MicrostructureProperties: II Fatigue - PowerPoint PPT Presentation

1 / 52
About This Presentation
Title:

MicrostructureProperties: II Fatigue

Description:

also, crack length. E := Young's modulus. b := exponent in Basquin Eq. ... the origin of the crack. Striations corresponding to slow, intermittent crack growth ... – PowerPoint PPT presentation

Number of Views:605
Avg rating:3.0/5.0
Slides: 53
Provided by: adrol
Category:

less

Transcript and Presenter's Notes

Title: MicrostructureProperties: II Fatigue


1
Microstructure-Properties IIFatigue
  • 27-302
  • Lecture 9
  • Fall, 2002
  • Prof. A. D. Rollett

2
Materials Tetrahedron
Processing
Performance
Properties
Microstructure
3
Objective
  • The objective of this lecture is to explain the
    phenomenon of fatigue and also to show how
    resistance to fatigue failure depends on
    microstructure.
  • For 27-302, Fall 2002 this slide set contains
    more material than can be covered in the time
    available. Slides that contain material over and
    above that expected for this course are marked
    .

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

5
Notation
  • sa Alternating stresssm Mean stressR
    Stress ratioe strainNf number of
    cycles to failureA Amplitude ratio??pl
    Plastic strain amplitude??el Elastic
    strain amplitudeK Proportionality constant,
    cyclic stress-strainn Exponent in cyclic
    stress-strainc Exponent in Coffin-Manson
    Eq. also, crack lengthE Youngs modulusb
    exponent in Basquin Eq.m exponent in
    Paris LawK Stress intensity
  • ?K Stress intensity amplitude
  • a crack length

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

7
Fatigue general characteristics
  • Primary design criterion in rotating parts.
  • Fatigue as a name for the phenomenon based on the
    notion of a material becoming tired, i.e.
    failing at less than its nominal strength.
  • Cyclical strain (stress) leads to fatigue
    failure.
  • Occurs in metals and polymers but rarely in
    ceramics.
  • Also an issue for static parts, e.g. bridges.
  • Cyclic loading stress limitltstatic stress
    capability.

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

9
S-N Curves
  • S-N stress-number of cycles to failure curve
    defines locus of cycles-to-failure for given
    cyclic stress.
  • Rotating-beam fatigue test is standard also
    alternating tension-compression.
  • Plot stress versus the log(number of cycles to
    failure), log(Nf). see next slide, also
    Courtney figs. 12.8, 12.9
  • For frequencies lt 200Hz, metals are insensitive
    to frequency fatigue life in polymers is
    frequency dependent.

Hertzberg
10
Fatigue testing, S-N curve
smean 3 gt smean 2 gt smean 1
The greater the number ofcycles in the loading
history,the smaller the stress thatthe material
can withstandwithout failure.
sa
smean 1
smean 2
smean 3
log Nf
Note the presence of afatigue limit in
manysteels and its absencein aluminum alloys.
Dieter
11
Endurance Limits
  • Some materials exhibit endurance limits, i.e. a
    stress below which the life is infinite fig.
    12.8
  • Steels typically show an endurance limit, 40
    of yield this is typically associated with the
    presence of a solute (carbon, nitrogen) that
    pines dislocations and prevents dislocation
    motion at small displacements or strains (which
    is apparent in an upper yield point).
  • Aluminum alloys do not show endurance limits
    this is related to the absence of
    dislocation-pinning solutes.
  • At large Nf, the lifetime is dominated by
    nucleation.
  • Therefore strengthening the surface (shot
    peening) is beneficial to delay crack nucleation
    and extend life.

12
Fatigue fracture surface
Hertzberg
13
Fatigue crack stages
Stage 1
Dieter
Stage 2
14
Fatigue Crack Propagation
  • Crack Nucleation ??stress intensification at
    crack tip.
  • Stress intensity ??crack propagation (growth)-
    stage I growth on shear planes (45),strong
    influence of microstructure Courtney
    fig.12.3a- stage II growth normal to tensile
    load (90)weak influence of microstructure
    Courtney fig.12.3b.
  • Crack propagation ??catastrophic, or ductile
    failure at crack length dependent on boundary
    conditions, fracture toughness.

