Residual stresses form in rolled sheet metal

[jb68021oh]

What are the residual stresses in flat sheet metal rolled into a cylindrical shape? My specific problem is 316 stainless steel, 0.090 in. thick, rolled to a diameter of 30 inches, but I would like to know in general what internal stresses are formed from the sheet metal rolling process.

 

[Dinosaur]

A simple calculation would show that the material has to yeild to get it into the round coil. I believe the formula for the strain is simply t/D, the thickness of the sheet divided by the diameter. A quarter inch thick sheet, rolled into a 30 inch diameter coil results in a strain of 0.00833. The yeild strain of 36 ksi steel is 0.00124. So you're about 6x the yeild strain.

This causes plastic bending in the sheet, which rebounds a small amount from the bending to form an equilibrated couple in the sheet permitting it to hold its new shape. A careful analysis could produce the degree of rebound that accommodates an equilibrium stress pattern (where the sum of the moments due to the residual stress is zero). This shouldn't take more than half to an hour of study. Good Luck.