Fatigue. 3. Final fracture (rough zone) 1. Fatigue origin. 2. Beach marks (velvety zone)

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1 Fatigue Term fatigue introduced by Poncelet (France) 1839 progressive fracture is more descriptive 1. Minute crack at critical area of high local stress (geometric stress raiser, flaws, preexisting cracks) 2. Crack gradually enlarges (creating beach marks ) 3. Final fracture (suddenly, when section sufficiently weakened) Fatigue: no or only microscopic distortion static failure: gross distortion 3. Final fracture (rough zone) 2. Beach marks (velvety zone) 1. Fatigue origin

2 Fatigue Repeated plastic deformation Thousands/millions of microscopic yielding (far below conventional yield or elastic point) Highly localized plastic yielding (holes, sharp corners, threads, keyways, scratches, corrosion) Strengthen vulnerable location often as effective as choosing a stronger material (If local yielding is sufficiently minute strain-strengthen may stop the yielding)

3 Standard Fatigue Strength S n Empirical data from R.R. Moore fatigue test (Highly standardized and restricted conditions) Rotating-beam fatigue-testing machine Pure bending (zero traverse shear) 1750 rpm various N cycles of tension-to-compression-to-tension

4 Standard Fatigue Strength S n Fatigue strength, or Peak alternating stress S (ksi) Linear coordinates (not used for obvious reason) Endurance Limit S n Scattered data Semilog coordinates Endurance Limit S n Knee: 10 6 < N <10 7 Log-log coordinates Endurance Limit S n Ferrous materials: for life cycle N > 10 6 σ < S n

5 S-N curve approximation for steel S n =0.5 x S u (0.4 x S u for cast iron) S u /ksi=0.5 x H B Brinell Hardness (also Bhn) Hence S n /ksi = 0.25 x H B for H B <400 S/S u (log) cycle fatigue: S 1000 = 0.9 x S u

6 Endurance Limit S-N curve for nonferrous metals No Sharply defined knee and No True endurance limit (Fatigue strength at N=5x10 8 often used) aluminum alloys Life N (cycles) Fatigue strength at N=5x10 8 S n = 0.4 x S u (for S u < 48 ksi) (like for cast iron) Tensile Strenght S u (ksi) S u (MPa)

7 Endurance Limit S-N curve approximation Endurance limit Steel S n = 0.5 x S N=10 6 Titanium S n = x S u Cast Iron Aluminum S n = 0.4 x S N=10 8 Magnesium S n = 0.35 x S u Nickel alloys S n = x S u Cooper alloys S n = x S u

8 Endurance Limit Rotating Bending (Moore testing) maximum stresses weakest point on surface fatigue start Reversed Bending (not rotating bending like in Moore testing) maximum stresses top and bottom high probability not weakest point Fatigue strength usually slightly greater deliberately neglected safe side Reversed Axial Loading Fatigue strength about 10% less eccentric loads about 20 30% less maximum stresses entire cross section no reserve! C G = gradient factor Reversed Torsional Loading maximum stresses shear stresses reversed biaxial stress distortion energy theory 58% on surface fatigue start C L =0.58 load factor

9 Endurance Limit

10 Juvinall p.312 Fig Steel S us =0.8 S u Other ductile material S us =0.7 S u

11 Influence of Surface So far special mirror polish surface (only in laboratory! ) Minimizes 1.) surface scratches (stress concentration) 2.) differences of surface & interior material 3.) residual stresses from finishing Commercial surfaces have localized points of greater fatigue vulnerability. Surface factor C S + cast iron Use only for endurance limit!

12 Influence of Size Reversed Axial Loading Fatigue strength about 10% less eccentric loads about 20 30% less maximum stresses entire cross section no reserve! Bending & Torsional Reversed Loading C G = gradient factor 0.3 test specimen large specimen > 0.4 C G = C G = C G = 0.7 Use equivalent round section! small specimen < 0.3 C G = 1

13 Summery use Table 8.1 Juvinall p cycle strength (endurance limit) S n = S n C L C G C S S n Moore endurance limit Bending Axial Torsion C L (load factor) C G (gradient factor) < r e d u c e r e d u c e C S (surface factor) see Fig cycle strength Bending Axial Torsion C L (load factor) 0.9S u 0.75S u 0.9S us steel: S us =0.8S u other ductile metals: S us =0.7S u

14 Example P 8.18 Known: D=25mm, Su = 950MPa, S y = 600MPa, reversed axially loaded, steel, hot-rolled surface Find: S n (2x10 5 life cycles)

15 Effect of mean stress Fatigue Strength Fluctuating stress = static stress + completely reversed stress mean + alternating

16 Effect of mean stress Static tensile stress reduces amplitude of reversed stress that can be superimposed S u empiric concept S y S n σ a σ m -S n Microscopic Yielding Macroscopic Yielding on first load application

17 Effect of mean stress Compressive mean stress does not reduce amplitude that can be superimposed Extends infinite for fatigue (only static failure S uc ) S y S n Values from S-N curve (σ m =0) No macroscopic yielding empiric concept Goodman lines σ a -S y -σ m (compression) σ m (tension) S y S u constant-life fatigue diagram Juvinall p.318 Fig. 8.16

18 Juvinall p.312 Fig. 8.12

19 Effect of mean stress S u σ max S n Goodman line test data steel alloy axial loading σ min σa σ m Note: Brittle materials are usually on Goodman line

20 Effect of mean stress S=0.75S u =0.75x150ksi =112ksi for N=10 6 & 10 3 d=? < 2in lb axial load SF=2 polished S y =120 ksi S u =150 ksi S n =S n C L C G C S =(0.5x150ksi)x1x0.9x0.9 =61ksi S y σ m SFxF m A m = = σ = a 6000lb A SFxF a = A 4000lb A σ σ a = m 0.67 σ a -S y -σ m (compression) σ m (tension) S y S u σ a (N=10 6 )=38ksi σ a (S y )=48ksi d=0.367in < 3/8 in d=0.326in <11/32in

21 Stress concentration K f = 1+ ( K 1) q t geometric or theoretic factor torsion K f <K t q sensitivity factor higly notch sensetive q 1 q S u / ksi bending axial load Cast iron q=0 notch r [in] Apply K f to mean stress σ m and to alternating stress σ a