Can stainless steel replace titanium for Mach 3+ speeds?

Question

In the documentary Wings of Russia: MiG-25 and MiG-31, they mentioned both aircraft had to use special stainless steel alloys and arc welding to withstand the Mach 2.83 - 3.2 speeds.

I couldn't help but recall the space pen vs. pencil myth. Could the SR-71 (Mach 3.3) have been built using such stainless steel alloys instead of covertly importing the titanium from Russia?

The major supplier of the ore was the USSR. Working through Third World countries and bogus operations, they were able to get the rutile ore shipped to the United States to build the SR-71.

Since the SR-71 flew higher, I'd guess both had comparable EAS / dynamic pressures. The titanium used on the SR-71 was an alloy, figuring out which alloy to use and how to shape it caused many challenges.

So gained knowledge and cool factor aside, what other factors are there?

Answer 1

Both the MiG-25 and MiG-31 designs had engines that would overheat and be damaged an anything past Mach 2.83, so both planes were limited by this. Typical speeds were closer to Mach 2.5 to extend the life of the planes. The highest aerodynamic heating occurs at the leading edges. It's possible that the MiG designs used titanium in these areas but opted for steel in most other areas, which was cheaper and easier to work with. This would have allowed the aircraft to reach speeds closer to the SR-71, even if the engines couldn't keep up.

The SR-71 was designed to cruise at up to Mach 3.3 at 80000ft, a similar altitude to the MiGs. Atmospheric heating is related to the cube of the speed. Mach 3.3 generates 10% more heat than Mach 3.2, and the SR-71 reached at least Mach 3.5. It seems the SR-71 flew faster and higher than the MiGs.

Heat is only one consideration though. Another big issue is weight. Steel is generally much heavier than a comparable structure made from titanium. The SR-71 empty weight was about 40% higher than the MiG-31, but the MTOW was 70% higher. This allows much more payload for mission equipment, but also fuel. The MiGs were designed to fly relatively short range interception or reconnaissance missions, having unrefueled ranges of 2000km or less. The MiG-31 could fly 3000km but only with drop tanks. The SR-71 was designed as a long range reconnaissance aircraft, and had a range of 5400km which enabled it to fly long missions over enemy territory.

Another consideration is size. The SR-71 was a larger plane than either the MiG-25 or MiG-31. It had a wingspan of 17m, compared to 14m of the MiGs, and a length of 33m, compared to 20m and 23m for the MiGs. This means higher forces on the aircraft structure.

Answer 2

Let's note some properties of steel and titanium. For steel, we choose 4340 alloy (oil-quenched and tempered); for titanium, we use the Ti-6Al-4V alloy (solution heat-treated and aged). These are not the 'default treatments' for either material, but put them both in a good light. Note that for titanium, the difference between low-grade and high-grade is not quite as significant as it is for steel.

                     | Steel  Titanium
------------------------------------------
Density:             | 7.85   4.43   g/cm3
E-modulus:           | 200    119    GPa
Yield strength:      | 1520   1103   Mpa
Thermal expansion:   | 12.3   8.6    10^-6 K^-1
Thermal conductivity | 44.5   6.7    W/mK
Cost                 | 3.60+  66-154 USD/kg

^{Data taken from Callister & Rethwisch, "Material Science and Engineering", 2011, and matweb.}

First, it is immediately clear why one would consider replacing titanium; it's mindbogglingly expensive. But is the alternative any good?

Let's look at what stresses heating could induce. We consider for simplicity a uniform rod clamped at both ends, heated up by a temperature difference $\Delta T$. The stress resulting from this temperature differential $\sigma = E\alpha_l\Delta T$ with $\alpha_l$ the thermal expansion coefficient. We rewrite for maximum allowable $\Delta T$ by equating $\sigma$ to the yield strength, $\sigma_y$. $$\Delta T_{max}=\max{\dfrac{\sigma_y}{E\alpha_l}}$$

Thanks to the low thermal expansion, Titanium is a clear winner here, with almost twice the maximum allowable temperature difference, at 1078 kelvin difference versus 618. Note however that steel does have a significantly higher thermal conductivity, so it may be able to transport heat away more efficiently (at the cost of things becoming hot where you don't want this...).

Of course, for various other parts, different guidelines exist; in simple tension loading, we could want to maximize ${\sigma_y}/{\rho}$ with $\rho$ the density (titanium is ~25% better than steel); in compression we could want ${\sqrt{E}}/{\rho}$ if we consider buckling (titanium ~35% better than steel). The key point here however is that none of them make a good match towards titanium, especially if we consider steel that is simply annealed or rolled rather than having special treatments. This is mostly due to its low density. Since making a plane fly at Mach 3 is quite an engineering challenge, the price-tag of the materials may be a lesser issue, and just making a feasible design given any material is quite the challenge.

The bottom line however is that everything is impossible until someone makes it, but until there is a very good incentive to make a supersonic aircraft from steel, it's not going to happen.

Answer 3

There has been a supersonic aircraft made from steel, the XB-70 Valkyrie, up there with the SR-71 in the exclusive club of awesomest planes. It was made of stainless steel/honeycomb (with a bit of titanium structure thrown in).

Take the strongest steel, strongest aluminium and strongest titanium and compare their strength-to-weight ratio. You will find that steel is 3 times heavier than aluminium, but also 3 times stronger: they have the same strength-to-weight ratio, which turns out to be the same ratio for titanium as well. Titanium is the most difficult to make into any desired shape at all, while stainless steel is a well known, benign pet: easy to weld, no fatigue problems if stresses are kept below the fatigue level etc.

So with equal strength-to-weight ratio's, you could make a steel structure that is as light as an aluminium one. That is, if the structure is loaded in tension, like a pressure vessel - which is what the fuselage actually is. With a metal sheet loaded in compression (the upper skin of a wing for instance) the sheet buckles before it reaches the yield strength: only thicker sheets help there, not stronger sheets. That is why aluminium wins when making the average holiday jet aircraft.

More info at this excellent answer from Peter Kämpf.