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1

Accounting for the random character of nucleation in the modelling of phase transformations in steels

Poloczek Łukasz, Kuziak Roman, Foryś Jakub, Szeliga Danuta, Pietrzyk Maciej

Computer Methods in Materials Science

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2023

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Vol. 23, No. 2

17--28

EN

In our earlier work, a stochastic model of multi-stage deformation at elevated temperatures was developed. The model was applied to calculate histograms of dislocation density and grain size at the onset of phase transformation. The histograms were used as input data for the simulation of phase transitions using the traditional deterministic model. Following this approach, microstructural inhomogeneity was predicted for different cooling conditions. The results obtained, showing the effect of dislocation density and inhomogeneity of austenite grain size on the microstructural inhomogeneity of the final product, can be considered reliable as they are based on material models determined in previous publications and validated experimentally. The aim of the present work was to extend the model by taking into account the stochastic nature of nucleation during phase transitions. The analysis of existing stochastic models of nucleation was performed, and a model for ferritic transformation in steels was proposed. Simulations for constant cooling rates as well as for industrial cooling processes of steel rods were performed. In the latter case, uncertainties in defining the boundary conditions and segregation of elements were also considered. The reduction of the computing costs is an important advantage of the model, which is much faster when compared to full field models with explicit microstructure representation.

2

Thermal-mechanical finite element simulation of flat bar rolling coupled with a stochastic model of microstructure evolution

Szeliga Danuta, Czyżewska Natalia, Kusiak Jan, Kuziak Roman, Morkisz Paweł, Oprocha Piotr, Pietrzyk Maciej, Piwowarczyk Michał, Poloczek Łukasz, Przybyłowicz Paweł, Rauch Łukasz, Wolańska Natalia

Computer Methods in Materials Science

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2022

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Vol. 22, No. 3

137--148

EN

It is generally recognized that the kinetics of phase transformations during the cooling of steel products depends to a large extent on the state of the austenite after rolling. Austenite deformation (when recrystallization is not complete) and grain size have a strong influence on the nucleation and growth of low-temperature phases. Thus, the general objective of the present work was the formulation of a numerical model which simulates thermal, mechanical and microstructural phenomena during multipass hot rolling of flat bars. The simulation of flat bar rolling accounting for the evolution of a heterogeneous microstructure was the objective of the work. A conventional finite-element program was used to calculate the distribution of strains, stresses, and temperatures in the flat bar during rolling and during interpass times. The FE program was coupled with the stochastic model describing austenite microstructure evolution. In this model, the random character of the recrystallization was accounted for. Simulations supplied information about the distributions of the dislocation density and the grain size at various locations through the thickness of the bars.

3

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

Szeliga Danuta, Czyżewska Natalia, Klimczak Konrad, Kusiak Jan, Kuziak Roman, Morkisz Paweł, Oprocha Piotr, Pietrzyk Maciej, Poloczek Łukasz, Przybyłowicz Paweł

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 3

art. no. e139

EN

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.

4

Processes simulations with multiscale materials models using a dedicated interface

Smyk Grzegorz, Szeliga Danuta

Computer Methods in Materials Science

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2021

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Vol. 21, No. 4

181--192

EN

The main goal of this work is the integration of in-house software with commercial numerical software based on the finite element method (FEM). The main idea is to develop a universal interface to perform process simulations with multiscale models. The interface allows the combination of external procedures with commercial software with minimum programmer’s work putting in integration. As an example, the model of material recrystallization of steel was implemented, added to the commercial application, and the software was tested for a process defined as a sequence of compression and cooling. The material model takes into consideration each type of recrystallization that occurs during a sequence of thermal and mechanical processing such as static recrystallization (SRX), dynamic recrystallization (DRX), and meta-dynamic recrystallization (MDRX). It allows the prediction of recrystallized volume fraction (X) and grain growth on each step of numerical simulation for each Gauss point in the computation domain. The presented multiscale model of process sequences not only allows to calculate microscale model parameters such as grain growth and recrystallized volume fraction, but also reflects the impact of the microscale model on macroscale parameters.

