Materials Issues in Fatigue and Fracture. 5.1 Fundamental Concepts 5.2 Ensuring Infinite Life 5.3 Failure 5.4 Summary
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1 Materials Issues in Fatigue and Fracture 5.1 Fundamental Concepts 5.2 Ensuring Infinite Life 5.3 Failure 5.4 Summary 1
2 A simple view of fatigue 1. Will a crack nucleate? 2. Will it grow? 3. How fast will it grow? Cyclic nucleation and arrested growth Crack growth 2
3 5.2 Ensuring Infinite Life Avoiding crack nucleation Avoiding crack growth Fatigue limit and the UTS UTS of structural materials 3
4 Avoiding crack nucleation Smooth specimen Infinite life At a sufficiently low alternating stress no fatigue cracks will form. 4
5 Cyclic hardening Development of cell structures (hardening) Increase in stress amplitude (under strain control) Break down of cell structure to form PSBs Localization of slip in PSBs cyclic hardening cyclic softening PSB 5
6 Cyclic Deformation Hysteresis loops? ε 6
7 Cyclic stress-strain curve? ε σ Cyclic stressstrain curve ε = σ E + σ K' 1/n' ε ε = σ E +2 σ 2K' 1/n' Hysteresis loops for different levels of applied strain 7
8 Cyclic stress-strain curves Maximum stress amplitude for infinite life. ε = σ E + σ K' 1/n' ε = σ E + σ K 1/n 8
9 5.2 Ensuring Infinite Life Avoiding crack nucleation Avoiding crack growth Fatigue limit and the UTS UTS of structural materials 9
10 Infinite life - no crack growth Infinite life Sharp notches may nucleate cracks but the remote, alternating stress may not be large enough to cause the crack to leave the notch stress field. 10
11 Threshold Stress Intensity The forces driving a crack forward are related to the stress intensity factor a?s At or below the threshold value of?k, the crack doesn t grow. K = Y S πa 11
12 Non-propagating cracks Endurance limit for smooth specimens Stress range,?s Non-propagating cracks Failure a th = 1 π K th S 2 Crack length 12
13 5.2 Ensuring Infinite Life Avoiding crack nucleation Avoiding crack growth Fatigue limit and the UTS UTS of structural materials 13
14 Fatigue limit related to UTS For wrought steel the fatigue strength at 1,000,000 cycles is about 0.5 UTS. For wrought aluminum the fatigue strength at 10,000,000 cycles is about 0.35 UTS. 14
15 5.2 Ensuring Infinite Life Avoiding crack nucleation Avoiding crack growth Fatigue limit and the UTS UTS of structural materials 15
16 Theo. shear stress of a solid τ τ ao x + b 2b τ b τm G 2š slip plane For iron (Fe), the theoretical shear stress is about 2,000,000 psi!?! 16
17 Dislocations τ y = G e 2πw b G e 4π 50 psi.!!! (Pierels stress) The concept of the dislocation explains why the theoretical shear strength is never achieved. However, dislocation theory would predict very low flow stresses!?! Pierels stress. 17
18 Strengthening mechanisms τ y = τ Pieierls + τ solution + τ dispersion + τ hardening Flow stress of a single crystal τ y solution α C 1 / 2 Solid solution strengthening - atomic misfits set up dislocation impeding stress fields 18
19 Strengthening mechanisms τ y dispersion = 2 T b L = G b L Dispersion (precipitate) strengthening - small second phase particles impede dislocation motion. 19
20 Strengthening mechanisms τ y hardening α γ m Work hardening - increasing number of dislocations reduces dislocation mobility due to dislocation interaction and entanglement. 20
21 Strengthening mechanisms F CC BCC H CP Face-centered B ody-centered Hexagonal Cubic Cubic close-packed A luminum I ron Titanium 12 S lip s ys tems 48 S lp s ystems 3 S lip s ys tems Slip system limitations lead to additional strengthening in polycrystalline metals 21
22 Strengthening mechanisms σ y = M τ y M = 3.02 (FCC ), M = 2.75 (BCC ) Polycrystalline metals require at least 5 independent slip systems. Thus grain boundaries and accommodation strains elevate the yield strength of polycrystals above that of single crystals 22
23 Strengthening mechanisms Dislocation pile-up at grain boundary σ y obstacle = σ i + k D 1/ 2 Hall-Petch relationship Flow stress for a poly-crystalline solid σ y = σ Pieierls + ( σ ss + σ dispersion + σ hardening )+ k D 1/ 2 σ y polycrystal = σ thermal + σ structural + k D 1/ 2 23
24 Aluminum fatigue limit Fatigue strength correlates with UTS and small grain size. 24
25 Influence of UTS and notches The fatigue limit of steel is a function of the UTS. However, stress concentrations resulting from either mechanical notches or corrosion pits greatly reduce the fatigue strength in proportion to the severity of the notch. 25
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