15
Fatigue Crack Nucleation
  • Flaws, cracks, voids can all act as crack
    nucleation sites, especially at the surface.
  • Therefore, smooth surfaces increase the time to
    nucleation notches, stress risers decrease
    fatigue life.
  • Dislocation activity (slip) can also nucleate
    fatigue cracks.

16
Dislocation Slip Crack Nucleation
  • Dislocation slip -gt tendency to localize slip in
    bands. see slide 10, also Courtney fig. 12.3
  • Persistent Slip Bands (PSBs) characteristic of
    cyclic strains.
  • Slip Bands -gt extrusion at free surface. see
    next slide for fig. from Murakami et al.
  • Extrusions -gt intrusions and crack nucleation.

17
Slip steps and the stress-strain loop
18
Design Philosophy Damage Tolerant Design
  • S-N (stress-cycles) curves basic
    characterization.
  • Old Design Philosophy Infinite Life design
    accept empirical information about fatigue life
    (S-N curves) apply a (large!) safety factor
    retire components or assemblies at the pre-set
    life limit, e.g. Nf107.
  • Crack Growth Rate characterization -gt
  • Modern Design Philosophy (Air Force, not Navy
    carriers!) Damage Tolerant design accept
    presence of cracks in components. Determine life
    based on prediction of crack growth rate.

19
Definitions Stress Ratios
  • Alternating Stress
  • Mean stress ? ?m (?max ?min)/2.
  • Pure sine wave ??Mean stress0.
  • Stress ratio ? R ?max/?min.
  • For ?m 0, R-1
  • Amplitude ratio ? A (1-R)/(1R).
  • Statistical approach shows significant
    distribution in Nf for given stress.
  • See Courtney fig. 12.6 also following slide.

20
Alternating Stress Diagrams
Dieter
21
Mean Stress
  • Alternating stress ? ?a (?max-?min)/2.
  • Raising the mean stress (?m) decreases Nf. see
    slide 19, also Courtney fig. 12.9
  • Various relations between R 0 limit and the
    ultimate (or yield) stress are known as Soderberg
    (linear to yield stress), Goodman (linear to
    ultimate) and Gerber (parabolic to ultimate).
    Courtney, fig. 12.10, problem 12.3

endurance limit at zero mean stress
sa
tensile strength
smean
22
Cyclic strain vs. cyclic stress
  • Cyclic strain control complements cyclic stress
    characterization applicable to thermal fatigue,
    or fixed displacement conditions.
  • Cyclic stress-strain testing defined by a
    controlled strain range, ??pl. see next slide,
    Courtney, figs. 12.24,12.25
  • Soft, annealed metals tend to harden
    strengthened metals tend to soften.
  • Thus, many materials tend towards a fixed cycle,
    i.e. constant stress, strain amplitudes.

23
Cyclic stress-strain curve
Courtney
Large number of cycles typically needed to
reach asymptotic hysteresis loop (100).
Softening or hardening possible. fig. 12.26
24
Cyclic stress-strain
  • Wavy-slip materials generally reach asymptote in
    cyclic stress-strain planar slip materials (e.g.
    brass) exhibit history dependence.
  • Cyclic stress-strain curve defined by the
    extrema, i.e. the tips of the hysteresis loops.
    Courtney fig. 12.27
  • Cyclic stress-strain curves tend to lie below
    those for monotonic tensile tests.
  • Polymers tend to soften in cyclic straining.

Courtney
25
Cyclic Strain Control
  • Strain is a more logical independent variable for
    characterization of fatigue. fig. 12.11
  • Define an elastic strain range as ?eel ?s/E.
  • Define a plastic strain range, ?epl.
  • Typically observe a change in slope between the
    elastic and plastic regimes. fig. 12.12
  • Low cycle fatigue (small Nf) dominated by plastic
    strain high cycle fatigue (large Nf) dominated
    by elastic strain.

26
Strain control of fatigue
Courtney
27
Cyclic Strain control low cycle
  • Constitutive relation for cyclic stress-strain
  • n 0.1-0.2
  • Fatigue life Coffin Manson relation
  • ?f true fracture strain close to tensile
    ductility
  • c -0.5 to -0.7
  • c -1/(15n) large n ? longer life.

