Constitutive Model for Coupled Inelasticity and Damage.

Abstract

Constitutive models to describe a coupling between deformation and damage due to creep of polycrystalline metallic materials are discussed 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. First, a new damage-coupled kinematic-hardening model is developed in the invariant form on the basis of the Malinin-Khadjinsky model. The evolution equation of the hardening variable is prescribed by the Bailey-Orowan format which includes the effects of isotropic damage. Then, an isotropic-hardening model taking damage into consideration is formulated by assuming a particular representation of the kinematic hardening variable. The evolution equation of the isotropic creep damage is analogous to that developed by Kachanov and Rabotnov. However, it takes into account a coupling with creep hardening and softening. The present models can describe primary, secondary and tertiary creep behavior, and they are applicable to variable loading conditions. The creep rupture time predicted, even in the simplest case, depends on the time and degree of damage at which the hardening variable reaches its saturation state under the applied stress conditions.