Analysis of the plane-strain bending of an orthotropic sheet in the elastic/plastic range

The problem considered in this paper is the elastic/plastic bending of a sheet metal, exhibiting planar anisotropy, under conditions of plane strain. The material is assumed to be elastically isotropic, and yielding according to Hill's quadratic yield criterion for orthotropic rolled sheets. For a given curvature of the bent sheet beyond the elastic limit, the strain distribution is obtained in closed form when the material is ideally plastic. The determination of the moment-curvature relationship in the elastic/plastic range requires numerical integration not only for a work-hardening sheet, but also for a non-hardening sheet. The numerical results are presented in a graphical form using selected values of the parameters which define the plastic properties of the material.