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7/29/2019 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)
Midwest Regional Office1117 S. Milwaukee Ave.Building B - Suite 13Libertyville, IL 60048-5258847-680-5493800-628-6437847-680-6012 (FAX)
Northeast Regional Office326 Clock Tower Commons
Route 22Brewster, NY 10509-9805914-279-6200800-628-5981914-279-7765 (FAX)
International Regional Office1-800-THE-ASME
Southern Regional Office1950 Stemmons Freeway Suite 5068Dallas, TX 75207-3109214-800-4900800-445-2388
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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Fatigue for Engineers
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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3
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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4
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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Fatigue for Engineers
Instructors Personal Notes
Instructors Outline
1. Introduce course title and yourself.
Major Learning Points
1
Fatigue for Engineers
Prepared by
A. F. Grandt , Jr.
Professor of Aeronautics and Astronautics
Purdue University
W. Lafayet te, IN 47907
June 1999
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Fatigue for Engineers
Instructors Personal Notes
Instructors Outline
1. Introduce course goals:
Overview of fatigue failure mode.
Crack initiation concepts.
Crack growth concepts.
Design implications of fatigue.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
Instructors Outline
1. The next section of charts deals with
methods to analyze fatigue crack formation .
Major Learning Points
11
Fatigue Crack Formation
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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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21
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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26
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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27
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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28
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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29
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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
Fatigue for Engineers
Instructors Personal Notes
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?
Major Learning Points
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
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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33
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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
Fatigue for Engineers
Instructors Personal Notes
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).
Major Learning Points
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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35
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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36
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
1. Now consider fatigue crack formation concepts.
30
Fatigue Crack Growth
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39
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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43
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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
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50
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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)
Number of Cycles (N)
da
dN
a*
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51
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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)
Number of Cycles (N)
da
dN
2a
2a
CrackLength(a
)
Number of Cycles (N)
da
dN
a*
KthKc
Log K
Logda/dN
K a=
KP
B a=
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Fatigue for Engineers
Instructors Personal Notes
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).
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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60
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
Instructors Outline
1. The final set of slides deal with fatigue design
concepts and a brief introduction to repairing fatigue
damage.
Major Learning Points
1. Transition slide to final portion of course.
53
Fatigue Design/Repair
Concepts
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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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66
Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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).
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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.
Major Learning Points
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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Fatigue for Engineers
Instructors Personal Notes
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