Creep and Fatigue

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An Introduction to the concepts

Text of Creep and Fatigue

  • BITSPilaniPilani Campus

    MATERIALS SCIENCE AND ENGINEERING

  • Creep

    Creep may be defined as a time-dependent

    deformation at elevated temperature and

    constant stress

    Occurs when material supports a load for very long

    period of time, and continues to deform until a

    sudden fracture or usefulness is impairedsudden fracture or usefulness is impaired

    Is only considered when metals and ceramics are

    used for structural members or mechanical parts

    are subjected to high temperatures

    Other materials (such as polymers & composites)

    are also affected by creep without influence of

    temperature

  • *3.7 FAILURE OF MATERIALS DUE TO CREEP & FATIGUE

    Creep

    Stress and/or temperature significantly affects the

    rate of creep of a material

    Creep strength represents the highest initial stress

    the material can withstand during given time

    Mechanical Performance of Materials

    the material can withstand during given time

    without causing specified creep strain

    Simple method to determine creep strength

    Test several specimens simultaneously

    At constant temperature, but

    Each specimen subjected to different axial stress

  • *3.7 FAILURE OF MATERIALS DUE TO CREEP & FATIGUE

    Creep

    Simple method to determine creep strength

    Measure time taken to produce allowable strain or

    rupture strain for each specimen

    Plot stress vs. strain

    Mechanical Performance of Materials

    Plot stress vs. strain

    Creep strength inversely proportional to

    temperature and applied stresses

  • *3.7 FAILURE OF MATERIALS DUE TO CREEP & FATIGUECreep

    Schematic creep curve for a constant load; a plot of the change

    in length verses time. The weight or load on the specimen is

    held constant for the duration of the test.

  • *3.7 FAILURE OF MATERIALS DUE TO CREEP & FATIGUECreep

    Creep deformation occurs by grain-boundary

    sliding. That is, adjacent grains or crystals move

    as a unit relative to each other

  • *3.7 FAILURE OF MATERIALS DUE TO CREEP & FATIGUECreep

    There are four portions of the curve

    that are of interest:

    An initial steep rate that is at least partly of

    elastic origin, from point "0" to point "A" in

    Figure.

    This is followed by a region in which the

    elongation or deformation rate decreases with

    time, the so-called transient or primary creep,

    from region "A" to "B". The portion from point from region "A" to "B". The portion from point

    "0" to point "B" occurs fairly quickly.

    The next portion of the creep curve is the area of engineering interest,

    where the creep rate is almost constant. The portion from "B" to "C" is

    nearly linear and predictable.

    The fourth portion of the creep curve, beyond the constant-creep-rate or

    linear region, shows a rapidly increasing creep rate which culminates in

    failure. Even under constant-load test conditions, the effective stress may

    actually increase due to the damage that forms within the microstructure.

  • Fatigue

    Fatigue is the lowering of strength or the failure of a

    material due to repetitive stress, which may be above

    or below the yield strength.

    Mechanical Performance of Materials

    Many engineering materials such as those used in

    cars, planes, turbine engines, machinery, shoes, etc

    are subjected constantly to repetitive stresses in the

    form of tension, compression, bending, vibration,

    thermal expansion and contraction or other stresses.

  • FATIGUE

    Fracture surface which usually exhibits:

    Smooth areas -correspond to the gradual crack growth stage, and

    Rough areas-correspond to the catastrophic fracture stage.

    The smooth parts of the fracture surface usually The smooth parts of the fracture surface usually exhibit beach marks which occurs as a result of changes in the magnitude of the fluctuating fatigue load.

    9

  • Fatigue Failures Are Often Easy To Identify

    10

  • *3.7 FAILURE OF MATERIALS DUE TO CREEP & FATIGUEMethod to Determine Fatigue

    Fatigue behavior of materials is usually described by

    means of the S-N diagram which gives the number

    of cycles to failure, N as a function of the max

    applied alternating stress.

    Subject series of

    specimens to specified

    Fatigue

    specimens to specified

    stress and cycle to failure

    Plot stress (S) against

    number of cycles-to-

    failure N

    (S-N diagram) on

    logarithmic scale

  • DESIGNING AGAINST FATIGUE

    S-N curve is a graphical representation of the maximum

    applied stress versus the number of stress cycles N before

    the fatigue failure on a semi-log graph. For ferrous metals

    like steel the curve becomes asymptotic at 106 cycles.

    The completely reversed stress which a material can

    withstand 106 cycles without failure is called ENDURANCE

    12

    withstand 106 cycles without failure is called ENDURANCE

    LIMIT of the material.

    For non ferrous materials, the curve slopes gradually even

    after 106 cycles. These materials do not have a limiting

    value of endurance in true sense. In these cases endurance

    limit is expressed as a function of number of cycles.

  • Fatigue

    Fatigue Limit:

    For some materials such as BCC steels and Ti alloys, the S-N

    curves become horizontal when the stress amplitude is

    decreased to a certain level.

    This stress level is called the Fatigue Limit, or Endurance

    Limit, which is typically ~35-60% of the tensile strength

    for steels.for steels.

    In some materials, including steels, the endurance limit is

    approximately half (50%) the tensile strength, given by:

    5.0strength tensile

    limit endurance ratio Endurance =

  • The S-N curves for a tool steel and an aluminum alloy showing the number of cycles to

    failure

  • DESIGNING AGAINST FATIGUE

    In the majority cases, the reported fatigue strength or endurance limits of the materials are based on the test of carefully prepared small samples under laboratory condition.

