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Department of Solid Mechanics

1

Course Notes

Hållfasthetslära Vk MHA100

Fatigue and Fracture AnalysisMHA140

School of Civil EngineeringPeriod II 1998

General

Additional and updated information about the course will be posted on the homepage of the course:http://www.solid.chalmers.se/anek/teaching/fatfract/

Teachers

The division of Solid Mechanics is situated at the ‘new’ M-building on Hörsalsvägen and can be reached by

phone 772 15 00fax 772 38 27E-mail [email protected] http://www.solid.chalmers.se

Goals

Within the field of fatigue and fracture mechanics, the goal of the course is to

·

Give an understanding of phenomena and theories.

·

Provide an orientation on classical and modern methods and design criteria.

Peter Möller Anders Ekberg

phone 772 15 05 772 34 80

home 12 64 27 703 44 76

E-mail [email protected] [email protected]

H�llfasthetsl�ra Vk / Fatigue and Fracture Analysis

2

C

OURSE

N

OTES

·

Teach basic numerical methods of design.

·

Serve as an introduction for possible further studies.

·

Give a brief introduction to current research trends in the area.

After completed course, the participants should have a good foundation for industrial fracture and fatigue design, as well as a basis for continued studies.

Literature

·

Peter W. Möller: Introductory Lecture Notes on Fracture Mechanics, CTH Solid Mechanics (15 SEK)

·

Compendium in Fracture Mechanics (50 SEK); (compiled by Tore Dahlberg)

·

Dahlberg, Ekberg, Möller: Exercises in Fracture and Fatigue Analysis, CTH Solid Mechanics U74 (20 SEK)

·

Tore Dahlberg: Material Fatigue, CTH Solid Mechanics U61 (40 SEK)

·

Anders Ekberg: Fatigue – a Survey,

2nd Edition

, CTH Solid Mechanics U67 (25 SEK)

Program

The course is divided into two main parts, viz. F

ATIGUE

A

NALYSIS

and F

RACTURE

M

ECHANICS

. Although each of these topics may be studied independent from each other, there are some natural connections.

Lectures and exercises are separated in the course program, some numerical examples may be provided in the lectures.

Examination

A written examination, embracing of five problems, is given December 16.

The problems may consist of numerical as well as theoretical parts.

The means of assistance that are allowed at the exam are

·

All the literature listed above except for the problems collection.

·

Handbooks and mathematical tables. This also includes textbooks on solid and structural mechanics, but no textbooks on fatigue and fracture (except for the textbooks listed above).

·

Dictionaries.

·

A calculator in one single unit and without external communication.

·

Distributed copies of slides

etc

.

This does not include distributed solved examples!

Minor notes, but no solved problems, in the listed material are allowed as well. If there are any questions regarding allowed means of assistance, please contact a teacher

prior to

the exam.


C

OURSE

N

OTES

3

Program

The course embrace 14 lectures and 14 exercises; 7 lectures and 6 exercises are devoted to fracture mechanics and another 7 lectures and 6 exercises treat fatigue. By the end of the course, about 1 week before the examination, 2 exercises are dedicated to repetition. Lectures take place in lecture hall VH, while exercises are conducted in VÖ12 and VÖ13 - any changes will be announced during the course.

Fracture Mechanics

L

ECTURE

1

Introduction to the course with emphasis on fracture mechanics

·

Mechanisms of failure

·

Equations of elasticity

·

Principal stress; Mohr’s circle

·

Effective stress

·

Energy and work

·

Tensor notation

L

ECTURE

2

Stress concentrations at voids and cracks

·

Mohr’s criteria for brittle fracture

·

Stress concentration factors

·

Stress intensity factors – modes of loading

L

ECTURE

3

Stress intensity factors Ð part I

·

Detailed study of mode III loading

·

Mode I and II solutions

·

The stress intensity factor as a failure criterion

E

XCERCISE

1

·

Equilibrium

·

Mohr’s criterion for brittle failure

·

Strain energy

L

ECTURE

4

Stress intensity factors Ð part II

·

Limitations of LFEM (Linear Elastic Fracture Mechanics)

·

Superposition – Mixed loading mode

·

Methods to determine stress intensity factors

E

XCERCISE

2

·

Stress concentration

·

Stress at crack tip


4

C

OURSE

N

OTES

L

ECTURE

5

Energy and energy balance

·

Surface energy

·

Potential and strain energy

·

Strain energy release rate –

G

·

The Griffith energy balance

·

Stable and unstable crack growth

· Relation between G and stress intensity factors

· Superposition revisited

· Methods to determine G

EXCERCISE 3 · Stress intensity factors

LECTURE 6 Correction for small scale yielding (ssy)· Irwin’s approach

· The Dugdale model

· Plastic zone – size and shape

· Limitation of LFEM revisited

· Size effects

EXCERCISE 4 · Surface energy

· Energy balance

· Strain energy release rate

LECTURE 7 Introduction to non-linear (elastic-plastic) fracture mechanics· Crack tip opening displacement – The CTOD criterion

· The J–integral and its relation to strain energy release rate

Fatigue

LECTURE 8 Introduction to fatigue analysis· Fatigue?!?

· History of fatigue

· Fatigue design philosophy

· An overview of fatigue design methods

· Complicating factors

· Dynamic loading

EXCERCISE 5 (FRACTURE MECHANICS)

· Irwin correction

· Plastic zone and the Dugdale model

LECTURE 9 High Cycle Fatigue (HCF) Design Ð part I· Underlying philosophy and physics


COURSE NOTES 5

· The Haigh diagram

· Finite / infinite fatigue life

· The Wöhler curve

· Limitations and difficulties

EXCERCISE 6 (FRACTURE MECHANICS)

· Crack tip opening displacement

· The J–integral

LECTURE 10 High Cycle Fatigue (HCF) Design Ðpart II· Multiaxial loading – complications

· Equivalent stress approaches

· Limited fatigue life in multiaxial loading


EXCERCISE 7 · HCF design

LECTURE 11 Low Cycle Fatigue (LCF) Design· Underlying philosophy and physics

· Morrow design rule

· Coffin – Manson design rule

· Multiaxial LCF


EXCERCISE 8 · HCF design

LECTURE 12 Fatigue Crack Propagation Ð part I· Underlying philosophy and physics

· Crack growth at cyclic loading

· Design against failure due to crack growth

· Basic analysis of crack growth rate


EXCERCISE 9 · LCF design

LECTURE 13 Fatigue Crack Propagation Ð part II· Influence of load magnitude

· Crack closure and arrestment

· Variable amplitude loading

· Short and long cracks

· Crack Growth Threshold

· Multiaxial Loading



6 COURSE NOTES

EXCERCISE 10 · LCF design

EXCERCISE 11 · Fatigue crack propagation

LECTURE 14 Concluding remarks of fatigue analysis· Fatigue of non-metallic materials

· Design codes (esp. BSK and BBK)

· Practical design

· Fatigue – a crash course

EXCERCISE 12 · Fatigue crack propagation

EXCERCISE 13 · Repetition of the course contents – problems from old exams

EXCERCISE 14 · Workshop – test exam and/or problems from old exams

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