asme 20- 20fatigue 20for 20engineers

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Fatigue for Engineers

Instructors Guide


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CONTACTINFORMATION

ASME Headquarters1-800-THE-ASME

ASME Professional Development1-800-THE-ASME

Eastern Regional Office8996 Burke Lake Road - Suite L102Burke, VA 22015-1607703-978-5000800-221-5536703-978-1157 (FAX)

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214-800-4902 (FAX)

Western Regional Office119-C Paul DriveSan Rafael, CA 94903-2022415-499-1148800-624-9002415-499-1338 (FAX)

You can also find information on

these courses and all of ASME,including ASME ProfessionalDevelopment, the Vice President ofProfessional Development, andother contacts at the ASME Website...

http://www.asme.org


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Prepared by:

A. F. Grandt, Jr.School of Aeronautics and Astronautics

Purdue University

Copyright 1999 by

All Rights Reserved


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TABLE OF CONTENTS

Abstract3

Introduction..4

Organizing Unit Responsibilities.. 5

Instructor Guidelines and Responsibilities. 6

Fatigue for Engineers Outline/

Teaching Plan. 8

Instructor Notes.. 9

Appendix A: Reproducible Overheads71

Appendix B: Course and Instructor Evaluation Form... 134

Appendix C: Continuing Education Unit (CEU) Submittal Form... 137

Course Improvement Form

Instructors Biography Form


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ABSTRACT

The ASME Fatigue for Engineers seminar provides an introduction to the fatiguestructural failure mode. Fatigue is caused by cyclic loading and results in the formationof cracks that can then propagate to fracture. It is a common failure mode for manytypes of structures and materials, and has been estimated to be the cause of over half ofall mechanical failures.

This four-hour course begins with a general description of the fatigue process and itscharacteristics. The stress-life and strain-life approaches for determining the number ofcycles required to form cracks in smooth and notched components are then presented.The next section deals with linear elastic fracture mechanics techniques to predictfatigue crack growth and subsequent fracture. The final section overviews variousfatigue design criteria and approaches for providing structural resistance to fatigue forlong service lives.

Who Should Attend

This course is directed to engineers involved with the design and/or maintenance ofmechanical components. It is assumed that the student is familiar with basic strength ofmaterials concepts.

Benefits of Taking the Course

The student will be exposed to a broad overview of the nature and consequences offatigue, one of the most common sources of structural failures. The student will also beintroduced to several different approaches for analyzing fatigue and for designing andmaintaining fatigue resistant structures for long service lives.


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INTRODUCTION

This Fatigue for Engineers course is part of the ASME International Career DevelopmentSeries an educational tool to help engineers and managers succeed in todaysbusiness/engineering world. Each course in this series is a 4-hour (or half-day) self-

contained professional development seminar. The course material consists of aparticipant manual and an instructors guide. The participant manual is a self-containedtext for students/participants, while the guide (this booklet) provides the instructionalmaterial designed to be presented by a local knowledgeable instructor with a minimumof preparation time.

The balance of this instructors guide focuses on:

1. Organizing Unit Responsibilities2. Instructor Guidelines and Responsibilities3. Comprehensive teaching materials which may be used as is or adapted toincorporate experiences and perspective of the instructor.

Welcome to the ASME International Career Development Series! We wish you all thebest in your presentation, operation and delivery of this course.


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ORGANIZING UNIT RESPONSIBILITIES

Detailed procedures for conducting professional development courses are available from theASME Professional Development or Member Affairs Departments, or from the ASME RegionalOffices (see the inside front cover for contact information). The key responsibilities and activitiesfor conducting a Career Development Series course falls with the organizing unit (Section,

Division, or other) and includes the items listed below.

1. Select the Course Content: Do this based upon member or industry input and use one ormore of the modules to create a course anywhere from 1/2 day to 2 days in length.

2. Select a Local Instructor: Find a technically qualified individual who is a good communicator,is knowledgeable, and is capable of generating participant interaction.

3. Materials: Arrange with ASME for the instructors guide and participant manuals (call 1-800-THE ASME to order).

4. Schedule the Event: A 6 month lead time is recommended so enough publicity can beperformed and accommodations and course details can be arranged.

5. Arrange a Site: Find a university, a company or a hotel, hopefully at low or no cost. Makesure the facility is good for an adequate table and chair arrangement to accommodate theexpected attendees (typically 10 - 25). Make sure you have access to proper audio-visualequipment, either supplied at the facility or brought with you.

6. Publicize the Event: Use your unit newsletter for several months; use mailings to selectedcompanies; use 3-fold brochures, fliers, etc. Three months of publicity is usually required tohold a very successful course.

7. Registration: Arrange for pre-registration by mail and on-site registration at a higher cost. Thiswill tend to encourage pre-registration.

8. Program Preparation: Follow up with the facility and the instructor to meet the needs of the

course. For example, name tags for the participants, tent cards for the table, overheadprojector w/extra bulbs), screen, large pad of paper or a whiteboard (could use clearoverheads and an overhead pen if necessary).

9. Site Management: Have at least one person on site to help the instructor and handle theaudio/visual requirements, facility logistics, on-site registration, refreshments, etc.

10. Wrap Up: Final resolution of any bills, arrangements, and materials including all CareerDevelopment Seminar costs.

11. ASME Feedback (REQUIRED): Return the following items to the ASME Regional Officeadministering to your region (if unsure which office this is, call one of the offices and ask orcontact InfoCentral at 1-800-THE-ASME).

Biography of the author (this is required for ASME to provide CEUs for thecourse... form in the back of this book).

Course/Instructor evaluation forms Course improvement form (if any comments)

The Career Development Series professional development courses are intended to be low cost($50 or less per 4-hour course) but also financially self-supporting; hopefully, generating revenuefor the organizing unit. Assistance in budgeting is available from your ASME Regional Office.


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INSTRUCTOR GUIDELINES AND RESPONSIBILITIES

Thank you for serving as an instructor for ASMEs Career Development Series, an excitingopportunity to help engineers and managers grow professionally to meet today's rapidly changingbusiness world. This Instructor's Guide is intended to provide the basic instructional materials fordirect use or for adaptation and expansion in teaching the course. While a separate document for

the participants contains the course text, this guide includes:

1. Options and Responsibilities: (These pages)

2. Teaching Plan: This is a preliminary plan that the instructor can use as is or adapt to meettheir experiences

3. Instructor Notes: This is a comprehensive page of information for each overhead andprovides the major learning points for the slide as well as some ideas on how to present it.

4. Reproducible Overheads: These are in the Instructors Guide and are here so the Instructorcan produce their own teaching tools (make their own plastic).

5. Course and Instructor Evaluation Form: This needs to be reproduced and handed out to theparticipants at the conclusion of the course.

6. Continuing Education Unit (CEU) Form: This form should be reproduced and handed out tothe participants at the conclusion of the course. To receive the CEUs for taking this course,this form must be filled out and sent with the indicated payment to the address on the form.

7. Course Improvement Form: This form should be completed by the instructor and theorganizing unit (if there are any comments) and submitted to the Regional Office, along withthe Instructors Bibliography Form and evaluations.

8. Instructors Bibliography Form: The biography section of this form must be filled out (orparticipants cannot get CEUs) and by the organizing unit to the Regional Office.

This Instructors Guide is intended to provide a reasonably complete basis for teaching thiscourse. The instructor may adapt the material to meet his/her style, or use it as is. Preparationsteps include:

Send the Organizing Unit Information: This includes the instructor biography, A/V needs,etc.

Read the Material: Review the Participant Manual and the Instructors Guide

Review and Adapt the Outline/Teaching Plan:- adapt as needed- 1-hour segments with breaks recommended- include in-class exercises

- frequent Q & A periodsPrepare Class Materials:- make transparencies from hard copies- add new overheads (if needed)- 2 blank transparency sheets per participant + marking pens- Diskettes with simple spreadsheets (Lotus/Excel)- Have students bring or supply annual reports (one per two students)- Have students bring laptops or have site provide them (optional)


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Prepare Your Teaching Notebook: Many instructors use a 3-ring binder to holdtransparencies, notes and examples in proper order. Review the course content andprepare a teaching plan for time verification. Other preparation options can be used tosuite the instructors style.

