eis paper july 2003 fatigue analysis testing dos donts

8/8/2019 EIS Paper July 2003 Fatigue Analysis Testing Dos Donts

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EIS Seminar, July 2003

2003Safe Technology LimitedPage 2

as a datum, and the effect of reducing this sample frequency is shown in Figure 2. It can be seen that sampling at 10

times the signal frequency gave calculated lives of 1.1 times the true value for a broad band signal, and up to 1.5

times the true value for a narrow band signal. A sample frequency of 10 points/cycle is now widely used in industry,

as it offers a reasonable compromise between accuracy of analysis and quantity of data (and hence analysis time).

2.2 Peak-valley extraction and cycle omission

Measured load histories can be truncated by extracting the peaks and valleys from the sampled signal. Because real

signals contain a large number of very small fluctuations, it may be convenient to omit them during the peak/valley

extraction. This process is known as cycle omission, or gating (Figure 3).

The cycle omission criterion, or gate level, must be chosen with care. Many materials exhibit an endurance limit

stress amplitude under constant amplitude testing. Figure 4 shows a measured strain history from a truck steering

arm (upper signal), and the strain history that is produced if all the cycles smaller than the constant amplitude

endurance limit are removed. Fatigue testing using the truncated signal produced fatigue lives which were 9 times

longer than those produced using the full signal [Kerr, 1992].

The reason for this result is that the conventional endurance limit is produced by constant amplitude testing. This

means that if all cycles have amplitudes smaller than the endurance limit amplitude, infinite life may be assumed.

However, if any cycles are larger than the endurance limit, the endurance limit amplitude is very much reduced

(Figure 5). It was shown by Conle [Conle, 1980], and in many papers by Topper et al (see for example [ DuQuesnay,

1993] ) that the first few small cycles which follow a larger cycle contribute significant fatigue damage. Subsequentsmall cycles cause less damage, and sufficient small cycles will return the endurance limit to its constant amplitude

position. The process then repeats following a subsequent large cycle. Standard text books, for example [Dowling,

1998] now recommend that the endurance limit is ignored when analysing variable amplitude signals. For testing, it

is recommended that an endurance limit amplitude equal to 25% of the constant amplitude value is assumed when

gating test signals to omit non-damaging cycles.

Peak-valley extraction can also be carried out on multiaxial loading signals. In this case it is necessary to retain the

phase relationship between the signals. To do this, each time a peak or valley occurs on one signal, the

corresponding data points on the other signal are also retained. The principle is illustrated in Figure 6. Gating to

omit small cycles can be integrated into this processing operation. The danger in this procedure is illustrated by

considering the way these signals are used in the fatigue analysis of a node in a finite element model.

(a) The unit load stress tensor for each node is multiplied by its corresponding load history, to produce timehistories of each stress tensor.

(b) The time histories of the stress tensors are superimposed.(c) The time histories of the principal stresses are calculated.

(d) The damage parameter (for example the time history of the shear strains on a critical plane) is calculated.The peak/valley procedure in Figure 6 therefore assumes that a peak or valley in the principal strains will alwayscoincide with a peak or valley in one of the load histories. In general this is far from true and serious errors in the

calculated fatigue lives can be produced by peak-valley extraction of multiaxial loading histories. The increase in

processing speed can be dramatic, but the potential errors are great. Safe Technologys fe-safe software does notpeak-valley multiaxial loading histories unless the user specifically requests it. A sensitivity analysis should always

be carried out to assess the effect on the calculated fatigue lives.

2.2 Length of load histories

Figure 7 shows fatigue damage histograms for a fatigue analysis of the first 3 000, 30 000 and 300 000 cycles of a

long signal. Although the calculated fatigue lives (adjusted for the different lengths of signal) were very similar, thefatigue damage distribution for the shortest signal is dominated by the largest few cycles. This is a characteristic of

short signals. It is possible to obtain quite adequate calculated fatigue lives from relatively short lengths of signals,

but these lives are much more dependant of the accuracy of measurement of the few largest cycles, and on thestatistical validity of their frequency of occurrence. The damage histogram from the shortest signal could also give

the misleading impression that the damage is dominated by low cycle fatigue and therefore a more ductile material is

required .