5

A dedicated sensitivity analysis and optimization application for industrial processes

Myczkowska Kamila, Szeliga Danuta

Computer Methods in Materials Science

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2021

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Vol. 21, No. 4

219--232

EN

The paper describes the architecture and the use case of the developed Modelbox system for sensitivity analysis (SA), uncertainty analysis (UA) and the subsequent optimization of industrial processes. The proposed solution addresses the most common practical and technical problems encountered by researchers and engineers when performing sensitivity analysis. It combines the functions from the numerical toolbox with a simulation management system. Maintaining usability and a good user experience while managing complex investigations of time-consuming industrial process simulations is a very important feature of the system. Several improvements were introduced to optimize the computation time of analysis/modelling tasks, including the automatization of distributed calculations, persistent, transparent caching of simulation data and duration estimations from collected statistics. The system has the ability to perform remote, parallel, asynchronous computations of both analytic algorithms and numerical simulations. The system is dynamically scalable horizontally by using serverless computing endpoints and thus it can be easily adapted to the user’s current needs in a flexible way. Modelbox provides web-based access to analysis/modelling tasks from sampling, SA/UA, optimization to metamodelling. It is extended with numerous interactive visualization components for effective results control. In addition, to access data from the completed analysis, the system supports convergence tracking for SA estimates and intermediate optimization results. The process of controlled cooling of rails was considered as a case study. The formulated optimization task was to find a combination of process parameters that ensures a minimum volume fraction of bainite along with required interlamellar spacing and optimal homogeneity of hardness. Different sensitivity analysis methods were used to evaluate the significance of all variables with respect to their influence on the model output.

6

Mean field and full field modelling of microstructure evolution and phase transformations during hot forming and cooling of low carbon steels

Szeliga Danuta, Bzowski Krzysztof, Rauch Łukasz, Kuziak Roman, Pietrzyk Maciej

Computer Methods in Materials Science

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2020

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Vol. 20, No. 3

121--132

EN

The paper describes a critical comparison of mean field and full field approaches to modelling hot deformation/controlled cooling sequences for steels. Classification of the models, based on the balance between predictive capabilities and computing costs, is presented. Mean field models, which describe microstructure evolution and phase transformations were connected with thermomechanical finite element program and applied to simulation of the hot strip rolling process and cooling of tubes after hot rolling. Full field model described in the paper is a connection of the finite element (FE) and level set (LSM) methods. These methods were used to simulate heating/cooling sequence in the continuous annealing line. A suggestion to use a stochastic model as a bridge between mean field and full field approaches is made.

7

Possibilities of the numerical solution of the dislocation evolution equation for stochastic variables

Milenin Ivan, Rauch Łukasz, Szeliga Danuta, Pietrzyk Maciej

Computer Methods in Materials Science

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2019

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Vol. 19, No. 4

169--173

EN

The model describing evolution of dislocation population based on fundamental works of Kocks, Estrin and Mecking (KEM) is a useful tool in modelling of metallic materials processing. In combination with the Sandstrom and Lagneborg approach it can predict changes of the dislocation density accounting for hardening, recovery and recrystallization. Numerical solutions of a one-parameter model (average dislocation density), as well as for two types of dislocations and three types of dislocation are described in the literature. All these solutions were performed for deterministic variables. On the other hand, an advanced modelling of materials requires often an information about distribution of parameters. This is the case when uncertainty of the model has to be evaluated or when an information about distribution of product properties is needed. The latter is crucial when deterioration of local formability is caused by sharp gradients of properties. Thus, the investigation of possibilities of numerical solution for the KEM model with stochastic variables was the main objective of the present work. Evolution equation was written for the distribution function and solution was performed using Monte Carlo method. Analysis of the results with respect to the reliability and computing costs was performed. The conclusions towards selection of the best approach were formulated.

PL

Model opisujący ewolucję populacji dyslokacji wykorzystujący fundamentalne prace Kocksa, Estrina i Meckinga (KEM model) jest użytecznym narzędziem w modelowaniu przetwórstwa materiałów metalicznych. W połączeniu z modelem Sandstroma i Lagneborga możliwe jest przewidywanie zmian gęstości dyslokacji uwzględniając zjawiska umocnienia, zdrowienia i rekrystalizacji. Numeryczne rozwiązania dla jednoparametrowego modelu (średniej gęstości dyslokacji), jak i dla dwóch lub trzech rozdajów dyslokacji, jest opisane w literaturze. Te rozwiązania zostały przeprowadzone dla zmiennych deterministycznych. Z drugiej strony zaawansowane modelowanie materiałów wymaga informacji o rozkładzie parametrów. Ma to miejsce np., kiedy potrzebna jest ocena niepewności wyników lub informacja o funkcji rozkładu własności materiału. To ostatnie jest ważne, kiedy obniżenie lokalnej odporności mateiału na pękanie jest powodowane przez ostre gradienty własności. Stąd celem niniejszej pracy była ocena możliwości numerycznego rozwiązania dla modelu KEM ze zmiennymi losowymi. Równanie ewolucji dyslokacji zapisano dla funkcji rozkładu prawdopodobieństwa i przeprowadzono rozwiązanie wykorzystując metodę Monte Carlo. Przeprowadzono analizę wyników w aspekcie ich dokładności oraz oceniając koszty obliczeń. Sformułowane zostały wnioski sugerujące dobór najlepszych parametrów modelu numerycznego.

