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FATIGUE MATERIALS SCIENCE & ENGINEERING Part of A Learner s Guide AN INTRODUCTORY E-BOOK Anandh Subramaniam & Kantesh Balani Materials Science and Engineering (MSE) – PowerPoint PPT presentation

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Fatigue of Materials (Cambridge Solid State
Science Series) S. Suresh Cambridge
University Press, Cambridge (1998) Atlas of
Fatigue Curves Ed. Howard E. Boyer American
Society of Metals, Metals Park, OH (1986)
Salient Features Overview Points
  • It is observed that materials subjected to
    dynamic/repetitive/fluctuating load (stress) fail
    at a stress much lower than that required to
    cause fracture in a single application of a
    load.? Damage of material due to varying load
    (of magnitude usually less than the yield stress)
    ultimately leading to failure is termed as
    fatigue of material (or fatigue failure).
  • It is estimated that fatigue accounts for 90 of
    all service failures due to mechanical causes.
    Corrosion being the other major cause of
  • The insidious part of the phenomenon of fatigue
    failure is that it occurs without any obvious
    warning. Usually, fatigue failures occur after
    considerable time of service.
  • The surface which has undergone fatigue fracture
    appears brittle without gross deformation at
    fracture (in the macroscale).
  • On a macroscopic scale the fracture surface is
    usually normal to the direction of the principal
    tensile stress.
  • Fatigue failure is usually initiated at a site of
    stress concentration (E.g. a notch in the
    specimen or an acicular inclusion).
  • The term fatigue is borrowed from human reaction
    of tiredness due to repetitive work!
  • Fatigue testing is often conducted in bending or
    torsion mode (rather than tension/compression
    mode). Bending tests are easy to conduct.
  • If the stress have a origin in thermal cycling,
    then the fatigue is called thermal fatigue.
  • Note Fatigue loading is sometimes used to get a
    sharp crack in a notched specimen? Called fatigue

Factors affecting fatigue failure
  • Three factors play an important role in fatigue
    failure (i) value of tensile stress (maximum),
    (ii) magnitude of variation in stress, (iii)
    number of cycles.
  • Geometrical (specimen geometry) and
    microstructural aspects also play an important
    role in determining fatigue life (and failure).
    Stress concentrators from both these sources have
    a deleterious effect. Residual stress can also
    play a role.
  • A corrosive environment can have a deleterious
    interplay with fatigue.

Sufficiently high maximum tensile stress
Factors necessary to cause fatigue failure
Large variation/fluctuation in stress
Sufficiently large number of stress cycles
Funda Check
If the value of the maximum stress experienced by
the material is less than the yield stress,
should not the material be in a purely elastic
state? (Why does failure occur in fatigue
  • Let us consider a uniaxial tensile loading. We
    have already noted that the yield stress (?y) is
    the macroscopic yield stress and microscopic
    yielding (by slip) is initiated at a much lower
    stress value. In uniaxial loading this slip
    usually does not lead to any appreciable effects
    or damage to the material/component.
  • In cyclic loading, on the other hand due to
    reversal of slip direction, intrusions can be
    caused on the surface, which are like small
    surface cracks (precursors to a full blown
  • Once a crack forms from these intrusions (due to
    further cyclic loading), local stress
    amplification takes place.
  • In the presence of the crack the relevant
    material property to be considered is fracture

Click here to know Where does yielding start?
Types of stress cycles and parameters
characterizing them
  • The pattern of loading experienced by a component
    may be complicated involving many frequencies and
    may include vibration (Fig.1 below). (If the
    frequency of loading is very high, it is referred
    to as vibration).
  • The essential effect of such a loading can be
    understood by simpler loading patterns like the
    sinusoidal wave (Fig.2 below). Tests involving
    such loading are easy to conduct and the results
    obtained is easy to interpret.

I. Completely reversed cycle of stress
  • The simplest loading one can conceive is a
    sinusoidal wave pattern loading, where the
    stress/load oscillates about a mean zero
    load/stress. The stress amplitude (?a) is marked
    in the figure.

II. Purely tensile cycles
  • The stress/load oscillation may be sinusoidal,
    but the mean stress/load may be such that the
    stress state during the entire cycle is tensile.
    Needless to say, for a given stress amplitude
    this type of loading is more severe (as maximum
    stress ?max is ?min ?r). Various parameters are
    defined in the equations below.

III. Random stress cycles
  • The stress/load oscillation may be sinusoidal,
    but the mean stress/load may be such that the
    stress state during the entire cycle is tensile.
    Needless to say, for a given stress amplitude
    this type of loading is more severe (as maximum
    stress ?max is ?min ?r).

