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Fatigue of Metals metals, Lecture notes of Engineering

lecturFatigue of Metals metals lecture e notes

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Suranaree University of Technology May-Aug 2007
Fatigue of metals
Fatigue of metals
Subjects of interest
Objectives / Introduction
Stress cycles
The S-N curve
Cyclic stress-strain curve
Low cycle fatigue
Structural features of fatigue
Fatigue crack propagation
Factors influencing fatigue properties
Design for fatigue
Chapter 12
Tapany Udomphol
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Suranaree University of Technology

May-Aug

Fatigue of metals^ Fatigue of metals Subjects of interest

-^ Objectives / Introduction •^ Stress cycles •^ The S-N curve •^ Cyclic stress-strain curve •^ Low cycle fatigue •^ Structural features of fatigue •^ Fatigue crack propagation •^ Factors influencing fatigue properties •^ Design for fatigue

Chapter 12

Tapany Udomphol

Suranaree University of Technology

May-Aug

Objectives^ Objectives^ • This chapter provides fundamental aspects of fatigue inmetals and the significance of fatigue failure.• Different approaches for the assessment of fatigueproperties, i.e., fatigue S-N curve and fatigue crack growthresistance will be introduced.• Discussion will be made on factors influencing fatigueproperties of metals, for example, mean stress, stressconcentration, temperature• Finally design against fatigue failure will be highlighted.

Tapany Udomphol

Suranaree University of Technology

May-Aug

Introduction^ Introduction Fatigue failure occurs at the outer rimof the wheel

Fatigue fracture area in a shaftcaused by corroded inside area

www.btinternet.com

Tapany Udomphol

Suranaree University of Technology

May-Aug

Introduction^ Introduction Fatigue failures are widely studiesbecause it accounts for 90% of all servicefailures due to mechanical causes.

  • Fatigue failures occur when metal issubjected to a

repetitive or fluctuating

stress

and will fail at a

stress much lower

than its tensile strength

  • Fatigue failures occur without any

plastic

deformation

(no warning).

  • Fatigue surface appears as a smoothregion, showing

beach mark

or origin of

fatigue crack.

Characteristics

mmd.sdsmt.edu Failure of crankshaft journal

www.capcis.co.uk Fatigue failure of a bolt

Tapany Udomphol

Suranaree University of Technology

May-Aug

Stress cycles^ Stress cycles^ Different types of fluctuating stress (a) Completely reversed cycle ofstress (sinusoidal)

(b) Repeated stress cycle

(c ) Irregular or random stress cycle

Tensile stress +Compressive stress -

σmax^ = -^ σ min

Tapany Udomphol

Suranaree University of Technology

May-Aug

2007

Stress cycles^ Stress cycles^ σσσσmax

σσσσmin

σσσσm

∆σ∆σ^ ∆σ∆σ

σσσσa

  • _^

cycles

Nomenclature of stress parameterin fatigue loading^ Fatigue stress cycle

Maximum stress,

σσσσmax

Minimum stress,

σσσσmin

min max

σ^

∆^

r or Stress rangeAlternating stress

2 2

min max

σ σ σ σ^

∆= a Mean stress

σ^ minmax 2 σ σ^

=m Stress ratio

σmin = σ^ max R

Amplitude ratio

R R

A

a m

−= + =^

1 1 σ σ

Eq.1 Eq.2 Eq.

Eq.

Eq.

Tapany Udomphol

Suranaree University of Technology

May-Aug

Basquin^ Basquin

equationequation

  • The

S-N curve

in the

high-cycle region

is sometimes described by

the^

Basquin equation

C N^

p= σ a^

Eq.

