FATIGUE

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FATIGUE
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)
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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
  failures.
• 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. In
  pipes fatigue tests may be done by internal
  pressurization with a fluid.
• 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
  pre-cracking.

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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
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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
loading?).

• 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
  crack).
• 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
  toughness.

Click here to know Where does yielding start?
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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.

Fig.1
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.

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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.

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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).

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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
  tests.
• 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 (strain control mode, instead of
  stress control).

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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
  category.
• 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).

400
Fatigue limit Endurance limit
Fatigue limit
Stress below Fatigue limit give infinite life
300
Mild steel
No fatigue limit ? fatigue strength is specified
for and arbitrary number of cycles ( 108 cycles)
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Bending stress (MPa) ?
Aluminium alloy
100

• Steel, Ti show fatigue limit
• Al, Mg, Cu show no fatigue limit(Might show a
  limit, but prohibitive to conduct such long time
  tests!)

Note that number of cycles is in log scale
Number of cycles to failure (N) ?
0
105
106
107
108
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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.

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Strain controlled cyclic loading
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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
  stress?.
• 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
Failure
Region of concentrated slip.
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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
Fig.1
Fig.3
Fine scale compared to static loading
Static loading
Fig.4
Fig.2
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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.
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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 I), 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
  specimen.

• 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 (including
the time involved).
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• 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
  blunting.
• Often the size of the plastic zone are small and
  hence the concepts of Linear Elastic Fracture
  Mechanics (LEFM) and hence K can be used as a
  characterizing parameter in fatigue.

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
  carefully.

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Fractography

• Often progress of fracture in due to fatigue
  loading is indicated in a fractograph by a series
  of rings (or beach marks).

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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. 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
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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
failure.