- The objective of this lecture is to explain fatigue and how resistance to fatigue failure depends on microstructure. Fatigue is failure due to alternating loads rather than static loads. - Fatigue is characterized by an S-N curve which plots the stress versus the log of the number of cycles to failure. It shows whether the material has an endurance limit below which it does not fail. - Fatigue failure involves crack initiation at a surface defect followed by crack propagation in stages I and II, with stage I influenced by microstructure and stage II less so. Modern damage tolerant design accepts the presence of cracks and predicts crack growth rates.

1. 1
Objective
Crack Microstructure-Properties: II
Initiation
S-N Fatigue
curves
Cyclic 27-302
stress-strn
Crack Lecture 9
Propagate
Fall, 2002
Microstr.
effects Prof. A. D. Rollett
Design

2. 2
Materials Tetrahedron
Processing
Performance
Objective
Crack
Initiation
S-N
curves
Cyclic
stress-strn
Crack
Propagate
Microstr.
Microstructure Properties
effects
Design

3. 3
Objective
• The objective of this lecture is to explain the
phenomenon of fatigue and also to show how
Objective
resistance to fatigue failure depends on
Crack
Initiation microstructure.
S-N • For 27-302, Fall 2002: this slide set contains
curves
Cyclic
more material than can be covered in the time
stress-strn available. Slides that contain material over
Crack
Propagate
and above that expected for this course are
Microstr. marked “*”.
effects
Design

4. 4
References
• Mechanical Behavior of Materials (2000), T. H.
Courtney, McGraw-Hill, Boston.
Objective • Phase transformations in metals and alloys, D.A.
Crack Porter, & K.E. Easterling, Chapman & Hall.
Initiation
• Materials Principles & Practice, Butterworth
S-N
curves Heinemann, Edited by C. Newey & G. Weaver.
Cyclic • Mechanical Metallurgy, McGrawHill, G.E. Dieter, 3rd
stress-strn Ed.
Crack
Propagate • Light Alloys (1996), I.J. Polmear, Wiley, 3rd Ed.
Microstr. • Hull, D. and D. J. Bacon (1984). Introduction to
effects Dislocations. Oxford, UK, Pergamon.
Design

5. 5
σa := Alternating stress
σm := Mean stress Notation
R := Stress ratio
ε := strain
Nf := number of cycles to failure
A := Amplitude ratio
Objective ∆ εpl := Plastic strain amplitude
Crack ∆ εel := Elastic strain amplitude
Initiation K’ := Proportionality constant, cyclic stress-strain
S-N n’ := Exponent in cyclic stress-strain
curves c := Exponent in Coffin-Manson Eq.;
Cyclic also, crack length
stress-strn E := Young’s modulus
Crack b := exponent in Basquin Eq.
Propagate m := exponent in Paris Law
Microstr. K := Stress intensity
effects ∆ K := Stress intensity amplitude
Design a := crack length

6. 6
Fatigue
• Fatigue is the name given to failure in response to
alternating loads (as opposed to monotonic
Objective straining).
Crack • Instead of measuring the resistance to fatigue
Initiation
failure through an upper limit to strain (as in
S-N
curves ductility), the typical measure of fatigue resistance
Cyclic is expressed in terms of numbers of cycles to
stress-strn failure. For a given number of cycles (required in
Crack an application), sometimes the stress (that can be
Propagate
safely endured by the material) is specified.
Microstr.
effects
Design

7. 7
Fatigue: general characteristics
• Primary design criterion in rotating parts.
• Fatigue as a name for the phenomenon based on the
Objective notion of a material becoming “tired”, i.e. failing at
Crack less than its nominal strength.
Initiation
• Cyclical strain (stress) leads to fatigue failure.
S-N
curves • Occurs in metals and polymers but rarely in
Cyclic ceramics.
stress-strn • Also an issue for “static” parts, e.g. bridges.
Crack
Propagate • Cyclic loading stress limit<static stress capability.
Microstr.
effects
Design

8. 8
Fatigue: general characteristics
• Most applications of structural materials involve cyclic
loading; any net tensile stress leads to fatigue.
Objective • Fatigue failure surfaces have three characteristic
Crack features: [see next slide, also Courtney figs. 12.1, 12.2]
Initiation – A (near-)surface defect as the origin of the crack
S-N – Striations corresponding to slow, intermittent crack growth
curves
– Dull, fibrous brittle fracture surface (rapid growth).
Cyclic
stress-strn • Life of structural components generally limited by
Crack cyclic loading, not static strength.
Propagate
• Most environmental factors shorten life.
Microstr.
effects
Design

