Course detail

Modelling of Phase Transformations

FSI-WFTAcad. year: 2010/2011

The course is oriented on the principles of modeling, on the models of the physical and technological processes, especially of the processes of a limit state of materials and the processes, which are influenced by means of the used technology. It will be explicated: the theory of the physical similarity, the dimension-less criteria (dimension-less numbers), the p - theorem and dimension analyses. The modeling of the processes and the behavior of the materials and technologies with the relation to the conditions (it means: temperature, pressure, material, physical and other parameters). The course presented same examples of the following models: the model of the blowing of the oxygen to the melt of the high alloy steel, the model of the nodular graphite growths, the model of the redistribution of interstitial elements (C, N and H) in the joints of the steels (in the steel weldments), the physical modeling and computer simulation of the temperature fields in the processes of the crystallization and cooling of metals, the influence of these processes on the phase transformation of steels, and the problems of the prediction of mechanical and physical properties of metal materials.

Language of instruction

Czech

Number of ECTS credits

Mode of study

Not applicable.

Guarantor

prof. Ing. Karel Stránský, DrSc.

Department

Institute of Materials Science and Engineering (ÚMVI)

Learning outcomes of the course unit

The knowledge of the following domain of the technical sciences in material engineering and their applications: physical, mathematical, geometrical, cybernetic and another models; physical and abstract models; the relation between the model and construction (or technological) work; the simulation of the relations and processes in material and technological engineering; the significance and using of the following dimension-les numbers (parameters): a) Reynolds number, Euler number, Froude number, Weber number, Mach number, Strouhal number (as a quantities of motion), b) Fourier number, Péclet number, Grashof number, Nusselt number, Stanton number (as a thermal quantities and quantities of mass transport in the systems) and c) Prandtl number, Schmidt number, Lewis number, Hooke number, Cauchy number, Poisson number, Newton number (as a material, substance quantities); the Fourier´s and Fick´s laws described by means of dimension-less numbers and their using for the solution of material and technological problems; the Nernst´s partition law and its using in the models; the Guldberg-Waage´s law in the solution of the chemical reactions and their using in the models and simulations; the models of quasi-stationary diffusion of carbon, nitrogen an hydrogen in steel weld joints and their using to the evaluation of the high temperature structural stability of steel weldments; the examples of the using of models and simulations in the technical praxis.

Prerequisites

Knowledge of the thermodynamic and kinetic of the liquid and solid phases. Knowledge of physical chemistry, physical metallurgy and chemical metallurgy of the liquid and solid phases of metals and alloys. Knowledge of the foundations of analytical and numerical mathematics and the solution of differential equations.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

Condition for awarding the course unit credit: Having done all the assigned topics in exercises and prepared the respective written individual tasks. Examination has a written and an oral part – the student answers three questions.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The course gives the possibility to obtain the knowledge about the following methods: how to make the modeling of the physical and technological processes, how to estimate the dimension-less criteria of the physical, mathematical, geometrical, thermal and another similarity, how to set up the dimension-less criteria equations and how to use these equations in the models. The course creates the possibilities to acquire know-how about: principals of modeling, modeling of physical and technological processing, using of the models to the describing of the behavior of metal materials, using of the models to the control of the technological processes.

Specification of controlled education, way of implementation and compensation for absences

Compulsory attendance at exercises, preparing written reading a paper on an assigned topics. Absence from exercises is resolved individually.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Type of course unit

Lecture

39 hod., optionally

Teacher / Lecturer

doc. Ing. Vít Jan, Ph.D.
prof. Ing. Karel Stránský, DrSc.

Syllabus

1) The theory of similarity in material engineering.
2) The dimension-less numbers (parameters), relation among number of values and dimension-less parameters.
3) The physical, mathematical and cybernetic modeling.
4) The dimensional analyze - the characteristic of this method. Theorem p (Bugingham).
5) The advantageous and the limiting factors of the dimensional analyze and theorem - p.
6) The analyze of the physical and mathematical models - the restrictions these models from the point of view of a theory of similarity.
7) Crystallization and the theory of nucleation from the point of view of a theory of similarity.
8) Thermodynamic activity and activity coefficient. Ideal solution - Raoult´s law.
9) No-ideal solution - Henry´s law. The using of Raoult´s a Henry´s laws.
10) Fick´s laws (I. and II. law) - their using in the theory of similarity.
11) Fourier´laws (I. and II. law), Stokes-Einstein´s equation, its important and using.
12) The problem of standard state and conversion from one standard state to another.
13) The redistribution of interstitial elements in the poly-component solid systems.
14) The model of quasi-stationary diffusion of carbon in steel welded joints.

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

prof. Ing. Karel Stránský, DrSc.
Ing. Simona Hutařová, Ph.D.

Syllabus

1) The definition and examples of models.
2) The transformation of one type of model (A) to another type of model (B).
3) The examples of the dimension analyze method – using in model constructions.
4) The models for mechanical properties of metals.
5) The examples of estimating of dimension-less numbers (criteria) from physical models.
6) The examples of estimating of dimension-less numbers (criteria) from mathematical models.
7) The examples of the theory of similarity to the describing of nucleation processes.
8) The examples of the estimating and applications of thermodynamic interaction coefficients.
9) The temperature effect on thermodynamic activity. The Arrhenius´s number – its significance.
10) The equilibrium constants of the physical and chemical reactions – examples.
11) Guldberg-Waage´s law and its using in models - examples.
12) Nernst´s partition law and the possibility using of this law in models.
13) The problems of interrelation between transport processes – viscosity, thermal conductivity, thermal diffusivity, temperature and pressure effect (examples).
14) The calculation of carbon redistribution in welded steel by means of special original software SVARY (WELDS).
15) The calculation of iron, carbon and additional elements in graphite cells by means of special original software U-GRAFIT (U-GRAPHITE).