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Fatigue Analysis Techniques · PDF fileFatigue Analysis Techniques! Load-Life! Stress-Life! BS 5400 ( Eurocode 3 )! Strain-Life! Crack Growth

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Text of Fatigue Analysis Techniques · PDF fileFatigue Analysis Techniques! Load-Life! Stress-Life! BS...

  • Fatigue Analysis Techniques

    Darrell Socie Mechanical Engineering

    University of Illinois

  • Fatigue Analysis Techniques

    ! Load-Life ! Stress-Life ! BS 5400 ( Eurocode 3 ) ! Strain-Life ! Crack Growth

  • Common Features

    ! Constant amplitude test data ! Rainflow ! Linear damage

  • Load-Life Data

    10

    100

    1000

    1E+0 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7

    Cycles

    L at

    er al

    F o

    rc e,

    kN

  • Stress-Life Data

    100

    1000

    10000

    1E+0 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7

    Cycles

    St re

    ss A

    m pl

    it ud

    e, M

    P a

  • BS 5400 ( Eurocode 3 ) Data

    100

    200

    300

    400

    B

    C

    D

    E

    F F2 G W 0

    105 106 107 108

    S tr

    es s

    R an

    g e ,M

    P a Steel

  • BS 5400 ( Eurocode 3 ) Data

    0

    25

    50

    75

    100

    125

    105

    B

    C

    D E

    F

    Aluminum

    106 107 108

    S tr

    es s

    R an

    g e ,M

    P a

    Cycles

  • BS 5400 ( Eurocode 3 ) Weld Class F

  • Strain-Life Data ∆ε - 2Nf

    0.00001

    0.0001

    0.001

    0.01

    0.1

    1

    1E+0 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7

    Reversals

    S tr

    ai n

    A m

    p lit

    u d

    e

  • Strain-Life Data σ − ε

    0

    100

    200

    300

    400

    500

    600

    0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

    Strain Amplitude

    S tr

    es s

    A m

    p lit

    u d

    e

  • Crack Growth Data

    1E-12

    1E-11

    1E-10

    1E-9

    1E-8

    1E-7

    1E-6

    1.00E+00 1.00E+01 1.00E+02

    Cyclic Stress Intensity, MPa m

    C ra

    ck G

    ro w

    th R

    at e,

    m /c

    yc le

  • Rainflow Counting

    A C

    B D

    E

    F

    G

    H

    I

  • Hysteresis Loops

    A C

    B D

    E

    F

    G

    H

    I

    A, I

    B

    C

    D, F

    E

    G

    H

  • Damage Accumulation

    ! Miner’s Linear Damage Rule

    " Σ Ni / Nf = 1

  • Load-Life

    ! Major Assumption " Loads used to generate

    baseline data are the same as service loading

  • Load-Life

    ! Advantages " Actual test of structure " Manufacturing and local stress

    concentration effects automatically included

    " Stress analysis is not needed

  • Load-Life

    ! Limitations " Actual test of structure " New tests required for each

    change in material, loading or geometry

    " Mean stress effects can not be included

  • Stress-Life

    ! Major Assumptions " Nominal stresses and material

    strength control fatigue life " Accurate determination of Kf

    for each geometry and material

  • Notched S-N Curve

    10

    100

    1000

    10000

    1E+00 1E+01 1E+02 1E+03 1E+04 1E+05 1E+06 1E+07

    Cycles

    S tr

    es s

    A m

    p lit

    u d

    e

    Kt or Kf

  • Stress-Life

    ! Advantages " Changes in material and

    geometry can easily be evaluated

    " Large emperical database for steel with standard notch shapes

  • Stress-Life

    ! Limitations " Does not account for notch

    root plasticity " Mean stress effects are often

    in error " Requires emperical Kf for good

    results

  • BS 5400 ( Eurocode 3 )

    ! Major Assumptions " Complex weld geometries can

    be described by a standard classification

    " Crack growth dominates fatigue life

    " Results independant of material and mean stress for structural steels

  • BS 5400 ( Eurocode 3 )

