Transcript Foundations of Materials Science and Engineering Third Edition

Fatigue
7-1
Fatigue of Metals
•
Metals often fail at much lower stress at cyclic loading
compared to static loading.
• Crack nucleates at region of stress concentration and
propagates due to cyclic loading.
• Failure occurs when
cross sectional area
of the metal too small
to withstand applied
Fracture started here
load.
Figure 6.19
Fatigue fractured
surface of keyed
shaft
Final rupture
7-13 (After “Metals Handbook,” vol 9, 8th ed., American Society of Metals, 1974, p.389)
Fatigues Testing
• Alternating compression and tension load is applied on
metal piece tapered towards center.
Figure 6.21
Figure 6.20
• Stress to cause failure S
and number of cycles
required N are plotted
to form SN curve.
Figure 6.23
7-14 (After H.W. Hayden, W.G. Moffatt, and J.Wulff, “The structure and Properties of Materials,” vol. III, Wiley, 1965, p.15.)
Cyclic Stresses
•
Different types of stress cycles are possible (axial,
torsional and flexural).
Figure 6.24
Mean stress =  m 
 max   min
2
Stress range =  r   max   min
7-15
Stress amplitude =  a 
 max   min
2
 min
Stress range = R 
 max
Structural Changes in Fatigue Process
•
•
Crack initiation first occurs.
Reversed directions of crack initiation caused surface
ridges and groves called slipband extrusion and
intrusion.
• This is stage I and is very slow (10-10 m/cycle).
• Crack growth changes
direction to be perpendicular to maximum tensile
stress (rate microns/sec).
Persistent slip bands
• Sample ruptures by ductile
In copper crystal
failure when remaining
cross-sectional area is small to withstand the stress.
Figure 6.26
7-16
Courtesy of Windy C. Crone, University of Wisconsin
Factors Affecting Fatigue Strength
•
Stress concentration: Fatigue strength is
reduced by stress concentration.
• Surface roughness: Smoother surface
increases the fatigue strength.
• Surface condition: Surface treatments like
carburizing and nitriding increases fatigue
life.
• Environment: Chemically reactive
environment, which might result in
corrosion, decreases fatigue life.
7-17
Fatigue Crack Propagation Rate
•
•
•
Notched specimen used.
Cyclic fatigue action is generated.
Crack length is measured by change in potential
produced by crack opening.
Figure 6.27
7-18(After “Metals Handbook,” Vol 8, 9th ed., American Society of Metals, 1985, p.388.)
Stress & Crack Length
σ2
Fatigue Crack Propagation.
σ1
Δa
ΔN
da
Figure 6.28
dN
Δa
ΔN  da 
 da

 dN


1
α f(σ,a)
 AK
m


dN

2
• When ‘a’ is small, da/dN
is also small.
• da/dN increases with increasing crack length.
• Increase in σ increases
crack growth rate.
da
= fatigue crack growth
rate.
dN
ΔK = Kmax-Kmin = stress
intensity factor range.
A,m = Constants depending on material, environment, frequency
temperature and stress ratio.
7-19
Fatigue Crack Growth rate Versus ΔK
 da 
  Log( AK m )
Log
 dN 
 m. Log( K )  Log( A)
Straight line with slope m
Limiting value of ΔK below
Which there is no measurable
Crack growth is called stress
intensity factor range
threshold ΔKth
Figure 6.29
7-20
(After P.C. Paris et al. Stress analysis and growth of cracks, STP 513 ASTM, Philadelphia, 1972, PP. 141-176
Fatigue Life Calculation
da
 AK m
dN
K  Y  a
But
m
m
Therefore K m  y m m 2 a 2
da
Therefore
m
m
 A( y m m 2 a 2 )
dN
Integrating from initial crack size a0 to final crack size af
at number of fatigue cycles Nf
af
m
m Nf
m m
2
2
da

A
y


a

 dN
a0
0
Integrating and solving for Nf
(Assuming Y is independent of crack length)
7-21
Nf 
af
(
m
2
) 1
 a0
m
m
Ay   ( 
m
m
m
(
2
2
2
) 1
 1)
Fatigue Behavior of Nanomaterials
• Nanomaterials and Ultrafine Ni are found
to have higher endurance limit than
microcrystalline Ni.
• Fatigue crack growth is increased in the
intermediate regime with decreasing grain
size.
• Lower fatigue crack growth threshold Kth
observed for nanocrystalline metal.