Ch Wang Fracture Mechanics

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Introduction to Fracture Mechanics

C.H. Wang

Airframes and Engines Division

Aeronautical and Maritime Research Laboratory

DSTO-GD-0103

ABSTRACT

This text is based on a series of lectures conducted on fracture mechanics. As anintroductory course, the test is focused on the essential concepts and analyticalmethods of fracture mechanics, aiming at painting a broad picture of the theoreticalbackground to fracture mechanics. While a brief review of some important issues in thetheory of elasticity is provided in the first chapter, the main focus of the test is centredon stress analysis and energetic approaches to cracked components, local plasticdeformation at crack tips, fracture criteria and fatigue life prediction.

RELEASE LIMITATION

Approved for public release

D E P A R T M E N T O F D E F E N C E

!

DEFENCESCIENCEANDTECHNOLOGYORGANISATION


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Published by

DSTO Aeronaut ical and M aritime Research LaboratoryPO Box 4331

Melbourne Victoria 3001

Telephone: (03) 9626 8111

Fax: (03) 9626 8999

Commonwealth of Australia 1996

AR No. AR-009-786

July 1996

APPROVED FOR PUBLIC RELEASE


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Introduction to Fracture Mechanics

Executive Summary

This text is prepared for a series of lectures on fracture mechanics. The main aimof the lectures is to provide AMRL staff who are involved in aircraft fatigue andfracture research with a broad picture of the theoretical background to fracturemechanics via a stress analysis viewpoint.

As an introductory course, the lectures are focused on the essential concepts andanalytical methods of fracture mechanics. A brief review of some importantissues in the theory of elasticity is provided in Chapter 1, while the remainingchapters deal with the stress analysis approach and the energy approach tocracked components, local plastic deformation at crack tips, fracture criteria andfatigue life prediction.


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Authors

C. H. Wang

Airframe and Engine Division

Chun-Hui Wang has a B.Eng and Ph.D (Sheffield, UK) in

Mechanical Engineering and is currently a member of the Institute

of Engineers, A ustralia. Prior to joining the A eronautical and

Maritime Research Laboratory in 1995 as a Senior Research

Scientist, Dr. Wang was a Lecturer at the Deakin University. He

has an extensive research record in fatigue and fracture mechanics,

stress analysis and constitut ive modelling, and biomechanics. Overthe last six years he also held academic/research positions at the

University of Sydney and the University of Sheffield, UK.

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Contents

1. FUN DAM ENTALS ............................................................................................................1

1.1 Historical Overview ......................................................................................................1

1.2 Notch es an d Stress Con centra tion .............................................................................. 2

1.3 Cracks an d Stress In ten sity Factor .............................................................................. 3

1.4 Plane Stress and Plan e Strain ...................................................................................... 4

1.5 Stress Functio n ............................................................................................................... 7

2. STRESS AN ALYSIS O F CRACKED CO MPONENTS .............................................10

2.1 Ene rgy Balance Durin g Crack Grow th ....................................................................10

2.2 Griff ith Th eory .............................................................................................................11

2.3 Energy Release Rate G an d Com plian ce ................................................................. 14

2.3.1 Constant Load Conditions .................................................................................... 15

2.3.2 Constant Displacement Condition.......................................................................15

2.3.3 Determination Of Energy Release Rate From Compliance ..............................16

2.4 Stress Intensity Factor K............................................................................................. 19

2.5 Su perp osit ion M eth od ................................................................................................28

2.6 Relationship Between G an d K................................................................................. 30

3. PLASTIC YIELDING AT CRACK TIP ........................................................................35

3.1 Irwin s Mod el ............................................................................................................... 35

3.2 Th e Strip Yield M od el ................................................................................................ 37

3.3 Plane Stress ver su s Plane Strain . .............................................................................. 39

3.4 Sh ap es o f Plast ic Zon e ................................................................................................40

3.5 Crack Tip Open in g Disp lacem en t ............................................................................43

4. FRACTURE CRITERIA .................................................................................................. 45

4.1 K as a Failu re Criter ion ...............................................................................................45

4.2 Residua l Stren gth an d Cri tical Crack Size..............................................................47

4.3 R -curve ...........................................................................................................................49

4.4 Mixed Mod e Load in g: Fracture an d Crack Path ....................................................52

5. FATIG UE AND LIFE PREDICTION ...........................................................................57

5.1 Fatig ue Crack Grow th Equ ation s..............................................................................57

5.2 Effect of Stress Rat io an d Crack Closu re ................................................................. 60

5.3 Var iab le Am plitude Load in g.....................................................................................62

5.3.1 First Generation Model and Palmgren-Miner Linear Rule .............................. 64

5.3.2 Wheeler Model........................................................................................................65

5.4 Dam age Toleran ce Design Meth od ology ................................................................ 67

6. REFEREN CES ...................................................................................................................69


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Ch Wang Fracture Mechanics

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