A two-site mean field model of discontinuous dynamic recrystallization

A mean field model of dynamic and post-dynamic recrystallization predicting kinetics, grain size and flow stress

“…The general equations describing the key physical phenomena occurring during recrystallization are presented from Sections 2.2-2.4, covering the evolution of dislocation density, grain boundary migration and nucleation. Except the static recovery equation, these equations were used in our dynamic recrystallization model [33], the interested reader is referred to the original publication for more details. A more general expression of the critical dislocation for dynamic recrystallization is proposed in Section 2.5, still taking into account of the effect of dynamic recovery.…”

“…The framework is based on a mean field approach [33], where each representative grain G i , defined by two state variables (the grain diameter D i and the grain average dislocation density q i ), is immersed in two HEMs (see Fig. 1).…”

“…Therefore, in some cases it may not be an accurate approximation for q DRX cr . Dynamic recovery was taken into account to calculate the critical dislocation density in (11) (see [33]), however, it was assumed that K 2 q DRX cr =K 1 was much smaller than 1. In the conditions used in [32], the approximation was appropriate.…”

“…The value for these parameters can be identified through purely numerical methods [33]. This approach yields multiple solutions in the form of Pareto optimal sets.…”

“…The framework of this model is based on a DDRX model [33] published by the current authors where the data structure is represented by a set of representative grains characterized by two state variables: grain size and dislocation density. Each representative grain is surrounded by two homogeneous equivalent media with high and low dislocation densities representing the average of recrystallized and non-recrystallized grains, respectively.…”