Shakedown-ratcheting analysis of Bree's problem by anisotropic continuum damage mechanics coupled with nonlinear kinematic hardening model

Abstract

In the present research, Bree's diagram, which has been used for ratcheting assessment of pressurized equipment in ASME III NH, has been developed when the pressure vessel contains discontinuities such as voids and microcracks. Nature of these defects leads to an anisotropic damage. Anisotropic Continuum Damage Mechanics (CDM) is considered to account effects of these discontinuities on the behavior of the structure. Shakedown – ratcheting response of a hollow sphere under constant internal pressure and cyclic thermal loadings is studied by using anisotropic CDM theory coupled with nonlinear kinematic hardening of Chaboche. Return mapping method is used to solve numerically the developed relations. Elastic, elastic shakedown, plastic shakedown and ratcheting regions are illustrated in the modified Bree's diagram. Influence of anisotropic damage due to the plastic deformation, is studied and it was shown that the plastic shakedown region is diminished because of the developed damage.