Marcin Hojny

The Physical and Computer Modeling of Plastic Deformation of Low Carbon Steel in Semisolid State

This paper reports the results of theoretical and experimental work leading to the construction of a dedicated finite element method (FEM) system allowing the computer simulation of physical phenomena accompanying the steel sample testing at temperatures that are characteristic for integrated casting and rolling of steel processes, which was equipped with graphical, database oriented pre- and postprocessing. The kernel of the system is a numerical FEM solver based on a coupled thermomechanical model with changing density and mass conservation condition given in analytical form. The system was also equipped with an inverse analysis module having crucial significance for interpretation of results of compression tests at temperatures close to the solidus level. One of the advantages of the solution is the negligible volume loss of the deformation zone due to the analytical form of mass conservation conditions. This prevents FEM variational solution from unintentional specimen volume loss caused by numerical errors, which is inevitable in cases where the condition is written in its numerical form. It is very important for the computer simulation of deformation processes to be running at temperatures characteristic of the last stage of solidification. The still existing density change in mushy steel causes volume changes comparable to those caused by numerical errors. This paper reports work concerning the adaptation of the model to simulation of plastic behavior of axial-symmetrical steel samples subjected to compression at temperature levels higher than 1400 ° C. The emphasis is placed on the computer aided testing procedure leading to the determination of mechanical properties of steels at temperatures that are very close to the solidus line. Example results of computer simulation using the developed system are presented as well.

Modeling of Strain-Stress Relationship for Carbon Steel Deformed at Temperature Exceeding Hot Rolling Range

The subject of the presented paper is the modeling of strain-stress relationship, which is the main mechanical property characteristic of the behavior of steel subjected to plastic deformation. The major cliallenge of the research is the temperature of the deformation, which significantly exceeds the hot rolling temperature range. This paper presents the results of work leading to the development of a rheological model describing the phenomena accompanying the deformation of 18G2A grade steel at temperature 1420°C and higher. Such temperature is a characteristic of the central parts of steel strands subjected to latest, very high temperature rolling technologies such as integrated rolling and casting processes. Rheological models have crucial influence on the results of the computer simulation of the mentioned processes. The methodology of yield stress curves development requires high accuracy systems of tension and compression test simulation. Hence, the proposed testing procedure is related to dedicated hybrid finite element method system with variable density, which was developed by the authors. The experimental work has been done using the Gleeble ® 3800 thermomechanical simulator in the Institute for Ferrous Metallurgy in Gliwice, Poland. The testing machine allows the physical deformation of samples while solidification of their central part is still in progress. The essential goal of the simulation was the computer reconstruction of both temperature changes and strain evolution inside a specimen subjected to simultaneous deformation and solidification. In order to verify the predictive ability of the developed rheological model, a number of compression tests using Gleeble ® 3800 simulator have been done, as well. The comparison between the numerical and the experimental results is also a part of the presented paper.

Inverse analysis applied for determination of strain–stress curves for steel deformed in semi-solid state

The integrated casting and rolling of plates in processes such as ISP or AST is the latest and very efficient method of hot strip production. The subject of the presented article is the modelling of steel behaviour at temperatures characteristic for the mentioned rolling technologies, which exceed the standard hot rolling temperature range. Numerical modelling can be very helpful in developing ‘know how’ theory for the mentioned processes. One of the most important relationships having a crucial influence on the metal flow path is the strain–stress curve. It is not easy to construct isothermal curves for a selected temperature range. The inverse method, which is usually applied for calculation of the real strain-stress relationship, needs a good mathematical model describing the plastic behaviour of the material. The model presented in the current article fills the gap in the modelling of plastic deformation of semi-solid materials. The methodology of constructing strain–stress curves is presented, as well. On the other hand, the mathematical modelling should be closely related to experiments. The only well-known method allowing laboratory tests in the discussed temperature range (over 1400°C) is the deformation of cylindrical samples using GLEEBLE thermo-mechanical simulator. However, experiments of steel deformation in semi-solid state by using this machine are very expensive. Therefore, application of a dedicated computer simulation system with an inverse method makes the tests possible in the first place and it also results in lowering testing costs.