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3. Fatigue testing

3.1 Equivalent damage

It is tempting to simplify fatigue tests by using simple constant amplitude loading instead of a representative serviceload history. The assumption is that the constant amplitude loading is equivalent, in fatigue damage terms, to the

more complex service load history. This approach is fraught with danger. Figure 8 shows S-N curves for three design

details on a component plain material, a geometric notch, and a welded joint. A constant amplitude stress cycle willproduce very different lives at each of these three design details. Clearly the constant amplitude loading can only be

equivalent to the service loading at one of these details, and must be very non-equivalent at the other two. A constantamplitude load history (rather than a stress history) may also produce different stress amplitudes at the three details,

complicating the situation further.

Constant amplitude testing may also rank materials and manufacturing processes in the wrong order. Figure 9 showsthe results of constant amplitude tests on riveted lap joints in aluminium alloy. The fabrication method which gave

the longest endurance in constant amplitude testing gave the shortest fatigue life when tested using flight-by-flight

service loading. This is very typical of the fatigue behaviour of complex joints.

3.2 Accelerated testing

Economic pressures may require that fatigue tests are accelerated in order to accumulate fatigue damage as rapidly as

possible. This may be required for reasons of cost, or in order to keep the fatigue test ahead of the components inservice. On method of accelerating tests is to increase the magnitude of the applied loads.

Figure 8 shows that applying the same scale factor to the stress amplitude will accelerate the fatigue damage of theweld to a much less extent than the fatigue damage at the other two details. It is clear therefore that fatigue damage

cannot be accelerated equally at all design details on a complex component. The danger then is that the order in

which cracks occur on an accelerated test will be different from the order of cracking in service. False hot-spots

may be identified, or real hot-spots missed.

There are other potential dangers in accelerated testing. Figure 10 shows test results from a specimen used toinvestigate fatigue failures on splined shafts. At realistic service torque loads, the failure site is correctly identified as

the root of the splines (A). Increasing the torque moves the failure site to the fillet radius (C), and further increasingthe torque moves the failure site to the shaft itself (B). This example shows that accelerating a fatigue test may

produce crack sites which are different from those which may occur in service.

3.3 Block loading test programmes.

In block loading tests, the service loading history is Rainflow cycle counted to produce a histogram of fatigue cycles.Cycles of similar range are grouped together and applied as blocks of constant amplitude loading. The order in which

the blocks are applied can have a significant influence on the test life. Referring to Figure 11, if the blocks are

arranged in a low-high sequence, where the smallest cycles are applied first, gradually increasing to the largest

cycles, then repeating the block, the fatigue life is similar to or shorter than the test life achieved using the original

signal. If the cycles are grouped into a high-low sequence, where the largest cycles are applied first, gradually

reducing to the smallest cycles, then the test life is very much longer. Other arrangements random order of blocks,or low-high-low, produce intermediate results. (The dramatic difference between the low-high and high-low

results is that in the low-high test the smallest cycles follow the largest cycles, and are therefore applied when the

endurance limit is at its most reduced value. Refer to Figure 5.)

4. FE mesh effects in FEA models

Fatigue cracks often initiate from the surface of a component. The accuracy of the surface stresses therefore has asignificant effect on the accuracy of the subsequent fatigue analysis. [Colquhoun, 2000] compared calculated fatigue

lives for a forged aluminium suspension component, using a preliminary and a final mesh, and found significant

differences (Figure 12). The final mesh produced fatigue lives which correlated very well with the results of a


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fatigue test of the component with a calculated life to crack initiation of 27 000 miles, compared to a test life of 41

000 miles at which quite long fatigue cracks were discovered. A difference of less than 15% between un-averaged

and averaged nodal stresses is a reasonable criterion for defining an adequate mesh density for fatigue analysis.

In selecting the parameter for analysis, possible options are integration point stresses (Gauss points), elemental

averaged stresses, nodal averaged stresses, or un-averaged nodal stresses.

Integration point and elemental averaged stresses do not normally give adequate estimates of the surface stresses,

and are not recommended.

With an adequate mesh, there should be little difference in the lives calculated from nodal averaged stresses, or un-averaged nodal stresses. In practice, mesh density is rarely ideal, and experience has shown that fatigue lives

calculated from un-averaged nodal stresses correlate most closely with test results. A recommended method of

assessing mesh density is to compare fatigue life contour plots, calculated from un-averaged nodal stresses, with

different amounts of averaging set in the contour plot software.

5. Choice of fatigue analysis method

5.1 Uniaxial fatigue

The use of uniaxial fatigue methods to analyse biaxially stressed components can give very optimistic life estimates.