Typically, it takes 1 to 2 days to evaluate the materials and prepare to give the course. Some finalhelpful hints include:

1. Keep it simple

2. Identify one key thought per visual

3. Remember... this is not a classroom... attendees do not have to listen

4. Pace yourself, speak slowly and distinctly

5. Avoid acronyms

6. Practice the presentation

7. Keep to the schedule or teaching plan

8. Encourage lots of class participation

9. Field questions throughout the class, but watch your time

10. Dont forget breaks

11. Challenge the participants to interact

12. Add humor to your presentation with things like cartoons, stories, etc.

13. Recommend to the participants that they take notes on the back side of the course text

pages... they have been left blank for this purpose!


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SUGGESTED OUTLINE/TEACHING PLAN

Time Major Interval

ClassSegment

Sub-segmentInterval

Sub-Segment Overheads

30 min. Introduction 2 min.

5 min.8 min.15 min.

Objectives

Failure MechanismsFatigue CharacteristicsExercises

1-2

3-45-78-10

30 min. CrackFormation

2 min.15 min.13 min.

ObjectiveStress-Life ConceptsStrain-Life Concepts

11-1213-1617-21

10 min. Break

45 min. Formation cont 10 min.10 min.10 min.5 min.10 min.

Strain-life continuedVariable AmplitudeNotchesSummary Initiation MethodsQuestions/discussion

17-2122-2526-2728-29

15 min. Crack Growth 10 min.5 min. Objectives/Damage ToleranceStress Intensity Factors 30-3334-35

Major Break

60 min. Crack Growth 5 min.10 min.15 min.15 min.15 min.

Crack tip Stress FieldsFractureFatigue Crack Growth RateCrack Growth LifeRetardation and Cycle-by-Cycle

3637-4041-4647-4950-51

10 min. Break

10 min. Crack Growth 4 min.6 min.

Summary Crack GrowthQuestions/discussion

52

40 min Design/Repair 30 min.10 min.

Design CriteriaLife Extension Techniques

53-5960

10 min. Summary &Closure Summary 61-62


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Instructors Personal Notes

Instructors Outline

1. Introduce course title and yourself.

Major Learning Points

1


Prepared by

A. F. Grandt , Jr.

Professor of Aeronautics and Astronautics

Purdue University

W. Lafayet te, IN 47907

June 1999


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Instructors Outline

1. Introduce course goals:

Overview of fatigue failure mode.

Crack initiation concepts.

Crack growth concepts.

Design implications of fatigue.


1. Overview course goals

2

Objective

Overview nature/consequences of thefatigue failure mechanism

Determine number of cycles required to

develop a fatigue crack

propagate a fatigue crack

Discuss implications of fatigue on

design and maintenance operations


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Instructors Outline

1. Review various structural failure modes. Set

context for discussion of fatigue.

2. Note failure modes may appear in combination

(i.e. corrosion-fatigue or creep-fatigue.

3. Ask students to give examples of the various

failure modes from their personal experience.

4. Ask students to discuss the material properties

associated with individual failure modes.

5. Point out this course deals with fatigue failure

mechanism.


1. Fatigue is one of sever

al failure modes that limit structural design

3

Structural Failure Modes

Excessive Deformation Elastic

Plastic

Buckling

Fracture

Creep

Corrosion

Fatigue

Force

Displacement

Yield

Permanent

displacement

displacement

Force


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Instructors Outline

1. Fatigue is associated with cyclic loading.

2. Fatigue can occur at small stress levels that

wont cause failure if only applied one time.

3. Although nominal stresses can be elastic, fatigue

results from local plastic deformation.

4. Point out the total fatigue process consists of

crack formation, growth, and fracture. This course

will introduce all 3 phases of fatigue life.

5. Pre-existent damage can shorten or eliminate

fatigue crack formation period.

6. Fatigue cracks may form, but then arrest in some

situations, so that fracture does not always result.

7. Another common scenario is for small cracks to

form separately, and this coalesce into larger

cracks.


1. Fatigue is due to repeated loading.

2. Fatigue process involves crack formation,

growth, and final fracture.

3. If the structure contains pre-existent damage, the

crack formation process may be greatly shortened

or eliminated entirely.

4

Fatigue Failure Mechanism

Caused by repeated (cyclic) loading Involves crack formation, growth, and final

fracture

Fatigue life depends on initial quality, load, . . .

S t

r e

s s

Time

Crack Nucleation

Fracture

Crack Growth

Elapsed Cycles N

CrackLength(a)

a

Crack


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Instructors Outline

1. Use exercise for students to become personally

familiar with fatigue.

2. Point out that the fatigue life will depend on how

much the wire is bent each cycle (I.e. applied load).

3. Also point out that surface damage (nicks &

dings) will shorten life by causing early crack

formation.

4. Heating of wire is due to plastic deformation.

Fatigue always involves plastic flow, although it may

be limited to a micro-level.

5. Note magnified photograph of fracture surface of

wire -- note fatigue cracks on top and bottom.

6. Next slide discusses fracture surface in more

detail.


1. Fatigue is a very common failure process that

requires repeated load applications to occur.

2. Although nominal loads may be elastic, plastic

deformation always occurs on a local level.

5

Paper Clip Experiment

Bend wire repeatedly until fracture

Note:

life (number of applied load cycles)

depends on:

applied stress amplitude

component quality (notches, scratches, etc.)

heat emitted >> plastic deformation


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Instructors Outline

1. Early engineers mistakenly thought that fatigue

crystallized the material, causing it to lose its

ductility. Brittle appearance actually due to crack

growth.

2. Fatigue cracks often form at free surfaces --

susceptible to surface damage, corrosion, plane

stress yielding. Individual cracks may form grow,

coalesce before fracture.

3. Macroscopic Beach marks are remnants ofthe crack tip location left when the load changed

significantly or result from environmental influences

-- visible to naked eye.

4. Striations often occur on microscopic level,

and record the crack advance per each cycle of

loading. Striations are positive proof of a fatigue

failure, although they may not always be present.


1. Fatigue fracture surfaces have a characteristic

appearance, both on a macroscopic and

microscopic scale.

2. Fatigue striations represent the crack advance

per cycle of loading (I.e. fatigue crack growth rate),

and offer conclusive evidence of a fatigue failure.

6

Characteristics of Fatigue

Brittle fracture surface appearance

Cracks often form at free surface

Macro/micro beach marks/ striations

0.3 in

Beach marks

20 m

Striations


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Instructors Outline

1. Many types of structures susceptible to fatigue.

2. Examples top row left-right:

fatigue crack between 2 fastener holes in aluminum

aircraft stringer.

fatigue crack surface at bolted fatigue specimen.

Note beach marks, crack origins.

cracked automobile piston.

3. Bottom row, left-right:

broken safety pin. Note is actually a corrosion

fatigue failure since cyclic loading occurs in

presence of aggressiveenvironment.

Cracked doorbell chime. Failure occurred as

stress waves caused by clapper met on opposite

side.

Cracked bicycle pedal crank.


1. Fatigue is a very common failure mode for a

wide variety of structures.

2. It has been estimated that 50 - 80% of all

structural failures are associated with fatigue.

7

Fatigue is problem for many

types of structures


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Instructors Outline

1. Encourage students to discuss their personal

experiences with fatigue failures or fatigue design

requirements.

2. Emphasize that cyclic loading was required, and

that fatigue may have been hastened by poor

quality control.

3. Have students discuss how problem detected --

were cracks easy to find?

4. What design changes or modifications werenecessary.


1. Fatigue is a common problem for many types of

structures.

