Course detail

Fracture mechanics

FAST-CD54Acad. year: 2012/2013

linear elastic fracture mechanics, fracture parameters of material – fracture toughness, fracture energy, characteristic length –, methods for determination of fracture parameters, function of geometry, two-parameters fracture mechanics, T-stress, biaxiality factor, non-linear fracture behaviour, approximate non-linear models, resistance curves and surfaces, toughening processes, brittleness, fractal dimension of crack and fracture surfaces, size effect theory, modelling of failure of concrete structures using FE method, constitutive laws for quasi-brittle materials, strain localization problems, crack band model, non-local continuum mechanics, fictitious crack model, ATENA – FEM software, application – modelling of experiments/structures

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

prof. Ing. Zbyněk Keršner, CSc.

Department

Institute of Structural Mechanics (STM)

Learning outcomes of the course unit

Students will be introduced to mechanics of material, theory of materials failures and linear/nonlinear fracture mechanics. Students will be acquainted with fracture parameters of materials (e.g. fracture toughness, fracture energy, characteristic length) and with methods for determination of these parameters. Students will be orientating in size effect models. They will be able to model of failure of concrete structures using finite element method software.

Prerequisites

Structural mechanics, meaning of quantities stress and strain, modelling, finite element method.

Co-requisites

Nonlinear structural analysis.

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

The subject is completed by credit and final examination. For credit the student should pass all written tests in selected exercises. The credit is the necessary condition for final examination entrance. The final examination consists of written and oral parts. The written examination part includes both examples and theory. The positive result in written examination allows the student to pass to oral part.

Course curriculum

1. Introduction to mechanics of material, theory of materials failures and fracture mechanics. Linear elastic fracture mechanics – energy/stress approach.
2. Fracture parameters of material, fracture toughness, fracture energy, characteristic length. Methods for determination of fracture parameters, function of geometry.
3. Two-parameters fracture mechanics – T-stress, biaxiality factor.
4. Non-linear fracture behaviour, approximate non-linear models, resistance curves and surfaces.
5. Toughening processes quantification. Determination of brittleness number. Fractal dimension of crack and fracture surfaces.
6. Size effect theory.
7. Modelling of failure of concrete structures using FE method. Constitutive equations for concrete and other quasi-brittle materials.
8. Strain localization problems. Crack band model, non-local continuum mechanics.
9. Fictitious crack model. Models of fixed/rotated crack.
10. ATENA – FEM software; application – modelling of experiments/structures.

Work placements

Not applicable.

Aims

Aim of the course is introduction to mechanics of material, theory of materials failures and linear/nonlinear fracture mechanics. Students will be acquainted with fracture parameters of materials (e.g. fracture toughness, fracture energy, characteristic length) and with methods for determination of these parameters. Students will be orientating in size effect models. They will be able to model of failure of concrete structures using FE method using ATENA.

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

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Bažant, Z.P., Planas, J.: Fracture and Size Effect in Concrete and other Quasibrittle Materials. CRC Press, Boca Raton, Florida, 1998. (EN)
Cotterell, B.: Fracture mechanics of cementitious materials. Chapman and Hall, Glasgow, 1996. (EN)
Karihaloo, B.L.: Fracture mechanics and structural concrete. Longman, New York, 1995. (EN)
Shah, S.P. et al.: Fracture mechanics of concrete. New York, 1995. (EN)
Z. P. Bažant, J. Planas: Fracture and size effect of concrete structures. CRC Boca Raton, 1999. (EN)

Classification of course in study plans

  • Programme N-K-C-SI Master's

    branch K , 2 year of study, winter semester, elective

  • Programme N-P-C-SI Master's

    branch K , 2 year of study, winter semester, elective

  • Programme N-P-E-SI Master's

    branch K , 2 year of study, winter semester, elective

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

prof. Ing. Zbyněk Keršner, CSc.

Syllabus

1. Introduction to mechanics of material, theory of materials failures and fracture mechanics.
2. Linear elastic fracture mechanics – energy/stress approach.
3. Fracture parameters of material, fracture toughness, fracture energy, characteristic length.
4. Methods for determination of fracture parameters, function of geometry.
5. Two-parameters fracture mechanics.
6. Non-linear fracture behaviour, approximate non-linear models, resistance curves and surfaces.
7. Toughening processes quantification. Determination of brittleness number.
8. Fractal dimension of crack and fracture surfaces.
9. Size effect theory.
10. Modelling of failure of concrete structures using finite element method. Constitutive equations for concrete and other quasi-brittle materials.
11. Strain localization problems. Crack band model, non-local continuum mechanics.
12. Fictitious crack model. Models of fixed/rotated crack.
13. Software; application – modelling of experiments/structures.

Exercise

13 hod., compulsory

Teacher / Lecturer

prof. Ing. Zbyněk Keršner, CSc.

Syllabus

1. Introduction to fracture mechanics, information sources.
2. Theoretical study of fracture experiment.
3. Fracture test - three-point bending of beam with central edge notch.
4. Test evaluation - determination of effective fracture toughness.
5. Test evaluation - critical crack opening displacement.
6. Test evaluation - specific fracture energy.
7. Resistence curves of selected fracture parameters.
8. Quantification of toughening processes.
9. Brittleness number determination.
10. Numerical simulation -- data preparation.
11. Software, simulation of fracture experiment.
12. Using parameters obtained in modeling of structural response.
13. Modeling of structural response (continuation). Credit.