Mean Stress & Fatigue: Material Behavior

Mechanical Behavior of Materials Effect of Mean Stress and Stress Amplitude Fatigue Cycles and process parameters ∆𝐾 = 𝐾𝑚𝑎𝑥 − 𝐾𝑚𝑖𝑛 𝐾𝑚𝑎𝑥 = 𝛼𝜎𝑚𝑎𝑥 𝜋𝑎 ∆𝐾𝑒𝑓𝑓 = 𝐾𝑚𝑎𝑥 − 𝐾𝑜𝑝 𝐾𝑚𝑖𝑛 = 𝛼𝜎𝑚𝑖𝑛 𝜋𝑎 𝜎𝑚𝑖𝑛 𝐾𝑚𝑖𝑛 𝑅= = 𝜎𝑚𝑎𝑥 𝐾𝑚𝑎𝑥 • ∆𝐾𝑜𝑝 is usually unknown, thus its dependence on ∆𝐾 and R is used • ∆𝐾𝑒𝑓𝑓 increases with ∆𝐾 and with the R ratio Mechanical Behaviour of Engineering Materials Metals, Ceramics, Polymers, and Composites: J. Rösler, H. Harders, M. Bäker Images are for educational and teaching purpose only 363 Effect of Mean Stress Stress + • Fatigue life decreases with increase in mean stress (𝜎mean or 𝜎m ) for a given stress amplitude (𝜎𝑎 ) Crack propagation When, 𝜎𝑚 ≠ 0 𝜎𝑎 𝐾𝑜𝑝 𝜎mean 𝜎ma𝑥 time - NO Crack propagation 𝐾𝑜𝑝 = stress intensity factor to open a crack 𝜎max + 𝜎min 𝜎𝑚 = 2 𝜎max − 𝜎min 𝜎𝑎 = 2 𝜎min Stress Amplitude, 𝜎𝑎 𝜎𝑚1 𝜎𝑚1 < 𝜎𝑚2 < 𝜎𝑚3 < 𝜎𝑚4 𝜎𝑚2 𝜎𝑚3 𝜎𝑚4 105 106 107 N, Cycles to failure As mean stress increases, fatigue life decreases for a given 𝜎𝑎 364 Effect of R ratio Let 𝜎ma𝑥 be the maximum allowable stress: 𝜎𝑎 + 𝜎m ≤ 𝜎ma𝑥 ∆𝐾𝑒𝑓𝑓 ∝ Δ𝐾 ∆𝐾𝑅=−1 > ∆𝐾𝑅=0 > ∆𝐾𝑅=0.5 Stress ∆𝐾𝑒𝑓𝑓|𝑅=−1 > ∆𝐾𝑒𝑓𝑓|𝑅=0 > ∆𝐾𝑒𝑓𝑓|𝑅=0.5 𝜎ma𝑥 ∆𝐾0.5 ∆𝐾0 time R = -1 R=0 R = 0.5 - ∆𝐾−1 Maximum Stress, 𝜎ma𝑥 + R = +0.3 R=0 R = -0.3 R = -1.0 105 106 107 N, Cycles to failure As ∆𝐾 increases, fatigue life decreases 365 Constant Life Diagram: Effect of 𝜎𝑎 and 𝜎𝑚 𝜎𝑚1 < 𝜎𝑚2 < 𝜎𝑚3 < 𝜎𝑚4 When, 𝜎𝑚 ≠ 0 Constant Life Diagram 𝜎𝑎1 > 𝜎𝑎2 > 𝜎𝑎3 > 𝜎𝑎4 𝜎𝑚2 N1 N2 N3 (𝜎𝑎1 ,𝜎𝑚1 ) 𝜎𝑚3 𝜎𝑚4 (𝜎𝑎2 ,𝜎𝑚2 ) (𝜎𝑎3 ,𝜎𝑚3 ) Failure line or Failure boundary (𝜎𝑎4 ,𝜎𝑚4 ) 105 106 107 N, Cycles to failure 𝜎max + 𝜎min 𝜎𝑚 = 2 𝜎𝑎 = Stress Amplitude, 𝜎𝑎 Stress Amplitude, 𝜎𝑎 𝜎𝑚1 For a constant life of N1 cycles Failure line or Failure boundary N1 < N2 < N3 (𝜎𝑎1 ,𝜎𝑚1 ) N2 (𝜎𝑎2 ,𝜎𝑚2 ) N3 (𝜎𝑎3 ,𝜎𝑚3 ) Safe region (𝜎𝑎4 ,𝜎𝑚4 ) Mean Stress, 𝜎𝑚 𝜎max − 𝜎min 2 366 Effect of 𝜎𝑎 and 𝜎𝑚 : Fatigue failure criteria