Where

σσσσa^

is the stress amplitude p^ and

C^ are empirical constants

HCF^ LCF

High cycle (low strain) fatigue Low cycle (high strain) fatigue

Log N

f

Stress level

HCF

LCF

Tapany Udomphol

Suranaree University of Technology

May-Aug

Construction of S^ Construction of S

  • N curve-N curve
    • The construction of

S-N curve

normally requires ~ 8-12 specimens

by first testing at a high level of stress ~ 2/3 of the tensile strength ofthe material.• The test is then carried out at lower levels of stress until

runout

  • The data obtained is normally scattered

at the same stress level

by using several specimens.• This requires

statistic approach

to define the

fatigue limit

www.statisticalengineering.com

S-N fatigue curve

Tapany Udomphol

Suranaree University of Technology

May-Aug

Effect of mean stress, stress range and stress^ Effect of mean stress, stress range and stressintensity (notch) on S^ intensity (notch) on S

  • N fatigue curve-N fatigue curve

Log N

f

σσσσa

σσσσm1 σσσσm2 σσσσm3 σσσσm

σσ>σσm^

σσσσm

^ σσσσ m

^ σσσσm

Mean stress Fatigue strength

Log N

f

σσσσa

loc app^ K= 1t^ K= 1.5t^

σK =t σ

Stress intensity Fatigue strength

Log N

f

σσσσmax

R = 0.3R = 0R = -0.3 R = -1.

Stress range Fatigue strength

Tapany Udomphol

Suranaree University of Technology

May-Aug

Goodman diagram^ Goodman diagram

Goodman diagram

-^ Goodman diagram

shows the variation of the limiting range

of stress (

σσσσmax

-^ σσσσ

) on mean stress.min

  • As the

mean stress

becomes more tensile the

allowable

range of stress

is reduced.

  • At tensile strength,
σσ, the stress range is zero.σσu^

Tapany Udomphol

Suranaree University of Technology

May-Aug

Master diagram for establishing influence^ Master diagram for establishing influenceof mean stress in fatigue^ of mean stress in fatigue^ Ex:

at^ σσσσ

max^

= 400 MPa,

σσσσmin

= 0, a fatigue limit of the notched

specimen is less than 10

6 cycles.

For the unnotched specimen is below the fatigue limit.

Tapany Udomphol

Suranaree University of Technology

May-Aug

Example:

A 4340 steel bar is subjected to a fluctuating axial load that

varies from a maximum of 330 kN tension to a minimum of 110 kNcompression. The mechanical properties of the steel are:

σσσσ= 1090 MPa,u^
σσσσ= 1010 MPa,o^
σσσσ= 510 MPae^

Determine the bar diameter to give infinite fatigue life based ona safety factor of 2.5. Cylindrical cross section of the bar =

A, the variation of stress will be^ MPa A A A

MPaA A A

MPaA

MPaA mean a

(^220). 0

2

)/ (^110). (^0) ( / 330

. 0 2

(^110). 0

2

)/ (^110). (^0) ( / 330

. 0 2

(^110). 0 , (^330). 0

min max

min max

min

max

= −−

= − =

= −+

=

=

−=

=^

σ σ σ

σ σ σ

σ

σ^ Using the

conservative Goodman line and

Eq.

.

mm A D

mm A

A

A

MPa

e m u e a

(^7). 38 11794

/ (^110). 0 1090 1 / (^220). 0 204

(^2045) 510.^2 , 1

(^2) = = =

−=

=

 ^ − =^ π

σ σ σ σ σ Tapany Udomphol

Suranaree University of Technology

May-Aug

Cyclic hardening and cyclic softening^ Cyclic hardening and cyclic softening

-^ Cyclic hardening would lead to adecreasing peakstrain with increasingcycles. (

n>0.

-^ Cyclic softening would lead to acontinually increasingstrain range and earlyfracture. (

n<0.

Tapany Udomphol

Suranaree University of Technology

May-Aug

Comparison of monotonic and cyclic^ Comparison of monotonic and cyclicstress^ stress

  • strain curves of cyclic hardened-strain curves of cyclic hardened materials^ materials Monotonic and cyclic stress-strain curves
  • The cycle stress-strain curve maybe described by a power curve asfollows

(^

' ) '^

n p K

σ^
∆^

Eq.

Where

n’

is the cyclic strain-hardeningexponent K’^ is the cyclic strengthcoefficient

For metals

n’^ varies between 0.10 -0.20. Sincestrain amplitude

' 1 ' 1 2 2 2

2 2 2

n p e

K E^

   ∆+  ∆= ∆

∆ + ∆= ∆

σ σ ε

ε ε ε

Tapany Udomphol