8

Exercise

Describe fatigue failures from yourpersonal experience

What was cause of fatigue failure?

What was nature of cyclic load?

Was initial quality an issue?

How was failure detected?

How was problem solved?


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Instructors Outline

1. Have students try to estimate how many cycles

of loading will occur for the various examples given.

(Only attempt crude order-of-magnitude estimates.)

2. Point out that not all structures require the same

fatigue life.

The space shuttle motor cases may be

used a dozen times, and only need a

fatigue life of a hundred or so cycles.

The lower wing skin on an aircraft may seemillions of repeated gust loading during the

aircrafts lifetime.

3. Often estimating how many loading cycles will be

required for a given application (or what the design

lifetime should be) is a difficult job.


1. Different components require different fatigue

lives.

2. Some components must resist millions of small

cycles (high cycle fatigue).

3. Other components only need to resist relatively

few large load cycles during their lifetime (low cycle

fatigue).

9

Exercise

Estimate the fatigue lifetime needed for:

Automobile axle Railroad rail

Commercial aircraft components

landing gear

lower wing skin

Highway drawbridge mechanism

Space shuttle solid propellant rocket motor

cases


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Instructors Outline

1. Emphasize that different applications require

different fatigue lives.

2. Roughly speaking, LCF applications are those

that see < 10,000 cycles of loading during the

component life.

3. HCF lives > 100,000 cycles


1. Discuss examples of structures with low cycle

fatigue and high cycle fatigue design requirements.

10

Exercise

Give an example of a High CycleFatigue (HCF) application.

What is the required lifetime?

What are consequences of failure?

Given an example of a Low Cycle

Fatigue (LCF) application.

What is the required lifetime?

What are consequences of failure?


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Instructors Outline

1. The next section of charts deals with

methods to analyze fatigue crack formation .


11

Fatigue Crack Formation


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Instructors Outline

1. The next section deals with methodology to

predict crack formation.

2. Assumes initial cracks/damage are not present

(note this assumption is not always true, and in that

case will employ crack growth methodology --

discussed later).

3. Will briefly examine both stress life and strain life

approaches here.

4. Stress life concepts are the oldest approach to

fatigue, beginning toward the end of the 19th

century.

5. The strain-life method is a more modern

approach developed inthe 1950s.


1. Introduce goals of fatigue crack formation

methodology.

12

Crack Formation

Fracture

Crack Growth

Elapsed Cycles N

CrackLength(a)

Fatigue Crack Formation

Objective Characterize resistance to fatigue crack formation Predict number of cycles to initiate small* fatigue crack

in component

*crack size ~ 0.03 inch

= committee crack

Approach Stress-life concepts

(S-N curves)

Strain-life concepts


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Instructors Outline

1. Original S-N approach developed by Wohler for

RR problems in the 1870s.

2. Test smooth specimen to repeated stress

amplitude -- measure cycles to failure.

3. Emphasize there will be lots of scatter in fatigue

life results. Scatter factors of 4 - 10 in life are not

uncommon. Often more scatter in HCF due to

longer initiation period.

4. Basic S-N curve is limited to constant amplitudeloading, same mean stress.

5. S-N curves are given in data handbooks.

6. Original fatigue work emphasized endurance

limit. Modern applications realize that infinite life

may not be achievable in practice.


1. Stress-life approach relates cyclic stress

amplitude to cyclic life.

2. Involves testing smooth, unnotched specimens

under load controlled conditions.

3. S-N curve may be viewed as a material property.

4. Endurance limit (infinite life) may exist under

some conditions.

13

Stress-life (S-N) Approach

Concept: Stress range controls fatigue life

S

S

Log cycles N

S/2

Note:

Life increases as load amplitude decreases Considerable scatter in data

Run-outs suggest infinite life possible

Life N usually total cycles to failure

S

time

S


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Instructors Outline

1. Note log-log format of S-N curve. Have also

changed life from cycles N to reversals 2N

1 cycle = 2 reversals

change in life units is to be consistent with

format used later in the strain-life method

2. Empirical estimate for endurance limit is based

on steel data. Other materials may not have

endurance limit.

3. Boxed equation is known as Basquins rule.

Simple straight line fit (power law) to log-log plot.

Only applies to stress amplitudes above endurance

limit.

4. Note definition of material properties:

endurance limit, fatigue strength coefficient, fatigue

strength exponent.


1. S-N data are often modeled with simple power

laws.

2. Define endurance limit, fatigue strength

coefficient, fatigue strength exponent.

14

Model Stress-li fe (S-N) Curve

Se = endurance limitfor steels

Se ~ 0.5 ultimate stress Sult Se ~ 100 ksi if Sult 200 ksi

Log reversals 2N

LogS/2

Se

S/2 = f (2N)b

f = fatigue strength coefficient b = fatigue strength exponent

typically -0.12 < b < -0.0

Note: Measure life in terms of reversals 2N

(1 cycle = 2 reversals)


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Instructors Outline

1. Original S-N curve usually established for

completely reversed loading (R = -1, mean stress =

0). Many applications involve other mean stress

levels.

2. Haigh diagram relates stress amplitude and

mean stress conditions that give same life.

3. To avoid measuring S-N curves for all possible

mean stresses, numerical models have been

formed. Models are collectively known asGoodman diagrams, and permit application of R =

-1 data to other mean stress conditions.

4. First boxed equation is Goodman diagram --

other forms exist. Usually applied to endurance

limit conditions.

5. Second boxed equation is mean stress corrected

version of Basquins law. Use for finite life.


1. Mean stress has a significant effect on fatigue

behavior.

2. Tensile mean stress decreases life (are bad).

3. Compressive mean stresses increase life (good).

4. Several numerical models have been proposed

for mean stress effect (see references for more

models).

15

S-N Curve: Mean Stress

Mean stress effects lifestress ratio R = Smin / Smax

Smean = 0.5(Smin + Smax)

Sa = 0.5(Smax - Smin) = S/2

Mean stress models

Sa/Se + Sm/Sult = 1

S/2 = (f - Smean)(2N)b

Mean StressStressAmplitude

N = 106

N = 103

Haigh constant life diagram

S

timeSmin

Smax

S = 2Sa


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Instructors Outline

1. Many other factors influence fatigue life.

2. S-N curves can be generated for various types of

coatings, notches, surface finishes, specimen sizes,

etc.

3. Reference books contain many empirical knock-

down factors for these effects -- detailed discussion

beyond scope of current notes --- see other texts.

4. S-N approach is original methodology for fatigue

problems. Initial emphasis was on characterizingthe endurance limit-- implied small stresses and

nominally elastic behavior.

5. Larger stress levels result in shorter lives and

more plasticity. S-N approach is not as accurate for

LCF applications.


1. S-N approach is simplistic model of fatigue

process.

2. Many practical considerations limit approach,

and result in empirical knock-down factors.

3. Problems associated with notches and variable

amplitude loading are discussed later.

4. S-N approach best suited for HCF problems

where plastic deformation is small.

5. Strain-life method developed for LCF

applications.

16

S-N Curve: Other Factors

S-N curves are very sensitive to

surface finish, coatings, notches

prior loading, residual stresses

specimen size effects, etc.

Many empirical knock-down factors

S-N approach best suited for HCF (High

Cycle Fatigue) applications

limited by local plastic deformation

strain-life approach better for LCF (Low

Cycle Fatigue)


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Instructors Outline

1. Strain life approach developed mid 1950s by

Coffin and Manson for LCF turbine engine

problems.

2. Oriented to situations involving considerable

plasticity.

3. Basic experiment involves subjecting smooth

specimen to controlled cyclic strain range.

4. Due to plasticity, the applied stress needed to

maintain strain limits can change initially.

If stress increases > hardens

If stress decreases > softens per example

on chart

5. Stress range needed to maintain strain limits

usually stabilizes by mid-life.

