0 DDas Fatigue Fracture

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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7/82Dr. D Das, BESUS, UG-2012



(R =0)

(R >0)

(R = -1)



Any varying stress with a nonzero mean

is considered a fluctuating stress.



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



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



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


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



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



Yield (Langer) Line

C it i f F ti F il


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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

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