Formulation, identification and validation of a stochastic internal variables model describing the evolution of metallic materials microstructure during hot forming

Szeliga, Danuta; Czyżewska, Natalia; Klimczak, Konrad; Kusiak, J.; Kuziak, R.; Morkisz, Paweł; Oprocha, Piotr; Pidvysotskyy, V.; Pietrzyk, M.; Przybyłowicz, Paweł

doi:10.1007/s12289-022-01701-8

Cited by 5 publications

(9 citation statements)

References 28 publications

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“…Details of the identification procedure are described in [2,6]. Inverse algorithm developed in [11] was applied.…”

Section: Fig 1 Selected Results Of a Comparison Of Measured And Calcu...mentioning

confidence: 99%

“…Advanced numerical models are needed to gain knowledge on the local heterogeneities of the microstructural features and resulting properties. As it was shown in [2] internal variable stochastic models, which can predict heterogeneity of the microstructure, would be a support for the design of multiphase materials.…”

Section: Introductionmentioning

confidence: 94%

“…These individual trajectories were then aggregated into histograms at consecutive time steps ti. Strictly speaking, we start with the grain size Dγ(t0) ≡ D0 which is a random variable described by the Weibull distribution with the shape parameter k = 10, which was determined on the basis of measured grain size distributions shown in [2]. The scale parameter of the distribution was established as the average grain size measured after roughing rolling.…”

Section: Modelmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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Through process stochastic model of hot strip rolling

Szeliga

2023

Materials Research Proceedings

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Abstract. Advanced numerical models, which predict heterogeneity of microstructural features, are needed to design modern multiphase steels. 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 to equations describing the evolution of the dislocations and the grain size during hot deformation. The idea of the internal variable model with the dislocation density and the grain size being stochastic variables is described briefly in the paper. Histograms of the grain size measured in the experimental compression tests were used to identify the coefficients in the model. Inverse analysis with the objective function based on the distance between histograms was applied. The model was used to simulation of the various technological routes in the industrial process of the hot strip rolling.

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“…Details of the identification procedure are described in [2,6]. Inverse algorithm developed in [11] was applied.…”

Section: Fig 1 Selected Results Of a Comparison Of Measured And Calcu...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 94%

Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Through process stochastic model of hot strip rolling

Szeliga

2023

Materials Research Proceedings

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“…Thus, the objective is to search for a fast mean-field model with extended predictive capabilities. As shown in [31], the internal stochastic variables can be used to describe the heterogeneous microstructures of alloys, leading to an interesting mean-field model. Such models can then be effectively used for prediction of gradients of microstructural features in designed final products.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2023

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Modern construction materials, including steels, have to combine strength with good formability. In metallic materials, these features are obtained for heterogeneous multiphase microstructures. Design of such microstructures requires advanced numerical models. It has been shown in our earlier works that models based on stochastic internal variables meet this requirement. The focus of the present paper is on deterministic and stochastic approaches to modelling hot deformation of multiphase steels. The main aim was to survey recent advances in describing the evolution of dislocations and grain size accounting for the stochastic character of the recrystallization. To present a path leading to this objective, we reviewed several papers dedicated to the application of internal variables and statistical approaches to modelling recrystallization. Following this, the idea of the model with dislocation density and grain size being the stochastic internal variables is described. Experiments composed of hot compression of cylindrical samples are also included for better presentation of the utility of this approach. Firstly, an empirical data describing the loads as a function of time during compression and data needed to create histograms of the austenite grain size after the tests were collected. Using the measured data, identification and validation of the models were performed. To present possible applications of the model, it was used to produce a simulation imitating industrial hot-forming processes. Finally, calculations of the dislocation density and the grain size distribution were utilized as inputs in simulations of phase transformations during cooling. Distributions of the ferrite volume fraction and the ferrite grain size after cooling recapitulate the paper. This should give readers good overview on the application of collected equations in practice.

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Sensitivity Analysis and Formulation of the Inverse Problem in the Stochastic Approach to Modelling of Phase Transformations in Steels

Szeliga,

Jażdżewska,

Foryś

et al. 2024

Lecture Notes in Mechanical Engineering

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The need for a reliable prediction of the distribution of microstructural parameters in metallic materials after processing was the motivation for this work. The model describing phase transformations, which considers the stochastic character of the nucleation of the new phase, was formulated. Numerical tests of the model, including sensitivity analysis, were performed and the optimal parameters such as time step, kind of the random numbers generator (RNG) and the number of the Monte Carlo points were determined. The validation of the model requires an application of proper coefficients corresponding to the considered materials. These coefficients have to be identified through the inverse analysis, which, on the other hand, uses optimization methods and requires the formulation of the appropriate objective function. Since the model involves stochastic parameters, it is a crucial task. Therefore, in the second part of the paper, a specific form of the objective function for the inverse analysis was developed. In the first approach, an objective function based on measurements of the average parameters was used and primary optimization was performed. Various optimization methods were tested. In the second approach, the hybrid objective function, which combined measured average transformation temperatures with a measure based on histograms, was used. Since, at this stage, we do not have measurements of the distribution of microstructural features, the basic histograms were generated by the model with the coefficients obtained in the first step of the optimization. The capability of finding the optimal solution for different starting points was evaluated and various approaches were compared. The elaborated original stochastic approach to modelling the phase transformations occurring during cooling after hot forming was validated on selected carbon steel.

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Formulation, identification and validation of a stochastic internal variables model describing the evolution of metallic materials microstructure during hot forming

Cited by 5 publications

References 28 publications

Through process stochastic model of hot strip rolling

Through process stochastic model of hot strip rolling

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

Sensitivity Analysis and Formulation of the Inverse Problem in the Stochastic Approach to Modelling of Phase Transformations in Steels

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