28
Cyclic Strain control high cycle
  • For elastic-dominated strains at high cycles,
    adapt Basquins equation
  • Intercept on strain axis of extrapolated elastic
    line sf/E.
  • High cycle elastic strain control slope (in
    elastic regime) b -n/(15n) Courtney,
    fig. 12.13
  • The high cycle fatigue strength, sf, scales with
    the yield stress ? high strength good in
    high-cycle

29
Strain amplitude - cycles
Courtney
30
Total strain (plasticelastic) life
  • Low cycle plastic control slope c
  • Add the elastic and plastic strains.
  • Cross-over between elastic and plastic control is
    typically at Nf 103 cycles.
  • Ductility useful for low-cycle strength for high
    cycle
  • Examples of Maraging steel for high cycle
    endurance, annealed 4340 for low cycle fatigue
    strength.

31
Fatigue Crack Propagation
  • Crack Length a.Number of cycles NCrack
    Growth Rate da/dNAmplitude of Stress
    Intensity ?K ?svc.
  • Define three stages of crack growth, I, II and
    III, in a plot of da/dN versus ?K.
  • Stage II crack growth application of linear
    elastic fracture mechanics.
  • Can consider the crack growth rate to be related
    to the applied stress intensity.
  • Crack growth rate somewhat insensitive to R (if
    Rlt0) in Stage II fig. 12.16, 12.18b
  • Environmental effects can be dramatic, e.g. H in
    Fe, in increasing crack growth rates.

32
Fatigue Crack Propagation
da/dN
  • Three stages of crack growth, I, II and III.
  • Stage I transition to a finite crack growth rate
    from no propagation below a threshold value of
    ?K.
  • Stage II power law dependence of crack growth
    rate on ?K.
  • Stage III acceleration of growth rate with ?K,
    approaching catastrophic fracture.

I
?Kc
II
III
?K
?Kth
33
Paris Law
  • Paris Law
  • m 3 (steel) m 4 (aluminum).
  • Crack nucleation ignored!
  • Threshold Stage I
  • The threshold represents an endurance limit.
  • For ceramics, threshold is close to KIC.
  • Crack growth rate increases with R (for Rgt0).
    fig. 12.18a

34
Striations- mechanism
  • Striations occur by development of slip bands in
    each cycle, followed by tip blunting, followed by
    closure.
  • Can integrate the growth rate to obtain cycles as
    related to cyclic stress-strain behavior. Eqs.
    12.6-12.8

35
Striations, contd.
  • Provided that mgt2 and a is constant, can
    integrate.
  • If the initial crack length is much less than the
    final length, c0ltcf, then approximate thus
  • Can use this to predict fatigue life based on
    known crack

36
Damage Tolerant Design
  • Calculate expected growth rates from dc/dN data.
  • Perform NDE on all flight-critical components.
  • If crack is found, calculate the expected life of
    the component.
  • Replace, rebuild if too close to life limit.
  • Endurance limits.

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

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

39
Microstructure affects Crack Nucleation
da/dN
  • The main effect of microstructure (defects,
    surface treatment, etc.) is almost all in the low
    stress intensity regime, i.e. Stage I. Defects,
    for example, make it easier to nucleate a crack,
    which translates into a lower threshold for crack
    propagation (?Kth).
  • Microstructure also affects fracture toughness
    and therefore Stage III.

I
?Kc
II
III
?K
?Kth
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 include
    extrinsic defects such as voids, inclusions,
    grain boundary films, and other types of
    undesirable second phases.
  • Voids are introduced either by gas evolution in
    solidification or by incomplete sintering in
    powder consolidation.
  • Inclusions are second phases entrained in a
    material during solidification. In metals,
    inclusions are generally oxides from the surface
    of the metal melt, or a slag.
  • Grain boundary films are common in ceramics as
    glassy films from impurities.
  • In aluminum alloys, there is a hierachy of names
    for second phase particles inclusions are
    unwanted oxides (e.g. Al2O3) dispersoids are
    intermetallic particles that, once precipitated,
    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
Metallurgical Control fine particles
  • Tendency to localization of flow is deleterious
    to the initiation of fatigue cracks, e.g. Al-7050
    with non-shearable vs. shearable precipitates
    (Stage I in a da/dN plot). Also Al-Cu-Mg with
    shearable precipitates but non-shearable
    dispersoids, vs. only shearable ppts.

