Constitutive Modeling of Creep and Damage Behaviors of the Non-Mises Type for a Class of Polycrystalline Metals

Phenomenological constitutive models to describe the creep and damage behaviors that deviate from the von Mises type for a class of polycrystalline materials are developed. Theoretical and empirical approaches are taken to the formulation. The effective stresses that govern the rates of creep and damage are scaled to describe any deviation from the response of the von Mises type. A general form of scaling parameter is proposed which can consider the hydrostatic stress and/or the third invariant of the stress deviator. A kinematic hardening model is first formulated on the basis of irreversible thermodynamics using the scaling parameters for creep and damage. Then, two kinds of empirical basis models are presented for cases of kinematic hardening and isotropic hardening, respectively. The proposed models can describe the primary, secondary and tertiary creep behaviors and distinguish between the creep and damage behaviors under different modes of loading. To illustrate the features of the proposed models, numerical simulations of the unequal creep behaviors under tension, compression, and torsion are carried out and compared with experimental results.