Elasto-plastic analysis of an internally pressurized thick-walled cylinder using a strain gradient plasticity theory

An analytical solution for the stress, strain and displacement fields in an internally pressurized thick-walled cylinder of an elastic strain-hardening plastic material in the plane strain state is presented. A strain gradient plasticity theory is used to describe the constitutive behavior of the material undergoing plastic deformations, whereas the generalized Hooke’s law is invoked to represent the material response in the elastic region. The solution gives explicit expressions for the stress, strain and displacement components. The inner radius of the cylinder enters these expressions not only in non-dimensional forms but also with its own dimensional identity, unlike classical plasticity-based solutions. As a result, the current solution can capture the size (strengthening) effect at the micron scale. The classical plasticity-based solution of the same problem is shown to be a special case of the present solution. Numerical results for the maximum effective stress in the cylinder wall are also provided to illustrate applications of the newly derived solution.