The plane-strain general yielding of notched members due to combined axial force and bending—II: Deep circular notches

The slip-line fields proposed by Green for the plane-strain general yielding of notched plates in pure bending are generalized to provide solutions for notched plates subjected to combined axial force and bending. Deep symmetrical circular notches and single circular notches are considered. For notched plates subjected to arbitrary combinations of axial force and bending, two constraint factors are obtained, T₁ due to the axial force and M₁ due to the bending moment. These constraint factors are shown to have characteristic relationships on the T₁−M₁ plane for the single notched plate and the symmetrically notched plate. The derivations of these general yielding loci are described in detail and the statical and kinematical limitations of the slip-line fields are discussed. Finally it is demonstrated that the corresponding strain-rate vectors are normal to these loci and that, therefore, these loci can be regarded as plastic potentials.