A new anisotropic continuum damage model was presented on the basis of irreversible thermodynamics. Second rank symmetric damage tensor, kinematic hardening tensor, and damage potential surface were introduced. The yield surface in this study has been modeled to distort in the stress space by the evolution of the damage tensor. The new model was applied in yield surface characterization and led to a well description of the subsequent yield surfaces. This model is then applied to predict experimental results of the cyclic nonproportional loading paths obtained by Kang et al. [2004], Hassan et al. [2002] and Taleb and Cailletaud [2011]. It is demonstrated that the new model can predict the yield surface distortion and the ratcheting strains of multiaxial nonproportional cyclic loading with acceptable accuracy and by using less material constants with respect to the previous models.
In cyclic loading and when plastic flow occurs, discontinuities grow. In this research, interaction diagram of Bree has been developed when the spherical pressure vessel contains discontinuities such as voids and microcracks. Bree’s diagram is used for ratcheting assessment of pressurized equipment in ASME III NH. 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 are studied by using anisotropic CDM theory coupled with nonlinear kinematic hardening of Armstrong-Frederick m’s model (A-F). 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.
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