(1)

where X is fraction recrystallized at time t and n is a constant. The recrystallization kinetics expressed as the time to reach a certain level of recrystallization depends on chemical composition, applied strain , strain rate , initial grain size D₀, and temperature T. According to Sellars [1979Sel], the time for 50% RX can be estimated by,

(2)

where p is an exponent, f(ζ_i ) a function of a parameter set ζ_i which often include strain rate, initial grain size and temperature. Z is the Zener-Hollomon parameter and is defined as

(3)

with is the strain rate, R is the gas constant and Q_d a deformation activation energy that is a material parameter. Then the recrystallized grain size D_RX can be estimated from a relation in the form,

(4)

here q is an exponent and f(ζ_j) a function of a parameter set ζ_j which often include the initial average grain size and the accumulated plastic strain. These parameters are defined in KDB file and can be adjusted based on the experimental data.

Thus, the average size of all grain D can be written as,

(5)

where D₀ and D_RX are initial and recrystallize grain sizes, respectively. X is recrystallized volume fraction.