636-3005/03 – Fracture mechanics (LMn)

Gurantor departmentDepartment of Material EngineeringCredits6
Subject guarantordoc. Ing. Stanislav Lasek, Ph.D.Subject version guarantordoc. Ing. Stanislav Lasek, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFMTIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
LAS40 doc. Ing. Stanislav Lasek, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+2
Part-time Credit and Examination 16+0

Subject aims expressed by acquired skills and competences

student will be able to use parameters and relations of fracture mechanics to determine the allowable stress or critical crack sizes in materials - student is able, on the basis of standard procedures, to determine the fracture toughness of the material and the associated FM parameters and assess the material resistance to brittle fracture. - student will be able to describe the causes of cracking and fracture of materials (components) based on fractographic analysis and knowledge of the failure mechanisms

Teaching methods

Project work


Fundamentals of the theory of elasticity, stress concentrations at notches and cracks, the stress intensity factors. Stress and energy approach to fracture problems. Fracture toughness test. The driving forces and crack resistance to the growth. Plastic zones. Nonlinear (elastoplastic) fracture mechanics – crack tip opening, J-integral. Application of fracture mechanics to fatigue cracks and stress corrosion cracking. Transit behaviour of steels. Influence of dynamic loading. Unstable crack problems and crack arrest. Using the fractography for failure analysis.

Compulsory literature:

ANDERSON, T. L. Fracture Mechanics. Fundamentals and applications. 4th ed. London: CRC Press, 2005. ISBN 978 142 0058215. FELBECK, D. K. and A. G. ATKINS. Strength and Fracture of Engineering Materials. 1st. ed. Englewood: Prentice Hall, 1984. ISBN 0-13-851709-6. CHIN-TECH, S. Fracture mechanics. 1st ed., Cambridge: Academic Press, Elsevier, 2012. ISBN 9780123850027.

Recommended literature:

LASEK, S. Fracture Mechanics. Ostrava: FMMI VŠB-TU Ostrava, 2015. Available from: http://katedry.fmmi.vsb.cz/Opory_FMMI_ENG/AEM/Fracture%20mechanics.pdf Engineering Fracture Mechanics. E- journal. Available from:: https://www.journals.elsevier.com/engineering-fracture-mechanics

Way of continuous check of knowledge in the course of semester

Continuous verification of learning outcomes: full-time study form - 2 written tests, 3 written programs during semester; combined study form - 1 semestral project. Final verification of study results: combined exam, decisive written part .


Other requirements

There are no further requirements.


Subject has no prerequisities.


Subject has no co-requisities.

Subject syllabus:

. Historical introduction and significance of fracture mechanics. Examples of structures damaged by crack or fractures. 2. Summary of the basic principles and concepts of the theory of elasticity. The stress concentrations in the vicinity of notches or holes. 3. The elastic stress field at the crack tip. Mathematical solutions. Mod (I-III) and the use of stress intensity factors. The influence of external multi-axial stress, superposition principle. Effect of finite dimensional elements, shape functions (factors). 4. Plastic zone at the crack tip, the size of the zones and the differences between the plane stress and plane strain state. Redistribution of stresses. The importance of plastic zones. 5. Mechanisms of initiation and growth of cracks.. Maps of fracture mechanisms. Methods of study of fractures, fractography, metallography. 6. Fracture toughness KIc, its determination to standards. The range of KIc values for materials, Ashby maps. Options of determine the critical stress or crack size. Effects of the structure of the material, temperature and thickness of the parts to the values Kc. 7. Energy approaches. Griffith´s theory. The driving force (energy) G of crack, crack propagation resistance R. Sih strain energy density factor and its applications. Critical values of stated parameters. Relations among fracture mechanics parameters. 8. Dynamics of fracture and crack arrest. The effect of shock loads and waves on crack. Impact testing of materials. Unstable crack propagation and the possibility of crack arrest. 9. Transit behaviour of metallic materials. Testing and determination of transition temperatures (DWT, DT, CAT). Standards and use in practice. 10. Nonlinear elastoplastic fracture mechanics. Crack opening displacement (COD), methods of measurement. Determination J-integral, its application examples. 11. Application of fracture mechanics to the growth of fatigue cracks. Paris relationship and possibility of prediction of cyclic life. 12. Crack growth under stress corrosion cracking and hydrogen embrittlement conditions. Application of LM parameters and thresholds values. 13. Calculation of critical defect size and service life of structures. Examples of pressure vessels and piping. Diagnosis of cracks. 14. Catastrophic fractures in practice, case study. The use of fractography in the analysis of material failure.

Conditions for subject completion

Full-time form (validity from: 2019/2020 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 35  21
        Examination Examination 65  30
Mandatory attendence parzicipation: 78% attendance on seminars and practical lessons. Elaboration of the projects.

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2020/2021 (N0715A270002) Materials Engineering (S01) Advanced engineering materials P Czech Ostrava 1 Compulsory study plan
2020/2021 (N0715A270002) Materials Engineering (S01) Advanced engineering materials K Czech Ostrava 1 Compulsory study plan
2020/2021 (N0788A270001) Biomechanical Engineering BDM P Czech Ostrava 1 Compulsory study plan
2019/2020 (N0715A270002) Materials Engineering (S01) Advanced engineering materials P Czech Ostrava 1 Compulsory study plan
2019/2020 (N0788A270001) Biomechanical Engineering BDM P Czech Ostrava 1 Compulsory study plan
2019/2020 (N0715A270002) Materials Engineering (S01) Advanced engineering materials K Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner