CHAPTER 6FATIGUE PROPERTIES OF MATERIALSME 215Machine parts are
rarely loaded in simple manner as the specimensin a tensile or
torsion test where load is usually constant or very slowly
varyingThe machine parts in real life are often subjected to loads
and stresses that varywith time either in magnitude or in
direction.In tensile (or compressive) tests of materials, loading
usually starts from zero and gradually goes up to a maimum value
where material no longer can resist the internal stresses and fails
!fractures around ultimate strength ("u) of material before the
load is removed. This type of failure is called the static
failure.In such tests, material is loaded only once but up to the
ultimate limit ("u) of the strength. #ife of the material is
therefore only half cycle of the loading.If we were to load the
material up to a point half the elastic limit (or ultimate
strength) and then remove the load material would not fail!fracture
and a second, third or more (n cycle) loading$unloading would be
possible. The life of the material then would be %n& cycle of
the loading until it fractures!fails.In such type of loadings where
the actual stresses are usually lower than ultimate strength of the
material, failure will not happen in the first cycle of loading and
will ta'e time. (fter a certain number of cycles of loading,
material would fail and the number of cycles to thefailure would
therefore be called the life of the part.This 'ind of failures with
a certain number of life cycles is thencalled the %fatigue
failure.The fatigue failure starts generally at stress levels below
the elastic limit of the material and result in an unepected
fracture of the component.Therefore, in engineering life it is
important that we care more about fatigue failure than static
failure since most of machine parts are re)uired to have a certain
life with stress level well below the ultimate strength (even below
elastic strength/limit) FATIGUE EXAMPLESA shaft fatigue failureA
bolt fatigue failureWelded art fatigue failure!orward"bac#ward
bendingA gear teeth fatigue failure $$$ A ship body fatigue
failure*atigue failure account for about +, - of part failure in
engineering and occurs in parts subjected to fluctuating
loads.enerally, fatigue fractures occurs as a result of crac' which
usually start at some discontinuity in the material, or at other
stress concentration location, and then gradually grow under
repeated application of load.(s the crac' grows, the stress on the
load$bearing cross$section increase until it reaches a high enough
level to cause catastrophic fracture of the part%rac#
initiation%rac# growthsmooth areas!racturerough areas&each
mar#s*racture surface which usually ehibits smooth areas which
correspond to the gradual crac' growth stage, and rough areas,
which correspond to the catastrophic fracture stage.The smooth
parts of the fracture surface usually ehibit beach mar's which
occurs as a result of changes in the magnitude of the fluctuating
fatigue load.*atigue behavior of materials is usually described by
means of a diagram called "$/ diagram which gives the number of
cycles to failure (/ ) as a function of the ma applied alternating
stress ("a)BASI !EFI"ITI#"SThe ti$e depe%de%t stresses causing
fatigue failure &a% be &lassi'ed i%to t(o $ai% groups)oA)
*a%do$ stresses+'g. b,.(no regular form or reetition e'ists)o&)
o%sta%t a$plitude a%d o%sta%t fre-ue%&y stresses +'g. a,(a
reeating form of the stress e'ists)BASI !EFI"ITI#"SA) *a%do$
stresses)The ti$e .ariatio% of su&h stresses does %ot follo( a