9. 9
S-N Curves
• S-N [stress-number of cycles to failure] curve defines
locus of cycles-to-failure for given cyclic stress.
Objective • Rotating-beam fatigue test is standard; also
Crack alternating tension-compression.
Initiation
• Plot stress versus the [Hertzberg]
S-N
curves log(number of cycles
Cyclic to failure), log(Nf).
stress-strn [see next slide,
Crack also Courtney figs. 12.8, 12.9]
Propagate • For frequencies < 200Hz,
Microstr. metals are insensitive to
effects
frequency; fatigue life in
Design
polymers is frequency
dependent.

10. 10
Fatigue testing, S-N curve
σmean 3 > σmean 2 > σmean 1
σa The greater the number of
cycles in the loading history,
Objective
σmean 1 the smaller the stress that
Crack
Initiation
σmean 2 the material can withstand
S-N
σmean 3 without failure.
curves log Nf
Cyclic
stress-strn Note the presence of a
Crack
Propagate fatigue limit in many
Microstr. steels and its absence
effects in aluminum alloys.
Design
[Dieter]

11. 11
Endurance Limits
• Some materials exhibit endurance limits, i.e.
a stress below which the life is infinite: [fig. 12.8]
Objective – Steels typically show an endurance limit, = 40% of
Crack yield; this is typically associated with the presence
Initiation of a solute (carbon, nitrogen) that pines
S-N dislocations and prevents dislocation motion at
curves small displacements or strains (which is apparent
Cyclic in an upper yield point).
stress-strn – Aluminum alloys do not show endurance limits;
Crack
Propagate this is related to the absence of dislocation-pinning
Microstr.
solutes.
effects • At large Nf, the lifetime is dominated by nucleation.
Design – Therefore strengthening the surface (shot peening) is
beneficial to delay crack nucleation and extend life.

12. 12
Fatigue fracture
surface
Objective
Crack
Initiation
S-N
curves
Cyclic
stress-strn
Crack
Propagate
Microstr.
effects
[Hertzberg]
Design

13. 13
Fatigue crack stages
Stage 1
Objective
Crack
Initiation
S-N [Dieter]
curves Stage 2
Cyclic
stress-strn
Crack
Propagate
Microstr.
effects
Design

14. 14
Fatigue Crack Propagation
• Crack Nucleation → stress intensification at crack tip.
Objective
• Stress intensity → crack propagation (growth);
Crack
Initiation
- stage I growth on shear planes (45° ),
S-N
strong influence of microstructure [Courtney: fig.12.3a]
curves - stage II growth normal to tensile load (90° )
Cyclic weak influence of microstructure [Courtney: fig.12.3b].
stress-strn • Crack propagation → catastrophic, or ductile failure
Crack
Propagate at crack length dependent on boundary conditions,
Microstr.
fracture toughness.
effects
Design

15. 15
Fatigue Crack Nucleation
• Flaws, cracks, voids can all act as crack nucleation
sites, especially at the surface.
Objective • Therefore, smooth surfaces increase the time to
Crack nucleation; notches, stress risers decrease fatigue
Initiation
life.
S-N
curves • Dislocation activity (slip) can also nucleate fatigue
Cyclic cracks.
stress-strn
Crack
Propagate
Microstr.
effects
Design

16. 16
Dislocation Slip Crack Nucleation
• Dislocation slip -> tendency to localize slip in bands.
[see slide 10, also Courtney fig. 12.3]
Objective • Persistent Slip Bands (PSB’s) characteristic of
Crack cyclic strains.
Initiation • Slip Bands -> extrusion at free surface. [see next slide
S-N for fig. from Murakami et al.]
curves
• Extrusions -> intrusions and crack nucleation.
Cyclic
stress-strn
Crack
Propagate
Microstr.
effects
Design

17. 17
Slip steps
and the
Objective stress-strain
Crack
Initiation loop
S-N
curves
Cyclic
stress-strn
Crack
Propagate
Microstr.
effects
Design

