Fatigue Lecture10

8/12/2019 Fatigue Lecture10

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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).

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

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

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.

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.

∆K ∆K th

∆K c

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

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.

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.

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.

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

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.

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

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.....

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

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.

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

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

Fatigue Lecture10

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