6. Measure stable stress range and fatigue life

(measured in reversals) for various strain

amplitudes.


1. Strain-life approach is based on strain amplitude

as key parameter that controls life.

2. Describe strain-life experiment.

3. Stress-strain response of material initially

changes due to plasticity, but eventually stabilizes.

17

Strain-life (- N) ApproachConcept: Strain range controls lifeExperiment

Control Measure

Reversals (2Nf)

to failure (1 cycle

= 2 reversals)

Stable stress range needed to maintain

Note: stable usually occursby mid-life (2Nf /2)

time

time


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Instructors Outline

1. Top schematic shows strain controlled test and

resulting stabilized stress range.

2. Stable stress-strain response for one cycle of

strain controlled loading is shown by hystersis

loop. Note plastic deformation.

3. Plot of stable stress amplitude that results as a

function of various applied strain amplitudes is

shown by cyclic stress-strain curve.

4. Cyclic stress-strain curve is a material propertythat indicates cyclic behavior. It may be compared

with conventional static (monotonic) stress-strain

curve to indicate whether material cyclically hardens

or softens.

5. Note numerical model of cyclic curve that defines

K and n. E is conventional elastic modulus.


1. Stress-strain response changes with cycling, but

stable response develops about mid-life.

2. Stable cyclic stress-strain response is shown in

hystersis loop and cyclic stress-strain curve.

3. Cyclic stress-strain curve may be modeled and

used to define cyclic material properties.

18

Cyclic Stress-Strain Curve

Relate stable cyclic stress and strain ranges

time

time

Hystersis loop

/2

/2

/2 = /2E + (/2K)1/n

Cyclic stress-strain curve

E = elastic modulus

K = cyclic strength coefficient

n = strain hardening exponent


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Instructors Outline

1. Coffin and Manson originally related plastic

strain life amplitude with life -- felt plastic strain was

most important parameter for LCF conditions.

2. Note power law model relating plastic strain-life

data. Defines material constants f and c.

3. Note how total strain range (which is applied

during test) is broken into elastic and plastic

components. For uniaxial loading, elastic strain is

simply stress/E.


1. Plastic strain-life curve.

2. Definition of fatigue ductility exponent and fatigue

ductility coefficient.

3. Resolution of total strain amplitude into plastic

and elastic components.

19

Plastic Strain-Life Curve

Relate plastic strain amplitude p/2with reversals to failure 2NfCompute p/2 = /2 - /2E = total - elastic strain amplitudes

Logp

/2

Log 2Nf

p/2 = f (2Nf)c

f = fatigue ductility coefficient

c = fatigue ductility exponent

typically -0.7 < c < -0.5


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Instructors Outline

1. The S-N curve and plastic strain-life curves may

be added to obtain total strain-life behavior.

2. Again note summation of elastic and plastic

strain amplitudes.

3. Elastic strain = stress/E. Dividing Basquins rule

(mean stress corrected version of stress-life) by E

gives elastic strain amplitude versus life.

4. Add to Coffin-Manson plastic strain life to get total

strain-life (note log-log scales).

5. Total strain life approach combines stress-life

and plastic strain live methods >> approach good

for both LCF and HCF problems.


1. Total strain-life approach combines stress-life

and plastic strain-life approaches.

20

Total Strain-Life CurvePlot total strain amplitudes versus life 2Nf

total /2 = /2 = 0.5 elastic +0.5 plastic = /2E + 0.5 plastic

/2 = {(f - Smean)/E}(2N)b + f (2Nf)c

p /2 = f (2Nf)c

/2E = {(f - Smean)/E}(2Nf)b

Log 2Nf

Logstrainamplitude

2Nt = transition life


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Instructors Outline

1. Note plastic-strain life curve dominates for short

lives (LCF).

2. Elastic strain life dominates for HCF.

3. Transition life life defined as life when elastic

and plastic strains are equal -- can be used to

separate HCF from LCF.

4. Material selection depends on life regime and

often involves trade-off.

LCF properties emphasize ductile behavior.

HCF properties emphasize high strength

behavior.


1. Total strain-life approach applicable to both HCF

and LCF problems.

2. Transition life separates HCF and LCF behavior.

21

Total Strain-Life

Note:

Plastic strain dominates for LCF

Elastic strain dominates for HCF

Transition life 2Nt separates LCF/HCF

p =f (2Nf)c

/2 = {(f - Smean)/E}(2N)b + f (2Nf)c

Log 2N f

Logstrainamplitude

/2E = {(f - Smean)/E}(2Nf)b

2Nt = transition life

LCF

HCF


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30



Instructors Outline

1. Discussion so far has focused on constant

amplitude loading --- many practical problems

involve variable amplitude loading (ask students for

examples).

2. Miners rule provides a simple way to estimate

variable amplitude lives from constant amplitude

data. Can be used with either stress-life or strain

life approaches.

3. Note that Miners rule must be used with caution,as it assumes linear cumulative damage that may

not occur in practice.

4. Load interaction effects are often observed in

variable amplitude fatigue tests (see later chart).

Miners rule ignores load interaction.


1. Many problems involve variable amplitude

loading conditions.

2. Miners rule provides simple method to predict

variable amplitude behavior from constant

amplitude stress-life or strain-life data.

3. Miners rule must be used with extreme caution.

4. Variable amplitude loading can lead to mean

stresses that result from plastic behavior during

large overloads.

22

Variable Amplitude Loading

Load amplitude varies in many applications

Use of constant amplitude S - N or- Ndata requires damage model

Miners rule*

(Ni/Nf) = 1

Ni = number of applied cycles of stress amplitude SaiNf= fatigue life for Sai cycling only

*Use with caution!

S

time

Ni

2Sai


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31



Instructors Outline

1. This example demonstrates Miners rule for

variable amplitude loading.

2. The example also demonstrates use of mean-

stress corrected Basquins rule.

3. Here, one duty cycle (1 block of loading) consists

of

100 reversals of +/- 80 ksi1000 reversals of 0 to 100 ksi

1000 reversals of -100 to 0 ksi

4. How many blocks can be repeated to a smooth

specimen before it fails?


1. Application of Miners rule to a variable

amplitude stress history.

2. Use of mean stress corrected version of

Basquins rule.

23

Example Problem

Assume:f = 220 ksi, b = - 0.1 stress history shown (1 block of loading)

Find: number of blocks to failure

+ 80 ksiS

time

- 80 ksi

- 100 ksi

+ 100 ksi

2N = 100

2N = 1000

2N = 1000S

S


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32



Instructors Outline

1. First two columns are given stress amplitudes

and mean stresses for parts of duty cycle.

2. Third column is fatigue life computed for

individual stress conditions in columns 1 and 2.

These lives are obtained from the Basquins rule

(upper right hand box).

4. Note big difference in life for 50 ksi stress

amplitude with + or - 50 ksi mean stress (206,000

vs 21 x 10

6

).3. Fourth column is number of applied stress

amplitude/mean stress combinations in one loading

block.

4. Fifth column is ratio of applied cycles/fatigue life

(column 2/3). Summation is damage per load

block. Inverse is number of blocks to failure.


1. Application of Miners rule.

2. Application of mean stress corrected Basquinsrule.

24

Solution

(N

i/N

f) = 1 2Nf= {(S/2) / (f - Smean)}1/b

(Ni/Nf) = 1

When:

1/0.0089

= 112.5

Answer

112 blocks

S/2(ksi)

Smean(ksi)

2Nf 2Ni Ni/Nf

80 0 24,735 100 0.0040

50 +50 206,437 1000 0.0048

50 -50 21 E6

1000 4.74 E-6

0.0089


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Instructors Outline

1. Note development of mean stresses in a hi-lo

block of strain controlled loading.

2. Note initial large completely reversed strain

amplitudes. Follow strain-time plot down to stress-

strain (hystersis curve) to obtain the resulting

completely reversed stable stress-time history.