For a given N cycles More conservative Goodman Line 𝜎𝑎 𝜎𝑚 + =1 𝜎𝑒 𝜎𝑈𝑇𝑆 Mostly used Gerber Parabola 𝜎𝑎 𝜎𝑚 + 𝜎𝑒 𝜎𝑈𝑇𝑆 Failure line or Failure boundary Alternating stress, 𝜎𝑎 𝜎𝑒 Goodman line Gerber parabola Soderberg 𝜎𝑦𝑠 Compression 𝜎𝑈𝑇𝑆 2 = 1 Goodman Diagram 𝜎𝑒 − Fatigue strength at N cycles or an endurance limit • Compressive mean stresses are beneficial to improve fatigue life. Tension 𝜎𝑚 = 0 Compression Mean stress, 𝜎𝑚 Compression Tension Test data of ductile materials fall closer to this Tension 0 Range of stress 𝜎𝑎 = 0 Soderberg Line 𝜎𝑚 𝜎𝑎 = 1 + 𝜎𝑦𝑠 𝜎𝑒 𝜎𝑚𝑎𝑥 0 𝜎𝑚𝑖𝑛 𝜎𝑎 𝜎𝑟 𝜎𝑦𝑠 𝜎𝑈𝑇𝑆 Mean stress, 𝜎𝑚 Safe region 367 Fatigue Lifetime Assessment Maximum Tension Climb Relative stress Cruise Turbulence • Varying cycles and loads • How to find the remanent life? Descent Taxing-to gate Taxi-runway Time Flight Profile Mean stress Landing Maximum Compression Images are for educational and teaching purpose only 368 Overstress cycle Miner’s Rule: Accumulative Damage during fatigue 𝑁2 𝑁3 𝑁𝑓2 𝑁1 𝑁4 𝑁𝑓3 𝑁𝑓1 Defect or Damage accumulation 𝑁1 during each overstress cycle 𝑁𝑓1 Time 𝑁𝑓4 𝑁2 𝑁𝑓2 𝑁3 𝑁𝑓3 𝑁4 𝑁𝑓4 𝑛 Linear Cumulative Damage, D 𝑁1 𝑁2 𝑁3 𝑁4 + + + =𝐷 𝑁𝑓1 𝑁𝑓2 𝑁𝑓3 𝑁𝑓4 𝑛 The component fails when the Total damage D equals one 𝑁𝑖 𝑁𝑓i 𝑫= 𝑖=1 𝑁𝑖 =1 𝑁𝑓i Miner’s Rule 𝐷 = 𝑖=1 Also called as Palmgren-Miner rule Find out what is “coaxing”? 369 Factors that influence fatigue life • Alloy strength: Yield strength or ultimate tensile strength • Fracture toughness: KIC • Mechanical design features that are stress concentrators o Inclusions and manufacturing defects (cracks, voids etc.,) o Surface defects, surface roughness or surface finish • Residual Stresses o Compressive residual stresses will enhance the fatigue life o Tensile residual stresses will decrease the fatigue life 370 Thank You!

Mean Stress & Fatigue: Material Behavior

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