The temperature of the Lockheed SR-71 Blackbird's fuselage never exceeded 500 Celsius, which, to my knowledge, would be perfectly tolerated by stainless steel. So, why titanium?
Because the specific strength of titanium at higher temperatures is better than that of steel (both are much better than that of aluminium).
Specific strength vs. temperature is shown on the above graph, from this site. Specific strength is the strength-to-mass ratio, which is the main factor in selecting aeroplane construction material, and it can be seen that:
- Titanium alloys have the upper hand until 500 - 600 °C
- Aluminium alloys are pretty good as long as the temp does not exceed about 100 °C
- For super high temperatures, steel is the only option.
The specific strength issue is of exponential importance for skin panels loaded under compression, as stated in this answer:
With a tension loaded construction, we're only concerned with the cross sectional area: how much force does it see, in order to get to the yield strength. With a compression loaded construction however, the failure mechanism is not yield strength but buckling.
In order to prevent buckling, we need a larger cross section than what would be necessary for pure yield strength, and this cross section is a function of the elasticity modulus, not the yield strength. So now the ratio of weight over elasticity sets the dimension. For compression, aluminium has the best ratio of the three metals mentioned above.
Steel would be the least suitable material for compression loaded panels - corrugating them does increase compression loading limits, but is detrimental for drag.
Plus the last factor: price. Al and Fe alloys cost much less than Ti alloys, and are easier to work with. Therefore, the order of selection of aeroplane construction material is aluminium alloy first, titanium alloy only if really required - which it absolutely was for the SR-71.
The Bristol 188 was intended to fly for extended periods at > M=2, for researching the effects of kinetic heating. The wiki article mentions how the buckling problem for compression loaded panels was tackled:
The 12% chromium stainless steel with a honeycomb centre was used for the construction of the outer skin, to which no paint was applied. Riveting was a potential method for construction but the new arc welding technique using an argon gas shield known as puddle welding was used. There were long delays with the method, which was less than satisfactory.... North American used the same methods of argon welding of stainless steel honeycomb sheet metal for the XB-70 Valkyrie bomber.
The aeroplane was unfortunately never able to fly at M > 2 for periods long enough to study the kinetic heating effects, and the project was abandoned after some time.
The XB-70 also experienced problems with the honeycomb structure, again quoted from the wiki:
The first aircraft was found to suffer from weaknesses in the honeycomb panels, primarily due to inexperience with fabrication and quality control of this new material.5 On two occasions, honeycomb panels failed and were torn off during supersonic flight, necessitating a Mach 2.5 limit being placed on the aircraft.
The deficiencies discovered on AV-1 were almost completely solved on the second XB-70, which first flew on 17 July 1965. On 3 January 1966, XB-70 No. 2 attained a speed of Mach 3.05 while flying at 72,000 ft (22,000 m). AV-2 reached a top speed of Mach 3.08 and maintained it for 20 minutes on 12 April 1966. On 19 May 1966, AV-2 reached Mach 3.06 and flew at Mach 3 for 32 minutes, covering 2,400 mi (3,900 km) in 91 minutes of total flight.
The Valkyrie was designed and operational earlier than the SR-71, and it looks like the issues with honeycomb structures plus the development of a more pliable titanium alloy prompted Lockheed to use titanium.
But, in reality, the strongest titanium alloys are only about as strong as the strongest steel alloys. In fact, their temperature tolerance is actually worse, while Aluminium is lighter. What makes titanium special is not it’s tensile strength, weight, or high-temperature performance. It is a combination of all of these material properties that made it perfect for the SR-71.
Even Lockheed notes here that it was not only the heat but the strength and durability under those conditions that made it the optimal choice.
With anticipated temperatures on the aircraft’s leading edges exceeding 1,000 degrees Fahrenheit, dealing with the heat raised a host of seemingly insurmountable design and material challenges. Titanium alloy was the only option for the airframe —providing the strength of stainless steel, a relatively light weight, and durability at the excessive temperatures.
Titanium, however, proved to be a particularly sensitive material from which to build an airplane. The brittle alloy shattered if mishandled, which meant great frustration on the Skunk Works assembly line, and new training classes for Lockheed’s machinists. Conventional cadmium-plated steel tools, it was soon learned, embrittled the titanium on contact; so new tools were designed and fabricated—out of titanium.