In [Devlukia, 1985] a welded steel bracket from a passenger car subjected to multiaxial loading developed fatigue

cracks at a life much shorter than that predicted by uniaxial local strain fatigue analysis. The component had also

been tested under two different service duties and uniaxial analysis failed to reproduce the relative severity of the

two duties.

[Bannantine, 1985] reported the following results from a multiaxial fatigue test programme (Table 1). The three

specimens were (i) simple bending, (ii) in-phase bending and torsion and (iii) axial and torsion loading with randomphase relationship. Fatigue life predictions using uniaxial methods were always non-conservative, with a predictions

up to 19 times the achieved test life.

5.2 Principal stress criterion

Early attempts to analyse biaxial fatigue were based on principal stresses, using a conventional S-N curve. For a

fatigue cycle, the stress range of 1 , or the stress amplitude1

2

, would be used with a stress-life curve obtained

by testing an axially loaded specimen. The (false) assumption in this procedure is that the fatigue life is always

determined by the amplitude of the largest principal stress 1 , and therefore that the second principal stress 2 has

no effect on fatigue life.

Consider a simple circular shaft loaded in pure torsion. If xy is the torsion stress, then the principal stresses are :

21,2 xy =

i.e. the maximum principal stress is equal to the torsion stress. A fatigue cycle of xy will produce a principal

stress cycle of 1 xy = . The use of the principal stresses therefore predicts that the fatigue strength in torsion is

the same as the fatigue strength under axial loading. This is not supported by test data, as Figure 14 shows.Figure 14 shows the results of fatigue tests on a commonly-used steel. It is clear that the torsion fatigue strength is

much lower than the axial fatigue strength - the allowable principal stress in torsion is approximately 60% of the

allowable axial stress. Calculating fatigue lives using principal stress will clearly be grossly optimistic for torsion

loading, and allowable torsion fatigue stresses will be overestimated by a factor of 1/0.6 = 1.66. This could mean the

difference between identifying and missing a potential fatigue 'hot spot'. (In 1927, Moore reported that From the

quite considerable amount of test data available for fatigue tests in torsion the general statement may be made that

under cycles of reversed torsion the endurance limit for metals ranges from 40 per cent to 70 per cent of the

endurance limit under cycles of reversed flexure [Moore, 1927]).


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It has been shown over the past 20 years that principal stresses should only be used for fatigue analysis of 'brittle'

metals, for example cast irons and some very high strength steels. A fatigue analysis using principal stresses tends to

give very unsafe fatigue life predictions for more ductile metals including most commonly-used steels and

aluminium alloys.

5.3 Principal strain criterion

This criterion proposes that fatigue cracks initiate on planes which experience the largest amplitude of principal

strain. The standard strain-life equation for unixial stresses is

(2 ) (2 )2

f

f f f b cN N

E

+

=

where is the applied strain range

2 fN is the endurance in reversals

f is the fatigue strength coefficient

f is the fatigue ductility coefficient

b is the fatigue strength exponent

c is the fatigue ductility exponent

Replacing the axial strain with the maximum principal strain gives :

1 (2 ) (2 )2

f

f f f b cN N

E

+

=

The SAE multiaxial test programme [Tipton, 1989] used a 40mm diameter notched shaft with 5mm fillet radii,

machined from SAE1045 steel. The specimens were tested under pure bending loads, pure torsion loads, and

combined bending-torsion with various proportions of bending and torsion. The test results have been compared

with life estimates made from measured strains at the notch. The maximum principal strain criterion produced lifeestimates which were non-conservative, particularly at lower values of endurance, and the scatter was large (Figure

15). Experience has shown that this criterion should be used only for fatigue analysis of brittle metals, for example

as cast irons and some very high strength steels.

5.4 von Mises Equivalent Strain

Because the von Mises criterion provides an estimate of the onset of yielding, it has been proposed as a criterion for

fatigue life estimation.

The strain-life equation in terms of von Mises equivalent strain is

(2 ) (2 )2

fEFFf f f

b cN NE

+

=

The von Mises equivalent strain, calculated from principal strains, is

( ) ( ) ( )( )0.52 2 2

1 2 2 3 3 1EFF = + +

The value of is chosen so that EFF has the same value as the principal strain 1 for the uniaxial stress condition.

