Fatigue - Nc State Universitymurty/NE509/NOTES/Ch4d-Fatigue.pdf · Fatigue Fatigue is failure under...
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Fatigue Fatigue is failure under cyclic loading • define various parameters (Fig. 8.17) : σ m - mean stress σ r - stress range σ a - stress amplitude R = σ min σ max • S - N curves : (Fig. 8.19) • fatigue strength • endurance-limit (35 - 60% of UTS) • low vs high cycle fatigue : LCF - ductility controlled HCF - strength controlled effects of CW / radiation ⇒ Coffin-Manson Equation (LCF) : ∆ε p 2 = A (2N) c , c ~ -0.5 - -0.7, A~ε f (Fig.12.13); similarly for hcf : ∆ε E 2 = B (2N) b , b ~ -0.05 - -0.12, B~σ f Characteristic slopes : ∆ε 2 = σ f E (2N) b + ε f (2N) c Universal slopes : ∆ε = 3.5 S u E N -0.12 + ε 0.6 f N -0.6 ∆ε 2 = ∆ε Ε 2 + ∆ε p 2 KL Murty page 1 NE 409/509
Transcript of Fatigue - Nc State Universitymurty/NE509/NOTES/Ch4d-Fatigue.pdf · Fatigue Fatigue is failure under...
Fatigue
Fatigue is failure under cyclic loading
• define various parameters (Fig. 8.17) :
σm - mean stress σr - stress range σa - stress amplitude R = σminσmax
• S - N curves : (Fig. 8.19) • fatigue strength • endurance-limit (35 - 60% of UTS)
• low vs high cycle fatigue : LCF - ductility controlled HCF - strength controlled effects of CW / radiation ⇒
Coffin-Manson Equation (LCF) :
∆εp2 = A (2N)c , c ~ -0.5 - -0.7, A~εf (Fig.12.13);
similarly for hcf : ∆εE2 = B (2N)b , b ~ -0.05 - -0.12, B~σf
Characteristic slopes :
∆ε2 =
σfE (2N) b + εf (2N)c
Universal slopes :
∆ε = 3.5 SuE N-0.12 + ε0.6
f N-0.6
∆ε2 =
∆εΕ2 +
∆εp 2
KL Murty page 1 NE 409/509
• mechanism (Fig. 8.22) crack initiation and propagation (Fig. 8.21) stage I (slow / along preferred crystallographic directions) stage II (relatively faster / ⊥r to the loading direction) beachmarks (Fig.8.23) & fatigue striations (Fig. 8.24)
• Crack propagation rate (Fig. 8.26)
No. of cycles to failure :
Paris law : dadN = A (∆K)m ⇔ Fig. 8.27
∫πσ∆
=∫∆
=∫=∴f
o
f
o
f a
a 2/m2/mmm
a
a m
N
of
a
da
)(AY
1
)K(A
dadNN
Nf = 1
Aπm/2(∆σ)m ⌡⎮⌠
ao
afda
Ym am/2 (Eq.8.21) ⇔⎪
⎪⎨⎧
=
≠
2m
2m
⎩
Factors Affecting Fatigue Life (& solutions to improve fatigue life)
1. Mean Stress (Fig. 8.29) 2. Surface Effects
(polished vs machined) 3. Design Factors (Fig. 8.30) 4. Surface Treatments
• shot peening (surface compressive stresses) • case hardening (carburization / nitriding - Fig. 8.31)
(Fig. 8.30)
vs
(Fig. 8.31)
KL Murty page 2 NE 409/509
Group Work
A steel has the following properties: Yield stress σo = 700 MPaToughness KIC = 165 MPa vm
A plate of this steel containing an edge crack was tested in fatigue under conditions where ao = 2 mm, R = 0.5 and σmax - σmin = 140 MPa.
This steel follows Paris law : da/dN = 0.66 x 10-8 (∆K)2.25 where da/dN is in m/cycle and ∆K is in MPa m .
a. Show that the critical crack size at failure af is 110 mm. First find σmax : from R and ∆σ ⇒ use relation between KIc , σ and af
b. Compute the fatigue life Nf In Eq. 8.21 we know A, m, ∆σ, ao, af and Y˜1
c. Compute tf at a cyclic frequency ν = 15 Hz
t = Nν
KL Murty page 3 NE 409/509
