Proportional loading of thick-walled cylinders

A generalized solution for small plastic deformation of thick-walled cylinders subjected to internal pressure and proportional axial loading is developed. The solution has been shown to reduce to the well-known Lamé's elastic solution and Nadai's general plane strain solution under appropriate assumptions. The influence of proportionality factor (ratio of axial strain to hoop strain) and hardening exponent on the induced strain, deformation fields and thickness reduction is systematically investigated. The formulation yields a singularity when the axial strain to hoop strain ratio is equal to '−2'. Based on the employed material parameters, power law constitutive model and proportionality factor, the maximum effective stress may occur at either the inside or outside of a tube shell. An equation to estimate ultimate internal pressure based on proportionality factor, material properties and tube geometry was derived. It is shown that maximum thickening occurs when the proportionality factor approaches '−2'.