graph courtesy of J. Staley, Alcoa
42
Coarse particle effect on fatigue
  • Inclusions nucleate cracks ??cleanliness (w.r.t.
    coarse particles) improves fatigue life, e.g.
    7475 improved by lower FeSi compared to 7075
    0.12Fe in 7475, compared to 0.5Fe in 7075
    0.1Si in 7475, compared to 0.4Si in 7075.

graph courtesy of J. Staley, Alcoa
43
Alloy steel heat treatment
  • Increasing hardness tends to raise the endurance
    limit for high cycle fatigue. This is largely a
    function of the resistance to fatigue crack
    formation (Stage I in a plot of da/dN).

Mobile solutes that pin dislocations ??fatigue
limit, e.g. carbon in steel
Dieter
44
Casting porosity affects fatigue
Gravity cast versussqueeze castversuswroughtA
l-7010
Polmear
  • Casting tends to result in porosity. Pores are
    effective sites for nucleation of fatigue cracks.
    Castings thus tend to have lower fatigue
    resistance (as measured by S-N curves) than
    wrought materials.
  • Casting technologies, such as squeeze casting,
    that reduce porosity tend to eliminate this
    difference.

45
Titanium alloys
Polmear
  • For many Ti alloys, the proportion of hcp (alpha)
    and bcc (beta) phases depends strongly on the
    heat treatment. Cooling from the two-phase
    region results in a two-phase structure, as
    Polmears example, 6.7a. Rapid cooling from
    above the transus in the single phase (beta)
    region results in a two-phase microstructure with
    Widmanstätten laths of (martensitic) alpha in a
    beta matrix, 6.7b.
  • The fatigue properties of the two-phase structure
    are significantly better than the Widmanstätten
    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
Design Considerations
  • If crack growth rates are normalized by the
    elastic modulus, then material dependence is
    mostly removed! Courtney fig. 12.20
  • Can distinguish between intrinsic fatigue use
    Eq. 12.4 for combined elastic, plastic strain
    range for small crack sizes and extrinsic
    fatigue use Eq. 12.6 for crack growth rate
    controlled at longer crack lengths. fig.
    12.21.
  • Inspection of design charts, fig. 12.22, shows
    that ceramics sensitive to crack propagation
    (high endurance limit in relation to fatigue
    threshold).

47
Design Considerations 2
  • Metals show a higher fatigue threshold in
    relation to their endurance limit. PMMA and Mg
    are at the lower end of the toughness range in
    their class. Courtney fig. 12.22
  • Also interesting to compare fracture toughness
    with fatigue threshold. Courtney fig. 12.23
  • Note that ceramics are almost on ratio1 line,
    whereas metals tend to lie well below, i.e.
    fatigue is more significant criterion.

48
Fatigue property map
Courtney
49
Fatigue property map
Courtney
50
Variable Stress/Strain Histories
  • When the stress/strain history is stochastically
    varying, a rule for combining portions of fatigue
    life is needed.
  • Palmgren-Miner Rule is useful ni is the number
    of cycles at each stress level, and Nfi is the
    failure point for that stress. Ex. Problem
    12.2

Courtneys Eq. 12.9 is confusing he has Nf in
the numerator also
51
Fatigue in Polymers
  • Many differences from metals
  • Cyclic stress-strain behavior often exhibits
    softening also affected by visco-elastic
    effects crazing in the tensile portion produces
    asymmetries, figs. 12.34, 12.25.
  • S-N curves exhibit three regions, with steeply
    decreasing region II, fig. 12.31.
  • Nearness to Tg results in strong temperature
    sensitivity, fig. 12.42

52
Fatigue summary
  • Critical to practical use of structural
    materials.
  • Fatigue affects most structural components, even
    apparently statically loaded ones.
  • Well characterized empirically.
  • Connection between dislocation behavior and
    fatigue life offers exciting research
    opportunities, i.e. physically based models are
    lacking!
Write a Comment
User Comments (0)
About PowerShow.com