    Such values cannot be directly used for design purposes because the behavior of a component or structure under fatigue loading does depend not only on the fatigue or endurance limit of the material used in making it, but also an several other factors including :endurance limit of the material used in making it, but also an several other factors including :

    Size and shape of the component or structure

    Type of loading and state of stress

    Stress concentration

    Surface finish

    Operating temperature

    Service environment

    Method of fabrication 15

  • Endurance-limit modifying factorsse = kakbkckdkekfkgkhse

    Where se = endurance limit of component

    se = endurance limit experimental

    ka = surface finish factor (machined parts have different finish)

    kb = size factor (larger parts greater probability of finding defects)

    DESIGNING AGAINST FATIGUE

    defects)

    kc = reliability / statistical scatter factor (accounts for random variation)

    kd = operating T factor (accounts for diff. in working T & room T)

    ke = loading factor (differences in loading types)

    kf = stress concentration factor

    kg = service environment factor (action of hostile environment)

    kh = manufacturing processes factor (influence of fabrication parameters)

    16

  • DESIGNING AGAINST FATIGUE

    ka = Surface finish factor

    17

  • DESIGNING AGAINST FATIGUE

    kb = Size factor

    Large engineering parts have lower fatigue

    strength than smaller test specimen

    Greater is the probability of finding metallurgical

    flaws that can cause crack initiation

    Following values can be taken as rough guidelines :

    kb = 1.0 for component diameters less than 10

    mm

    kb = 0.9 for diameters in the range 10 to 50 mm

    kb = 1 [( D 0.03)/15], where D is diameter

    expressed in inches, for sizes 50 to 225 mm.

    18

  • DESIGNING AGAINST FATIGUE

    kc = Reliability factor

    Accounts for random variation in fatigue

    strength.

    The following value can be taken as

    guidelinesguidelines

    kc = 0.900 for 90% reliability

    kc = 0.814 for 99 % reliability

    kc = 0.752 for 99.9 % reliability

    19

  • DESIGNING AGAINST FATIGUE

    kd = Operating temperature factor

    Accounts for the difference between the test

    temperature and operating temperature of the

    component

    For carbon and alloy steels, fatigue strength not

    affected by operating temperature 45 to affected by operating temperature 45 to

    4500C kd = 1

    At higher operating temperature

    kd = 1 5800( T 450 ) for T between 450 and

    550oC, or

    kd = 1 3200( T 840 ) for T between 840 and

    1020oF20

  • DESIGNING AGAINST FATIGUE

    ke = Loading factor

    Different type of loading, give

    different stress distribution

    ke = 1 for application ke = 1 for application

    involving bending

    ke = 0.9 for axial loading

    ke = 0.58 for torsional loading

    21

  • DESIGNING AGAINST FATIGUE

    kf = Fatigue stress concentration factor

    Accounts for the stress concentration

    which may arise when change in cross-

    section

    kf = endurance limit of notch-free partkf = endurance limit of notch-free part

    endurance limit of notched part

    Low strength, ductile steels are less

    sensitive to notch than high-strength

    steels

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  • DESIGNING AGAINST FATIGUE

    kg = Service environment factor

    Accounts for the reduced fatigue strength

    due to the action of a hostile environment.

    23

  • DESIGNING AGAINST FATIGUE

    kh = Manufacturing process factor

    Accounts for the influence of fabrication

    parameter

    Heat treatment, cold working, residual

    stresses and protective coating on the stresses and protective coating on the

    fatigue material.

    It is difficult to quantify, but important to

    be included.

    24

  • Fatigue Failures

    Types of stresses for fatigue tests include,

    axial (tension compression)

    flexural (bending)

    torsional (twisting)

    From these tests the following data are generated.

    +

    By convention, tensile stresses are positive and compression stresses are

    negative.

    max

    min

    minmaxr

    minmaxa

    minmaxm

    Ratio, Stress

    Range, Stress

    2 Amplitude, Stress

    2 Stress,Mean

    =

    =

    =

    +=

    R

  • Fatigue Failures

    Examples of stress

    cycles where a) shows

    the stress in

    compression and

    tension, b) shows

    a

    tension, b) shows

    theres greater tensile

    stress than

    compressive stress

    and in c) all of the

    stress is tensile.

    b

    c

  • Fatigue Failures

    As the mean stress, m, increases, the stress amplitude, a,must decrease in order for the material to withstand the

    applied stress. This condition is summarized by the

    Goodman relationship:

    = mfsa 1 Amplitude, Stress

    Where fs is the desired fatigue strength for zero mean stress and TS is the tensile strength of the material.

    TS

    fsa

  • Fatigue FailuresCrack Growth Rate

    To estimate whether a crack will grow, the stress intensity

    factor (K), which characterizes the crack geometry and the stress amplitude can be used.

    Below a threshold K a crack doesnt grow.

    For somewhat higher stress intensities, the cracks grow

    slowly.slowly.

    For still higher stress-intensities a crack grows at a rate

    given by:

    Where C and n are empirical constants that depend

    on the material.

    When DK is high, the cracks grow in a rapid and

    unstable manner until fracture occurs.

    ( )nKCdN

    da=

  • Fatigue Failures

  • Fatigue Failures

    if we integrate between the initial size of a crack and the

    crack size required for fracture to occur, we find that the

    number of cycles to failure is given by

    ( )nKCdN

    da=

    From the steady state crack growth relationship of

    number of cycles to failure is given by

    where C and n are empirical constants that depend on the

    material.

    [ ]2/

    2/)2(2/)2(

    )2(

    )()(2nnn

    n

    i

    n

    c

    Cfn

    aaN

    =