Fatigue Life Prediction Based on Variable Amplitude Testsaila/Smogen_PJ_2004-08-17.pdf · Fatigue...
Transcript of Fatigue Life Prediction Based on Variable Amplitude Testsaila/Smogen_PJ_2004-08-17.pdf · Fatigue...
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Fatigue Life Prediction Based on Variable Amplitude Tests
Pr Johannesson Thomas SvenssonJacques de Mar
Acknowledgements
Atlas Copco, Bombardier, Sandvik, Volvo PV, SP, STM,
Smgen Workshops
104
105
106
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1
2
3
N / Antalet cykler till brott
Feq
/ E
kviv
alen
t vid
d [k
N]
N = 7.11e+006 S5.74
Gaussiskt (R=0)Liniljrt (R=0)Hllered (R=1)
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Outline
What is metal fatigue?
Life Prediktion & Testing Traditional Method
Life Prediktion & Testing Proposed Method
Examples
Extensions of the model
Conclusions
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What is Fatigue?
Fatigue is the phenomenon that a material gradually deteriorateswhen it is subjected to repeated loadings.
Whler (1858), Railway engineer Model for fatigue life: Whler-curve
number of cycles N to failure as function of cycle amplitude S.
log(S)
log(N)106103
fatigue limit
finite life
infinite life
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SN-curve:
, material parameters.
Cycle counting Convert a complicated load function to
equivalent load cycles. Load X(t) gives amplitudes S1, S2, S3,
Palmlgren-Miner damage accumulation rule Each cycle of amplitude Si uses a fraction 1/Ni of the total life. Damage i time [0,T]:
Failure occurs when all life is used, i.e when D>1.
Fatigue Life, Load Analysis, and Damage
==i
ii i
T SND 11
time
2S
= SN
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Life Prediktion & Testing Traditional Method
CAConstant Amplitude
Fatigue testing
Predicted life
VA Variable Amplitude
Analysis Basquin
105 106 107
1
2
N
S
= SN
Prediktion Palmgren-Miner Rainflow count
Basquin
Whler-curve
Disadvantages: Often systematic prediction errors. Model errors!Could depend on sequence effects, residual stresses, and threshold effects.
Empirical correction: Change damage criterion, e.g. D = 1 D = 0.3
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Estimated SNcurve from constant amplitude tests
N / Number of cycles to failure
Seq
/ E
quiv
alen
t am
plitu
de [M
Pa]
N = 7.23e+012 S3.07
Constant amplitudeNarrowBroadPM mod
Example: Agerskov Data Set
Welded steel, non load carrying weld.
Estimation from CA: Linear regression.
Here it gives non-conservative predictions.
Solution suggested by Schtz(1972): Relative Miner-rule. Calculate a correction factor based on VA tests, i.e. change but keep fixes.
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Life Prediktion & Testing Proposed Methodology
VAVariable
Amplitude
Fatigue testing
Predicted life
VA Variable Amplitude 105 106 107
1
2
N
S
Whler-curve
Advantage: Same load type at both testing and prediction. Should reduce possible model errors, and give better predictions.
Inspiration: - Gassner-line (1950) - Relativ Miner (1972) - Omerspahic (1999)
Analysis Palmgren-Miner
Basquin
Prediktion Palmgren-Miner Rainflow count
Basquin
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Problem Description
Model SN-curve, Basquin: A VA load is specified through a load spectrum, i.e.
the frequencies j of the load amplitudes sj, L=(sj,j) An equivalent load amplitude is defined as
Damage equivalent to load spectrum.(Palmgren-Miner damage accumulation)
= jjeq sS
iii eSN =
Estimation Maximum Likelihood non-linear regression. Uncertainty in estimates. Uncertainty in prediction.
sj
vi
log(N)
S
Load spectrum
log(Seq)
log(N)
Basquin curve
Equivalent Amplitude:
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( ) iiiieqi fSN +=+= ,;lnlnln ,
( )[ ]2
1),(,;lnminarg),(
=
=n
iii fN
( )[ ]2
1
22 ,;ln2
1
=
==n
iii fNn
s
/1
1
= =
a
m
iieq SS{ }miskk ,2,1;, ==
Condense the VA load to a spectrum of counted load cycles and define its equivalent load amplitude
eqS
Formulate the logarithm of the Basquin equation ...
and ML estimate of the parameters from n reference spectrum tests
),0(ln 2 Neii =
iii eSN =
Estimation of Whler curve for variable amplitude loads
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105
106
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50
100
200
500
Estimated SNcurve from constant amplitude tests
N / Number of cycles to failure
Seq
/ E
quiv
alen
t am
plitu
de [M
Pa]
N = 7.23e+012 S3.07
Constant amplitudeNarrowBroadPM mod
Example: Agerskov
Estimated SN-curve from CA-tests, predictions for VA.