18. 18
Design Philosophy: Damage Tolerant
Design
• S-N (stress-cycles) curves = basic characterization.
• Old Design Philosophy = Infinite Life design: accept
Objective empirical information about fatigue life (S-N curves);
Crack apply a (large!) safety factor; retire components or
Initiation
assemblies at the pre-set life limit, e.g. Nf=107.
S-N
curves • *Crack Growth Rate characterization ->
Cyclic • *Modern Design Philosophy (Air Force, not Navy
stress-strn
carriers!) = Damage Tolerant design: accept
Crack
Propagate presence of cracks in components. Determine life
Microstr. based on prediction of crack growth rate.
effects
Design

19. 19
Definitions: Stress Ratios
• Alternating Stress
Objective • Mean stress ≡ σm = (σmax +σmin)/2.
Crack
Initiation
• Pure sine wave ≡ Mean stress=0.
S-N • Stress ratio ≡ R = σmax/σmin.
curves
Cyclic • For σm = 0, R=-1
stress-strn
Crack • Amplitude ratio ≡ A = (1-R)/(1+R).
Propagate
Microstr. • Statistical approach shows significant
effects
distribution in Nf for given stress.
Design
• See Courtney fig. 12.6; also following slide.

20. 20
Alternating Stress Diagrams
Objective
Crack
Initiation
S-N
curves
Cyclic
stress-strn
Crack
Propagate
Microstr.
effects
Design
[Dieter]

21. 21
Mean Stress
• Alternating stress ≡ σa = (σmax-σmin)/2.
• Raising the mean stress (σm) decreases Nf. [see slide 19,
Objective also Courtney fig. 12.9]
Crack • Various relations between R = 0 limit and the ultimate
Initiation (or yield) stress are known as Soderberg (linear to
S-N yield stress), Goodman (linear to ultimate) and
curves
Gerber (parabolic to ultimate). [Courtney, fig. 12.10, problem
Cyclic 12.3]
stress-strn
Crack
Propagate
endurance limit at zero mean stress
Microstr. σa
effects
Design
tensile strength
σmean

22. 22
Cyclic strain vs. cyclic stress
• Cyclic strain control complements cyclic
stress characterization: applicable to thermal
Objective
fatigue, or fixed displacement conditions.
Crack
Initiation • Cyclic stress-strain testing defined by a
S-N controlled strain range, ∆ εpl. [see next slide,
curves
Courtney, figs. 12.24,12.25]
Cyclic
stress-strn • Soft, annealed metals tend to harden;
Crack
Propagate
strengthened metals tend to soften.
Microstr. • Thus, many materials tend towards a fixed
effects
cycle, i.e. constant stress, strain amplitudes.
Design

23. 23
Cyclic stress-strain curve
Objective
Crack [Courtney]
Initiation
S-N
curves
Cyclic
stress-strn
Crack
Propagate
Microstr.
effects • Large number of cycles typically needed to reach
Design asymptotic hysteresis loop (~100).
• Softening or hardening possible. [fig. 12.26]

24. 24
Cyclic stress-strain
• Wavy-slip materials [Courtney]
generally reach
asymptote in cyclic stress-
Objective strain: planar slip
Crack materials (e.g. brass)
Initiation exhibit history
dependence.
S-N
curves • Cyclic stress-strain curve
defined by the extrema,
Cyclic
i.e. the “tips” of the
stress-strn
Crack hysteresis loops. [Courtney
fig. 12.27]
Propagate
• Cyclic stress-strain curves
Microstr.
tend to lie below those for
effects
monotonic tensile tests.
Design • Polymers tend to soften in
cyclic straining.

25. 25
Cyclic Strain Control
• Strain is a more logical independent variable
for characterization of fatigue. [fig. 12.11]
Objective
Crack
• Define an elastic strain range as ∆ εel = ∆σ/E.
Initiation
• Define a plastic strain range, ∆ εpl.
S-N
curves • Typically observe a change in slope between
Cyclic the elastic and plastic regimes. [fig. 12.12]
stress-strn
Crack • Low cycle fatigue (small Nf) dominated by
Propagate
Microstr. plastic strain: high cycle fatigue (large Nf)
effects dominated by elastic strain.
Design

26. 26
Strain control
of fatigue
Objective
Crack
Initiation
S-N [Courtney]
curves
Cyclic
stress-strn
Crack
Propagate
Microstr.
effects
Design

27. 27
Cyclic Strain control: low cycle
• Constitutive relation
for cyclic stress-strain:
Objective
Crack
• n’ ≈ 0.1-0.2
Initiation
• Fatigue life: Coffin Manson relation:
S-N
curves
Cyclic
• εf ~ true fracture strain; close to tensile
stress-strn
Crack
Propagate
Microstr.
ductility
effects • c ≈ -0.5 to -0.7
Design
• c = -1/(1+5n’ ); large n’ → longer life.

