I have a doubt on the concept of elastic shakedown. The concept is explained in books as below :
If the stress due to temperature is raised from initial value (say room temp) to a value SIG1, which is above the yield stress, SIGY, then a plastic strain of e1 corresponding to SIG1 will be produced. On coming back to zero strain condition the piping will have a residual compressive stress of SIG1 - SIGY.
If SIG1 is less than 2SIGY, then there will be elastic behaviour in subsequent cycles so long as the maximum stress value is less than 2SIGY.

The doubt is as follows :
Suppose a piping system at room temperature is heated to a temperature where the stress is SIG1 < 2SIGY. On cooling back to room temperature i.e. shutdown statethe residual strain will not be zero but e1-ey. As a result if you apply a stress 2SIGY, won't this result in further plastic deformation AND NOT ELASTIC BEHAVIOUR ?

Please explain

TIA

regards
R2D2

Your e1-ey equates to a residual stress less than or equal to -SIGY. Adding 2SIGY to -SIGY you have a maximum of +SIGY. On subsequent cycles the pipe will alternate between +SIGY and -SIGY, thus the limit of 2SIGY for the total stress range.

Dear Mr Brown
Thank you for the response.

rd2d