Exact solutions for the elastic-plastic response of functionally graded pipe under external pressure

This study investigates the influence of material gradient on the elastoplastic response of functionally graded (FG) thick-walled pipes subjected to external pressure. Closed-form solutions are derived for radial and circumferential stresses across various stages: purely elastic, partially plastic, and post-unloading from plastic regimes. Both the elastic modulus and yield stress exhibit radial variation defined by power-law functions, while Poisson's ratio remains constant. The stress distribution within the pipe depends not only on the external pressure but also on the material gradient index and the geometric dimensions of the pipe. A method is presented to accurately determine the first yielding position in a thin-walled tube based on the material gradient index by employing Tresca's yield criterion. Plastic zones nucleate at one or both surfaces as external pressure increases. The propagation of elastoplastic interfaces and stress distributions within each zone are examined in detail. Notably, following plastic deformation and complete unloading, FG thick-walled pipes may exhibit re-emergence of plastic deformation, depending on the pre-unloading stress state and the gradient of the elastic modulus. The conclusions of this work expected to aid in the design of FG pressure vessels and improve their load-carrying capacity and safety.