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Over the Next Several Days

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1 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

2 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

3 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

4 Identifying Fatigue Fractures
beachmarks

5 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

6 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

7 Types of Fatigue Loading
Fully Reversed Repeated Fluctuating stress range amplitude ratio alternating component mean component stress ratio

8 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

9 Testing Fatigue Properties
Rotating Beam – most data is from this type Axial lower or higher? Why? Cantilever Torsion

10 Fully Reversed Empirical Data
An S-N Curve (Stress-Life) Wrought Steel

11 Fully Reversed Empirical Data
Aluminum

12 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)

13 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

14 Types of Fatigue Loading
Fully Reversed Repeated Fluctuating stress range amplitude ratio alternating component mean component stress ratio

15 Getting Fatigue Data Test a prototype Test the exact material used
Published fatigue data Use static data to estimate

16 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

17 Correction Factors talk about each of these pages in your book

18 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

19 Fatigue Stress Concentration
Kf = 1+q(Kt-1) q = notch sensitivity function of material, Sut, Neuber constant, a notch radius, r

20 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

21 Types of Fatigue Loading
Fully Reversed Repeated Fluctuating stress range amplitude ratio alternating component mean component stress ratio

22 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)

23 Uniaxial, Fully Reversed Strategy Fatigue Half
Se´ or Sf´ Cload Csurf Csize Ctemp Creliab Se or Sf Estimated S-N Curve

24 Uniaxial Fully Reversed Strategy
Nf = fatigue safety factor; Sn = Fatigue strength at n cycles;  ´= largest von Mises alternating stress

25 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

26 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

27 Types of Fatigue Loading
Fully Reversed Repeated Fluctuating stress range amplitude ratio alternating component mean component stress ratio

28 Does Mean Stress Matter?

29 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

30 The Data

31 “Augmented” Modified-Goodman Plot
Sy Se or Sf m Syc Sy Sut von Mises calculated for a and for m separately

32 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)

33 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)

34 Uniaxial Fluctuating Strategy Fatigue Aspects
Se´ or Sf´ Cload Csurf Csize Ctemp Creliab Se or Sf Modified-Goodman Diagram

35 Uniaxial Fluctuating Strategy
Nf

36 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*

37 Strategy Find ´a and ´m with appropriate stress concentration factors Find Se Plot modified-Goodman diagram Find factor of safety

38 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

39 Types of Fatigue Loading
Fully Reversed Repeated Fluctuating stress range amplitude ratio alternating component mean component stress ratio

40 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

41 Fully Reversed Multiaxial
Find von Mises equivalent stress for alternating component Cload implications

42 Fluctuating Multiaxial
Sines Method Von Mises Method modified-Goodman diagram

43 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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