Propagation Failure is a term used to describe a type of failure in many various forms of engineering. From what I gathered while listening in on the class (that is way above me and in a field of study I know virtually nothing about), this type of failure is one of the worst kinds of structural failure possible. What happens is there are two sides of a metal sheet, say in a nuclear reactor, like so :
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A |<---L--->| B
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Side A is the outside of the sheet and Side B is the inside of the sheet, that is of any length (width?), L, that is within reason for a metal sheet. The sheet is heated to a temperature T, usually for demonstration purposes this temperature is at least 600 degrees (Celsius, presumably, but the professor never said one way or the other, and it's not like 600 degrees Fahrenheit is cold). The heat of the sheet is caused by immense temperature from inside it, from side B. Side A is surrounded by air, which is greatly heated because of heat transfer.
Propagation Failure occurs when side A is subjected to immediate and immense cooling, a tank of water for example, and the lack of elasticity by the metal sheet, and the still immense heat of both the sheet and side B result in a stress fracture being created horizontally along length L in the sheet.
This fracture can be microscopic in size at first, but it can grow. there have been ships in artic waters that have been split in half and sunk because of Propagating Failure. Logically, it is also a problem with airplanes and large buildings in colder climates, or anything with rapid cooling.