Also worth noting, and mentioned here, the expansion characteristics made it ideal for actually construction the aircraft.
All metal expands when heated, it is a part of the chemical property. Titanium, unlike most metals out there, expands relatively little, making it the best option for the SR-71 Blackbird. Lockheed knew this when it designed the plane and specifically designed the aircraft to fit together better when in flight. When the plane was sitting on the ground before a flight, it was “cool” and the parts fit loosely into one another. It wouldn’t be until the plane was in flight and “heated” up that everything fit snuggly into each other. The large, “cool” surfaces on the aircraft had a corrugated texture that allowed the metal to expand as it heated up.
It's worth mentioning, as a general engineering idea, often the material choices are a matter of the best all around optimization of parameters and not a single parameter optimization. There are lots of materials that can withstand high heat, but they are not all practical for building planes.
NASA was the final operator of the Blackbird and this NASA report contains several valuable information about the SR-71. Just download and read it, it has no equation in it and it's written in a really fluent way :) I report here under some parts from the chapter about its structure.
It's worth noting that even if the main requirement driving the choice of the material was obviously the retention of good structural characteristics at high temperature, anyway what tipped the scale was at the end the ability to work with the chosen material: for the North American the scale tipped toward stainless steel when developing the XB-70 Valkyrie; just a couple of years afterwards the scale tipped toward titanium when Lockheed developed the Blackbird; and maybe in the future it will tip toward plastic as Lockheed also explored in the design phase.
Lockheed engineers faced unique challenges in designing and building the Blackbirds. Aerodynamic friction and continuous engine operation during high-speed flight subjected some parts of the airplane to temperatures as high as 1,050 °F. Average surface temperatures ranged from 462 to 622 °F. This precluded the use of aluminum as a basic structural material. The Skunk Works team turned instead to titanium, stainless steel, and other advanced alloys, as well as to high-temperature plastics. Only titanium and steel could withstand the expected operational temperatures, but steel was extremely heavy and Lockheed had little experience with lightweight stainless steel honeycomb structures. Skunk Works technicians realized aged B-120 titanium had nearly twice the strength/density ratio of stainless steel per cubic inch, but weighed approximately half as much. They also found they could manufacture titanium structures with fewer parts using conventional construction methods than were necessary with steel. High-strength composites were not available in 1960. While the Blackbirds featured an abundance of composite plastic laminates as anti-radar treatments, those substances were not used as primary structure.
Fully 93 percent of the Blackbird’s structural weight consisted of titanium alloys. Three types of titanium alloys were used in the Blackbirds. The first, designated A-A110AT, contains approximately 5 percent aluminum and 2.5 percent tin. The second, B-120VCA, contains approximately 13 percent vanadium, 11 percent chromium, and 3 percent aluminum. Finally, C-120AV contains approximately 6 percent aluminum and 4 percent vanadium. Most of the Blackbirds’ titanium skin, ranging in thickness from 0.020-inch to 0.040-inch, consisted of B-120VCA fastened to the frame by riveting or spot-welding.
Large sections of the leading and trailing edges, vertical stabilizers, chines, and inlet spikes were made of “plastic” laminates of phenyl silane, silicone-asbestos, and fiberglass. These materials – featured primarily on the A-12 and SR-71 families – helped reduce the aircraft’s radar signature.
Areas subject to extremely high temperatures, such as the engine nacelle exhaust ejector section incorporated two types of nickel alloys. René 41 is a nickel base metal alloyed with chromium, iron, molybdenum, cobalt, titanium, and aluminum. It can withstand temperatures up to 1,600 °F. Hastelloy-X – nickel alloyed with chromium, iron, and molybdenum – can withstand approximately 2,200 °F.
Assuming comparable steel alloy from the heat resistance point of view, titanium will be roughly 50% lighter for same structural strength. Considering this, it will become self evident why titanium was chosen over steel or nickel alloys for SR-71, or rather the A-12, the "original" Blackbird.
The Blackbirds were real gas guzzlers simply because of the drag at high speeds, so a lightweight fuselage was a must to enable large enough fuel capacity for meaningful mission radius.