Link Between Fatigue and Fracture
σapplied
Static loading:
Kapplied = Yσ applied πa ≤ K IC
Cyclic loading:
∆K = K max − Kmin
b
≡ Y σ max − σ min
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g
σapplied
πa
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Week 10
Link Between Fatigue and Fracture
Crack length, a
σ2 >σ1
FG da IJ
H dN K
a1 ,σ 2
log
FG da IJ
H dN K
da
dN
a1 ,σ 1
I
II
Cycle N
b g
da
= A ∆K
dN
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log ∆K
m
No growth
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SS
Rapid
22
1
Q?
How does material fail by fatigue?
Metals: (sequence of events)
1.
2.
Ceramics:
1.
2.
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Week 10
Example:
Fatigue Strength, F.S. (MPa)
For an alloy with T.S.= 800MPa, Estimate σapplied Maximum
Use safety factor = 2.
Fig. 8-16
F.S.= 1/2 T.S.
F.S.= 1/4 T.S.
Tensile strength T.S. (MPa)
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2
6.5 Creep and Stress Relaxation
ØIncreased Strain with time under constant stress
• Continuous plastic deformation of materials subjected
to a constant stress at T > 0.4Tm
– Occurs at stresses well below room temperature yield
strength
• Both temperature and applied stress influence creep
behavior
• Alloys resistant to creep have
- high E
- high melting T
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Stages of Creep
Load cell
Grip
Specimen
Grip
Dead weight
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Creep depends on σ and T
ε
Increasing σ
Creep rate affected by
changes in applied stress
time
ε
Increasing T
Creep rate affected by
changes in temperature
time
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Creep Mechanisms
Ø.
• vacancy diffusion
• grain boundary diffusion
• dislocation motion
• grain boundary sliding
- Different for different materials
- Creep Strain rate follow the Arrhenius expression
ε& = Ce − Q
RT
For the needed activation energy to move any of these defects
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4
High Temperature Alloys
o Improve creep resistance
• higher Tm (less diffusional creep)
• greater E (harder)
• larger grain size (reduce grain boundary sliding)
o Metals include
• stainless steel
• refractory metals
• superalloys
(e.g. Co-Ni superalloys)
o Processes include
• addition of insoluble
dispersed phase
• directional solidification
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Stress Relaxation:
ØDecrease Stress with time under constant strain
Creep
Stress
Stress
Relaxation
Strain
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Strain
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5
Summary of Mechanical Properties of Metals
• Describe the concepts of Stress and Strain
• Differentiate between Elastic and Plastic Deformation
• Quantify Elastic Properties of Materials
• Describe measures of hardness
• Describe different modes of failure
• Explain fatigue and creep
ØRead Class Notes and Relevant portions of Shackelford 2001
Ch. 6:186-200, 210-230, Ch. 8:270-288
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6