When a fast-breeder reactor is shut down quickly, the temperature of the surface of a number of components drops from 600°C to 400°C in less than a second. These components are made of a stainless steel and have a thick section the bulk of which remains at the higher temperature for several seconds. The low-cycle fatigue life of the steel is described by:
Nr1/2Δεpl = 0.2
where Nr is the number of cycles to failure and Δεpl the plastic strain range. Estimate the number of fast shut-downs the reactor can sustain before serious cracking or failure will occur. [Hint: The thermal expansion coefficient of stainless steel is 1.2 x 10-5 / K; the yield strain at 400°C is 0.4 x 10-3].