STRESS CYCLES

Repeated Stress Cycle

Completely Reversed Stress Cycle

σm = 0

R = -1

Random Stress Cycle

STRESS-LIFE DIAGRAM

(HIGH CYCLE FATIGUE)

Basquin Relation

NF (σa)p = C

Stress – Life Approach

Endurance Limit or Fatigue Limit

Yield Strength

There is a strong correlation between fatigue

strength and tensile strength.

(From Forrest, Fatigue of Metals, Pergamon Press, London, 1962)

σe ≈ 0.5 σu for steels

σe (for 108 cycles)≈ 0.35 σu

for non-ferrous alloys

Statistical Nature of Fatigue

Ti6Al4V

Statistical Nature of Fatigue

Effect of mean stress on fatigue

GOODMAN DIAGRAM

(gives the maximum allowable stress amplitude

for a different mean stress)

GOODMAN DIAGRAM

x = 1 for Goodman line

x = 2 for Gerber parabola

σu = σo for Soderberg line

Effect of mean stress on fatigue

EXAMPLE

SOLUTION

STRESS STRAIN LOOP FOR CONSTANT

STRAIN CYCLE

STRAIN-LIFE DIAGRAM

(LOW CYCLE FATIGUE)

Coffin- Manson Relation

(Low cycle fatigue)

STRAIN-LIFE EQUATION

(FOR ALL FATIGUE LIVES)

CUMULATIVE FATIGUE DAMAGE

CUMULATIVE FATIGUE DAMAGE

CUMULATIVE FATIGUE DAMAGE

A multipurpose traffic bridge has been in service for three years and

each day carries a large number of trains, trucks, and automobiles. A

subsequent highway analysis reveals a sharp difference between

expected actual traffic patterns that threatens to shorten the usefull life

span of the bridge. Fortunately, a nearby second bridge was recently

completed that can assume all of the train traffic. Given the following

fatigue information, estimate the remaining lifetime for the first bridge,

assuming that it will carry only truck and automobile traffic.

VEHICLE FATIGUE

LIFETIME

VEHICLES/

DAY

Automobiles 108 5000

Trucks 2x106 100

Trains 105 30

CUMULATIVE FATIGUE DAMAGE

Example

Trains

Trucks

a) First establish the amount of fatigue damage

accumulated during the initial 3-year service period:

Accumulated damage in initial 1095 days: 0.438.

That is 43.8% of the combined fatigue lifetime.

b) Remaining fatigue lifetime: 56.2% of the combined

fatigue lifetime.

D= remaining days of service

D= 5620 days(15.4 years) for automobile + truck traffic

only.

D= 3.85 years, if the train traffic were to be continued.

FRACTURE MECHANICS

APPROACH TO FATIGUE

(Damage Tolerant Design)

C-T SPECIMEN

Crack Growth Rate Measurement

1) Crack length, a is

measure against

number of cycles, N

2) a vs N diagram is

drawn

3) Crack growth rate,

da/dN is calculated

from the slope.

STUDY:

http://aluminium.matter.o

rg.uk/content/html/eng/d

efault.asp?catid=176&pa

geid=2144416584

a vs N DIAGRAM

Driving Force for Crack Growth

• The driving force for crack growth is the in

the stress intensity factor range during

cycling.

0Rfor

0Rfor

a(a/W)K

max

minmax

f

Crack Growth Rate Diagram

(da/dN vs ΔK)

REMAINING FATIGUE LIFE

ac

ac

General Solution:

c

o

a

a

mp

a(a/W)A

daN

)f

co

3323pa

1

a

1

YA

2N

)(/

m=3;; constant Y= f(a/W) :

NF

NF

EXAMPLE PROBLEM

• A relatively large sheet of steel is to be exposed to cyclic tensile and compressive stresses of magnitudes +100 MPa and -50 MPa respectively. Prior to testing, it has been determined that the length of the largest straight-through center crack is 2.0 mm. Estimate the fatigue life of this sheet if its plane strain fracture toughness is 25 MPa.m1/2 and the values of m and A are 3 and 1X10-12

respectively for Δσ in MPa and a in mm. Assume Y=1.

• Answer: 2ao= 2 mm, so ao= 1 mm

ac= 0.01989 m = 19.89 mm

NF= 8.81 X 106 cycles

TF= 204 days (For a loading frequency of 0.5 Hz)

AN EXAMPLE FROM DIETER

AN EXAMPLE FROM DIETER

FACTORS AFFECTING THE

FATIGUE LIFE

• Geometrical Design

• Surface Roughness

• Surface Strength

• Residual Stresses

• Size

• Environment

• Metallurgical Structure

GEOMETRICAL DESIGN

(Remove stress concentrators)

BAD

BETTER

EFFECT OF STRESS CONCENTRATION

SURFACE ROUGHNESS

Reduction factor for fatigue limit of steel due to

various surface treatments (Surface Finish)

• Sensitivity to

surface condition

increases with

increasing

strength.

• Corrosion has a

significant effect

on fatigue limit

SURFACE TREATMENT

Shot Peening

Carburizing, Nitriding, Induction Hardening, Electroplating

Decarburization?

COMPRESSIVE RESIDUAL STRESS

(Put surface into compression)

EFFECT OF CORROSION

TOPICS TO THINK ABOUT

1) Why does shot peening improve the fatigue life

of a metal component?

2) Why does carburizing increase the fatigue life of

a steel component?

3) What microstructure is the best for the optimum

fatigue properties in heat treated low alloy

steels?

4) What kind of fatigue (low cycle or high cycle)

should be considered for the ribbed steels in

steel reinforced concrete during an earthquake?

5) What effect will have the decarburization of a

steel component on the fatigue performance of

it?