    10

    100

    1000

    1E+05 1E+06 1E+07 1E+08

    Cycles

    S tr

    es s

    R an

    g e,

    M P

    a

    Fatigue Limit

    No Fatigue Limit

  • BS 5400 ( Eurocode 3 )

    ! Advantages " Manufacturing effects are

    directly included " Large emperical database

    exists

  • BS 5400 ( Eurocode 3 )

    ! Limitations " Difficult to determine weld

    class for complex shapes " No benifit for improving

    manufacturing process

  • Welded Structure

  • Strain-Life

    ! Major Assumptions " Local stresses and strains

    control fatigue behavior " Accurate determination of Kf

  • Strain-Life

    ! Advantages " Plasticity effects " Mean stress effects

  • Mean Strain Example

  • Tensile Mean Stress

  • Compressive Mean Stress

  • Neuber’s Rule

    0

    200

    400

    600

    800

    1000

    0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

    Strain

    S tr

    es s

    K S ef 2 ∆ ∆ ∆σ ∆ε=

  • Strain-Life

    ! Limitations " Requires emperical Kf " Long life situations where

    surface finish and processing variables are important

  • Crack Growth

    ! Major Assumptions " Nominal stress and crack size

    control fatigue life " Accurate determination of

    initial crack size

  • Crack Growth

    ! Advantage " Only method to directly deal

    with cracks

  • Crack Growth

    ! Limitations

    " Sequence effects ∆Keff = f ( ∆K )

    " ∆K = E ∆e Y( a ) √ a " Accurate determination of ai

  • Crack Closure

    Crack Opened Crack Closed

  • Crack Opening Load

    Damaging portion of loading history

    Nondamaging portion of loading history

    Opening load

  • Applications

    ! Material Selection / Improvement

    ! Fillet Weld ! Scaling / Editing Load

    Histories ! Crack Size / Shape

  • Transmission History

    -600

    -400

    -200

    0

    200

    400

    600

    800

    1000

    N o

    m in

    al S

    tr ai

    n

  • Material Properties

    BHN 187 277 336 410 545

    σ f ' ,MPa 1668 2978 3902 4593 5666

    b -0.149 -0.158 -0.159 -0.167 -0.170

    ε f ' 0.556 0.700 0.563 0.381 0.068

    c -0.522 -0.578 -0.595 -0.589 -0.603

    K’, MPa 1460 1743 2051 2381 4438

    n’ 0.234 0.189 0.163 0.172 0.169

    E, GPa 206 206 208 206 205

  • Strength Variation

    0

    100

    200

    300

    400

    500

    600

    1E+03 1E+04 1E+05 1E+06 1E+07

    Blocks

    H ar

    d n

    es s,

    B H

    N

  • Kf Variation

    1.5

    2

    2.5

    3

    3.5

    4

    4.5

    1E+03 1E+04 1E+05 1E+06 1E+07

    Blocks

    F at

    ig u

    e N

    o tc

    h F

    ac to

    r

  • Scale Factor Variation

    0

    0.5

    1

    1.5

    2

    1E+03 1E+04 1E+05 1E+06 1E+07

    Blocks

    S ca

    le F

    ac to

    r

  • Cycle Histogram

    0

    1500

    range (uE)

    -1000

    1000

    mea n (u

    E)

    0

    25

    co un

    ts

  • ε-N Damage

    0

    1500

    range (uE)

    -50

    50

    mea n st

    ress

    0

    10

    % da

    m ag

    e

  • Weld Geometry

    Crack Depth

  • Geometry Factor

    0.0

    0.5

    1.0

    1.5

    2.0

    2.5

    3.0

    0.0 0.2 0.4 0.6 0.8 1.0 a/W

    Y (

    a/ W

    )

  • Crack Length

    0

    0.001

    0.002

    0.003

    0.004

    0.005

    0 200 400 600 800 1000

    Blocks

    C ra

    ck L

    en g

    th ,m

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