A SELF-CONSISTENT RELATION FOR THE TIME-DEPENDENT CREEP OF POLYCRYSTALS

A self-consistent relation with a weakening constraint power in the matrix is derived for the primary and steady-state creep of polycrystals. This derivation makes use of a linear viscoelastic comparison material, under which the constraint power of the creeping matrix is found to decrease exponentially with the ratio of the elastic shear modulus to the secant creep modulus, or when expressed alternately, with the ratio of the creep strain to the elastic strain. Such a dramatic decrease leads one to believe that the overall creep strain of the polycrystal as calculated by the traditional elastic-constraint model could be far too low; a direct comparison between the two, however, quickly reveals that the accuracy of the elastic-constraint model is better than what is initially thought, and certainly far better than in the rate-independent plasticity. With this new relation, the creep heterogeneity among the constituent grains are then studied in details. It is demonstrated that while the creep strains of the more favorably oriented grains tend to increase, and those of the less favorably oriented ones decrease, their creep rates become virtually uniform during the long-term, steady-state creep. This suggests that grain compatibility, instead of stress equilibrium, is the more dominant factor governing the grain-boundary condition during the steady-state process.