Modelling the Deformation and Annealing Processes: Physical and Regression Approaches
The flow stress behaviour of ferrite under abruptly reduced strain rate has been modelled by employing the relatively simple approach of the Bergström’s model for plastic deformation of metals. This physical model considers the rate of change of dislocation density as a difference of the rate of dislocation immobilisation and remobilization, estimated as a function of a recovery parameter. The concept of average rest time of immobilized dislocations prior to remobilization has been suitably employed to estimate the transient times and the enhancement of recovery rates after the strain rate change. The transient friction stress was estimated by using equations given in the literature and some mathematical factors concerning the estimated dislocation densities and the net rates of dislocation immobilization at the high and low strain rates. The present authors have also developed a new unique regression model that is able to predict the static recrystallisation kinetics of most of the common carbon steel grades (including microalloyed steels). A linear regression equation was established to predict the activation energy of static recrystallisation for hot-worked austenite as sum effects of potent solute elements. Further, the power of grain size in the equation was found to be a strong grain-size dependent variable. The model was later validated for several special steel grades, as well as including the consideration for an upper limit for Nb and Si in retarding recrystallisation.
P. B. Prangnell and P. S. Bate
M. C. Somani and L. P. Karjalainen, "Modelling the Deformation and Annealing Processes: Physical and Regression Approaches", Materials Science Forum, Vol. 550, pp. 583-588, 2007