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Over the Next Several Days
What is fatigue? Types of Fatigue Loading Empirical Data Estimating Endurance/Fatigue Strength Strategies for Analysis Uniaxial Fully Reversed Uniaxial Fluctuating Multiaxial Crack Growth
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Some History Rail car axles The all-important microcrack
Role of stress concentrations Comet airplanes rail car axles failed below Sy, brittle-like – and the static strength was not reduced! fatigue begins at a crack stress concentrations can play a big role in starting a crack
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Three Stages of Fatigue Failure
Crack Initiation Crack Propagation oscillating stress… crack grows, stops growing, grows, stops growing… with crack growth due to tensile stresses Fracture sudden, brittle-like failure
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Identifying Fatigue Fractures
beachmarks
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Three Theories Stress-Life Strain-Life LEFM (Fracture Mechanics)
stress-based, for high-cycle fatigue, aims to prevent crack initiation Strain-Life useful when yielding begins (i.e., during crack initiation), for low-cycle fatigue LEFM (Fracture Mechanics) best model of crack propagation, for low-cycle fatigue
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Low vs. High Cycle >103 cycles, high cycle fatigue
car crank shaft – manufacturing 100 rpm – ~2.5 E8 Rev/105 miles 1.25 E8 Rev/year <103 cycles, low cycle fatigue ships, planes, vehicle chassis
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Types of Fatigue Loading
Fully Reversed Repeated Fluctuating stress range amplitude ratio alternating component mean component stress ratio
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Update What is fatigue? Types of Fatigue Loading Empirical Data
Estimating Endurance/Fatigue Strength Strategies for Analysis Uniaxial Fully Reversed Uniaxial Fluctuating Multiaxial Crack Growth
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Testing Fatigue Properties
Rotating Beam – most data is from this type Axial lower or higher? Why? Cantilever Torsion
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Fully Reversed Empirical Data
An S-N Curve (Stress-Life) Wrought Steel
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Fully Reversed Empirical Data
Aluminum
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Endurance Limit A stress level below which a material can be cycled infinitely without failure Many materials have an endurance limit: low-strength carbon and alloy steels, some stainless steels, irons, molybdenum alloys, titanium alloys, and some polymers Many other materials DO NOT have an endurance limit: aluminum, magnesium, copper, nickel alloys, some stainless steels, high-strength carbon and alloy steels for these, we use a FATIGUE STRENGTH defined for a certain number of cycles (5E8 is typical)
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Update What is fatigue? Types of Fatigue Loading Empirical Data
Estimating Endurance/Fatigue Strength Strategies for Analysis Uniaxial Fully Reversed Uniaxial Fluctuating Multiaxial Crack Growth
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Types of Fatigue Loading
Fully Reversed Repeated Fluctuating stress range amplitude ratio alternating component mean component stress ratio
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Getting Fatigue Data Test a prototype Test the exact material used
Published fatigue data Use static data to estimate
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Estimating Se´ From Static Data
see page 345 in your book… steels irons aluminums BUT, these are all for highly polished, circular rotating beams of a certain size
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Correction Factors talk about each of these pages in your book
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Constructing Estimated S-N Curves
The material strength at 103 cycles, Sm: Sm=0.9Sut for bending Sm=0.75Sut for axial loading The line from Sm to Se or Sf, Sn=aNb or logSn=loga + blogN
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Fatigue Stress Concentration
Kf = 1+q(Kt-1) q = notch sensitivity function of material, Sut, Neuber constant, a notch radius, r
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Update What is fatigue? Types of Fatigue Loading Empirical Data
Estimating Endurance/Fatigue Strength Strategies for Analysis Uniaxial Fully Reversed Uniaxial Fluctuating Multiaxial Crack Growth Uniaxial Multiaxial
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Types of Fatigue Loading
Fully Reversed Repeated Fluctuating stress range amplitude ratio alternating component mean component stress ratio
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Uniaxial, Fully Reversed Strategy Loading & Stress Half
N (umber of cycles) Fluctuating Load (Fa) Tentative Design Tentative Material Kt a (nominal) Kf a 1, 2, 3 (principal) ´ (von Mises)
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Uniaxial, Fully Reversed Strategy Fatigue Half
Se´ or Sf´ Cload Csurf Csize Ctemp Creliab Se or Sf Estimated S-N Curve
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Uniaxial Fully Reversed Strategy
Nf = fatigue safety factor; Sn = Fatigue strength at n cycles; ´= largest von Mises alternating stress
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Uniaxial, Reversed Example
B C D (mm) 3mm fillets 6.8 kN 250 125 10 75 100 10 30 30 32 35 A B C D MB Mc Mmax 38 Sut=690 MPa Sy=580 Mpa
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Update What is fatigue? Types of Fatigue Loading Empirical Data
Estimating Endurance/Fatigue Strength Strategies for Analysis Uniaxial Fully Reversed Uniaxial Fluctuating Multiaxial Crack Growth Uniaxial Multiaxial
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Types of Fatigue Loading
Fully Reversed Repeated Fluctuating stress range amplitude ratio alternating component mean component stress ratio
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Does Mean Stress Matter?
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Fluctuating Stress Failure Plot
constructed for a given number of cycles N Sy Yield Failure Safety Se or Sf modified-Goodman Soderberg Gerber m Sy Sut
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The Data
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“Augmented” Modified-Goodman Plot
Sy Se or Sf m Syc Sy Sut von Mises calculated for a and for m separately
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Factors of Safety Four cases
a constant, m varies a varies, m constant a and m increase at constant ratio a and m increase independently If you know how the stress can vary, only use one of four cases If stress can vary in any manner, Case 4 should be used (the most conservative)
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Uniaxial Fluctuating Strategy Stress & Loading
N (umber of cycles) Fluctuating Load (Fa) Tentative Design Tentative Material a m (nom) a (nom) m Kf Kt Kfm 1a, 2a, 3a; 1m, 2m, 3m (principal) ´a, ´m (von Mises)
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Uniaxial Fluctuating Strategy Fatigue Aspects
Se´ or Sf´ Cload Csurf Csize Ctemp Creliab Se or Sf Modified-Goodman Diagram
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Uniaxial Fluctuating Strategy
Nf
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Uniaxial, Fluctuating Example
B Fm=1 kN Fa= 2 kN C D (mm) 3mm fillets 250 125 10 75 100 10 30 30 32 35 A B C D MB Mc Mmax 38 Sut=690 MPa Sy=580 Mpa *NOT a rotating shaft*
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Strategy Find ´a and ´m with appropriate stress concentration factors Find Se Plot modified-Goodman diagram Find factor of safety
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Update What is fatigue? Types of Fatigue Loading Empirical Data
Estimating Endurance/Fatigue Strength Strategies for Analysis Uniaxial Fully Reversed Uniaxial Fluctuating Multiaxial Crack Growth Uniaxial Multiaxial
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Types of Fatigue Loading
Fully Reversed Repeated Fluctuating stress range amplitude ratio alternating component mean component stress ratio
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Multiaxial Fatigue simple multiaxial stress complex multiaxial stress
periodic, synchronous, in-phase complex multiaxial stress everything else assuming synchronicity and being in-phase is usually conservative
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Fully Reversed Multiaxial
Find von Mises equivalent stress for alternating component Cload implications
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Fluctuating Multiaxial
Sines Method Von Mises Method modified-Goodman diagram
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Fatigue Recap What is fatigue? Types of Fatigue Loading Empirical Data
Estimating Endurance/Fatigue Strength Strategies for Analysis Uniaxial Fully Reversed Uniaxial Fluctuating Multiaxial Crack Growth Uniaxial Multiaxial
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