Estimated median life.
Confidence interval for median life.
Prediction interval (for future tests).
Relative life, Nrel=N/Npred, a way to examine systematic prediction errors.
Non-conservative predictions. Broad: Nrel = 0.38; (0.31, 0.47)Narrow: Nrel = 0.53; (0.41, 0.69) PM mod: Nrel = 0.46; (0.37, 0.59)
95% intervals.
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Example: Agerskov
Estimated SN-curve from Broad, prediction for CA.
Estimated median life.
Prediction interval.
Conservative predictions. Nrel = 2.57; (1.82, 3.63)
No statistically significant difference for the damage exponent .
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106
107
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200
500
Estimated SNcurve from variable amplitude tests (Broad)
N / Number of cycles to failure
Seq
/ E
quiv
alen
t am
plitu
de [M
Pa]
N = 1.49e+012 S2.96
Constant amplitudeBroad
95% intervals.
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Example: Agerskov
Estimated SN-curve from Broad, prediction for Narrow.
Estimated median life.
Prediction interval.
No statistically significant systematic errors. Nrel = 1.42; (0.98, 2.05)
Prediction based on CA gives systematic errors. Nrel = 0.53; (0.41, 0.69)
Prediction for PM mod: Nrel = 1.23; (0.86, 1.74)
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106
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50
100
200
500
Estimated SNcurve from variable amplitude tests (Broad)
N / Number of cycles to failure
Seq
/ E
quiv
alen
t am
plitu
de [M
Pa]
N = 1.49e+012 S2.96
NarrowBroad
95% intervals.
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106
107
50
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200
500
Estimated SNcurve
N / Number of cycles to failure
Seq
/ E
quiv
alen
t am
plitu
de [M
Pa]
N = 1.09e+012 S2.87
Constant amplitudeNarrowBroadPM mod
Estimated median life.
Prediction interval.
Possible to combine different types of load spectra when estimating the SN-curve.
Systematic prediction errors. Nrel = 2.11; (1.69, 2.64)
No difference seen in !
Example: Agerskov
Estimated SN-curve from all VA, prediction for CA.
95% intervals.
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Extended Fatigue Model Mean Value Influence
Mean value correction Include mean value correction when calculating Seq. Use existing models, e.g. mean-stress-sensibility (Schtz, 1967)
Possible to estimate the correction M together with SN-curve.
Crack closure models Include crack closure when calculating Seq.
Use existing models variable closure level, or constant closure level.
Possible to estimate a constant level Sop together with SN-curve.
( ) += jmjajeq sMsS ,,
( ) = jopjjeq SSS ,max,
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SP: Convex spectrum Mean stress correction
Mean-Stress-SensibilitySa=Sa+MSm
Uncertainty in parameters = 5.74;
4.74 < < 6.75 (95%) M = 0.17;
0.073 < M < 0.251 (95%)
Scatter is reduced from s=0.51 to s=0.38.
We should include the extra parameter M.
Optimal model complexity?104
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200MeanStressSensibility (MSS)
N / Number of cycles to failure
Seq
/ E
quiv
alen
t am
plitu
de [M
Pa]
N = 2.06e+017 S5.74
s = 0.38214, M = 0.16179
Convex 1Convex 0.5
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Conclusions
Estimation of SN-curve from spectrum tests. Methodology based on equivalent load, Seq. Can combine different types of load spectra. Analysis of uncertainties in estimates and predictions. Possible to distinguish systematic deviances form random variations.
Difference between CA and VA? Yes, often! (same ) Difference between load spectra? No, for Agerskov! Influence from mean value, irregularity, or level crossings?
Extensions Mean value influence.
Further work. Combined estimation of SN-curves for CA and for VA (same slope ).
Estimate two SN-curves (CA and VA) at the same time, with some common parameters.
Parameters: (CA, VA, , ) different Parameters: (CA, VA, , CA, VA) different and
Different classes of service loads. same slope ,different ?