Constitutive Model for Coupled Inelasticity and Damage

A constitutive model to describe a coupling between deformation and damage due to creep of polycrystalline metallic materials is developed from phenomenological and continuum mechanics points of view. The constitutive modeling is based on the irreversible thermodynamics for internal state variable theories, where the thermodynamic potentials, i.e., free energy and dissipation energy functions, are defined using hardening and damage variables. The material damage is assumed to be isotropic. We first derive a damage coupled kinematic-hardening model in the invariant form on the basis of the Malinin-Khadjinsky model. Then, an isotropic-hardening model which includes a coupling with damage is formulated by assuming a particular representation of the kinematic hardening variable. The evolution equation of the hardening variable is prescribed by the Bailey-Orowan format which includes the effect of damage. The damage rate is governed by the magnitude of the assumed strain hardening variable. These models can describe a transition from primary to tertiary creep stages, and it is applicable to variable loading conditions. In a particular case the expression for the creep rupture time has a similar form to the Kachanov-Rabotnov type, although it depends on the time and damage at the instant of a hardening saturation under the applied stress condition.