Course detail

Theory of Metal-forming

FSI-HTAAcad. year: 2020/2021

Complex engineering solutions of the technological processes of metal-forming are based on the theory of plasticity and theory of metal-forming with systems of computer support. The content of the course starts from selected chapters of the physical essence of plastic strain, formability of metals and alloys, fundamentals of mathematical theory of plasticity, and experimental/analytical methods for the theoretical solution of metal-forming processes. The course provides the basic knowledge of and skills in mathematically describing metal-forming processes while applying the physical, chemical, mechanical and thermodynamic principles of the transition of metallic bodies from elastic into plastic state in the course of their plastic deformation into the required shape. The course also addresses the problem of determining the loading of metal-forming tools and machines, carries out analyses of deformation, establishes critical strain values and offers an introduction to computer-aided modelling of metal-forming processes.

Learning outcomes of the course unit

The course offers students the knowledge necessary for simplified mathematical representation of forming processes while applying the physical, chemical, mechanical and thermodynamic principles of metallic bodies changing from the elastic into the plastic state, and when these bodies are plastically deformed into the required shape. Students will learn how to determine the loading of the forming tool or machine, and how to determine the critical values of deformation.


Successful completion of the course is conditional on the knowledge of applied mathematics and physics, materials science, elasticity, strength, and plasticity, and a grasp of metal-forming technologies.


Consultations with teachers after mutual agreement and according to schedule in semester. Distance learning form by e-mail.

Recommended optional programme components

Not applicable.

Recommended or required reading

FOREJT, Milan. Teorie tváření. Učební texty. 2. vyd. VUT Brno : AN CERM, s.r.o. Brno, 2004. 167 s. ISBN 80-214-2764-7. (CS)
Metals handbook, Ninth Edition: Forming and Forging. Vol 14. Metals Park, Ohio: American Society for Metals, c1988, 17 v. ISBN 0-87170-007-7. (EN)
LANGE, Kurt. Handbook of metal forming. New York: McGraw-Hill, c1985, 900 p. ISBN 00-703-6285-8. (EN)
FOREJT, Milan. Teorie tváření, Návody do cvičení. Studijní opora FSI VUT, říjen 2004 (novela 2020) (CS)
FARLÍK Alois a Emanuel ONDRÁČEK.Teorie dynamického tváření. sv.6137. Praha: SNTL, 1968, 315 s., DT 621.7.014 (CS)
MIELNIK, Edward M. Metalworking science and engineering. New York: McGraw-Hill, c1991, 976 p. McGraw-Hill. ISBN 00-704-1904-3. (EN)
ASM handbook: Metalworking, Bulk Forming. Vol.14A, Editor: ASM International, 2005, 888 s. ISBN 08-717-0708-X. (EN)
FOREJT, Milan a Miroslav PÍŠKA. Teorie obrábění, tváření a nástroje. Brno: A N CERM, 2006. ISBN 80-214-2374-9. ( dotisk 2008, 2012, 2015, 2018) (CS)
MARCINIAK, Z. Mechanics of sheet metal forming. Oxford: Butterwort-Heinemann, 2002. ISBN 0-7506-5300-0. (EN)

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Teaching is suplemented by practical laboratory work.

Assesment methods and criteria linked to learning outcomes

Conditions of awarding the course-unit credit: participation in exercises, working out 10 accepted reports concerning individual assignments, using recommended computer support. If this condition is not satisfied, the teacher may in justified cases assign alternative exercise programs. The examination is in public, testing the knowledge of three basic areas of the course, namely
1) the physical essence of plastic deformation and formability of metals and alloys,
2) mathematical theory of plasticity,
3) methods for solving metal-forming processes. Oral examination follows a preliminary written preparation answering the drawn complex question with 3 sub-questions concerning the basic areas of the course. The main emphasis is on understanding the method of solution and the ability to apply the known analytical and experimental calculation models.
The exam is public, it will have written preparation and oral part. It is classificated to the ECTS grading scale.

Language of instruction


Work placements

Not applicable.


The main objective of the course is to provide students with the theoretical foundations and methodology necessary for solving metal-forming technologies on the principles of plastic deformation and theory of plasticity. Students will acquire knowledge necessary for a creative and complex engineering solution of the technologies of metal-forming processes.

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

Attendance in lectures is recommended.
Attendance in exercises is compulsory.
The attendance to the seminar is regularly checked and the participation in the lesson is recorded.
Absence from laboratory exercises is compensated for via make-up topics of exercises and consultations.

Classification of course in study plans

  • Programme N-STG-P Master's

    specialization STG , 1. year of study, summer semester, 6 credits, compulsory
    specialization STM , 1. year of study, summer semester, 6 credits, compulsory-optional

Type of course unit



26 hours, optionally

Teacher / Lecturer


1. Physical substance of plastic deformation. Formability of metals and alloys.
2. Resistance to deformation, effect of basic parameters. Deformation work and force.
3. Summary of the fundamentals of mathematical theory of plasticity. Partial theories.
4. Conditions of the appearance of plastic deformation. Analysis of the deformation process.
5. Analytical and analytical-experimental methods for solving metal-forming processes.
6. Upsetting between parallel planes, the Siebel and the Unksov solutions.
7. Forward extrusion, stress and strain analysis.
8. Backward extrusion, solution after Dipper, Sachs and Siebel.
9. Die forging, solution after Tomlen, Gubkin, Gelei and Storozhev
10. Bending of thin bars and wide bands.
11. Deep drawing, stress and strain, calculation after Sachs and Sofman.
12. Method of resistance to deformation. Theory of small elastic-plastic deformations.
13. State of stress in free and closed shear and in precise shearing.

Laboratory exercise

26 hours, compulsory

Teacher / Lecturer


1. Problems of the physical substance of plastic deformation, demonstrations, report.
2.Evaluation of the parameters of deformation, deformation rate, report. 3.Calculation of main and effective stress, graphic interpretation, report. 4.Evaluation of resistance to deformation curves obtained from experiments. 5.Calculation of resistance to deformation and forces in upsetting, report.
6.Stress and forces in forward extrusion, report.
7.Stress and forces in backward extrusion, report.
8.Die forging, calculation of forging forces, report.
9.Calculation of bending forces and springing-back, report.
10.Stress, forces and number of drawing operations, report.
11.Evaluation of stress and strain on a drawn part, report.
12.Stress in current and precise shearing, report.
13.Conclusion of exercises, discussion of reports. Course-unit credit.