Quantification of multi-stage recrystallization in low-alloy steel under varying deformation conditions using inhomogeneous-dislocation-density 3D cellular automaton

In the thermoforming process, alloys experience severe plastic deformation under varying temperatures and strain rates, complicating dynamic recrystallization (DRX) behavior. Current DRX models developed under constant deformation conditions have limited accuracy in predicting complex stress and microstructure evolutions. This work develops a 3D cellular automaton (CA) model to precisely predict the DRX microstructure and flow stress of low-alloy steel under varying deformation conditions. The model incorporates dislocation density gradients and grain-boundary sliding to quantify dislocation density evolutions in matrix and multi-stage recrystallization grains during hot compression. Parameter variables related to dislocation accumulation and annihilation are derived from a new phenomenological constitutive model, in which the variation of the time for 50% DRX fraction and the residual softening induced by the first-stage recrystallization are considered. CA simulation results illustrate that the stress softening following peak stress after transiently increasing the Zener-Hollomon parameter $Z_P$$Z_P$ is attributed to the refinement of matrix and first-stage DRX grains (DRXGs_I) resulting from dislocation differences. DRXGs_I cannot be fully refined due to delayed nucleation of second-stage DRX grains (DRXGs_II), resulting in a greater final grain size. After decreasing $Z_P$$Z_P$, even if the DRX fraction increases to levels under constant conditions, some matrix still exhibits higher dislocation density due to an inhomogeneous-dislocation-density distribution. This accelerates DRXGs_I growth to a size similar to that under the constant condition, producing a stress-decreasing rate that closely matches experimental findings. The proposed simulation framework not only contributes to visualizing multi-stage recrystallization but also aids in quantitative microstructure control during hot forging.