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7/29/2019 0 DDas Fatigue Fracture
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Dr. D Das, BESUS, UG-2012
Fatigue FailureFailures occurs under conditions of dynamic loadings
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Failure even at low Stresses
Failure often occurs even when:
applied < fracture and applied < yielding
90% of all mechanical failures are
related todynamic loading.
Dynamic Loading -> Cyclic Stresses
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(R =0)
(R >0)
(R = -1)
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Any varying stress with a nonzero mean
is considered a fluctuating stress.
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Plot of Fatigue Failures for Mean (Midrange) Stresses in both Tensile andCompressive Regions
Plot of fatigue failures for midrange stresses in both tensile and compressive
regions. Normalizing the data by using the ratio of steady strength components to
tensile strength Sm/Sut, steady strength component to compressive strength Sm/Suc,
and strength amplitude component to endurance limit Sa/Se enables a plot ofexperimental results for a variety of steels.
COMPRESSIVE
mean stressesareBENEFICIAL(or have noeffect) in
fatigue
TENSILEmeanstresses areDETRIMENTALfor fatigue
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Mean stress, m
Alternativestress,a
e
0
o u
2
minmax
m
minmax a
0
Yield stress uniaxial tension
e Fatigue limit determined for
completely reversed loading1
max
min
R
0
Ultimate tensile stress
Criteria of Fatigue Failure
m
ar
Load line, Slope
C i i f i il
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Dr. D Das, BESUS, UG-2012Mean stress, m
Alternativestress,a
e
0
o u
Criteria of Fatigue Failure
Unsafe
Safe
Load line
m
a
M difi d G d ThC it i f F ti F il
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Modified Goodman Theory
Mean stress, m
Alternativestress,a
e
0
o u
Load line
m
a
u
m
ea
1
A
O
B
Factor of safety = OA/OB
For infinite life, Failure occurs when
Criteria of Fatigue Failure:
Germany, 1899
Modified Goodman line
Th S d b ThC it i f F ti F il
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The Soderberg Theory
Mean stress, m
Alternativestress,a
e
0
o u
Load line
m
a
0
1
m
ea
C
O
B
Factor of safety = OC/OB
For infinite life, Failure occurs when
Criteria of Fatigue Failure:
USA, 1933
Soderberg line
Th G b ThC it i f F ti F il
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The Gerber TheoryCriteria of Fatigue Failure:
Germany, 1874
Mean stress, m
Alternativestress,a
e
0
o u
Load line
m
a
2
1
u
mea
D
O
B
Factor of safety = OD/OB
For infinite life, Failure occurs when
Gerber line
Th ASME Elli tiC it i f F ti F il
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The ASME Elliptic
Mean stress, m
Alternativestress,a
e
0
o u
Load line
m
a
2
1
2
0
1
m
ea
E
O
B
Factor of safety = OE/OB
For infinite life, Failure occurs when
Criteria of Fatigue Failure:
ASME Elliptic line
Th L Yi ld liC it i f F ti F il
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The Langer Yield line
Mean stress, m
Alternativestress,a
e
0
o u
Load line
m
a
0
01
m
a
F
O
B
Factor of safety = OF/OB
For infinite life, Failure occurs when
Criteria of Fatigue Failure:
Yield (Langer) Line
C it i f F ti F il
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Criteria of Fatigue Failure:
Mean stress, m
Alternativestress,ae
0
o uO
Yield (Langer) Line
ASME Elliptic line
Gerber line
Modified Goodman line
Load line
1u
m
e
a
Soderberg line1
0
m
e
a
1
2
u
m
e
a
1
00
ma
1
2
0
2
m
e
a
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At max = 400 MPa and min = 0 MPa, Nf< 106 cyclesAt min = - 400 MPa and R = -1.0, Nf< 104 cycles
At min = +150 MPa and R = +0.33 Nf> 107 cycles
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Surface roughness
Surface properties
Surface residual stress
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Kfis usually less than Kt and ration ofKf/ Ktdecreases with increasing Kt.
Materials that experiences no reduction in
fatigue due to notch (Kf= 1) and hence, q = 0.
In material in which the notch has its full
theoretical effect (Kf= Kt) and thus q =1.
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Notch radius
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High stacking fault energy Easy cross slip of dislocation (Wavy slip)that promotes ..
Avoid slip band formation
Minimize plastic zones at the tips of cracks
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Grain size
For materials with low SFE (planer slip)
Fatigue life is proportional to (grain size)-1/2
For material with high SFE (wavy slip)
Fatigue life is independent on grain size
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For better fatigue properties at same strength/hardness level
bainitic structure is better than hardened and tempered structure
Spheroidite structure is better than course peartlite
due to lowering of stress concentration site life sharp and thin cementite
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Mainly for Fe and Ti
Addition of interstitial elements
raises yield strength and makes it
more difficult to initiate slip band
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Ratio of UTS to YS (in monotonic loading)
> 1.4 Cyclic hardening
< 1.2 Cyclic softening
1.2-1.4 no change
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Coffin-Manson relation
Lower value ofc for better fatigue life
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(monotonic true fracture stress)
Lower value ofb for better fatigue life
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Fatigue Life: HCF and LCF
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g
18%-Ni maraging steel
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Fatigue crack can be formed before 10% of the NfIf tensile stress is high, as in the fatigue of sharply notched specimens, stage-I
crack may not be observed at ll
In LCF, large portion of Nfare involved in the propagation ofstage-II cracking
In HCF, large portion of Nfare involved in the propagation ofstage-I cracking
The Process of Fatigue
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g
The Materials Science Perspective:
Cyclic slip,
Fatigue crack initiation, Stage I fatigue crack growth,
Stage II fatigue crack growth,
Stage III Brittle fracture or ductile rupture
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Interface
like,
carburized
layer/basemetal
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Woods model of fatigue crack initiation from microdeformation
Surface notch (intrusion) Surface ridge (Extrusion)
Formation of slip bands in fatigue is the result of a systematic buildup of fine slip movement(in the order ofonly 1 nm in comparison to 100 to 1000 nm in static loading)
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Cyclic deformation generates vacancies, cold worked becomes softer as a result
of fatigue, peak aged Al-alloy overaged at room temperature by fatiguedeformation.
But the generation of vacancy is not essential for fatigue failure.
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At the start of the loading cycle the crack
tip is sharp
As tensile loading is applied the small double
notch at the crack tip concentrates the slip
along planes 45o to the plane of the crack
As tensile loading increases, the cracks
widens to its maximum extension. It grows
longer by plastic shearing and at the sametime its tip becomes blunter
When load is compression, the slip direction
in the end zones is reserved. The crack are
crushed together and the new crack surface
created in tension is forced into the plane of
the crack where it partly folds by buckling toform a resharpened crack tip
The resharpened crack is ten ready to advanced
and be blunted in the next stress cycle.
Schematic of Fatigue Crack Initiation Subsequent Growth
C di d T iti F M d II t M d I
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Locally, the crack grows in shear;
macroscopically it grows in tension.
c
Corresponding and Transition From Mode II to Mode I
Stages I, II, and III of fatigue crack propagation
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Fatigue Damage
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Intrinsic and extrinsic mechanisms of fatigue damage.
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pKAdN
da Paris Law
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General solution
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Features of the Fatigue Fracture Surface of a Typical Ductile MetalSubjected to Variable Amplitude Cyclic Loading
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Subjected to Variable Amplitude Cyclic Loading
A fatigue crack area
B area of the final static failure
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Fatigue property map
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Fatigue property map