3. When strain changes to the smaller completely

reversed amplitudes.

Stable hystersis loop is now small redloop inside the original large loop.

Although applied strain is completely

reversed, stress amplitude has

compressive mean and big effect on life.

4. If hi-lo change had occurred after tension peak

>> tensile mean stress.


1. Demonstrate how the sequence of applied loads

can introduce mean stresses that can have large

influence on life.

2. Point out limitation of Miners rule.

25

Load Sequence Effects Hi-lo strain sequence

results in compressive

mean stress increases life Note last large peak

was compression here

If last peak had beentension, would result in

tensile mean stress

decreases life

Load sequence important!

t

t

Mean stress


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34



Instructors Outline

1. Notches represent a difficult, but practical fatigue

problem.

2. Schematic S-N curves are shown for notched

and smooth fatigue specimens (nominal stress

amplitudes shown in both cases).

3. Notches usually more effective in reducing HCF

than LCF life.

4. Influence of notch depends on material

response. Define this effect by fatigue notchconcentration factor = ratio of smooth/notched

fatigue strengths at some reference life (usually 106

cycles).

4. Note if Kf= 1, the notch has no effect in reducing

fatigue life. This is desirable property, and may

occur in ductile materials.

5. If Kf= elastic Kt notch significant in reducing life

(often occurs in high strength materials).


1. Point out influence of notches on fatigue life.

2. Define fatigue notch concentration factor

(distinguish from elastic stress concentration factor).

26

Notch Fatigue Notches can reduce life

Define Fatigue Notch Factor

Kf

Kf = Smooth/notch fatigue

strength at 106 cycles

= Ss /Sn1 < Kf< Kt

(Kt = elastic stress

concentration factor)

Kf= 1 no notch effectKf= Kt full notch effect

Smooth

Notch

S/2

Log cycles N

Ss /2

Sn /2

106


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Instructors Outline

1. Are several approaches to analyzing notch

problem.

2. This slide shows use of Neubers rule to relate

nominal stress/strain amplitudes away from notch

(where behavior is often elastic) with larger

stress/strain at tip of notch.

3. Fatigue life is controlled by notch stress/strains,

which are often plastic.

4. The three boxed equations can be solved to findfatigue life for notched member.

Obtain Kffrom testing or handbook.

Stress analysis gives nominal stress/strain

amplitudes awary from notch (may be

elastic).

The 3 unknowns are usually notch

stress/strain amplitudes and fatigue ife.


1. Application of Neubers rule to notch fatigue

problem.

27

Neubers Rule

Kf= fatigue notch concentration factor

(s,e) = nominal stress/strain ranges(away from notch)

(,) = notch stress/strain rangesNeubers rule relates notch and

nominal stress/strain behavior

Solve with:

Kf2se =

/2 = /2E + (/2K )1/n

/2 = {(f - Smean)}(2Nf)b + f (2Nf)c

(,)

(s,e)


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Instructors Outline

1. Next two slides summarize the stress-life and

strain-life approaches to fatigue initiation life. Will

discuss crack growth life next.

2. Point out have only provided brief introduction to

approaches, and that many other details are

available in the literature.

3. Definition of initiation or crack formation life is

problematic.

S-N or strain-life tests are usuallyconducted to failure (I.e. total life).

Specimens are small, however, so crack

growth portion usually short >> often treat

as initiation methods.

Unless crack length actually measured

during test, often assume committee crack

at end of these lives.


1. Summarize stress-life and strain-life approaches

to fatigue.

28

Summary Initiation Methods Total strain-life approach combines:

original S-N curve (best suited for HCF) and

plastic strain-life method developed for LCF

problems

S-N and strain-life often viewed as crack

initiation approaches

actually deal with life to form small crack

crack size implicit in specimen/test procedure

typically assume committee crack ~ 0.03 in.


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37



Instructors Outline

1. Point out that notch fatigue and sequence effects

are complex problems that are only introduced here.

2. Encourage students to read more on these

subjects.


1. Summarize notch fatigue and sequence effects.

29

Initiation Summary Cont

Notches increase local stress/strain andoften are source for crack formation

complex problem leads to local plasticity

characterize by fatigue notch concentration

factor Kf,, Neubers rule

Load interaction effects result in local

mean stress

can increase/decrease life

invalidate Miners rule


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38



Instructors Outline

1. Introduction to the next group of slides that deal

with methodology to predict fatigue crack growth.

2. This will involve a different viewpoint about

fatigue, and will entail a different technical

approach.

3. The focus will be entirely on the crack growth

phase of fatigue.


1. Now consider fatigue crack formation concepts.

30

Fatigue Crack Growth


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39



Instructors Outline

1. Assume now that the component is cracked

before subjected to cyclic loading.

2. The crack initiation phase is ignored entirely. In

many cases this will be a conservative assumption,

but it is based on prior experience where several

new structures failed prematurely by fatigue that

initiated at pre-existent defects associated with poor

quality control.

3. The fatigue crack growth approach wasdeveloped in the 1960s where conventional fatigue

design procedures (i.e. S-N approach) resulted in

several designs that could not resist pre-existent

structural damage.

4. Fatigue crack growth concepts are a key

element of damage tolerant design methods.


1. Focus on fatigue crack growth process.

2. Introduction to goals of a damage tolerant

design.

31

Crack Growth Approach

Assumes entire lifefatigue crack growth

ignores initiation

assumes component

cracked before cycling begins

Used with damage tolerant design

protects from pre-existent (or service) damage

based on linear elastic fracture mechanics

Elapsed Cycles N

Crack Growth

CrackLength(a)

Fracture

Initial crack


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40



Instructors Outline

1. Define damage tolerance: ability to resist pre-

existent damage for given period of service.

2. Is a measure of the safety provided to

unanticipated damage occurrence. Damage

tolerance is essential for structures whose failure

can result in loss of life (e.g. aircraft, nuclear power

plants, etc.).

3. Initial damage can be due to material

imperfections (inclusions, porosity, etc.),manufacturing problems (poor welds, burrs, etc.), or

it may be induced during service (e.g. foreign object

damage--bird strikes by aircraft, battle damage,

corrosion, etc.)

4. Damage tolerant design codes specify the initial

crack size to be considered. Based on what can be

missed by inspection, experience, etc.


1. Definition of damage tolerance.

2. Discussion of the types of initial damage that

might be present in a new structure.

32

Damage Tolerance

The ability of a structure to resist priordamage for a specified period of time

Initial damage

material

manufacturing

service induced

size based on

inspection capability,

experience, . . .time

Cracksize

Desired Life


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41



Instructors Outline

1. Establish the two major goals for this section:

Determine crack size that will cause

fracture (i.e. end of fatigue life).

Determine how long it takes for a fatigue

crack to grow to this size.

2. Also will establish the material properties related

to fatigue crack growth.

3. Will use linear elastic fracture mechanicsconcepts developed in the 1950s and 60s to

analyze cracks.

4. Key parameter will be the stress intensity factor

K. Both fracture and fatigue crack growth rate will

be expressed in terms of this parameter.


1. Objective is to predict fracture and fatigue crack

growth rate.

2. Will employ linear elastic fracture mechanics

concepts.

33

Fatigue Crack Growth

Objective Characterize material resistance to fatigue crack growth

Predict catastrophic fracture and subcritical crack

growth

Approach Assume crack growth

controlled by stress

intensity factor K

fracture

growth rate da/dNElapsed Cycles N

Crack Growth

CrackLength(a)

Fracture

Initial crack


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42



Instructors Outline

1. The stress intensity factor is the key parameter

for analyzing fatigue crack growth.

2. It relates crack length, remotely applied stress,

and crack geometry . (point out is dimensionlessfunction of crack length).

3. Emphasize that this is a crack term. Make sure

students dont confuse with the familiar stress

concentration factor Kt.

