fatigue lecture10
TRANSCRIPT
8/12/2019 Fatigue Lecture10
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1
Defects in Materials
• Defects in materials - intrinsic defects (vacancies,dislocations). For the materials engineer, however, defectsinclude extrinsic defects such as voids, inclusions, grainboundary, and other types of undesirable second phases.
• Voids are introduced either by gas evolution in solidificationor by incomplete sintering in powder consolidation.
•
Inclusions are second phases entrained in a material duringsolidification. In metals, inclusions are generally oxides fromthe surface of the metal melt, or a slag.
• Grain boundary films are common in ceramics as glassy filmsfrom impurities.
•
In aluminum alloys – inclusions are oxides (e.g. Al2O3)
– dispersoids are intermetallic particles that, once precipitated, arethermodynamically stable (e.g. AlFeSi compounds)
– precipitates are intermetallic particles that can be dissolved or precipiateddepending on temperature (e.g. AlCu compounds).
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Environmental effects
Corrosion fatigue• cyclic stress and chemical attack• pit formation and pits act as cracks
• metals do not show definite fatigue limit in corrosion environment
• fatigue frequency dependent
•
evidence of corrosion at room temp at well• a reduction of 50% fatigue life due to corrosion
Methods to minimize corrosion-fatigue
• Choice of material- corrosion resistant properties
SS, bronze, Be, Cu preferred over heat-treated steel• coating – metallic or nonmetallic
Zn and Cd coating on steel, Al on Al alloys
• Inducing surface compressive residual stresses
• Nitriding, shot peening
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Effect of temperature of fatigue
– Low temp fatigue
• Fatigue strength increases with decreasing temp
• Fatigue strength less affected below DBTT, unlike tensile strength in steels
– High temp fatigue
– Fatigue strength decreases with increasing temp
– Mild steel is exceptional which shows maximum fatigue strength at 200 –
300°C due to strain aging.
– At high temp (> 0.5Tm) creep dominants (failure from transgranular fatigue
failure to intergranular creep failure)
– Higher the creep strength, higher will be high-temp fatigue strength
– Fine grain size is good for low temp fatigue
– Coarse-grain exhibits high temp strength
– Compressive residual stresses do not help in high-temp fatigue properties
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Thermal fatigue
– Induced at elevated temp by fluctuating thermal stresses
– The magnitude of thermal stress is given by
Where ΔT = temp change, αl = coeff of thermal exp, E =
modulus
• If failure occurs by one application of thermal stress thecondition is called thermal shock .
• If failure occurs after repeated applications of thermal stress,
of lower magnitude then it is called thermal fatigue.• Thermal fatigue failure is related to σ f k /E α , σ f is fatigue
strength and k = thermal conductivity.
T E l
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Effect of microstructure crack nucleation
•
The main effect ofmicrostructure (defects,surface treatment, etc.) isalmost all in the low stressintensity regime, i.e. Stage I.Defects, for example, make it
easier to nucleate a crack,which translates into a lowerthreshold for crack propagation( ∆K th).
• Microstructure also affectsfracture toughness andtherefore Stage III.
da/dN
∆K ∆K th
∆K c
I
IIIII
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Design for fatigue
• Infinite life design
– Keeping the stresses at some fraction of the fatigue limit
• Safe-life design
– Aircrafts designed to a safe-life of ¼ of the life
• Fail-safe design
– Inspection, detection of cracks and repaired well before
failure
• Damage tolerant design
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Damage Tolerant Design
• Calculate expected growth rates from dc/dN data.
• Perform NDE on all critical components.
• If crack is found, calculate the expected life of the
component.
• Replace, rebuild if too close to life limit.
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8
Microstructure-Fatigue Relationships
• What are the important issues in microstructure-fatiguerelationships?
• Answer: three major factors.1: geometry of the specimen (earlier slide); anything on the
surface that is a site of stress concentration will promote crackformation (shorten the time required for nucleation of cracks).
2: defects in the material; anything inside the material that canreduce the stress and/or strain required to nucleate a crack(shorten the time required for nucleation of cracks).
3: dislocation slip characteristics; if dislocation glide is confined to
particular slip planes (called planar slip) then dislocations canpile up at any grain boundary or phase boundary. The head ofthe pile-up is a stress concentration which can initiate a crack.
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Coarse particle effect on fatigue
• Inclusions nucleate cracks improves fatigue life, e.g.
fatigue life of 7475 Al alloy improved by loweringFe+Si compared to 7075:
0.12Fe in 7475, compared to 0.5Fe in 7075;
0. 1Si in 7475, compared to 0.4Si in 7075.
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Alloy steel heat treatment
• Increasing hardness tends to raise the endurance limit
for high cycle fatigue. This is largely a function of the
resistance to fatigue crack formation (Stage I in a plot
of da/dN).
Mobile solutes that pin
dislocations fatigue limit, e.g.
carbon in steel
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Variable Stress/Strain Histories
• Complex loading conditions
• Overstressing is the process of testing a virgin specimen for some number
of cycles less than failure at a stress above the fatigue limit, subsequently
running the specimen to failure at another test stress.
• The ratio of the cycles of overstress to the virgin fatigue life at the same
stress is called cycle ratio.
• When the stress/strain history is stochastically varying, a rule for
combining portions of fatigue life is needed.
• Miners’ rule assumes that total life of a part can be estimated by adding
up percentage of life consumed by each over stress cycle: ni is the number
of cycles at each overstress level, and Nfi is the failure point for that stress.
ni
N f i
1
i
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Cumulative damage and life exhaustion
• Components in real life situations are
subjected to a range of fluctuating loads,
mean stress levels, and variable frequencies.
• It is important to predict the fatigue life of
such a component.
Damage accumulation in a high to low loading sequences
• The cumulative damage
theory attempts predict
that.
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Cumulative damage... (contd...)
• The ratio of the cycles of overstress tothe virgin fatigue life at the same stress
is called cycle ratio.• Palmgren-Miner rule or linear
cumulative damage theory assumes thattotal life of a part can be estimated byadding up percentage of life consumedby each over stress cycle and is given by,
1.....
1
3
3
2
2
1
1
1
k
k
k
i i
i
N
n
N
n
N
n
N
n
N
n
Where k is the number of stress levels in the block spectrum loading.
N1, N2, N3....Ni are the fatigue lives corresponding to stress levels σ 1, σ 2, σ 3.... σ i,
respectively and n1, n2,...ni are the no of cycles carried out at the respective
stress levels.
Sequences of block loadings at
four different mean stresses and
amplitudes
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Coaxing
• If a specimen is tested without failure for alarge number of cycles below the fatigue limit
and the stress is increased in small increments
after allowing a large number of cycles tooccur at each stress level, it was found that
the resulting fatigue limit is ~ 50% greater
than the initial fatigue limit. This procedure is
called coaxing.
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Example
The S-N curve of a material is described by the
relationship
Where N is the number of cycles to failure, S is the
amplitude of the applied cyclic stress and σ max is
the monotonic fracture strength, i.e., S = σ max at N
= 1. A rotating component made of this material
is subjected to 104 cycles at S = 0.5 σ max. If thecyclic load is now increased to S = 0.75 σ max, how
many more cycles will the material withstand?
)/1(10log max S N
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Example
• A solid round Al alloy shaft must withstand acompletely reversed bending moment of 8000
in.-lb or 55 Nm for an estimated 107 cycles. Factor
of safety of 1.25 is to be used.• Find the required shaft diameter.
• Assume that the previous estimate is doubled,
i.e., N =20,000,000. find the new diameterrequired and calculate the percentage increases
in the diameter and volume of the shaft
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