How does thermal shock affect pans made of different materials?

Coated (e. g. enamel, PTFE, ceramic)

I can't answer in general, but that one's easy. Sudden thermal shock causes strain in a material by unequal expansion, either in the same material by high thermal gradients, or in interfaces between materials with different coefficients of thermal expansion. The strain in this case (two different materials) can be very high. If the material in question is not elastic (e.g. enamel + ceramic; I would think PTFE is different, but I'm not sure), then the bonds between the coating and the metal would be severely strained and it would likely crack and chip.

I can tell you from personal experience that I have actually used this to my advantage:

In the spring, I produce a small quantity of maple syrup by boiling sap in an uncoated stainless steel pan. On rare occasions, accompanied by the release of many expletives, I have let the syrup boil down too far, at which point it burns and seems to coat the bottom of the pan with a thin but hard and very resilient layer of carbon black. The trick to removing this stuff is to get some kind of stress crack started, e.g. by scrubbing w/ steel wool or a copper pad, and then what I do is I put the pan on the stove for a while to let it heat up hot (but not red hot), and then bring it over to the sink and spray cold water on the inside pan bottom where the carbon black has stuck to. After a few times, the carbon black will start to flake off and then it becomes easier to remove by a combination of abrasion and thermal shock. (The two pans I've done this on have been fine; both are stainless steel with a thick (>8mm) bottom, and I've put them through at least 30 or 40 thermal cycles of this type.)

edit re: general topic:

Wikipedia says this:

The robustness of a material to thermal shock is characterized with the thermal shock parameter:

where

• k is thermal conductivity,
• ?T is maximal tension the material can resist,
• ? is the thermal expansion coefficient
• E is the Young's modulus, and
• ? is the Poisson ratio.

Higher thermal conductivity means it's more difficult to get a large thermal gradient across the material (less prone to shock); higher thermal expansion means more strain (more prone to shock), and higher Young's modulus means more stress for a given strain (more prone to shock).

So theoretically you could compare the different materials. (exercise for the reader ;) Most likely copper would be more resilient than the other metals, because of its higher thermal conductivity and higher ductility.

Thermal conductivity k: Copper = 401, Aluminum alloys = 120-180, stainless steel = 12-45 (units = W/m*K)

?T: no idea:

Coefficient of thermal expansion ?: Copper = 17, Aluminum = 23, iron = 11.1, stainless steel = 17.3 (units = 10?6/°C)

Young's modulus E: Copper = 117, Aluminum = 69, iron/steel = around 200 (units = GPa)

Poisson's ratio ?: Copper/stainless steel/aluminum are all around 0.3-0.33, cast iron = 0.21-0.26

So stainless steel is worse than aluminum or copper (much lower thermal conductivity, higher Young's modulus).

I have never conducted scientific tests on pans, but from many years of experience I have observed this using domestic electric stove, oven, and gas hobs

Cast Iron: A good quality pan seems indestructible, low quality with flaws will crack randomly, but more often when suddenly heated or cooled. When you buy a new cast iron pan give it a few extreme thermal shocks on your domestic stove before you bother seasoning it. If it cracks send it back under warranty. I have a pan that is older than me that has been thermally shocked repeatedly including tossed into super hot fires, and shows no sign or damage. In fact it's seasoned surface is better than some PTFE pans

Coated Aluminium: (PTFE) The aluminium quickly becomes weaker and warps with thermal shock. Just using too high a heat will cause warping and the coating rapidly deteriorates as well. After a while you can use hand pressure to 'reshape' the bottom :-)

Stainless Steel: Good quality seems indestructible, this pas may warp very slightly but tend to settle back with regular use. Pans that are used for de-glazing seem to get slicker (less sticky) over time (this is good). I have a 55cm stainless steel wok that has had regular use over the last ten years, and is washed every time by dumping in cold water and scrubbing immediately after serving

Sandwiched bottom: I have never thermally shocked this type of pan intentionally, not normally used for this type of cooking. Used for low even heat

I would be surprised if a domestic stove could get to 400°C let alone 500°C. Most ovens can't go past 260°C (500°F) and that's in a closed box

Steels are generally hardened above 500°C (930°F), typically above 700°C (1300°F). This also make them brittle. The hardening processes ends with the hot metal being rapidly cooled with air, oil, or water. For high stability steel the parts may be cooled to below -75°C (-100°F)

They are them tempered from 230°C (445°F), typically 270°C (520°F). Tempering makes metal tough but not brittle. The tempering process ends with gradual cooling to room temperature

The 400°C (750°F) - 510°C (950°F) range is avoided for any length of time as this can cause embrittlement

Treated an inexpensive white ceramic coated pan like that (not knowing whether it would take that treatment, and wanting to find out), regularly cooled it under running water (first applied to the base) so i could clean and store it right after emptying. After 10-20 such treatments, anything that would stick to stainless steel would stick to the ceramic, so nonstick properties went kaputt very quickly. No visible chipping, but noticeably the coating easily stained from turmeric, caramel etc... in a way that you could hardly get it white again.

Yes thermal shock damaged nonstick ceramic coating. if the bottom is sandwich there are more chances of not only loosing nonstick but also getting micro cracking.

In the case of normal water based ptfe coating you wont observe same.