Influences of Material Variations of Functionally Graded Pipe on the Bree Diagram

The present research is concerned with the elastic–plastic responses of functionally graded material (FGM) pipe, undergoing two types of loading conditions. For the first case, the FGM is subjected to sustained internal pressure combined with a cyclic bending moment whereas, in the second case, sustained internal pressure is applied simultaneously with a cyclic through-thickness temperature gradient. The properties of the studied FGM are considered to be variable through shell thickness according to a power-law function. Two different designs of the FGM pipe are adopted in the present research, where the inner surface in one case and the outer surface in the other are made from pure 1026 carbon steel. The constitutive relations are developed based on the Chaboche nonlinear kinematic hardening model, classical normality rule and von Mises yield function. The backward Euler alongside the return mapping algorithm (RMA) is employed to perform the numerical simulation. The results of the proposed integration procedure were implemented in ABAQUS using a UMAT user subroutine and validated by a comparison between experiments and finite element (FE) simulation. Various cyclic responses of the two prescribed models of FGM pipe for the two considered loading conditions are classified and brought together in one diagram known as Bree’s diagram.