How does thermal shock affect pans made of different materials? In another question, I had a little comment-discussion with TFD on the effect of shock cooling on pans. In a nutshell, I said that it is bad for the pan, and he said that especially if the pan is made of steel, it should have been at 500°C for the shocks to have consequences, not at candy cooking temperature. I think that if it happens often, even at low temperatures, the internal structure of the pan would be less even (because of microcracks, or maybe some difference in the crystalline structure of the metal), leading to hot spots.

I'd like to broaden the question a bit. I think we will all agree that big temperature shocks have bad consequences on metals (think forging). I think that smaller shocks will have some (but smaller consequences), but after TFD's comments I am not sure. Could please somebody with better knowledge about metals explain what happens in different combinations of following combinations: 


Cooling method


Immersion of the whole pan in cold water (as in, I have hot sugar syrup in it, and want to stop the heating immediately).
Pouring a small amount of cold liquid into the empty hot pan (as in deglazing). 

Pan material 


Stainless steel 
Aluminum 
Sandwiched bottom 
Coated (e. g. enamel, PTFE, ceramic) 
Copper 
Iron 

Temperature difference (our cold water is in all cases in the range 5°C (fridge) - 15°C (tap)) 


Steak/candy temperature (let's pick a range of 160°C - 200°C because of caramelisation and Leidenfrost)
Hottest stove temperature (because I want to know about the extreme case. 400°C or 500° should do, the first because that's what I am sure have had on my stove, the second because TFD mentioned it). 



Let's assume not a single shock, but regular shocks (maybe two shocks a week over the lifetime of the pan). What will be the effects? And also, is there a combination which can (but will not always result in) crack a cast iron pan immediately?
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 (&gt;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,
σT is maximal tension the material can resist,
α is the thermal expansion coefficient
E is the Young's modulus, and
ν 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)
σT: no idea:
Coefficient of thermal expansion α: 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 ν: 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).