1fatigue theory developed by scott civjan university of massachusetts, amherst
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1Fatigue Theory
Developed by Scott CivjanUniversity of Massachusetts, Amherst
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Fatigue - Definitions
Typical of bridge loading, vibrating equipment, wind loading on signage.
High Cycle FatigueFormation of a crack due to cyclic elastic loading below design stress levels.
20,000 to millions of cycles
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Fatigue - Definitions
Typical of seismic loading of connections.NOT COVERED IN THE FOLLOWING SLIDES
Low Cycle FatigueFormation of a crack due to cyclic inelastic loading.
Less than 20,000 cycles to failure
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Prefer ductile failures if fracture occurs.
Brittle FractureSudden failure, often with minimal plastic deformation.
Ductile FractureProgressive failure, often with minimal plastic deformation.
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Fatigue - Definitions
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Brittle Fracture
More likely with:Stress ConcentrationsHigh ConstraintHigh Load RateLow Material ToughnessLow Temperature
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Fatigue - Definitions
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Time1 cycle
Stress range
For a constant amplitude stress range
Stress Range: The difference between maximum and minimum stress values.
Cycle: one application and unloading of stress range.
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Fatigue - Definitions
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To predict the fatigue life, S-N curves typically are used.
These are log-log plots of stress range versus number of cycles expected to cause fatigue fracture.
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Fatigue - Definitions
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Linear Relationship for design life on log-log plot
Number of Cycles (log scale)
Threshold Stress Range
S-N CurveFatigue Life
8Fatigue Theory
Fatigue - Definitions
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Fatigue Life: The number of stress cycles to cause fracture.
Threshold Stress Range: A stress range below which fatigue life is expected to be infinite.
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Fatigue - Definitions
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Design Life: The expected number of stress cycles applied.
Design Category: A grouping of design details with similar fatigue parameters, such as stress concentrations and constraints.
The S-N curve can be related to the actual stress range and expected design life.
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Fatigue - Definitions
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Fatigue - Design
Fsr = Design stress rangeN = Design lifeFth = Threshold stress rangeCf = Constant dependent on design category
th
.
fsr F
N
CF
333
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Typical equation for steel design is shown, others exist for different conditions or materials.
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Given a detail and design life, can calculate the allowable stress range.
Given a detail and applied stress range, can calculate the design life.
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Fatigue - Design
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Unfortunately, the stress range history for a given structure typically is irregular unless fatigue is caused by machinery.
Need to transform irregular stress range pattern into an equivalent constant amplitude stress range.
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Fatigue - Design
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Transferring Variable Amplitude Stress Ranges to Constant Amplitude Stress Range
Miner’s Rule 33α
isriisr FF
Fsr = Design Stress Rangei = number of cycles at stress range Fsri divided by the
total number of cyclesFsri = Individual stress range within load historyFsrmax = Maximum stress range within load history
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Fatigue - Design
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Finite life if Fsr>Fth Base fatigue life on S-N curve.
Infinite life if Fsr ≤ Fth AND Fsrmax ≤ Fth.
Finite life if Fsr ≤ Fth but Fsrmax > Fth. In this case use extension of fatigue life curve for design. May define acceptable risk of exceedance for limited number of cycles of Fsrmax.
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Fatigue - Design