In internal pressure design of piping, Y is the correction factor for temperature. So, it is not simple just considering the failure criterion based on elastic stress behavior on the cylindrical shell due to internal pressure.
The following is the another story regarding the establishment how Y is determined.
For thick wall cylindrical shell,
Shoop,average=P(D/2t − 1)
Sradial,average=-0.5P
The maximum shear stress failure criterion, Tresca's is as follows:
Saverage=Shoop,average-Sradial,average=P(D/2t − 0.5P)
In 1943, a factor of 0.4 was recommended in place of 0.5 in the stress formula [Boardman].
Resulting from burst test data available, ASME task group judged that the choice of Y being 0.4 while adequate for temperatures up to 900°F. However, it would result in excessively thick pipe for service above 900°F.
This would in turn lead to unnecessarily heavy and costly pipe, less flexibility to absorb thermal expansion and also larger through-wall thermal gradients. To avoid these difficulties, and based on burst test results, it was decided that between 900°F and 1150°F the 0.4 factor is gradually increased to 0.7.
This was the origin of the Y factor in today’s ASME B31.1 and ASME B31.3 pressure design equations.
Bend Burst by Overpressure
Chapter IX High Pressure Piping