Understanding Dynamic Recrystallization Behavior through a Delay Differential Equation Approach

Jong K. Lee

doi:10.4028/www.scientific.net/MSF.558-559.441

Paper Titles

Application of FIB-EBSD Tomography for Understanding Annealing Phenomena in a Cold Rolled Particle-Containing Nickel Alloy
p.413

Recrystallization Behaviour of Cold Rolled Low Carbon Steel Strip with Various Starting Microstructures
p.419

Effect of Niobium Addition on the Texture Formation of High Strength Cold-Rolled Low Carbon Steel Sheets
p.425

Grain Size in Mg Alloys: Recrystallization and Mechanical Consequences
p.433

Understanding Dynamic Recrystallization Behavior through a Delay Differential Equation Approach
p.441

Dynamic Recrystallization in Copper and Copper-Tin Alloys
p.449

Nucleation of Dynamic Recrystallization at the Grain Boundaries of Copper Bicrystals
p.457

Atomistic Processes of Phase Transformation and Dynamic Recrystallization during Hot-Working of Intermetallic Titanium Aluminides
p.465

Formation of Ultrafine Ferrite Grains during Interrupted Multi-Pass Deformation under Hot Torsion
p.471

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Understanding Dynamic Recrystallization Behavior through a Delay Differential Equation Approach

Abstract:

During hot working, deformation of metals such as copper or austenitic steels involves features of both diffusional flow and dislocation motion. As such, the true stress-true strain relationship depends on the strain rate. At low strain rates (or high temperatures), the stress-strain curve displays an oscillatory behavior with multiple peaks. As the strain rate increases (or as the temperature is reduced), the number of peaks on the stress-strain curve decreases, and at high strain rates, the stress rises to a single peak before settling at a steady-state value. It is understood that dynamic recovery is responsible for the stress-strain behavior with zero or a single peak, whereas dynamic recrystallization causes the oscillatory nature. In the past, most predictive models are based on either modified Johnson-Mehl-Avrami kinetic equations or probabilistic approaches. In this work, a delay differential equation is utilized for modeling such a stress-strain behavior. The approach takes into account for a delay time due to diffusion, which is expressed as the critical strain for nucleation for recrystallization. The solution shows that the oscillatory nature depends on the ratio of the critical strain for nucleation to the critical strain for completion for recrystallization. As the strain ratio increases, the stress-strain curve changes from a monotonic rise to a single peak, then to a multiple peak behavior. The model also predicts transient flow curves resulting from strain rate changes.