THE PLASTIC YIELDING OF NOTCHED BARS DUE TO BENDING

Abstract

Extremum principles are applied to the problem of estimating loads sufficient to cause pronounced plastic yielding in notched bars. The theory is two-dimensional and an ideal plastic-rigid material is assumed. Upper bounds to the constraint factors in pure bending are obtained for deep notches with circular and wedge-shaped roots, and for shallow notches of any shape. The estimates for deep notches are calculated by means of slip-line fields constructed to satisfy all conditions in the plastic region; but since the associated stress distributions in the rigid zones are not examined, it is not known theoretically whether these are complete solutions. A simple method is presented for ascertaining whether the rate of plastic work is positive in a given slip-line field. Experiments are described in which wide bars of copper, stainless steel, and mild steel, deeply notched on one side only with a single wedge-shaped notch, were bent by pure couples applied at each end. The yield-point couples, the surface deformation, and the regions of plastic deformation (revealed by etching bent mild steel specimens) agreed closely with the theory.