Implementation of Precipitation and Ripening of Second-Phase Particles in the Constitutive Modelling of Creep

Abstract

Recent developments in constitutive modeling make it possible to directly incorporate microstructural features of a material in the constitutive equations describing its mechanical behavior. For a precipitation hardened material, the most relevant microstructural characteristic is the average particle spacing in the dislocation glide plane. A model describing the effect of this parameter on the strain hardening and creep behavior proved to have a good predictive capability for the case when the particle arrangement does not change during the deformation. This becomes particularly important for high-temperature deformation when an interplay between second-phase precipitation and particle ripening may produce a complex time dependence of the particle strengthening effect. A reliable description of the deformation behavior then requires the use of a constitutive model in which the kinetics of the particle evolution is accounted for. Such an attempt can be based on the model developed by Mecking and Estrin, in which the dislocation density is treated as a single internal variable. The formulation contains the distance of free dislocation glide, which is affected by the presence of second-phase particles. The new feature is that a variable second-phase particle spacing is now considered. The two concurrent processes, viz. precipitation and ripening of particles, aremore » described in a unified way in that the time dependence of the average particle spacing is presented in an analytical form. Schwarze et al. tried to apply this concept modeling the mechanical behavior of INCOLOY alloy 800H, a carbide precipitation strengthened high temperature alloy. For the present paper the model was developed more rigorously and simplifying assumptions, which may be allowed at lower temperatures, are avoided.« less