A Micromechanical Theory of High Temperature Creep

Based on the mechanism of dislocation climb-plus-glide, a micromechanical theory is developed for the high-temperature creep of polycrystals. This model assumes that dislocation climb is responsible for the release of dislocations and whose subsequent glide provides the only significant contribution to the overall creep strain. Taking into consideration the forces acting on both dislocation climb and dislocation glide, a microconstitutive equation is introduced to describe the transient and steady-state creep of slip systems. Together with the self-consistent relation, the creep property of a polycrystal is determined by an averaging process over the behavior of its constituent grains. The developed micromechanical theory is then applied to model the creep behavior of lead at 0.56 Tm, under both tension and shear. Based on these micromechanical analyses, a macroscopic multiaxial theory—involving an effective normal stress to reflect the climb force on the microscale as well as the usual effective shear stress—is also developed. It is found that the effective normal stress, which is independent of the hydrostatic pressure, depends primarily on the second invariant of the deviatoric stress, and only weakly so on the third invariant. Thus despite the distinct presence of two types of microstress, the constitutive equations on the macroscale can still be reasonably described by the second invariant alone even at high temperature.