Strain gradient plasticity solution for an internally pressurized thick-walled spherical shell of an elastic linear-hardening material

An elastic-plastic analytical solution is derived for an internally pressurized thick-walled spherical shell of an elastic linear-hardening material using a strain gradient plasticity theory. Closed-form expressions are obtained for the stress, strain and displacement components. The inner radius of the shell enters the solution with its own dimensional identity as well as in non-dimensional forms, unlike that in classical plasticity-based solutions. As a result, the current solution can capture the size 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. To further illustrate the capability of the newly derived solution, formulas and numerical results for the plastic limit pressure are provided. These results reveal that the load-carrying capacity of the shell indeed increases with decreasing inner radius at the micron scale. The current solution can be employed to construct improved expanding cavity models in indentation mechanics that incorporate both the strain-hardening and indentation size effects.