Influence of continuum damage mechanics on the Bree’s diagram of a closed end tube

This paper extends the Bree’s cylinder behaviors, which is subjected to the constant internal pressure and cyclic temperature gradient loadings, with considering continuum damage mechanics coupled with nonlinear kinematic hardening model. The Bree’s biaxial stress model is modified using the unified damage and the Armstrong–Frederick nonlinear kinematic hardening models. With the help of the return mapping algorithm, the incremental plastic strain in axial and tangential directions is obtained. Continuum damage mechanics approach can be used to extend the Bree’s diagram to the damaging structures and reduce the plastic shakedown domain. Kinematic hardening behavior was considered in the material model which shifts the ratcheting zone. The role of the material constants in the Bree’s diagram is also discussed.