Residual Stresses in Bending

If a sufficiently large bending moment is applied to an elastoplastic member, plastic zones will develop in the member.

Now, if the bending moment is reduced to zero, the stress and strain reduction can be plotted as a straight line on the stress-strain plot.

Applying the bending moment from zero to its maximum value is called the loading phase, and the decrease in the bending moment from its maximum value to zero is called the unloading phase.

During the unloading phase, the stress will not be zero at any given point and may not have the same sign as during the loading phase, resulting in a residual stress.

The stress and strain have a linear relationship during the unloading phase, and elastic flexure formulas can be applied.

The residual stresses can be calculated using the superposition principle. First, the stresses due to the bending moment during the loading phase, corresponding to the elastoplastic nature, and the stresses due to the opposite bending moment during the unloading phase, corresponding to the elastic nature, are added to get the residual stress.