Fatigue Life Prediction Based on Variable Amplitude Testsaila/Smogen_PJ_2004-08-17.pdf · Fatigue Life Prediction Based on Variable Amplitude Tests Pär Johannesson Thomas Svensson

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

107

108

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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105

106

107

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 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

107

50

100

200

500

Estimated SNcurve from constant amplitude tests


Seq

/ E

quiv

alen

t am

plitu

de [M

Pa]

N = 7.23e+012 S3.07


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.


Prediction interval.

Conservative predictions. Nrel = 2.57; (1.82, 3.63)

No statistically significant difference for the damage exponent .

105

106

107

50

100

200

500

Estimated SNcurve from variable amplitude tests (Broad)


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.



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)

105

106

107

50

100

200

500

Estimated SNcurve from variable amplitude tests (Broad)


Seq

/ E

quiv

alen

t am

plitu

de [M

Pa]

N = 1.49e+012 S2.96

NarrowBroad

95% intervals.

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105

106

107

50

100

200

500

Estimated SNcurve


Seq

/ E

quiv

alen

t am

plitu

de [M

Pa]

N = 1.09e+012 S2.87




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

105

106

107

50

100

200MeanStressSensibility (MSS)


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 ?

Documents

Fatigue Life Prediction Based on Variable Amplitude Testsaila/Smogen_PJ_2004-08-17.pdf · Fatigue Life Prediction Based on Variable Amplitude Tests Pär Johannesson Thomas Svensson