28. 28
Cyclic Strain control: high cycle
• For elastic-dominated strains
at high cycles, adapt
Objective
Crack
Basquin’s equation:
Initiation • Intercept on strain axis of extrapolated
S-N
curves
elastic line = σf/E.
Cyclic • High cycle = elastic strain control:
stress-strn
Crack slope (in elastic regime) = b = -n’ /
Propagate (1+5n’ ) [Courtney, fig. 12.13]
• The high cycle fatigue strength, σf,
Microstr.
effects
Design scales with the yield stress ⇒ high
strength good in high-cycle

29. 29
Strain amplitude - cycles
Objective
Crack [Courtney]
Initiation
S-N
curves
Cyclic
stress-strn
Crack
Propagate
Microstr.
effects
Design

30. 30
Total strain (plastic+elastic) life
• Low cycle = plastic control: slope = c
• Add the elastic and plastic strains.
Objective
Crack
Initiation
S-N
curves • Cross-over between elastic and plastic control is
Cyclic typically at Nf = 103 cycles.
stress-strn • Ductility useful for low-cycle; strength for high cycle
Crack
Propagate • Examples of Maraging steel for high cycle
Microstr. endurance, annealed 4340 for low cycle fatigue
effects strength.
Design

31. 31
Fatigue Crack Propagation
• Crack Length := a.
Number of cycles := N
Crack Growth Rate := da/dN
Objective Amplitude of Stress Intensity := ∆ K = ∆ σ√ c.
Crack • Define three stages of crack growth, I, II and III,
Initiation in a plot of da/dN versus ∆ K.
S-N • Stage II crack growth: application of linear elastic fracture
curves mechanics.
Cyclic • Can consider the crack growth rate to be related to the applied
stress-strn stress intensity.
Crack
• Crack growth rate somewhat insensitive to R (if R<0) in Stage II
Propagate
[fig. 12.16, 12.18b]
Microstr. • Environmental effects can be dramatic, e.g. H in Fe, in
effects
increasing crack growth rates.
Design

32. 32
Fatigue Crack Propagation
• Three stages of crack da/dN
growth, I, II and III.
• Stage I: transition to a
Objective finite crack growth rate
Crack from no propagation
I
∆Kc
Initiation below a threshold value
S-N
of ∆K. II
curves • Stage II: “power law”
dependence of crack III
Cyclic growth rate on ∆K.
stress-strn • Stage III: acceleration
Crack
of growth rate with ∆K,
Propagate
approaching
Microstr. catastrophic fracture.
effects
Design
∆Kth ∆K

33. 33
*Paris Law
• Paris Law:
Objective
Crack
• m ~ 3 (steel); m ~ 4 (aluminum).
Initiation
• Crack nucleation ignored!
S-N
curves • Threshold ~ Stage I
Cyclic
stress-strn • The threshold represents an endurance
Crack
Propagate
limit.
Microstr. • For ceramics, threshold is close to KIC.
effects
Design
• Crack growth rate increases with R (for
R>0). [fig. 12.18a]

34. 34
*Striations- mechanism
• Striations occur by development of slip bands
in each cycle, followed by tip blunting,
Objective
followed by closure.
Crack
Initiation • Can integrate the growth rate to obtain cycles
S-N as related to cyclic stress-strain behavior. [Eqs.
curves 12.6-12.8]
Cyclic
stress-strn
Crack
Propagate
Microstr.
effects
Design

35. 35
*Striations, contd.
• Provided that m>2 and α is constant, can integrate.
Objective
Crack
Initiation
S-N
curves • If the initial crack length is much less than the final
Cyclic length, c0<cf, then approximate thus:
stress-strn
Crack
Propagate
Microstr.
effects
Design • Can use this to predict fatigue life based on known
crack

36. 36
*Damage Tolerant Design
• Calculate expected growth rates from dc/dN
data.
Objective
Crack
• Perform NDE on all flight-critical components.
Initiation • If crack is found, calculate the expected life of
S-N
curves
the component.
Cyclic • Replace, rebuild if too close to life limit.
stress-strn
Crack • Endurance limits.
Propagate
Microstr.
effects
Design