For design analysis based on stresses, at high endurance where the plastic component is small, the von Mises

equivalent stress is


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( ) ( ) ( )( )0.5

2 2 2

1 2 2 3 3 11

2EFF = + +

and fatigue lives could be calculated using (2 )2EFF

f fbN

=

or using EFF with a conventional S-Ncurve.

A major problem with the practical application of von Mises criteria to measured signals is that the von Mises stressor strain is always positive, even for negative values of stress or strain, and so Rainflow cycle counting cannot be

applied directly. Some approximations have been proposed, such as to assign the sign of the largest stress or strain tothe von Mises stress or strain, or alternatively to assign the sign of the hydrostatic stress or strain to the von Mises

stress or strain. These are termed signed von Mises criteria. The different methods of determining the sign can give

significantly different life estimates.

The von Mises criteria correlate poorly with test data, particularly for biaxial stresses when the two in-plane

principal stresses change their orientation during the fatigue loading.

5.5 Brown-Miller criterion.

The Brown-Miller equation proposes that the maximum fatigue damage occurs on the plane which experiences the

maximum shear strain amplitude, and that the damage is a function of both this shear strain max and the strain

normal to this plane, N

max 1.65 (2 ) 1.75 (2 )2 2

fNf f f

b cN NE

+

+ =

This formulation of the Brown-Miller parameter was developed by Kandil, Brown and Miller [Kandil, 1982].

The Brown-Miller criterion is attractive because it uses standard uniaxial materials properties. Figure 16 shows the

results from the SAE test programme [Tipton, 1989]. In general, test results and predictions agreed to within a factor

of 3. The Brown-Miller criterion is widely accepted for the analysis of most metals with the exception of verybrittle metals such as cast irons.

More recently, Chu, Conle and Bonnen [Chu, 1993] have shown improved correlation if the mean shear stress is

included, and have proposed the following extension to the Brown-Miller equation, using a mean stress correctionsimilar to a Smith-Watson-Topper correction

( )2

max ,max

21.02 (2 ) 1.04 (2 )2 2

fNN f f f f

b b cN NE

+

+ = +

where max is the maximum shear stress

and , maxN is the maximum normal stress.

Again, this equation uses standard uniaxial materials properties.

Varvani-Farahani has further extended the Brown-Miller equation, by weighting the contribution of the normal and

shear stress/strains using the axial and torsion fatigue strength coefficients. [Varvani-Farahani, 2000], [Varvani-

Farahani, 2003].

6. Concluding remarks

This paper has given some guidelines to be followed when planning a fatigue investigation. Many of the guidelines

are set as defaults in fe-safe, allowing engineers with relatively little fatigue experience to carry out successful

analyses.


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Processing speeds are also impressive. To give two examples: the fatigue analysis in fe-safe of a 700 000 element

model (4-noded solid elements) containing two load steps, in a 3 GByte file, took 35 minutes on a UNIX

workstation. For an 8 GByte FEA results file containing 36 load steps, the total fe-safe time for read-in, fatigue

analysis of the 36 load steps in sequence, and export of results, was 1 hour 15 minutes on a PC running Windows.

7. References

Bannantine J A, Socie D F. A variable amplitude multiaxial fatigue life prediction method.

Fatigue under biaxial and multiaxial loading, Proc. Third International Conference on Biaxial/Multiaxial Fatigue,Stuttgart, 1989. EISI Publication 10, MEP, London.

Chu C-C, Conle F A and Bonnen J F. Multiaxial stress-strain modelling and fatigue life prediction of SAE axle

shafts. American Society for Testing and Materials, ASTM STP 1191, 1993 pp 37-54

Colquhoun C, Draper J. Fatigue analysis of an FEA model of a suspension component, and comparison withexperimental data. Proc. NAFEMS Conference 'Fatigue analysis from finite element models', Wiesbaden,

November 2000.

Conle A and Topper T.H. Overstrain effects during variable amplitude service history testing. InternationalJournal of Fatigue, Vol 2, No.3, pp130-136, 1980

Dowling N. Mechanical Behavior of Materials. 2 nd edition. Prentice-Hall. 1998/9

Devlukia J, Davies J. Fatigue analysis of a vehicle structural component under biaxial loading.