Kt is for notches, not cracks. It is the ratioof local to remote stress (is dimensionless)

Stress intensity factor is a crack term. Note

that it has units of stress-length1/2 (i.e., ksi-

in1/2 or Mpa-m1/2.

4. Stress intensity factor has a rigorous definition in

the context of crack tip stress fields.


1. Stress intensity factor is key parameter for

analyzing crack growth.

34

Stress Intensi ty Factor K IKI is key linear elastic fracture mechanics

parameter that relates:

applied stress: crack length: a

component geometry: (a)((a) is dimensionless) a

Crack

= 1.12

aK=I

Note units: stress-length1/2


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Instructors Outline

1. Two sample stress intensity factor solutions are

given.

2. When cracks are small in both cases (a/W ~0),

the terms simplify.

= Secant term ~ 1 for center crack

~ 1.12 for edge crack

3. While the particular solutions given here, will be

used later, emphasize that many solutions areavailable for other crack configurations (see

reference handbooks). Its shown later that one can

characterize fracture and fatigue in terms of the

stress intensity factor.

4. The examples discussed here are all for Mode I

loading (remote stress applied perpendicular to

crack plane). See references for modes II and III

results which entail shear loading.


1. Examples of stress intensity factors for two

specific crack geometries.

2. Handbooks contain solutions for many other

crack configurations.

35

Stress Intensity Factors

2a

W

K a Seca

W

=

1

2

= Remote Stress

20 95

a

W .

W

a

h

a

W

0 6.

a

W

h

W

10.

K a

aW

aW

=

= +

112 0 231 10. 55. . aW

aW

aW

+ 2173 30 392 3 4

. .

For and

Many KIsolutions

available


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44



Instructors Outline

1. These equations indicate that the stress intensity

factor is related to the stress distribution near the

crack tip, and that KI has a rigorous mathematical

basis.

2. Point out that all crack configurations have same

elastic stress field at tip. All differences between

various crack problems are contained in the stress

intensity factor KI term.

3. Point out that these elastic results give infinitestresses at crack tip (examine limit as distance r

from crack tip approaches 0). Although yielding will

occur at tip, it is often small, and the stress intensity

factor remains a useful parameter.

4. Derivation and interpretation of these equations

is beyond current scope. See references.


1. The stress intensity factor is related to the elastic

stress filed near a crack tip.

2. It can be rigorously proven (see references) that

crack tip stresses for all crack problems are

characterized by the stress intensity factor.

3. Thus, stress intensity factor is a key crack

parameter.

4. The following sections demonstrate how fracture

and crack growth can be characterized by K.

36

Crack tip Stress Fields

( )

+==

==

=

+=

=

yxz

z

yzxz

Ixy

Iy

Ix

r

Kr

K

r

K

strainplane

0stressplane

02

3cos

2cos

2sin

2

2

3sin

2sin1

2cos

2

2

3sin

2sin1

2cos

2

Theory of elasticity gives elastic stresses near crack tip in

terms of stress intensity factor KI

All crack configurations have same singular stress field at tip(are similar results for other modes of loading, i.e., modes II and III)

Crack

x

y

r

xy

y

x


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45



Instructors Outline

1. Schematic representation of fracture stress

versus critical crack size for center crack specimen.

Note K equation for infinite sheet width ( =1).

Line gives condition that K = constant =

material toughness -- fits most data except

for small cracks.

2. Crack tip plasticity limits application of Kc

fracture criterion for small cracks.

Note deviation in small crack regime.

Fracture stress when there is no crack is

tensile ultimate

3. Emphasize that this simple criterion is quite

powerful. Relates crack length, stress, crack

geometry, and material in simple statement.


1. Kc Fracture criterion to determine fracture

conditions for cracked member.

2. Fracture toughness as material property.

3. Crack tip plasticity limits small crack

applications.

37

Kc Fracture Criterion

Fracture occurs whenK > constant = Kc

Kc = material property

= fracture toughness

Criterion relates:

crack size: a

stress: geometry: (a) material: Kc

Plasticity limits small

crack applications

2a

ult

FractureStress

Crack Size a

( )K a ac =


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47



Instructors Outline

1. This example demonstrates how fracture

toughness concepts can be used to predict fracture.

2. Point out there are two different specimen

configurations made from the same material (same

plate thickness).

3. Use the results of the edge- cracked specimen to

predict fracture for the center-cracked member.


1. Example of fracture toughness criterion.

39

Fracture Example

Member A fractures whencrack length a = 2.0 inch

and remote stress = 5 ksi

What stress will fracture

member B (assume same

material)?

2.0 in

4.0 in

5 ksi

5 ksi

A

5 in

8 in

= ?

= ?

B


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48



Instructors Outline

1. Begin solution by obtaining stress intensity factor

solutions for the two specimens -- given in earlier

charts. Note that there are handbooks that have

these types of solutions for many other crack

configurations.

2. Compute the stress intensity factor that causes

fracture for the edge-crack solution.

Note that the beta value in this case is 2.83.

The stress intensity factor for the load/cracklength that causes fracture is 35.4 ksi-in1/2.

This is Kc = value that will cause fracture in

all members made from this plate.

3. Compute K for center-crack specimen. Set = Kcand solve for fracture stress. Note total crack length

2a = 5, so a = 2.5.


1. Calculation of stress intensity factors.

2. Use of fracture toughness concepts to predict

fracture load.

40

Fracture Example SolutionEdge crack

K = (a)1/2(a) = Kc at fracture

a/w = 2/4 = 5 a = 2 = 2.83Kc = 35.5 ksi-in

1/2 = constant

Center Crack

K = ( a)1/2(a) (a) = [Sec ( a/W)]1/2

a = 2.5 W = 8 = 1.34K = Kc at fracture = 35.5

2.0 in

4.0 in

5 ksi

5 ksi

5 in

8 in

= ?

= ?

a

W

a

W

=

+ 1 12 0 231 10. 55. .

a

W

a

W

a

W

+

21 73 30 39

2 3 4

. .

f = 9.5 ksi


51/144


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50



Instructors Outline

1. Although both experiments involve constant

amplitude loads, they give entirely different crack

growth behaviors.

2. For remote loading, the crack growth rate da/dN

increases as crack length a increases. Also note

from K solution that cyclic K increases as a

increases.

3. For crack face loading, growth rate da/dN

decreases as crack length increases (i.e. rate slowsdown). Note, however, that the cyclic K also

decreases in this case as the crack length gets

larger (a is in denominator, B = thickness).

4. Crack face pressure K solution may seem

strange to students, but is correct solution for this

configuration (note has same units as before).

5. Note cyclic K here = K at max load - K at minload per cycle.


1. Cyclic K controls fatigue crack growth rate.

42

Measure Crack Growth

2a

Remote Load

2a

P

Crack Face Load

da

dN

CrackLength(a)

Number of Cycles (N)

=K PBa

K =

a

CrackLength(a)


da

dN

a*


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51



Instructors Outline

1. Prior chart indicated that the two specimens

gave entirely different fatigue crack growth rate

behavior under constant amplitude loading. It was

noted, however, that cyclic K controlled fatigue

crack growth rate.

2. Now plot crack growth rate at a given crack

length versus the cyclic K for that crack length.

Use K solutions given for the two

specimens.Now the fatigue crack growth behavior for

these specimens is identical when plotted

versus K.

3. Thus, K is key parameter that controls rate.


1. Fatigue crack growth rate is controlled by cyclic

stress intensity factorK.

2. The da/dN - K plot is the material property thatcharacterizes fatigue crack growth.

43

Correlate Rate da/dN vs K

CrackLength(a)


da

dN

2a

2a

CrackLength(a

)


da

dN

a*

KthKc

Log K

Logda/dN

K a=

KP

B a=


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52



Instructors Outline

1. The da/dN - K plot is a material property --- isgiven in material handbooks.

2. Note upper asymptote (Kc) where fracture

occurs.

