Fatigue Part 1

7/27/2019 Fatigue Part 1

1/41

Fatigue Part 1

Dr. Nuri Ersoy


2/41

Fatigue, Damage, Durability Fatigue is the process where repeated variations

in loading cause failure even when the nominalstresses are below the material yield strength;

Damage is the inverse of life for a given strain

amplitude and is cumulative until failure

Durability is the capacity of an item to survive its

intended use for a suitably long period of time,so that good durability minimises the cost ofmaintaining and replacing the item


3/41

Approaches to Analysing and

Designing Against Fatigue Failure Stress Based Aproach: Analysis is based on the nominal

(average) stresses in the region of the component beinganalysed. The nominal stresses that can be resistedunder cyclic loading is determined by considering meanstresses and by making adjsutments for the effects ofstress raisers, such as grooves, holes, fillets, andkeyways

Strain Based Approach: involves more detailed analysisof the localised yielding that may occur at stress raisers

during cyclic loading. Fracture Mechanics Approach: treats growing cracks

using fracture mechanics approach


4/41

Definitions and Concepts Constant Amplitude Stressing

2

:StressgAlternatin

2:StressMean

:RangeStress

minmax

minmax

a

mean


5/41

Fatigue Testing Rotating Bending Testing


6/41

Fatigue Testing Servohydraulic Testing


7/41

Metallurgical Fundamentals Persistent Slip Band Formation


8/41

Stages of Fatigue Initiation Stage I Stage II


9/41


10/41

Stages of Fatigue Crack Initiation: Early development of fatigue

damage which can be removed by suitablethermal annealing

Slip band crack growth: deepening of the initialcrack on planes of high shear stress Stage I

crack growth Crack growth on planes of high tensile stress:

growth of well-defined crack in direction normalto maximum tensile stress Stage II crack growth

Ultimate ductile failure: occurs when the crackreaches a sufficient length so that the remainingcross section cannot support the applied load.


11/41

Fatigue Stages and

Fatigue Surfaces


12/41


13/41

Fatigue Striations


14/41

Stage II Crack Growth


15/41

Low Cycle vs High Cycle Fatigue Low Cycle

Y50% of life spent for initiation

Many cracks nucleate

High Cycle

>104 cycles


16/41

Fatigue Testing Rotating Bending Testing


17/41

Stress-Life Curve (S-N curve)

constantsmaterial

areand

)2(

b

N

f

b

ffa


18/41

Prime indicates that it is obtained from rotating-bending tests

Stress level below which fatigue failure does not occur (plaincarbon and low alloy steels)


19/41

Fatigue Strength Stress amplitude value from an S-N curve at a

particular life of interest


20/41

S-N Curve


21/41

S-N Curve

a, MPa Nf, cycles

948 222

834 992

703 6004

631 14130

579 43860

524 132150


22/41

Probabilistic Nature Of Fatigue

Scatter in rotating bending S-N data for an unnotched aluminum alloy


23/41

Distr ibution of fatigue lives for 57 small specimens of

7075-T6 aluminum tested at Sa=207 MPa


24/41

Probabilistic Nature of Fatigue


25/41

Safety Factors

B -1/B XN

for XS

=2 XS

for XN

=10

-0.1 10 1024 1.26

-0.2 5 32 1.58

-0.333 3 8 2.15

a=ANfB


26/41

Endurance Limit versus UTS


27/41

Endurance LimitsWrought Steel

Cast Steel and Cast Iron

Aluminium Alloys

Wrought Aluminium Alloys

Magnesium Alloys

Copper and Nickel Alloys

Titanium Alloys

1400MPafor700MPa

1400MPafor5.0

u

uu

eS

SSS

MPa403for130MPa

MPa403for40.0

u

uu

eS

SSS

MPa006for275MPa

MPa600for45.0

u

uu

eS

SSS

ue SS 35.0

moldpermanentfor100MPa-70

castsandfor75MPa-05eS

uue SSS 50.0to25.0

uue SSS 65.0to45.0


28/41

Generalized S-N Curve for

Wrought Steel


29/41

Factors Affecting the Endurance

Limit

factornotchfatigue

factoryreliabilit

factorloading

factor(Gradient)Sizefactorsurface

/

f

R

L

G

S

fRSGLee

k

C

C

CC

where

kCCCCSS


30/41

S-N Diagrams for Other Types

of Loading (Loading Factor, CL)


31/41

Influence of Surface Finish on Fatigue

Strength (Surface Factor,Cs)


32/41

Influence of Size on Fatigue

Strength (Size Factor, CG)


33/41

Size Factor, CG

in bending or torsion

in axial loads

independent of size

1bk

1 0.4 (10 )

.85 0.4 (10 ) 2 (50 )

.75 2 (50 )

b

for d mm

k for mm d mm

for d mm


34/41

Reliability Factor, CR

Reliabilityck

50%

90%95%

99%

99.9%

99.99%

1.00

.90

.85

.80

.75

.70


35/41

Fundamentals of Machine Component Design, 4/E by Robert C. Juvinall and Kurt M. Marshek

Table 8.1a (p.

303)Generalized Fatigue

Strength Factors for

Ductile Materials

(S-N curves).

(Continued on nextslide.)


36/41

Fundamentals of Machine Component Design, 4/E by Robert C. Juvinall and Kurt M. Marshek

Table 8.1b (cont.)


37/41

Effect of Mean Stress


38/41

Presentation of Mean Stress Data Constant life Diagram


39/41

Presentation of Mean Stress Data Normalized Amplitude-Mean Diagrams

0for

stressgalternatintheis

stressmeananyforstressgalternatintheis

1

ParabolaGerber

)0(1

LineGoodmanModified

2

m

ar

m

a

u

m

er

e

m

u

m

ar

a


40/41

Life Estimates Any combination of mean

stress m and amplitude a is

thus expected to produce the

same life as the stress

amplitude applied at zero

mean stress, ar. Hence armay be thought of as an

equivalent completely

reversed stress, with respect

to the life produced. bff

f

mar

b

ffar

f

m

aar

f

m

ar

a

N

N

)2(1

)2(

1

1

ApproachMorrow


41/41

Life Estimates

)0()2(

Approach(SWT)Topper-Watson-Smith

maxmax

max

b

ffa

aar

N

Fatigue Part 1

Documents

Transcript of Fatigue Part 1