Computer-Aided Physical Simulations Within the Context of New Technology Development

A new category has appeared in the experimental research for evaluation of material properties. It is called “physical simulation” and is directly related to a new type of computer controlled testing machine, able to change experiment conditions automatically during the experiment progress according to the assumed programme. It allows the course of industrial processes to be reconstructed in laboratory conditions, and, more precisely, the dynamics of changes in the tested material properties to be reconstructed as in the actual industrial process. So, the laboratory test results may be applied directly for commercial purposes.

Physical Simulation of Steel Deformation in the Semi-solid State

A new category has appeared in the experimental research for evaluation of material properties. It is called “physical simulation” and is directly related to a new type of computer controlled testing machine, able to change experiment conditions automatically during the experiment progress according to the assumed programme.

Multiscale Modelling of Mechanical Properties of Steel Deformed in Semi-Solid State – Experimental Background

The paper reports the results of experimental and theoretical work leading to the construction of a multiscale mathematical model describing the phenomena accompanying the steel deformation in semi-solid state as well as at extra-high temperatures. Conducted experiments and simulations confirms the need to seek new methods to obtain precise characteristics in the context of detailed computer simulations. The investigations presented in the current paper has shown, that temperature distribution inside the controlled semi-solid volume is strongly heterogeneous and non-uniform. Axial-symmetrical model (core of the old methodology) does not take into account all the physical phenomena accompanying the deformation. Finally, the error of the predicted strain-stress curves can still be improved. The proposed solution of the presented problem is application of both fully three-dimensional solution and more adequate solidification model taking into consideration evolution of forming steel microstructure. Contrary to the current model the new approach should allow to better capture the physical principles of semi-solid steel deformation in micro-scale. Additionally, the new complex methodology should allow to transfer the characteristics of the material behaviour between the micro-and macro-scale. As a consequence the final results should be more precise and accurate.

Spatial Solutions Based on the Smoothed Particle Method and the Finite Element Method—A Hybrid Approach

This chapter presents a numerical model of fluid flow (SPH method) and solidification model on the basis of the smoothed particle method and the finite element method (hybrid approach FE+SPH). The formulated models constitutes the foundation of a new conceptual hybrid model combining the advantages of the finite element method and mesh-free methods. Examples of test simulations were presented, and the implemented model in the DEFFEM system was validated by comparing the obtained simulation results with the analytical solution based on the common laws of physics (fluid flow) and physical simulation (solidification).

Spatial Solutions Based on the Finite Element Method and the Monte Carlo Method—A Multi-scale Approach

This chapter presents a 3D solution to the problem of medium deformation in conditions of its simultaneous solidification. The proposed solution consists of four sub-models. These are a mechanical model based upon a rigid-plastic solution, and a thermal model based on the Fourier equation solution. Another key component model is the model of function of stress versus strain change. The developed methodologies of determining the mentioned functions are presented in details in Chap. 8.

An Integrated Modelling Concept Based upon Axially Symmetrical Models

The present chapter presents identification strategies of yield stress investigation of steels based on tensile and compression tests at very high temperatures as well as in the semi-solid state. The methodologies of stress-strain curves investigation combine the possibility of direct simulation using the Gleeble 3800 thermo-mechanical simulator with the developed dedicated DEFFEM system with implemented axial-symmetrical solutions. The constitutive parameters identified by these procedures have been successfully applied in additional three-dimensional tests (see Chap. 9)

An Integrated Modelling Concept Based upon Three-Dimensional Models

The chapter presents sample physical and computer simulation results, conducted based on the modelling concept utilising full three-dimensional solutions. In the first part of the chapter, the initial results were presented, verifying the developed three-dimensional solutions spanning high-temperature processes for the macro scale: heating/melting/solidification as well as deformation. In the subsequent part, results of microstructure tests were presented, indicating high variability of the achievable cooling rates in the analysed medium volume. The research is supplemented by the developed concept method of estimation of the microstructure based on special “high-temperature” CCT diagrams. The final part presents results of experimental trials concerning verification of the developed grain growth model for the micro scale. The developed model is a unique one, spanning in a comprehensive manner the growth of grain in an integrated heating-melting-cooling process in the Gleeble 3800 simulator equipment.