This doesn't answer your question but may help lead you to the formula you are looking for. This was taken from a 1930 locomotive superheater patent (US1784378A):

"The superheater headers and elements are usually made of iron or steel casting or plates or of cold or hot drawn seamless steel tubing, but we propose when advisable or necessary, to produce these headers and elements from high heat resisting alloys. Several such alloys have been developed in recent years. For instance, these alloys exploited under the trade names of ascoloy, duralloy, fabrite, thermalloy, hardite, Beckett metal, and Elesco metal are suitable. for such purpose."

Likely considered "trade secrets" would the formulae be found in some metallurgy publication or research paper? Good luck.

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A problem here is that Elesco (The Superheater Company) famously kept element metallurgy information close to their collective chests. The T1 Trust hosts a review of information on the construction of the UP Wahsatch 4-8-8-4s -- this goes into great detail on the metallurgy of the studs, washers, and other paraphernalia in the superheater arrangement, but is silent on the element material.

A relatively late printing of the Superheater Company book "Superheat Engineering Data" (which I advise anyone interested in steam technology read and bookmark) is here, at Hathitrust in page images that can be read online:

https://babel.hathitrust.org/cgi/pt?id=wu.89089671895

As with the advertised Superheater Company design services made available to railroads... this did not extend to providing the materials to fabricate either the elements/cast ends or the erosion shielding to be tack-welded to the element bends going up to the header.

A 1942 copy of Woldman's Engineering Alloys, a book containing much proprietary alloy data from that era, is accessible here:

https://automaterials.files.wordpress.com/2018/09/woldmans-engineering-alloys.pdf

You will find this references Elesco 600 and 600 H.T. [note the periods]. While there is a space to 'write in' the data if you could secure it from the Superheater Company or, post-merger, Combustion Engineering, nothing whatever is disclosed; I cannot prove this alloy is similar to "other" 600.

Many of the other alloys referenced in this and the two 'Big Boy' patents concerning the throttle header (1712928 and 1863020) can be found with a little intelligent cross-referencing. I don't think this really satisfies what's being researched here, which is the definitive compositions of historical record that were used in 'modern' Superheater Company Schmidt-type elements (either E or A type) but it was a useful starting place to research how to specify modern materials to do the job.

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I am sharing an experiance to possibly add to this thread.

I was (now retired) a mechanic at a well known museum and had a lot of time making repairs on steam locomotives. I want to report on my incidents of repairs (removals in service) of a few failed superheater elements from a particular locomotive. Keeping in mind, I am not a metalurgist, just a mechanic. (Circa 2012) During my "weekly Tuesday after weekend operation inspection" (boiler with no pressure, but still luke warm but touchable) I discovered there is water trickling out of the rear of a superheater flue and visibly running down the rear tube sheet. Many folks were suggesting a cracked flue, but, there wasn't a leak while firing up, or while running. This water was flowing with 0 psi on the gauge. I did a close examination of the firebox end of the flue and could see that the origin of leak was in front of the end of the superheater element. There was quite a puddle in the law part of the swaged end. I wanted to see if the leak increased when there was pressure in the boiler, so I pressurized with house air, but the leakage rate did not increase. With the brakes full on and the reverser in neutral, I cracked the throttle. Much to my suprize, After a much larger flow of water ended, there was a distinct hiss of air coming from the leaking flue. This was a case of a leaking superheater element. The water was from the remaining steam in the "post throttle" part of the system, condensing, and leaking out of a hole in the element. It was decided to cut off the element (folded over and welded per standard RR repair practice) and remove the element for inspection (I did this - not fun!!) We found the leak, a 1/16" hole, in the lower point of the tube, in the lowest part of the element. More curiosity lead me to split the entire tube pass, only to find "many" pits, just waiting to break through the wall. Even though the outside of the tube looked fine, the ID was failing at an alarming rate. This was most likely caused by the condensed steam (water) sitting in the lowest part of the elements, and due to the elements having no way to drain this sitting water, and the concentrated boiler treatment remaining after most of the water vapor rose to the top elements after cool down.