37. 37
Geometrical effects
• Notches decrease fatigue life through stress
concentration.
Objective • Increasing specimen size lowers fatigue life.
Crack • Surface roughness lowers life, again through stress
Initiation concentration.
S-N • Moderate compressive stress at the surface
curves increases life (shot peening); it is harder to nucleate a
Cyclic crack when the local stress state opposes crack
stress-strn opening.
Crack
Propagate • Corrosive environment lowers life; corrosion either
Microstr. increases the rate at which material is removed from
effects the crack tip and/or it produces material on the crack
Design surfaces that forces the crack open (e.g. oxidation).
• Failure mechanisms

38. 38
Microstructure-Fatigue Relationships
• What are the important issues in microstructure-
fatigue relationships?
Objective • Answer: three major factors.
Crack 1: geometry of the specimen (previous slide); anything on the
Initiation surface that is a site of stress concentration will promote
S-N crack formation (shorten the time required for nucleation of
curves cracks).
Cyclic 2: defects in the material; anything inside the material that can
stress-strn reduce the stress and/or strain required to nucleate a crack
Crack (shorten the time required for nucleation of cracks).
Propagate
3: dislocation slip characteristics; if dislocation glide is confined
Microstr. to particular slip planes (called planar slip) then dislocations
effects
can pile up at any grain boundary or phase boundary. The
Design head of the pile-up is a stress concentration which can
initiate a crack.

39. 39
Microstructure affects Crack Nucleation
• The main effect of da/dN
microstructure (defects,
surface treatment, etc.)
Objective is almost all in the low
Crack stress intensity regime, I
i.e. Stage I. Defects,
Initiation
S-N
for example, make it II ∆Kc
easier to nucleate a
curves crack, which translates
into a lower threshold
III
Cyclic
stress-strn for crack propagation
Crack (∆ Kth).
Propagate • Microstructure also
Microstr. affects fracture
effects toughness and
therefore Stage III.
Design
∆Kth ∆K

40. 40
Defects in Materials
• Descriptions of defects in materials at the sophomore level
focuses, appropriately on intrinsic defects (vacancies,
dislocations). For the materials engineer, however, defects
Objective include extrinsic defects such as voids, inclusions, grain
Crack boundary films, and other types of undesirable second phases.
Initiation • Voids are introduced either by gas evolution in solidification or
by incomplete sintering in powder consolidation.
S-N
curves • Inclusions are second phases entrained in a material during
solidification. In metals, inclusions are generally oxides from the
Cyclic surface of the metal melt, or a slag.
stress-strn • Grain boundary films are common in ceramics as glassy
Crack
films from impurities.
Propagate
• In aluminum alloys, there is a hierachy of names for second
Microstr. phase particles; inclusions are unwanted oxides (e.g. Al2O3);
effects
dispersoids are intermetallic particles that, once precipitated,
Design are thermodynamically stable (e.g. AlFeSi compounds);
precipitates are intermetallic particles that can be dissolved or
precipiated depending on temperature (e.g. AlCu compounds).

41. 41
Metallurgical Control: fine particles
• Tendency to localization of flow is deleterious to the
initiation of fatigue cracks, e.g. Al-7050 with non-
Objective shearable vs. shearable precipitates (Stage I in a da/
Crack dN plot). Also Al-Cu-Mg with shearable precipitates
Initiation but non-shearable dispersoids, vs. only shearable
S-N ppts.
curves
Cyclic
stress-strn
Crack
Propagate
Microstr.
effects
graph courtesy of J.
Design Staley, Alcoa

42. 42
Coarse particle effect on fatigue
• Inclusions nucleate cracks → cleanliness (w.r.t.
coarse particles) improves fatigue life, e.g. 7475
Objective improved by lower Fe+Si compared to 7075:
Crack 0.12Fe in 7475, compared to 0.5Fe in 7075;
Initiation 0.1Si in 7475, compared to 0.4Si in 7075.
S-N
curves
Cyclic
stress-strn
Crack
Propagate
Microstr.
effects
graph courtesy of J.
Design Staley, Alcoa

43. 43
Alloy steel heat treatment
• Increasing hardness tends to raise the endurance
limit for high cycle fatigue. This is largely a function
Objective
of the resistance to fatigue crack formation (Stage I in
a plot of da/dN).
Crack
Initiation
S-N
curves Mobile solutes that pin
Cyclic dislocations → fatigue
stress-strn limit, e.g. carbon in steel
Crack
Propagate
Microstr.
effects
Design
[Dieter]

44. 44
Casting porosity affects fatigue
Gravity cast
versus
Objective squeeze cast
[Polmear]
Crack versus
Initiation
wrought
S-N Al-7010
curves
Cyclic
stress-strn
Crack
Propagate
• Casting tends to result in porosity. Pores are effective sites for
Microstr. nucleation of fatigue cracks. Castings thus tend to have lower fatigue
effects resistance (as measured by S-N curves) than wrought materials.
Design • Casting technologies, such as squeeze casting, that reduce porosity
tend to eliminate this difference.

