On the development of shear bands in pure bending

Abstract

The development of shear bands in a plate subject to pure bending is analyzed numerically. For a plate with an initial periodic imperfection, the course of shear band development is determined for three material models; an elastic-plastic solid with a rather sharp vertex on its yield surface, an elastic-plastic solid with a more blunt vertex on its yield surface and a nonlinear elastic solid. The uniaxial stress-strain behavior of these material models is taken to be identical. In each case, the initial imperfection leads to the development of surface undulations on both the compressive and tensile sides of the plate and, subsequently, shear bands initiate at points of strain concentration induced by these surface undulations. The course of shear band development is found to depend on the constitutive law employed to characterize the material behavior. For the elastic-plastic solid with the sharper vertex, the effect of additional longer wavelength imperfections is considered. These additional long wavelength imperfections enhance the process of shear band development by focussing the deformation into one or a few shear bands. In pure bending, the shear bands must propagate into the plate against an adverse deformation gradient so that the peak straining within the bands always occurs at the free surface and the shear bands end inside the plate.