Observations: I cannot say when the last time the elements were replaced or tested (last 1472 day I assume). Not aware of the supplier. The boiler still had a couple of years before the next 1472 day inspection was due. There was very little wear on the return ends, the tube OD themselves, or the bands. The wall thickness for the most part was still acceptable, except in the areas around the pits. These pitted areas were funnel like and very random in placement other than mostly in the lowest part of the tube.

After actions: After the 3rd element failed over the course of 2 months, it was decided to take the locomotive out of service not knowing when the next superheater element would fail (as well as other items of concern). Circa fall of 2012

My additions: Internal corrsion is an issue. Perhaps because of the removal of some key, costly, elements from the alloy by the manufacturer that were included in older alloys may be the cause. I do notice that copper is rarely found in newer chemical analysis of boiler tube steels.

Textbook oxygen cell corrosion due to improper layup.

Copper was specified in some water tank steel plate by some railroads, thinking it gave better service. Not scientifically proven or widely accepted.

To read along with the 1939 'Superheat Engineering Data' linked from HathiTrust, here is a PDF of a 1947 copy of the MeLeSco "locomotive Superheaters: that may contain material of value:

https://boomerdownunder.com/wp-content/uploads/2018/09/melesco_superheaters.pdf

Note that, as in the American ('Elesco") version, the Superheater Company notes that its elements "are prepared from cold drawn weldless steel tubing of the best quality, to conform with a Specification prepared by the [Superheater] Company. This Specification will be forwarded upon request."

Sadly, as with current requests for the Superheater Company's mail-in service for superheater specification and design, obtaining a copy of this Specification is no longer as straightforward as it might have been.

Something I think hasn't been mentioned as much as it ought to be is the amount of creative metallurgy that probably went into this. There are some similarities with the B&W 'Croloys' for panel or pendant superheaters like the one Mr. Austin pictured, but there may be some interest in the stated difference (in 1942) between Elesco 600 and Elesco 600HT, the implied difference being added (and greater-cost) alloy elements to permit either a higher degree of superheat or better resistance to transient overheating conditions (which occurred much more often than likely recorded in late American large locomotive practice!). Some part of a historical analysis of superheater metallurgy should involve just how 'built to a price' the specification for a given element design was.

UP Class 4-6-6-4-4&5 had their superheaters shortened 9" as soon as they hit the property in 1943. Shortened again in 1950 by another 12".

In preservation, there’s definitely no need for the highest superheat temperature you can manage, so this is mainly an academic point.

The main problem with US steam lubrication practice and high steam temperatures is the use of atomizers to distribute the lubricant. When the oil is sprayed in fine droplets into red-hot steam, it gets “cooked” (carbonized) and loses most of its lubricating properties. The later German steam designs and IIRC the British Rail standard steam designs supplied lubricant directly to the rubbing surfaces of the valve chambers and cylinders. This allowed these engines to operate with higher steam temperatures for best efficiency and power while maintaining proper lubrication.

Now, if you get the temperature of the rubbing surfaces high enough you also destroy the lubrication, but the rubbing surface temperatures are less than the steam temps. David Wardale pushed the limits on this with his modified SAR 4-8-4 #3450 the Red Devil. He added cooling passages on the outside of the valve rubbing surfaces (which will be hotter than the cylinder rubbing surface temperatures), cooling them with saturated steam. This seems counterproductive, but it allowed very high superheat temperatures without destroying conventional lubricating oils.

Again, none of this should come up in steam preservation, but it’s interesting.

"Old" Elesco return bends were forged from two tubes. These days the return bends are cast and then welded on. Even if the material is adequate you have the variables of casting quality and attachment welding quality. This photo shows a pinhole failure due to botched weld. Welds have to have a nearly perfect root profile on the steam side to eliminate steam erosion due to globs hanging into the steam flow. Most powerplant superheater welds are 100% x-rayed to eliminate this type of failure.

One powerplant reheater replacement I was involved in, found one of the welders was using 1/16" TIG wire snips as a root gap spacer. X-rays showed welds with porcupine quills which would have caused pinholes or ended up traveling supersonic through the steam turbine nozzles.