fe post processing plotting campbell diagram goodman diagram fracture yield principal stress
Post on 16-Dec-2015
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Campbell Diagram
0
500
1000
1500
2000
2500
3000
3500
0 2000 4000 6000 8000 10000 12000 14000
Fre
qu
en
cy -
Hz
Rotation Rate - RPM
Mode 1
Mode 2
Mode 3
EO: 1
EO: 3
EO: 6
EO: 10
EO: 11
EO: 12
EO: 15
Idle
Red Line
Probabilistic Campbell Diagram
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500
1000
1500
2000
2500
3000
3500
0 2000 4000 6000 8000 10000 12000 14000
Fre
qu
en
cy -
Hz
Rotation Rate - RPM
Mode 1
Mode 2
Mode 3
EO: 1
EO: 3
EO: 6
EO: 10
EO: 11
EO: 12
EO: 15
Idle
Red Line
Inputs Include
• Material:– Ultimate tensile strength, – Yield stress – 0.2%,– High cycle fatigue strength,
• Loads– Steady stress,– Vibratory,
• Half amplitude, zero-peak, • Full amplitude, peak-peak,
UTS
Y
1R
0
pp
HCF Test Data
• Fit R=-1 data– For example:
• Pick number of cycles to failure: Nf
• Solve for corresponding half-amplitude stress:
110 /log Rf BAN
1R
Stress Intensity FactorMode I
Stresses near crack tip are singular and vary as the inverse square root of distance from crack tipKI is the stress intensity factor
Von Mises Stress
zzyzxz
yzyyxy
xzxyxx
is the stress tensor
3zzyyxxp
is the equivalent hydrostatic pressure
p
p
p
sss
sss
sss
s
zzyzxz
yzyyxy
xzxyxx
zzyzxz
yzyyxy
xzxyxx
is the deviatoric stress
Invariants of Stress
• Invariants do not change values when coordinate system is rotated.
• The first invariant of the stress is
• The second invariant of the deviatoric stress is
• The third invariant of the deviatoric stress is the determinant.
.31 pI zzyyxx
.2
1 2222222222 zzyzxzyzyyxyxzxyxx sssssssssJ
Uniaxial Tension
000
000
00y
33yzzyyxxp
y
y
yp
zzyzxz
yzyyxy
xzxyxx
p
p
p
s
3
100
03
10
003
2
22222 3
1
9
1
9
1
9
4
2
1yyyyJ
:yield stressy
Equivalent Mises Stress
• Yielding occurs when
• Or when equivalent stress
• When yielding occurs
• Stress ratio is
03
1 22 yJ
23JvM
yvM
yvM /
Principal Stresses
• Eigenvalues of stress tensor (matrix) are principal stresses– All values are real– Order is 1:maximum, 2: intermediate, 3:minimum
• Associated eigenvectors are normal to face• Use maximum principal stress for fracture
1
2
3
x
y
z
FE Post Processing• Plotting
– Includes displaced, contour, and scatter plots• Campbell Diagram
– Finds important resonances• Goodman Diagram
– Predicts high cycle fatigue life• Fracture
– Indicates failure due to crack propagation• Yield
– Establishes yield through the use of equivalent (Mises) stress• Principal Stress
– Aids in determining failure due to presence of flaws
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