MS temperature (Change per weight percent).

N	C	Ni	Co	Cu	Mn	W	Si	Mo	Cr	V	Al
-450	-450	-20	+10	-35	-30	-36	-50	-45	-20	-46	-53	P-1976

• P-1976 F.B. pickering, `Physical metallurgy of stainless steel developments’, Int. Met. Rev., 21, pp 227-268, 1976.
• 8 P. Payson and C. H. Savage. Trans. ASM, 33:261-281, 1944.
• 9 R. A. Grange and H. M. Stewart. Trans. AIME, 167:467-494, 1945.
• 10 A. E. Nehrenberg. Trans. AIME, 167:494-501, 1945.
• 11 W. Steven and A. G. Haynes. JISI, 183:349-359, 1956.
• 12 K. W. Andrews. JISI, 203:721-727, 1965.
• 13 C. Y. Kung and J. J. Rayment. Metall. Trans. A, 13:328-331, 1982.

Neural network models have been developed to predict both martensite start and bainite start temperatures. It is also possible to calculate these using ‘physically’ based models based on thermodynamics.

They’re all just maths!