Over the Next Several Days

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

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

ships, planes, vehicle chassis 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

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

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 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

Tentative Material Tentative Design a (nominal) Kt Kf a 1, 2, 3 (principal) ´ (von Mises) Uniaxial, Fully Reversed StrategyLoading & Stress Half N (umber of cycles) Fluctuating Load (Fa)

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

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

Mmax MB Mc A B C D Uniaxial, Reversed Example A B C D (mm) 3mm fillets 6.8 kN 250 125 10 75 100 10 30 30 32 35 38 Sut=690 MPa Sy=580 Mpa

Does Mean Stress Matter?

Failure Yield modified-Goodman Gerber Soderberg Safety Fluctuating Stress Failure Plot a constructed for a given number of cycles N Sy Se or Sf m Sy Sut

The Data

“Augmented” Modified-Goodman Plot a 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)

Tentative Material Tentative Design m (nom) Kt a (nom) Kf Kfm a m 1a, 2a, 3a; 1m, 2m, 3m (principal) ´a, ´m (von Mises) Uniaxial Fluctuating StrategyStress & Loading N (umber of cycles) Fluctuating Load (Fa)

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

Uniaxial Fluctuating Strategy Nf

Mmax MB Mc A B C D Uniaxial, Fluctuating Example A B Fm=1 kN Fa= 2 kN C D (mm) 3mm fillets 250 125 10 75 100 10 30 30 32 35 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

Multiaxial Fatigue • simple 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

Over the Next Several Days