Discrete micro-scale cellular automata model for modelling phase transformation during heating of dual phase steels

Physical and numerical simulations of the hot rolling and laminar cooling of DP steel strips are presented in the paper. The objectives of the paper were twofold. Physical simulations of hot plastic deformation were used to identify and validate numerical models. Validated models were applied to simulate the manufacturing of DP steel strips. Conventional flow stress model and microstructure evolution model were used in the hot deformation part. The approach to the complex systems analysis based on global thermodynamic characterization and detailed microstructure characterization was applied to determine equilibrium state at various temperatures. Finally, two numerical models were used to simulate kinetics of austenite decomposition at varying temperatures: the first, conventional model based on the Avrami equation, and the second, the discrete Cellular Automata approach. Plastometric tests and stress relaxation tests were used for identification of the hot rolling model for the DP steel. Dilatometric tests were performed to identify the phase transformation models. Verification confirmed good accuracy of all models. Validated models were applied to simulate the manufacturing of DP steel strips. Influence of technological parameters (e.g., strip thickness and velocity, active sections in the laminar cooling, and water flux in the sections) on the DP microstructure was analyzed. The cooling schedules, which give required microstructures were proposed. The numerical tool, which simulates manufacturing chain for DP steel strips is the main output of the paper.

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“…The effect of diffusion is indirectly accounted for by relation of the phase boundary mobility on the diffusion coefficient in Eq. [18].…”

Section: Ca Model For Phase Transformationsmentioning

confidence: 99%

Conventional and Multiscale Modeling of Microstructure Evolution During Laminar Cooling of DP Steel Strips

Pietrzyk

Kusiak

Kuziak

et al. 2014

Metall Mater Trans A

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“…Different numerical simulation methods are used to support the experimental research on these steels. Present investigation is a continuation of earlier work 1) and focuses on phase transformation during heating.…”

Section: Introductionmentioning

confidence: 83%

“…The developed CA model is described in detail in an earlier work, 1) while main assumptions are summarized below to clearly highlight model parameters investigated during sensitivity analysis.…”

Section: Description Of Phase Transformation Model During Heatingmentioning

confidence: 99%

“…Increase at least one k components of x* by Δ, forming new sampling vector x (1) which is still in Θ. (1) , x (2) , …, x (k+1) are produced, forming a trajectory leading to one orientation matrix B*.…”

Section: Appendixmentioning

confidence: 99%

“…However, majority of publications describing application of CA to materials processing deals with recrystallization or phase transformations during cooling. [13][14][15] That is why, in the previous paper 1) authors proposed a model of phase transformation during heating. The model was based on combined CA-FDM method, which has good predictive capabilities but at the same time is quite complex and potentially requires a large number of input parameters related with material property, initial condition and boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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Sensitivity Analysis of the Finite Difference 2-D Cellular Automata Model for Phase Transformation during Heating

et al. 2015

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Sensitivity analysis of the Finite Difference Cellular Automata model for Dual Phase steel phase transformation during heating was performed in the present work. The main goal of the work was to determine the process parameters that are most important throughout transformation and should be particularly considered during the identification of model parameters: deformation, coefficients related with grains nucleation, activation energy, pre-exponential factor, and curvature parameters. The Morris OAT is a screening method capable of recognising the important factors of model and global sensitivity analysis was computed using this method. Different responses of the model outcomes were obtained by changing subsequent model input parameters. Results from Morris OAT design showed that deformation and activation energy have the most significant impact on the kinetics of phase transformation whereas average grain size strongly depends on all of the model parameters. Next, local sensitivity analysis was considered to check the behavior of each parameter locally. Finally both global and local sensitivities were compared and it was found that local sensitivity analysis in the case of such complex models can lead to inaccurate results.

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A cellular automata‐based deterministic inversion algorithm for the characterization of linear structural heterogeneities

Fischer

Jardani

Masséi

2017

Water Resources Research

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Inverse problem permits to map the subsurface properties from a few observed data. The inverse problem can be physically constrained by a priori information on the property distribution in order to limit the nonuniqueness of the solution. The geostatistical information is often chosen as a priori information; however, when the field properties present a spatial locally distributed high variability, the geostatistical approach becomes inefficient. Therefore, we propose a new method adapted for fields presenting linear structures (such as a fractured field). The Cellular Automata‐based Deterministic Inversion (CADI) method is, as far as we know when this paper is produced, the first inversion method which permits a deterministic inversion based on a Bayesian approach and using a dynamic optimization to generate different linear structures iteratively. The model is partitioned in cellular automaton subspaces, each one controlling a different zone of the model. A cellular automata subspace structures the properties of the model in two units (“structure” and “background”) and control their dispensing direction and their values. The partitioning of the model in subspaces permits to monitor a large‐scale structural model with only a few pilot‐parameters and to generate linear structures with local direction changes. Thereby, the algorithm can easily handle with large‐scale structures, and a sensitivity analysis is possible on these structural pilot‐parameters, which permits to considerably accelerate the optimization process in order to find the best structural geometry. The algorithm has been successfully tested on simple, to more complex, theoretical models with different inversion techniques by using seismic and hydraulic data.

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Discrete micro-scale cellular automata model for modelling phase transformation during heating of dual phase steels

Cited by 31 publications

References 25 publications

Conventional and Multiscale Modeling of Microstructure Evolution During Laminar Cooling of DP Steel Strips

Conventional and Multiscale Modeling of Microstructure Evolution During Laminar Cooling of DP Steel Strips

Sensitivity Analysis of the Finite Difference 2-D Cellular Automata Model for Phase Transformation during Heating

A cellular automata‐based deterministic inversion algorithm for the characterization of linear structural heterogeneities

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