Enlargement of a circular hole in a disc of plastically compressible material

A semi-analytic solution for the elastic/plastic distribution stress and strain in a thin annular disc subject to pressure over its inner radius is presented. It is assumed that a pressure-dependent yield criterion and its associated flow rule are valid in the plastic zone. Thus, the material is plastically compressible, which is a distinguished feature of the solution. Also, in contrast to most studies on elastic/plastic deformation of thin plates and discs under plane stress conditions, the flow theory of plasticity is adopted in conjunction with a smooth yield surface. Numerical methods are only necessary to evaluate ordinary integrals and to solve simple transcendental equations. It is shown that the stress path is not proportional and, therefore, the application of deformation theories of plasticity widely used to calculate the distribution of stresses and strains in thin plates and discs is not justified.