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

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

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

Identifying Fatigue Fractures beachmarks

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

Low vs. High Cycle >103 cycles, high cycle fatigue car crank shaft – manufacturing equipment @ 100 rpm – ~2.5 E8 Rev/105 miles 1.25 E8 Rev/year <103 cycles, low cycle fatigue ships, planes, vehicle chassis

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

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

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

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

Fully Reversed Empirical Data Aluminum

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)

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

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

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

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

Correction Factors talk about each of these pages 348-353 in your book

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

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

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

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

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)

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

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

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

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

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

Does Mean Stress Matter?

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

The Data

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

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)

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)

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

Uniaxial Fluctuating Strategy Nf

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*

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

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

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

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

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

Fluctuating Multiaxial Sines Method Von Mises Method modified-Goodman diagram

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