Non-proportional stress and stress-strain controlled paths cyclic loading modeling by using anisotropic continuum damage model

Abstract

In this study, the effect of developed anisotropic damage on the ratcheting is studied. Damage occurs during extra loading in an anisotropic manner. A modified anisotropic continuum damage model of Murakami is developed in this paper and combined with nonlinear kinematic hardening model of Chaboche. The constitutive relations for anisotropic damage of elastoplastic materials are developed based on irreversible thermodynamics. 2nd rank symmetric damage tensor, the kinematic hardening tensor and tensor of damage potential surface movement are specified according to the internal state manifold which is consistent to the thermodynamic state of solids. The symmetrization of effective stress tensor is carried out by the proposed method of Cordebois and Sidoroff (1982). The proposed yield surface distortion model consists of equivalent effective stress and it distorts in the stress space by evolution of damage parameter. Thus, the induced anisotropy is due to plastic deformation and damage evolution. Combination of the nonlinear kinematic hardening model of Chaboche and the model of anisotropic continuum damage is applied to cyclic loading modeling and the ratcheting strains are predicted under various loading paths.