fatigue fatigue life and design fatigue mechanisms factors...
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Chapter 8 Failure (Fatigue and creep)
Fatigue Fatigue life and designFatigue mechanismsFactors that affect fracture lifeGeneralized creep behavior Stress and temperature effects
Fatigue
Fatigue = failure under cyclic stress.
tension on bottom
compression on top
countermotor
flex coupling
bearing bearing
specimen
Stress varies with time. --key parameters are S and σm
σmax
σmin
σ
time
σmS
Key points: Fatigue...--can cause part failure, even though σmax < σc.--causes ~ 90% of mechanical engineering failures.
Fatigue life
Stress amplitude (S) versus number of cycles to fatigue failureσmax=2/3 σFatigue limits =35-60% of tensile strengthFatigue life
Fatigue design parameters
Fatigue limit, Sfat:--no fatigue if S < Sfat
Sometimes, thefatigue limit is zero!
Sfat
case for steel (typ.)
N = Cycles to failure103 105 107 109
unsafe
safe
S = stress amplitude
case for Al (typ.)
N = Cycles to failure103 105 107 109
unsafe
safe
S = stress amplitude
Fatigue mechanism
Crack grows incrementally
dadN
= ∆K( )mtyp. 1 to 6
~ ∆σ( ) aincrease in crack length per loading cycle
Failed rotating shaft--crack grew even though
Kmax < Kc--crack grows faster if
• ∆σ increases• crack gets longer• loading freq. increases.
crack origin
Improving fatigue life
Impose a compressivesurface stress(to suppress surfacecracks from growing)
--Method 1: shot peening
Remove stressconcentrators
--Method 2: carburizing
C-rich gasput
surface into
compression
shot
N = Cycles to failure
moderate tensile σmlarger tensile σm
S = stress amplitude
near zero or compressive σm
Adapted fromFig. 8.22, Callister 6e.
Factors that affect fatigue life
Mean stressSurface effects• Design factors• Surface treatments• Case hardening
Carburizedsteel
Core steel
Environmental effects
Thermal fatigue: induced at elevated temperatures by fluctuatingthermal stresses.
Corrosion fatigue: failure occurs by the simultaneous action of a cyclic stress and chemical attack
TEl ∆=ασ
Generalized creep behavior
Conditions for creep to occur• elevated temperature• static mechanical stresses
Creep behavior• primary creep • steady-state creep• tertiary creep• rupture
Creep
timeelastic
primary secondary
tertiary
T < 0.4 Tm
INCREASING T
0
strain, ε
Occurs at elevated temperature, T > 0.4 TmeltDeformation changes with time.
Adapted fromFigs. 8.26 and 8.27, Callister 6e.
σ,εσ
0 t
Creep Failure
Most of component life spent here.Strain rate is constant at a given T, σ--strain hardening is balanced by
recovery stress exponent (material parameter)
strain rateactivation energy for creep(material parameter)
applied stressmaterial const.
Strain rateincreasesfor larger T,
σ10
20
40
100
200
Steady state creep rate (%/1000hr)10-2 10-1 1
ε s
Stress (MPa)427C
538 C
649 C
εs = K2σn exp −
QcRT
⎛
⎝ ⎜
⎞
⎠ ⎟ .
Examples
Failure:along grain
boundaries.
time to failure (rupture)
function ofapplied stress
temperature
T(20 + log t r ) = L
L(103K-log hr)
Str
ess
, ksi
100
10
112 20 24 2816
data for S-590 Iron
20appliedstress
g.b. cavities
• Time to rupture, tr
Estimate rupture timeS 590 Iron, T = 800C, σ = 20
ksi
T(20 + log t r ) = L
1073K
24x103 K-log hr
Ans: tr = 233hr
Summary
Failure type depends on T and stress:
- for noncyclic σ and T < 0.4Tm, failure stress decreases with:increased maximum flaw size,decreased T,increased rate of loading.
- for cyclic σ:cycles to fail decreases as ∆σ increases.
- for higher T (T > 0.4Tm):time to fail decreases as σ or T increases.