How to estimate those internal stresses after cold-work bending?

[designsimply]

One of my clients asked for some estimation on internal stresses/residual stresses after bending a 3/4" dia. mild steel rod at 165 degree. I think there should be a minor internal tensile and compression stresses at each side respectively after bending. However, does anyone know a simple formula to estimate them? My client likes to know them quantitatively. Thanks.

 

[JStephen]

I've worked this out in times past for plate bending and I assume you could do the same for bending of a round rod. But I didn't get a simple formula out of it.

The way I worked that, I first assumed that the stress-strain curve was two straight lines, uniform modulus up to the yield stress, then uniform yield stress beyond that point. For a given angular deflection in the rod, you can then calculate the amount of permanent deformation induced. Use the permanent deformation to recalculate internal stresses as the rod deflection is reduced, and find the point at which the internal moment is zero. This probably sounds more complicated than the idea really is. In my case, seems like I wound up with residual stresses of around 7,000 or 8,000 psi with bending 36,000 psi yield plate.