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Fatigue Life Evaluation

S-N Curve (alternating stress amplitude (Sa) versus number of cycles (Nf)to failure)

310

410

510

610

710

810

400

600

800

Sa = a(MPa)

Nf , cycles to failure

e= Se endurance limit

Some materials, such as steel, show an endurance limit stress

below which the fatigue life is essentially infinite. Other materialsmay not show such behavior but an effective endurance limit maybe specified at some large number of cycles

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time

stress

P

a

a

S-N testing is done under alternating(completely reversed) loading andstress

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Mean Stress Effects

max

min

m

a

max min

max min

max min

2 2

2

a

m

=

= =

+=

stress range

alternating stress

mean stress

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max

min

m

a

max

min

a

m

R

A

=

=

stress ratio

amplitude ratio

fully reversed

1R A= =

zero to max

1R A= =

0 1R A= =

zero to min

Mean Stress Effects

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Mean Stress Effects

m

fN610 710

400m

MPa =

200

100

0

100

a

a

-100 0 200 400 600

Constant Life Diagram

uultimate stress

usual S-N curve

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Empirical curves to estimate mean stress effects on fatigue life

m

a

f

y

u

a. Soderberg (USA, 1930)

b. Goodman (England, 1899)

c. Gerber (Germany, 1874)

d. Morrow (USA, 1960s)

1a m

e u

+ =

1a m

e y

+ =

1a m

e f

+ =

2

1a m

e u

+ =

a b

c

d

e

y

u

f

e

yield stress

ultimate stress

true fracturestress

effectivealternating

stress at failurefor a lifetime of

Nf cycles

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General observations

1. Most actual test data tend to fall between the Goodman and Gerbercurves.

2. For most fatigue situations R

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Use of empirical curves for an infinite life design

Use a particular curve such as the Goodman with ( the

endurance limit, )

m

a

u

e e =

e

"infinite" life curve"safe"

"unsafe"

any combination of mean and alternating stresses that are to

the left of the curve are deemed safe, those to the right are not

fN =

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Use of empirical curves and S-N data for an finite life design

1. A given combination of mean and alternating stresses is taken

to lie on a constant life curve such as the Goodman line:

m u

e

constant life of Nf cyclesa

2. That curve is then used to solve for the effective purelyalternating stress, , that will cause failure at this same lifetime:e

1a m

e u

+ =

solve for

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3. Using this effective alternating stress, determine the lifetime forthis stress (and the corresponding original alternating and mean

stresses) from the S-N diagram for the given material:

cycles to failure

e

Nf

a

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Some References on Fatigue Design

C.C. Osgood Fatigue Design, 2nd Ed. 1982

R.C. Juvinall Engineering Considerations of Stress, Strain, andStrength, 1967

H.O Fuchs and R. I. StephensMetal Fatigue in Engineering, 1980

J.A. Graham Fatigue Design Handbook, SAE, 1968

A.F. Madayag Metal Fatigue: Theory and Design 1969

J.A. Ballantine, J.J. Conner, and J.L. HandrockFundamentals of Metal Fatigue Analysis, 1990

N.E. Dowling Mechanical Behavior of Materials, 1993