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lecturFatigue of Metals metals lecture e notes
Typology: Lecture notes
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Suranaree University of Technology
May-Aug
-^ 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
Tapany Udomphol
Suranaree University of Technology
May-Aug
Fatigue fracture area in a shaftcaused by corroded inside area
www.btinternet.com
Tapany Udomphol
Suranaree University of Technology
May-Aug
repetitive or fluctuating
stress
and will fail at a
stress much lower
than its tensile strength
plastic
deformation
(no warning).
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
(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
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
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
S-N curve
in the
high-cycle region
is sometimes described by
the^
Basquin equation
C N^
p= σ a^
Eq.
Where
is the stress amplitude p^ and
C^ are empirical constants
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
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
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
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^
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 (
-^ σσσσ
) on mean stress.min
mean stress
becomes more tensile the
allowable
range of stress
is reduced.
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:
max^
= 400 MPa,
= 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:
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
(^
' ) '^
n p K
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