3. The lower asymptote defines a threshold Kth.

IfK < Kth, da/dN = 0.

This result is analogous to the S-N curve

endurance limit, except here we have thesituation where a cracked member does not

fail under cyclic loading.

The Kth threshold is usually a smallnumber, and it is difficult to design for zero

crack growth (would involve very small

stress levels).


1. The da/dN - K plot is a material property.

2. Definition of threshold Kth.

44

da/dN Vs K

KthKc

LogK

Logda/dN

Note:

K correlates fatiguecrack growth rate da/dN

K accounts for crackgeometry

No crack growth for

da/dN


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53



Instructors Outline

1. Note sample da/dN - K data taken from Mil-Handbook 5.

2. Similar data are available for other materials in

this and several other handbooks. Thus, the da/dN

delta K curve is a common format for documenting

fatigue crack growth data.

3. Note the effect of stress ratio R.

In general, increasing R increases the

fatigue crack growth rate at the same deltaK level.

Thus, attempts to model the fatigue crack

growth data will need to include the R ratio

(or some other measure of mean stress) as

a parameter.


1. Example of actual fatigue crack growth data

taken from a handbook.

2. Increasing the stress ratio increases fatigue

crack growth rate at same level of stress intensity

factor.

45

Sample Crack Growth Data

da/dN - K data for7075-T6 aluminum

Note effect of stress

ratio R = min/max

stress (da/dN as R) Reference: Military

Handbook-5

Other handbook data

are available


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54



Instructors Outline

1. The objective now is to model the da/dN - Kdata with equations that can be used for subsequent

analysis. Note this is primarily a curve fitting

exercise.

2. The Paris and Forman equations are two simple

growth rate models.

Note the Paris law is a straight line on the

log-log plot, and does not show the

asymptotic behavior at small and largecyclic Ks or depend on R.

Forman equation has upper asymptote and

depends on R.

3. These are only two examples of the many

equations that have been used to model fatigue

crack growth data (see Refs. for more).

4. All of the models will involve determining some

empirical constants such as those shown here.


1. Introduction to modeling the da/dN - K data.

46

Model da/dN - K CurveFit test data with numerical

models such as:

KthKc

LogK

Logda/dN

da

dNF K= ( ) da

dNC K

m=

da

dN

C K

R K K

m

c

=

( )1

Here C, m, Kc are

empirical constants

R = min/max stress

(are many other models)

Paris

Forman


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55



Instructors Outline

1. Return to the main objective of determining the

crack growth life.

2. The key concept is based on the fact that the

fatigue crack growth rate is a function of the stress

intensity factor da/dN = F(K).

The particular function will be determined

with baseline experiments that establish the

da/dN - K data.

In addition to K, F(K) could depend on Ror other values.

3. Integrating the da/dN law gives the boxed

equation. Crack length a is the variable of

integration and initial/final crack lengths are the

integration limits.

af is specified by Kc condition if life is to

fracture

ao is set by inspection, code, etc.


1. Calculation of fatigue crack growth life by

integrating da/dN model.

47

Compute Fatigue Life Nf

ao, af = initial, final crack sizes

F(K) = function of:

cyclic stress: , R, . . . crack geometry: (a) crack length: a

material

N

da

F Kf

a

a

o

f

= ( )da

dN F K= ( )

time

2a


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56



Instructors Outline

1. Now demonstrate the life calculation procedure

with a simple example that can be solved closed

form.

2. Note given geometry, stress, da/dN model, etc.

3. Final crack size af= 10 is computed from the

fracture toughness Kc criterion.

Note that = 1.12 for an edge-crack in asemi-infinite sheet. See earlier K solution

for edge-crack when a/W ~ 0.

4. Results are desired for two initial crack sizes.


1. Demonstrate fatigue life calculation.

48

Example Life Calculation

a

Crack

= constant

time

Given: edge crack in wide plate

Kc= 63 ksi-in1/2

initial crack ai = 0.5 inchcyclic stress = 10 ksi, R = 0

( = max = 10 ksi)

da/dN = 10-9K4

Find: a) cyclic life Nf

b) life if initial crack size

decreased to ai = 0.1 inch

Note: at fracture

K = Kc = 63 = 1.12max (a)1/2

final crack af= 10 inch


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Instructors Outline

1. Solution is obtained by integrating basic da/dN =

F(K) model.

2. Note in this case that Paris model is used for

F(K) = CKm

3. Since and are constant in this case(independent of a), the integration is quite simple,

and a closed form solution results.

4. In other situations, closed form integration is not

possible

The expression may be a function ofcrack length a (see earlier expression).

F(K) may be more complex (see Forman

model)

Applied stress may not be constantamplitude.

4. In those cases numerical integration is readily

accomplished with a computer program.


1. Example life calculation involving direct

integration of da/dN model.

49

Solution

[ ] = =

da

C K

da

C am ma

a

a

a

o

f

o

f

112. Nf

( ) ( )[ ]N

C m

a af m fm

o

m=

1

112 1 5

1 5 1 5

. .

. .

K a= 112.da

dNC Km

=

a) Nf= 12,234 cycles (ai = 0.5)

b) Nf= 63,747 cycles (ai = 0.1)

Note: big influence of initial crack length!


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58



Instructors Outline

1. Load interaction effects can complicate fatigue

crack growth life calculation for variable amplitude

loading.

2. The fatigue crack retardation phenomenon can

be significant.

Note peak overload can increase life

(assuming it is not large enough to cause

fracture)

Fact that large tensile load can be beneficialis not intuitive, but is readily explained by

crack tip plasticity considerations that are

beyond present scope.

There are several numerical models for

crack retardation (encourage students to

examine references).

Retardation can be analyzed and

accounted for.


1. Fatigue crack retardation can delay subsequent

crack growth.

2. Retardation is a load interaction effect that must

be accounted for.

50

Fatigue Crack Retardation

Time

AppliedStre

ss()

Overload

Without Overload

With Overload

RetardationCrackLength(a)

Elapsed Cycle (N)

Note load interaction effect Tensile overload can retard crack growth (increase life)

Life increase due to crack tip plasticity

Depends on magnitude/sequence of overload, material,

Are empirical retardation models


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Instructors Outline

1. For variable amplitude loading, the life cannot be

calculated by direct integration between initial and

final crack lengths (i.e. stress depends on crack

length a, and must remain under integral sign).

2. For these cases, crack growth is computed on a

cycle-by-cycle basis.

Note that K will change with each cycle as

the crack length a increases (since , a,

and all change with each cycle).F(K) and da/dN can be computed for each

cycle, however, and summed for the total

life.

One can also account for crack retardation

in this calculation.

3. Many computer programs are available for these

calculations.


1. Cycle-by-cycle calculation schemes are a

powerful and general approach to accomplish

fatigue crack growth life calculation.

2. Many general computer codes are available for

the engineer to make black box life calculations for

complex fatigue crack growth problems.

51

Cycle-by-Cycle Calculation

Compute cycle-by-cycle growth in crack length a

acurrent = aprior+ da/dNcurrent

da/dNcurrent = F(Kcurrent) * Retardation term

Sum for all cycles in spectrum

Powerful technique for computer programming

n

n+1AppliedStress()

Time (t)

Variable amplitudeloading prevents

simple life integration


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Instructors Outline

1. Summarize the fatigue crack growth analysis

procedure.

2. Method is used with damage tolerant design

concepts that conservatively assume the structure

contains pre-existent cracks.

3. Key point is the stress intensity factor controls

fracture and fatigue crack growth in many practical

situations.

4. Method is limited by crack tip plasticity in somecases that require more complex analysis

procedures (see references).

5. Encourage students to consult references for

more details of crack growth methodology.

6. Emphasize, however, that analysis of fatigue

crack growth is possible for many engineering

applications.


1. Summary of key concepts related to fatigue

crack growth.

