COUPLED 2023

Exploring a possibility of an application of the statistical methods to modelling thermomechanical processing of steels with heterogeneous microstructure

  • Bzowski, Krzysztof (AGH University of Science and Technology)
  • Pietrzyk, Maciej (AGH University of Science and Technology)
  • Szeliga, Danuta (AGH University of Science and Technology)
  • Rauch, Lukasz (AGH University of Science and Technology)

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Exploring a possibility of a stochastic modelling of thermomechanical processing is the objective the work. Our motivations were twofold. Firstly, the development of the industry is associated with the search for construction materials with exceptional properties. Heterogeneous materials meet these requirements and they are now widely used in forms of metallic alloys, among which multiphase steels are a leading example [1]. Secondly, a problem of the uncertainty of predictions of product microstructure and properties is important today [2]. Investigation of both these aspects requires advanced models, which can describe distribution of microstructural features instead of their average values. Full field models based on representation of the microstructure using the RVE meet this requirement but they require long computing times. Our objective was to search for faster models, which, however, will still have a capability to describe the heterogeneous microstructure. A model based on the Statistically Similar RVE was proposed in [3]. The idea was to replace a RVE with a complex morphology by a simple periodic one composed of optimal unit cells. Significant reduction of the computing costs was obtained while good predictive capabilities were maintained [3]. Further reduction of the computing costs can be obtained by an application of the stochastic methods without explicit representation of the microstructure. It is shown in [4] that the model with internal stochastic variables allows description of the heterogeneous microstructure accounting for distributions of various features. The stochastic model, which describes evolution of the dislocation density and the grain size during hot deformation was proposed in [4]. Since the final microstructure and properties of product are obtained by a control of phase transformations during cooling after hot forming, the model was now extended by accounting for a random character of the nucleation during transformations in the process of cooling. The cooling model uses the stochastic initial conditions in the form of dislocation density and grain size histograms calculated by the hot deformation model. Results of case studies for the two models will be presented and compared. REFERENCES [1] Chang Y., et al., Mat. Design, 203, 2021, 109620. [2] Henke T., et al., CIRP Annals – Manuf. Technology, 62, 2013, 287–290. [3] Bzowski K., et al., Materials, 2021, 14, 5363. [4] Szeliga D., et al., Int. J. Mater. Form., 15, 2022, 53.