Stochastic model describing evolution of microstructural parameters during hot rolling of steel plates and strips

Abstract

Enhancing strength-ductility synergy of materials has been for decades an objective of research on structural metallic materials. It has been shown by many researchers that significant improvement of this synergy can be obtained by tailoring heterogeneous multiphase microstructures. Since large gradients of properties in these microstructures cause a decrease of the local fracture resistance, the objective of research is to obtain smoother gradients of properties by control of the manufacturing process. Advanced material models are needed to design such microstructures with smooth gradients. These models should supply information about distributions of various microstructural features, instead of their average values. Models based on stochastic internal variables meet this requirement. Our objective was to account for the random character of the recrystallization and to transfer this randomness into equations describing the evolution of dislocations and grain size during hot deformation and during interpass times. The idea of this stochastic model is described in the paper. Experiments composed of uniaxial compression tests were performed to supply data for the identification and verification of the model in the hot deformation and static recrystallization parts. Histograms of the grain size were measured after hot deformation and at different times after the end of deformation. Identification and validation of the model were performed. The validated model, which predicts evolution of heterogeneous multiphase microstructure, is the main output of our work. The model was implemented in the finite element program for hot rolling of plates and sheets and simulations of these processes were performed. The model’s capability to compare and evaluate various rolling strategies are demonstrated in the paper.

Through process stochastic model of hot strip rolling

“…3 variable γ represents a mobile fraction of the recrystallized grain boundary and depends on the distribution of ξ(ti-1) in previous step, as it is explained in [6]. In the work [7] the model was further extended by including interpass times and static phenomena into simulations. Several trajectories of Eq.…”

“…Our objective was to account for the random character of the recrystallization which occurs during deformation and after deformation at elevated temperatures and to transfer this randomness to equations describing evolution of the dislocation populations and the grain size. The idea of the model is presented in [6] and its identification for hot deformation processes is described in [2,7]. Since the model incorporates stochastic character of the phenomena, it may predict the distribution of parameters instead of their average values.…”

Conditional Optimization of Algorithms for Estimating Distributions of Solutions to Stochastic Differential Equations

“…As such an estimate, the histogram is usually considered [11][12][13][14][15], which is a statistical analogue for the probability density of the SDE solution. Note that histograms are used not only when solving SDEs but also when analyzing various data [16][17][18]. However, this article studies estimating distributions in the context of SDEs.…”

A Comparative Study of Deterministic and Stochastic Models of Microstructure Evolution during Multi-Step Hot Deformation of Steels

“…This model was identified based on the experimental data [31]. In publication [36], the model was utilized to conduct simulations of multi-step hot forming processes.…”