Bending of an Ideal Plastic Metal

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Abstract
The stresses and strains in plastically bent parts have been analyzed for the two limiting conditions of (a) a very wide plate (plane strain), and (b) a very narrow bar (plane stress). The complete solution is presented for a hypothetical metal with no strain-hardening, and the method is described for treating any actual metal. The solution was obtained by a method of successive approximations, each approximation employing various graphical processes. The gradual change in cross-sectional contour with progressive bending was obtained by considering small successive intervals of increasing curvature. The final solution shows the movement of the neutral axis toward the compression surface, the decrease in the radial dimension of the part, and the gradual divergence between the tangential strains at the inside and outside surfaces. The solutions for plane stress and plane strain were nearly identical as regards the tangential strains and the changes in the radial dimension. Experimental measurements of surface strains and cross-sectional contour of bends conformed well with the results of the calculations.

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