45. 45
Titanium alloys
[Polmear]
Objective
Crack
Initiation
S-N
curves
Cyclic
stress-strn
Crack • For many Ti alloys, the proportion of hcp (alpha) and bcc (beta) phases
Propagate depends strongly on the heat treatment. Cooling from the two-phase region
results in a two-phase structure, as Polmear’s example, 6.7a. Rapid cooling
Microstr. from above the transus in the single phase (beta) region results in a two-
effects phase microstructure with Widmanstä tten laths of (martensitic) alpha in a
beta matrix, 6.7b.
Design
• The fatigue properties of the two-phase structure are significantly better than
the Widmanstä tten structure (more resistance to fatigue crack formation).
• The alloy in this example is IM834, Ti-5.5Al-4Sn-4Zr-0.3Mo-1Nb-0.35Si-0.6C.

46. 46
*Design Considerations
• If crack growth rates are normalized by the elastic
modulus, then material dependence is mostly
Objective removed! [Courtney fig. 12.20]
Crack • Can distinguish between intrinsic fatigue [use Eq.
Initiation
12.4 for combined elastic, plastic strain range] for
S-N
curves
small crack sizes and extrinsic fatigue [use Eq. 12.6
for crack growth rate controlled] at longer crack
Cyclic
stress-strn lengths. [fig. 12.21….]
Crack • Inspection of design charts, fig. 12.22, shows that
Propagate
ceramics sensitive to crack propagation (high
Microstr.
effects
endurance limit in relation to fatigue threshold).
Design

47. 47
*Design Considerations: 2
• Metals show a higher fatigue threshold in
relation to their endurance limit. PMMA and
Objective
Mg are at the lower end of the toughness
Crack
Initiation range in their class. [Courtney fig. 12.22]
S-N • Also interesting to compare fracture
curves
toughness with fatigue threshold. [Courtney fig.
Cyclic
12.23]
stress-strn
Crack • Note that ceramics are almost on ratio=1 line,
Propagate
Microstr.
whereas metals tend to lie well below, i.e.
effects fatigue is more significant criterion.
Design

48. 48
*Fatigue
property map
Objective
Crack
Initiation
S-N
curves
Cyclic
stress-strn
Crack
Propagate
Microstr.
effects
Design
[Courtney]

49. 49
*Fatigue
property map
Objective
Crack
Initiation
S-N
curves
Cyclic
stress-strn
Crack
Propagate
Microstr.
effects
Design
[Courtney]

50. 50
*Variable Stress/Strain Histories
• When the stress/strain history is
stochastically varying, a rule for combining
Objective
portions of fatigue life is needed.
Crack
Initiation • Palmgren-Miner Rule is useful: ni is the
S-N number of cycles at each stress level, and Nfi
curves
Cyclic is the failure point for that stress.
stress-strn [Ex. Problem 12.2]
Crack
Propagate
Microstr.
effects
Design * Courtney’s Eq. 12.9 is confusing; he has Nf in the numerator also

51. 51
*Fatigue in Polymers
• Many differences from metals
• Cyclic stress-strain behavior often exhibits
Objective
Crack
softening; also affected by visco-elastic
Initiation effects; crazing in the tensile portion
S-N produces asymmetries, figs. 12.34, 12.25.
curves
Cyclic
• S-N curves exhibit three regions, with steeply
stress-strn decreasing region II, fig. 12.31.
Crack
Propagate • Nearness to Tg results in strong temperature
Microstr.
effects
sensitivity, fig. 12.42
Design

52. 52
Fatigue: summary
• Critical to practical use of structural materials.
• Fatigue affects most structural components,
Objective
Crack
even apparently statically loaded ones.
Initiation • Well characterized empirically.
S-N
curves • Connection between dislocation behavior and
Cyclic fatigue life offers exciting research
stress-strn
Crack
opportunities, i.e. physically based models
Propagate are lacking!
Microstr.
effects
Design