Quantifying Fatigue Failure

Quantifying Fatigue Failure: Stress-Life Method for

Non-Zero Mean Stress (Failure Surface = lGoodman Diagramz)

Terms for Stress Cycling

maximum stress, max

minimum stress, min

Stress at A

load reversals (2 reversals = 1 cycle)

stress amplitude, a

mid-range stress, m

t

Follow a material point A on the outer fiber

6-11 Characterizing Fluctuating Stresses

Variation in cyclic stress.

Fm

=

Fmax

+ 2

Fmin

Fa

=

Fmax - Fmin 2

Mean stress:

m

= max + min 2

Stress Stress

Amplitude:

a =

ratio:

R = min

max

- min 2

max

Amplitude ratio:

A = a = max - min = 1- R

m max + min 1+ R

Schematic: Effect of Midrange Stress Sm = m|Nf =

Sf = Sa|Sm=0

Sut

S-N diagram for Sm = 0

Sa

Alternating stress amplitude (a ) at failure,

or fatigue strength Sa

Sf|Nf <

N f <

Se

Se

N

(Se = Sf|Nf ) =

f =

103

106

N

Su

Mid-range stress (m S) m

at failure, or mid-range

strength Sm

7

Data: Effect of Midrange Stress m

That is: the endurance limit drops as m|Nf = Sm increases

Simple Model to Account for Midrange Stress m

That is: the endurance limit drops as m|Nf = Sm increases

Goodman Diagram for Fatigue

This line is known as the Goodman diagram

Goodman diagram lendurance limit as a function of mean stressz

Goodman diagram = drop in Se for rise in tensile Sm

Goodman Diagram: Fatigue Failure with m 0

Sa

Alternating stress amplitude, a ,

as fatigue strength Sa

Sf = a|Nf <

Se

(Se = Sa|Nf ) =

Mean stress, m , as mid-range strength Sm

N f

<

N f

=

Equation of Goodman line:

Sa + Sm = 1 Se Su

Su

Sm

lGoodman Criterionz for finite life:

Sa + Sm = 1 S f Su

or

a

(S f

n)

+

m

(Su n)

=

1

failure surface

design equation

(i.e., shrink failure surface until you hit service loads)

lGoodman Criterionz for --life:

Sa + Sm = 1 Se Su

or

a

(Se n)

+

(Su

m

n)

=

1

failure surface

design equation

8

Goodman Diagram: Fatigue Failure with m 0

Sa

Alternating stress amplitude, a ,

as fatigue strength Sa

Sf (Nf ................
................

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