8

Framework for fast simulations of material science phenomena with Cahn-Hilliard equations

Gurgul Grzegorz, Paszyński Maciej, Szeliga Danuta, Puzyrev Vladimir

Computer Methods in Materials Science

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2019

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Vol. 19, No. 1

12--20

EN

This paper presents the framework for executing Cahn-Hilliard simulations through a web interface which is based on a popular continuous integration tool called Jenkins. This setup allows launching computations from any machine, in the client mode, and without the need to sustain a connection to the computational environment. It also isolates the researcher from the complexity of the underlying infrastructure and reduces the number of steps necessary to perform the simulations. Moreover, the results of the computations are automatically post-processed and stored upon job completion for future retrieval in the form of raw data, a sequence of bitmaps, as well as a video sequence illustrating changes in the material structure over time. The Cahn-Hilliard equations are parameterized with mobility and chemical potential function, allowing for several numerical applications. The discretization is performed with Isogeometric finite element method, and it is parameterized with the number of time steps, the time step size, the mesh size, and the order of the B-spline basis functions using for the approximation of the solution. The interface is linked with the alternating direction semi-implicit solver, resulting in a linear computational cost of the simulation.

PL

W niniejszej pracy przedstawiamy framework służący do przeprowadzania symulacji opartych o wzory Cahna-Hilliarda poprzez wygodny interfejs webowy. Wykorzystujemy do tego popularne narzędzie służące do ciągłej integracji o nazwie Jenkins. Tego typu konfiguracja pozwala na uruchamianie obliczeń z dowolnej maszyny w trybie klienckim bez konieczności utrzymywania połączenia do środowiska obliczeniowego. Dzięki temu naukowiec wykonujący obliczenia jest odizolowany od skomplikowanej infrastruktury obliczeniowej, a uruchomienie symulacji wymaga mniejszej liczby czynności. Ponadto, wyniki symulacji są automatycznie przetwarzane i prezentowane w formie tabularycznej, sekwencji bitmap oraz filmu, który odzwierciedla zmiany zachodzące w strukturze badanego materiału w czasie. Równania Cahna-Hilliarda są parametryzowane poprzez funkcje mobilności i potencjału chemicznego, co pozwala na przeprowadzanie symulacji wybranych zjawisk dla wielu materiałów. Dyskretyzacja jest wykonywana z wykorzystaniem Izogeometrycznej Metody Elementów Skończonych i jest uzależniona od liczby i rozmiaru kroków czasowych, wielkości siatki oraz rzędu krzywych B-sklejanych, użytych do aproksymacji rozwiązania. Interfejs, o którym mowa, konfiguruje solwer zmienno-kierunkowy z dyskretyzacją czasową schematem wprost, co skutkuje liniowym kosztem obliczeniowym symulacji.

9

Fast model for phase transformations during cooling of pre-annealed multiphase steels

Szeliga Danuta, Kuziak Roman, Zalecki Władysław, Pidvysotskyy Valeriy, Chang Yuling, Bleck Wolfgang, Bachniak Daniel, Pietrzyk Maciej

Computer Methods in Materials Science

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2019

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Vol. 19, No. 4

150--161

EN

A thorough experimental and numerical analysis of phase transformations in a selected CP800 steel was the general objective of the paper. Dilatometric tests were performed for a wide range of cooling rates. Two models based on a mean field approach were considered. The first was an upgrade of the Johnson-Mehl-Avrami-Kolmogorov equation. The second model was based on the Leblond equation. Both models were identified using inverse analysis of the experimental data. Simulations of various cooling schedules were performed to validate the models. Phase compositions for these cooling schedules were determined. Following this the effect of elements' segregation during solidification of steel on the occurrence of marteniste/bainite bands was accounted for using the developed models.

PL

W artykule opisano doświadczalną i numeryczną analizę przemian fazowych w wybranej stali o podwyższonej wytrzymałości. Próby dylatometryczne wykonano w szerokim zakresie prędkości chłodzenia. Rozważono dwa modele wykorzystujące metodę średniego pola. Pierwszym modelem była zmodernizowana wersja modelu JMAK (Johnson-Mehl-Avrami-Kolmogorov). Drugim modelem było rozwinięcie równania Leblonda. Przeprowadzono identyfikację modeli wykorzystując rozwiązanie odwrotne dla prób dylatometrycznych. W celu walidacji modeli wykonano symulacje różnych schematów chłodzenia. Wyznaczono skład fazowy dla tych schematów. Następnie oszacowano wahania składu chemicznego w badanej stali i wykorzystano opracowane modele do określenie wpływu segregacji pierwiastków podczas krzepnięcia stali na powstawanie pasm martenzytu/bainitu.