S-N Curve
  • Engineering fatigue data is usually plotted as a
    S-N curve. Here S is the stress and N the number
    of cycles to failure (usually fracture). The
    x-axis is plotted as log(N).
  • The stress plotted could be one of the following
    ?a, ?max, ?min. Each plot is for a constant ?m, R
    or A.
  • It should be noted that the stress values plotted
    are nominal values and does not take into
    account local stress concentrations.
  • Most fatigue experiments are performed with ?m
    0 (e.g. rotating beam tests).
  • Typically the stress value chosen for the stress
    is low (lt ?y) and hence S-N curves deal with
    fatigue failure at a large number of cycles (gt
    105 cycles). These are the high cycle fatigue
  • It is to be noted that the nominal stress lt ?y,
    but microscopic plasticity occurs, which leads to
    the accumulation of damage.
  • As obvious if the magnitude of Stress increases
    the fatigue life decreases.
  • Low cycle fatigue (N lt 104 or 105 cycles) tests
    are conducted in controlled cycles of elastic
    plastic strain (instead of stress control).

S-N Curve
  • Broadly two kinds of S-N curves can be
    differentiated for two classes of materials. (1)
    those where a stress below a threshold value
    gives a very long life (this stress value is
    called the Fatigue Limit / Endurance limit).
    Steel and Ti come under this category.(2) those
    where a decrease in stress increases the fatigue
    life of the component, but no distinct fatigue
    life is observed. Al, Mg, Cu come under this
  • From a application point of view having a sharp
    fatigue limit is useful (as keeping service
    stress below this will help with long life (i.e.
    large number of cycles) for the component).

Fatigue limit Endurance limit
Fatigue limit
Mild steel
Stress below Fatigue limit give infinite life
No fatigue limit ? fatigue strength is specified
for and arbitrary number of cycles ( 108 cycles)
Bending stress (MPa) ?
Aluminium alloy
Note that number of cycles is in log scale
  • Steel, Ti show fatigue limit
  • Al, Mg, Cu show no fatigue limit

Number of cycles to failure (N) ?
S-N Curve Basquin equation
  • S-N curve in the high cycle region can be
    described by the Basquin equationwhere, ?a is
    the stress amplitude, p C empirical constants.
  • The S-N curve is usually determined using 8-12
    specimens. Starting with a stress of two-thirds
    of the static tensile strength of the material
    the stress is lowered till specimens do not fail
    in about 107 cycles. As expected, there is
    usually there is considerable scatter in the data.

Strain controlled cyclic loading
Microstructural aspects of fatigue failure
  • One of the important mysteries related to
    fatigue is how does fatigue failure occur if
    the stress value used is below the yield
  • Fatigue failure occurs because of microscopic
    plasticity (which can occur below the yield
    stress) and damage accumulation with time (i.e.
    number of cycles of loading).
  • Four important stages of fatigue can be
    identified1? Crack initiation (in notched
    specimens this stage may be absent). This occurs
    mostly at surfaces or sometimes at internal
    interfaces. Crack initiation may take place
    within about 10 of the total life of the
    component. 2? Stage-I crack growth (Slip-band
    crack growth) growth of crack along planes of
    high shear stress. This can be viewed as
    essentially extension of the slip process which
    lead to crack formation (something like deepening
    of the crack formed). 3? Stage-II crack growth
    in this stage the crack grows along directions of
    maximum tensile stress. Hence, crack propagation
    is trans-granular.4? Ductile failure reduction
    in load bearing area (due to crack propagation)
    leads to ultimate failure.
  • The crack which forms after stage-1 can be
    removed by annealing (i.e. the damage is
    reversible at that stage).
  • In parallel with dislocation activity, fatigue
    loading can give rise to an increased
    concentration of vacancies (as compared to
    uniform loading). These vacancies can further
    play a role in processes like climb, over-aging
    of precipitates, etc. (depending on the material
    and context).

Crack initiation
Crack deepening
Crack growth
Slip and fatigue crack initiation
  • When a specimen (Fig.1) is subjected to uniform
    loading (e.g. pure shear in Fig.2), dislocations
    moving on parallel slip planes leave the free
    surface of crystal/grain, giving rise to slip
    lines on the surface of the specimen (Fig.2). The
    surface steps in static loading are typically
    100-100nm high. Slip is prevalent in all grains
    of the specimen uniformly.
  • In fatigue loading on the other hand some grains
    may show slip while others may not. Due to
    accumulation of slip, slip bands form (within
    about 5 of the total number of cycles to
    failure), which increase with number of cycles.
    The surface steps created in this case are fine
    (1nm) and further due to oscillatory loading
    this can lead to extrusions (Fig.3) and
    intrusions (Fig.4). The intrusions can act like a
    notch, which is a stress concentrator and are a
    precursor to a full blown crack.