de'%ite patter%. The a$plitude of the /u&tuati%g stress
&ha%ges together (ith its fre-ue%&y.A ra%do$ stress is
&hara&terised by a &o%ti%uous &ha%ge i% a$plitude
a%d fre-ue%&y so that i%sta%ta%eous .alues ha.e %o $ea%i%g.BASI
!EFI"ITI#"S&) o%sta%t a$plitude a%d &o%sta%t fre-ue%&y
stresses These are spe&ial &ase of ra%do$ stresses (ith a
si%usoid (a.e for$.oAlter%ati%g stresses +rotati%g shaft
e0a$ple1,oFlu&tuati%gstresses +%o regular diagra$1,o*epeated
stresses +bet(ee% 2ero a%d pea3 .alue1,BASI !EFI"ITI#"S(egarding
reeating (non"random) stresses there are some basic arameters to
#ee in mind)oS$a0 Ma0i$u$ stress) The stress ha.i%g the highest
algebri& .alue i% the stress &y&le. Te%sile stress
bei%g &o%sidered positi.e a%d &o$pressi.e stress
%egati.e.oS$i%4 Mi%i$u$ stress) The stress ha.i%g the lo(est
algebri& .alue i% the stress &y&le."m, Mean stress0 The
average of "ma and "min."M0("M(12"MI/)!3"r , 4ange of stress0 The
difference between the ma and min stresses in one
cycle."r0"ma$"min"a , "tress amplitude0 5ne half of range of
stress."a6("r!3)67("ma$"min)!38BASI !EFI"ITI#"S9hile the amplitude
of a sinusoidal (non$random) stress is easily measured , the
amplitude of a random stress can only be epressed and measured as
the average of the instantaneous amplitudes over a certain time
period.:lassic eamples of random stress producing loading
conditions are sea waves, atmospheric disturbances and road induced
vibrations in ground vehicles.FATIGUE P*#ESS STAGESFatigue failure
pro&ess is basi&ally a $i&ros&opi& pro&ess.
The i%itiatio% a%d progress of fatigue pro&ess depe%s upo% the
$i&ros&opi& .ariables The fatigue pro&ess
&o%sists of .arios stages asfollo(s)o*A5 I"ITIATI#"oSTAGE 6 *A5
G*#7T8oSTAGE 9 *A5 G*#7T8 oF*ATU*E123%rac# initiation%rac#
growth*tage 1 + 2fracture123%rac# initiation%rac# growth*tage 1 +
2fractureFATIGUE P*#ESS STAGESra&3 i%itatio%)The progressi.e4
lo&ali2ed4 per$a%e%t stru&tural &ha%ge (hi&h
i%itiates fatigue failure is the
:microplasticity.Mi&roplasti&ity is the o%set of
plasti&ity at $i&ros&opi& le.el (hile $aterial is
still %o$i%ally elasti&;oThe usual $ethod of
$i&roplasti& defor$atio% i% $etals is by slidi%g of
blo&3s of &rystal grai% o.er o%ea%other4 li3e a de&3 of
&ards. oThe e0te%t of the plasti& /o( is li$ited by the
surrou%di%g elastic matrix. o7he% the load or stress is re$o.ed4
ba&3 stresses arisi%g fro$ the elasti& $atri0 for&e the
plasti& defor$atio% to retur% to their orgi%al state. o#% high
stresses, the elasti& $atri04 ho(e.er4 &a%%ot restore the
plasti& /o( a%d a $i&roplasti& defor$atio% starts at
&rystal grai% le.el.FATIGUE P*#ESS STAGESFATIGUE P*#ESS
STAGESThis phenomenon of microplastic deformation is called
;deformation by slip and involves three important
consideration0o"lip planeso4esolved shear stresso:ritical "hear
"tressFATIGUE P*#ESS STAGESStage 6 &ra&3 gro(th)The
persistent slip bands are embryonic fatigue crac's.( series of
intrusions and etrusions are developed during load cyclingwhich are
peculiar to the fatigue process. 5ne simple eplanation of crac'
formation that suggests itself is that these etrusions and
intrusions build up a notch FATIGUE P*#ESS STAGESThe initial crac's
form along the slip planes and usually at clevage>planes from
grain to grain and maintains a general direction perpendicular to
the maimum tensile stressFATIGUE P*#ESS STAGESoGe%eral
dire&tio% of &ra&3s is perpe%di&ular to the $a0i$u$
te%sile stress as see% i% a bifra&ture e0a$plesFATIGUE P*#ESS
STAGES o%sideri%g the life of parts4 fatigue pro&ess $ay be
di.ided i%to t(o $ai% &atogories o% the S