Biaxial Fatigue Conference, Sheffield University, Dec 1985

DuQuesnay D.L, Pompetzki M.A, Topper T.H. Fatigue life prediction for variable amplitude strain histories. SAEPaper 930400, Society of Automotive Engineers

Kandil F A, Brown M W, Miller K J. Biaxial low cycle fatigue fracture of 316 stainless steel at elevatedtemperatures. Book 280, The Metals Society, London, 1982

Kerr W. 1992. Final year undergraduate project. Unpublished

Moore H F. Manual Of Endurance Of Metals Under Repeated Stress. Engineering Foundation Publication Number13, 1927.

Morton K, Musiol C, Draper J. Local stress-strain analysis as a practical engineering tool.

Proc. SEECO 83 Digital Techniques in Fatigue. City University, London 1983. Society of EnvironmentalEngineers

Tipton S M, Fash J W. Multiaxial fatigue life predictions for the SAE specimen using strain based approaches.Multiaxial Fatigue: Analysis and Experiments, SAE AE-14, 1989

Varvani-Farahani A and Topper TH. A new energy-based multiaxial fatigue parameter.

Fatigue 2000: Fatigue and Durability Assessment of Materials, Components and Structures.

4th International Conference of the Engineering Integrity Society, Cambridge UK. pp313-322.

Bache MR, Blackmore PA, Draper J, Edwards JH, Roberts P, Yates JR (eds.). EMAS 2000.


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Varvani-Farahani A. Critical plane-energy based approach for assessment of biaxial fatigue damage where the

stress-time axes are at different frequencies . 6th International Conference on Biaxial/Multiaxial Fatigue and

Fracture, Lisbon, Portugal, 2001. Carpinteri A, de Freitas M, Spagnoli A (eds.). pp203-221. ESIS Publication 31,

Elsevier 2003.


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Table 1. Uniaxial fatigue life predictions for various multiaxial conditions.(Lives are repeats of the test signal).

TEST LIFE PREDICTION

UNIAXIAL FATIGUE

600 5000

200 450

4000 53000

1700 30000

1000 19000

Figure 1. Possible samples from a signal sampled at four times the signal frequency

Poin ts/ cycle

Relativelife

Narrow band

Broad band

Figure 2. Effect of sampling frequency on fatigue life estimation (Narrow band data from[Morton,1983])

(i)

(ii)

(iii)


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Figure 3. Measured signal (top) and the same signal after peak-valley and cycle omission(bottom)

Figure 4. Measured truck steering arm loading (top) and the same signal after omitting cyclesbelow the endurance limit (bottom)


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Figure 5. Effect of variable amplitude loading on the constant amplitude endurance limit

Figure 6. Multi-channel peak-valley


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Figure 7. Fatigue damage histograms from the first 3000 (top), 30000 (centre) and 300000 cyclesof a long load history

Damage

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

Mean:uERange:uE

0

721

1443

2164

2885

-1417

-703

11

726

1440 Mean ()Range ()

Damage

0

0.00002

0.00004

0.00006

0.00008

0.0001

0.00012

0.00014

0.00016

Mean:uERange:uE

0

703

1406

2109

2812

-1344

-648

48

744


Damage

0

0.000005

0.00001

0.000015

0.00002

0.000025

0.00003

Mean:uERange:uE

0

605

1209

1814

2419

-1167

-568

30

629



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Figure 8. Notional S-N curves for three design details.

Figure 9. S-N curves and flight-by-flight test results for three lap joints.

10-2

10-1

100

101

102

103

100 102 104 106 108

Life (2nf)

Sa(SN):MPa

Weld Notch

Plain


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Figure 10 Accelerated testing can change the failure location

Figure 11 Block loading effect of block sequence on test life


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Figure 12. Effect of mesh refinement on calculated fatigue lives

Figure 13. Principal stresses for a shaft under axial load and torsion load

0

10

20

30

40

50

60

1.0E+04 1.0E+06 1.0E+08 1.0E+10 1.0E+12 1.0E+14 1.0E+16

Predicted Fatigue Life (repeats).

Applied%ofServiceLoa

Standard Mesh - Max Shear Strain

Refined Mesh - Max Shear Strain


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100

1000

1.0E+04 1.0E+05 1.0E+06 1.0E+07

Cycles

StressA

mplitudeMPa

Axial stress

Torsional stress

Figure 14. Stress-life curves for axial and torsion loading

Figure 15. SAE notched shaft test results, principal strain theory


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Figure 16. SAE notched shaft, Brown-Miller parameter

eis paper july 2003 fatigue analysis testing dos donts

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