Dynamic/fatigue loading
Fine scale compared to static loading
Static loading
Fatigue crack propagation
  • Once a crack has formed its growth can be
    understood in two stages. (i) Stage-I. Growth
    along slip bands due to shear stress (which lead
    to the formation of the intrusions), which can be
    thought of as crack deepening. The extension of
    the crack is only a few grain diameters during
    this stage at the rate of few nm per cycle. (ii)
    Stage-II marks faster crack growth of microns per
    cycle and is dictated by the maximum normal
    stress present. Striations characteristic of
    fatigue crack propagation are seen in this stage
    (fatigue striations). Each striation is produced
    by one cycle of stress. Sometimes these
    striations are difficult to detect and hence if
    striations are not found it does not imply that
    fatigue crack propagation was absent. The
    standard mechanism used to explain this
    phenomenon is shown in figure below (the tensile
    part of the cycle). During the compressive
    portion of the cycle the crack faces tend to
    close and the blunted crack tends to re-sharpen.
  • The important portion of the fatigue failure is
    the Stage-II crack growth and hence understanding
    the same helps one predict the failure
    cycles/time and hence plan for fail safe design
    (the component can be replaced before the crack
    grows to a critical value leading to failure the
    concept of preventive maintenance).

Formation of double notch concentrating slip at
45? due to tensile loading
tensile part of the cycle
Crack tip extension and blunting
Crack widening.
Fatigue crack propagation
  • As we have seen stage II crack growth occupies
    the predominant portion of the fatigue life of a
    sample/component. Empirically it is seen that the
    crack growth rate (da/dN) follows a double power
    law equation.
  • ?a ? the alternating stress
  • a ? the crack length
  • A,B ? constants
  • m ? ranges from 2-4
  • n ? ranges from 1-2
  • In terms of the total strain (?) this can be
    expressed as
  • We have noted that once the crack nucleates (as
    has already happed in stage II), the relevant
    parameter characterizing the mechanical behaviour
    of the material is the stress intensity factor
    and not the stress (alone). So a logical plot
    should be between da/dN and the range of stress
    intensity factors (?K) experienced by the
  • A range of K (i.e. ?K) has to be considered as we
    are in fatigue loading mode.
  • Use of ?K further gives a crucial link between
    fatigue and fracture mechanics.

Note in compression K is not defined and hence
Kcompression is taken to be zero. However, the
compressive part of the loading is important from
mechanistic and other points of view.
  • A plot of da/dN vs ?K can the divided into three
    regions. Region-1 ? slow or negligible crack
    growth.Region-2 ? stable crack growth with power
    law behaviour (linear behaviour between crack
    growth rate and log of stress intensity factor
    range (log?K) (called Paris law)).Region-3 ?
    unstable crack growth leading to failure (as Kmax
    exceeds the Kc of the material).
  • We have noted that the materials we are dealing
    with are ductile with appreciable crack tip
  • However, Linear Elastic Fracture Mechanics (LEFM)
    and hence K can be used as a characterizing
    parameter (as plastic zone sizes are often small).

Approximately linear curve in region-2
  • C ? a constant in region-2
  • ?K ? (Kmax ? Kmin)
  • p ? 3 for steels, 3-4 Al alloys
  • It is important to note that S-N curves are
    usually determined with R ?1 (fully reversed
    stress cycles) and (da/dN)-?K curves are
    determined with R 0 (pulsating tension). Hence,
    comparison of data and curves should be done

(No Transcript)
  • Often progress of fracture in due to fatigue
    loading is indicated in a fractograph by a series
    of rings (or beach marks).

Effect of Metallurgical Variables
  • Fatigue related properties are sensitive to (i)
    specimen geometry (with special reference to
    stress raisers) (ii) microstructure (including
    residual stress and microstructural stress
    raisers)(iii) surface finish.
  • Smooth surface finish and compressive residual
    stress improve fatigue properties (i.e increase
    fatigue life).
  • In some cases correlation is found between
    properties determined from static tensile tests
    (like UTS) with that determined from fatigue
    testing (e.g. fatigue limit). However, there is
    no universality to the behaviour.
  • As we have observed localization of slip is a key
    feature of fatigue crack nucleation. This implies
    that if slip can be spread out more uniformly
    (homogenization of slip) then fatigue life with
    improve. This is more prevalent in low stacking
    fault energy (SFE) materials (like Ag),
    cross-slip is more difficult (as the spacing
    between partials is more) and hence obstacles
    cannot be overcome easily by cross-slip. The
    opposite is true for high SFE materials (like
    Al), where cross-slip can lead to a set of
    parallel slip planes operating extensively.

High SFE material
Effect of Metallurgical Variables
  • Further, in low SFE materials, the grain size
    plays an important role in determining the
    fatigue life. This role is important only under
    conditions of low stress (where number of cycles
    to failure is high and stage-I cracking is
    predominant). Under such circumstances the
    following relation is often observed
  • In high SFE materials, dislocation cell
    structures form on deformation and these play a
    more important role in stage-I cracking as
    compared to grain size.
  • The presence of interstitial and substitutional
    alloying elements play an important role in
    determining the S-N curve (fatigue life).
    Interstitial solutes, which contribute to strain
    aging give rise to a fatigue limit in the S-N
    curve. Substitutional elements increase fatigue
    life without introducing a fatigue limit.

Enhanced strain aging effect (due to increased
solute content or aging time) gives tolerance to
higher stress values, for a given fatigue life
Interstitial solute elements (like C in steel)
introduce fatigue limit due to strain aging
For a given stress, more number of cycles to
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