52

Crack Growth Summary

Fracture mechanics approach assumes

entire fatigue life is crack growth Stress intensity factor K controls fracture

and growth rate da/dN

K = [a]1/2(a) Fracture: K = Kc

Fatigue: da/dN = F(K) Integrate da/dN for life

Are load interaction and other effects (see

references)


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Instructors Outline

1. The final set of slides deal with fatigue design

concepts and a brief introduction to repairing fatigue

damage.


1. Transition slide to final portion of course.

53

Fatigue Design/Repair

Concepts


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Instructors Outline

1. Several different design criteria have been

developed to design fatigue resistant structures (i.e.

determine component dimensions and materials).

2. These approaches differ in the philosophy one

takes regarding the presence of initial fatigue cracks

and the desired final life.

3. Companies follow different design concepts

depending on the application. One may, in fact, use

different fatigue design criteria for differentcomponents in the same structure.

4. The following slides attempt to overview several

common approaches to fatigue design.

5. Ask students to give examples from their

personal experience as the various approaches are

described.


1. Introduce various design criteria that have been

employed for fatigue resistant structures.

54

Design Philosophies

Fatigue Design Criteria Infinite Life

Safe-Life

Damage Tolerant

Fail-safe

Slow crack growth

Retirement-for-cause

a

Crack

S t r

es

s

Time

Crack Formation

Fracture

Crack Growth

Elapsed Cycles N

Pre-CrackC rackLength(a)


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Instructors Outline

1. To achieve infinite life, the material needs a well

defined endurance limit, the component must

remain in pristine condition, and service loads can

never exceed those assumed in design.

2. Unfortunately, these assumptions often cannot

be achieved in practice. Other factors also make

infinite life impractical for complex components:

Low stress levels lead to heavy and/or

expensive components.Manufacturing or service induced damage

often lead to early crack formation.

Service loads often exceed those assumed

in design.

3. Engineers must recognize infinite life is probably

impossible, and most components will have a finite

life that they must determine.


1. Infinite life design criteria are based on

endurance limits or threshold K concepts.

2. Although a laudable goal, infinite life is usually

not achievable in practice.

3. The engineer must determine what the actual

component life could be, and make sure it is retired

or repaired before failure occurs.

55

Infinite Life Criterion

Design Goal: prevent fatigue damage from everdeveloping (i.e. infinite life)

Usually based on endurance limit

Could also employ threshold K concepts

Leads to small design stresses/heavy members

Limited to simple components/loading

Often impractical/not achievable in practice

Weight critical structure

Complex loads


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Instructors Outline

1. Safe-life design recognizes the component will

have a finite fatigue life and that there is much

scatter in fatigue behavior.

2. Safety is provided by determining the variability

in the component fatigue life through test and/or

analysis.

The mean life is then divided by a safety

factor to determine the safe operating life.

Safety factors of 4 are common, but couldbe as large as 10.

3. Safe-life has been used for aircraft design, but

has been unreliable due to the possibility of initial or

service induced damage that eliminates the crack

formation period of fatigue life and defeats the

safety factor. It is being replaced by damage

tolerance designs.


1. Description of the safe-life design procedure.

2. Potential shortcomings of safe-life designs.

56

Safe-Life Criterion

Design goal: component is to remain crack free for

finite service life Assumes initial crack-free structure

Establish mean life by test/analysis

Safety factors account for scatter

predicted mean

Desired life = mean/S.F.

Design Life

Failure

Occurrence

1 32 4

Problems:

large safety factor

no protection from

initial damage


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Instructors Outline

1. The remaining criteria are all forms of damage

tolerance where pre-existent cracks are assumed.

One designs/manages the structure so that these

cracks cannot cause catastrophic failure during

service.

2. The fail-safe criterion employs redundant

components for safety. Although an initial crack in

one component could cause it to fail prematurely

(first crack growth curve), adjacent members pick

up the failed components load.

3. The second crack growth curve is for the

redundant member. Again, for safety, it is assumed

to contain a small pre-crack. Since the loads in the

redundant member increase, it will fail earlier than

normal.

4. Note that for approach to be successful, the

original failure must be detected and repaired.


1. The fail-safe design criterion is a form of damage

tolerant design that protects from unforeseen

damage.

2. This is a preferred design approach for many

aircraft components.

57

Fail-Safe CriterionDesign goal: contain single component failure

without losing entire structure Assumes crack is present

Provide alternate load paths, redundant structure, crack

stoppers, etc.

Requires detection of 1st failure

Time

Cracksize

1st member

2nd memberCrack arrest


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Instructors Outline

1. The slow crack growth approach is for the

situation where redundant components are not

possible.

2. Safety is provided by ensuring that the crack

growth lives of all critical members exceed the

desired service life by some specified safety factor

(typically 2).

3. Note that materials selection and component

dimensions are based on crack growth analyses.4. The initial crack size assumption is based on the

largest possible crack that could missed by

inspection and wind up in a new component.


1. The slow crack growth design criterion is a form

of damage tolerance employed for primary

structural members that cannot be protected by

redundant load paths.

58

Slow Crack Growth Criterion

Design goal: prevent initial crack from growing tofracture during life of structure

Pre-existent crack size specified by inspection

limits, experience

Crack growth life

> service life x S.F.

Based on fatigue

crack growth

resistance

Emphasizes nondestructive inspection

Cracksize

Desired Life

time

Fracture


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Instructors Outline

1. Periodic inspection and repair are used to obtain

the desired life.

2. The first inspection period could be based on

fatigue crack growth concepts (as shown here) or

on crack formation methods (stress-life or strain-life)

where the component was originally assumed to be

crack free.

3. Following the first inspection, all cracked

members are repaired or retired, and thecomponent(s) returned to service.

4. The second inspection is based on crack growth

analyses, assuming an initial crack that could have

been missed by the original inspection.

5. The process can be repeated indefinitely until

the cost of inspection and repair becomes

unacceptable (note that eventually there will be

many cracks to repair).


1. Retirement-for-cause is a life management

philosophy that incorporates repeated inspection

and repair periods to obtain the desired service life.

59

Retirement-for-Cause

Failure size

Crack

Length

Time

inspect/repair

Design goal: Use periodic inspection/repairto achieve desired fatigue lives

Limited by repeated maintenance economics


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Instructors Outline

1. Outline life extension concepts.

2. Following inspection, uncracked members are

assumed to contain crack sizes below the

inspection threshold.

3. Life extension can be achieved by reducing

applied stresses or by introducing beneficial (i.e.

compressive) residual stresses. Common residual

stresses techniques are indicated.

4. Reducing applied stresses is achieved by localreinforcement or by restrictions on usage.

5. Patching or stop drilling are particularly effective

crack repairs. (Stop drilling entails drilling a hole at

the crack tip -- turns it into a notch. A temporary fix

since new fatigue crack can form at the stop drill

hole.) Composite or metal patches can be bonded

or mechanically fastened.


1. Several methods are provide to solve fatigue

problems and to increase component life.

60

Life Extension Concepts

Shot peenHole coldwork

Interference fastenersOverstress, etc.

Introduce BeneficialResidual Stresses

MetalComposite

Mechanical FastenBond

Doublers

HCF damping materials

Reduce Stressvia Reinforcement

Weight limitsFlight restrictions

etc.

Reduce OperatingLoads

No Cracks Found(assume small cracks)

MetalComposi te Mechanical Fasten

Bond

Patches

Replace componentStop drill cracks

Welding

Repair CrackedStructure

Cracks Found

ComponentInspection


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Instructors Outline

1. Fatigue is a complex problem that is aggravated

by many factors and can occur in many types of

structures.

2. Several methods have been developed to

analyze/design for fatigue. Methods differ primarily

in the philosophy one has regarding the possibility

for pre-existent damage and the resulting

consequences.

3. Fatigue is a process that involves muchvariability. Although not emphasized here,

probabilistic tools are available in the literature to

charac

asme 20- 20fatigue 20for 20engineers

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