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Archive for the ‘Fatigue’ Category

Here is a paper showing how fatigue damage can be calculated from a stress response PSD for a plate excited by an acoustic pressure field:  acoustic_fatigue_plate.pdf

The calculation method is given at:
Fatigue Damage for a Stress Response PSD

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The Matlab scripts for calculating the plate responses are included in the vibroacoustics section of the Vibrationdata GUI package, available at:   Vibrationdata Signal Analysis Package

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See also:

Steady-State Response of a Rectangular Plate Simply-Supported on All Sides to a Uniform Pressure:  ss_plate_uniform_pressure.pdf

Steady-State Vibration Response of a Plate Fixed on All Sides Subjected to a Uniform Pressure: fixed_plate_uniform_pressure.pdf

- Tom Irvine

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Here is a paper.

Estimating Fatigue Damage from Stress Power Spectral Density Functions: estimate_fatigue_psd.pdf

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This following Matlab program calculates the cumulative rainflow fatigue damage for an input stress PSD using the following wideband methods:

1. Wirsching & Light
2. Ortiz & Chen
3. Lutes & Larsen, Single-Moment
4. Benasciutti & Tovo, alpha 0.75
5. Dirlik
6. Zhao & Baker

Reference:

Random Vibrations: Theory and Practice (Dover Books on Physics)

The stress PSD and the fatigue strength coefficient must have consistent stress units.

The input PSD must have two columns: freq(Hz) & stress(unit^2/Hz)

* * *

Main scripts:

stress_psd_fatigue.zip

Vibrationdata Signal Analysis Package

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The following values are “For Reference Only.”

m = fatigue exponent
A = fatigue strength coefficient

Aluminum 6061-T6 with zero mean stress

m=9.25
A=9.7724e+17 (ksi^9.25)
A=5.5757e+25 (MPa^9.25)

Butt-welded Steel Joints

m=3.5
A=1.255e+11 (ksi^3.5)
A=1.080e+14 (MPa^3.5)

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See also:

Rainflow Fatigue

Mrsnik, Janko Slavic, Boltezar, Frequency-domain methods for a vibration-fatigue-life estimation – Application to real data:  mrsnik_article_vib_fatigue.pdf

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- Tom Irvine

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Here is an empirical method for directing calculating a fatigue damage spectrum from a shock response spectrum: srs_fds.pdf

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See also:

Using Random Vibration Testing to Cover Shock Requirements

- Tom Irvine

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Aerospace and military components must be designed and tested to withstand shock and vibration environments.

Some of this testing occurs as qualification, whereby a sample component is tested to levels much higher than those which it would otherwise encounter in the field. This is done to verify the design.

Now consider a launch vehicle component which must withstand random vibration and pyrotechnic shock. The random vibration specification is in the form of a power spectral density (PSD). The shock requirement is a shock response spectrum (SRS).

Pyrotechnic-type SRS tests are often more difficult to control and thus more expensive than shaker table PSD tests. Furthermore, some lower and even mid-level SRS specifications may not have the true damage potential to justify shock testing.

The fatigue damage spectrum (FDS) can be used to further determine whether the PSD specification covers the SRS requirement.  If so, then shock testing can be omitted in some cases.

Here is a paper: random_cover_shock.pdf

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See also:

Shock Severity Limits for Electronic Components

Rainflow Cycle Counting

Fatigue Damage Spectrum

Matlab Mex – fds_main script

SDOF Response to an acceleration PSD Base Input – VRS script with FDS option

Matlab script: Vibrationdata Signal Analysis Package  – SRS damped sine time history synthesis function

Direct Fatigue Damage Spectrum Calculation for a Shock Response Spectrum

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- Tom Irvine

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There is an occasional need to compare the effects of two different power spectral density (PSD) base input functions for a particular component. This would be the case if the component has already been tested to one PSD but now must be subjected to a new PSD specification.

A comparison can readily be performed using a Vibration Response Spectrum (VRS) if the PSDs have the same duration. This requires estimates of the bounds for both the amplification factor Q and the natural frequency.

The task is more complex if the PSDs have different durations. A Fatigue Damage Spectrum (FDS) comparison can be performed as an extension of the VRS method. This also requires estimates of the fatigue exponent.

The method is demonstrated using an actual case history: psd_fatigue_comparison.pdf

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Here is the source code for a C++ vibration response program which has a fatigue damage spectrum option: vrs.cpp

The calculation can also be performed using the Matlab script set: VRS.zip

The main script is:  VRS.m

But the C++ version is much faster!

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See also:

Rainflow Fatigue Cycle Counting

Dirlik Rainflow Counting Method from Response PSD

SDOF Response to an acceleration PSD Base Input

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- Tom Irvine

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Aircraft Fatigue

Malaysia Airlines Flight 370

b777

The leading news story the last few days has been Malaysia Airlines Flight 370 which mysteriously disappeared on March 8, 2014, somewhere over the South China Sea or perhaps the Strait of Malacca. The aircraft was a Boeing 777-200ER.

The cause or causes of the disappearance and presumed crash are simply unknown at this time.

But fatigue failure is one possible cause. Note that the Federal Aviation Administration (FAA) had previously issued the following warning regarding potential fatigue cracking in Boeing 777 aircraft.

Airworthiness Directives; The Boeing Company Airplanes
Document Number: 2013-23456
Type: Proposed Rule
Date: 2013-09-26

Agency: Federal Aviation Administration, Department of Transportation
We propose to adopt a new airworthiness directive (AD) for certain The Boeing Company Model 777 airplanes. This proposed AD was prompted by a report of cracking in the fuselage skin underneath the satellite communication (SATCOM) antenna adapter. This proposed AD would require repetitive inspections of the visible fuselage skin and doubler if installed, for cracking, corrosion, and any indication of contact of a certain fastener to a bonding jumper, and repair if necessary. We are proposing this AD to detect and correct cracking and corrosion in the fuselage skin, which could lead to rapid decompression and loss of structural integrity of the airplane.

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Pressurization Cycles

Aircraft fuselages undergo repetitive cycles of differential pressure with each flight. The difference between the cabin and the external ambient pressure is about 6 or 7 psi at an altitude of 36,000 feet.

Note that cabin pressure at high altitudes is maintained at about 75% of sea level pressure, which corresponds to the air pressure at 8000 ft. This is done by pumping air into the cabin. Note that there is some variation in these numbers depending on the aircraft model.

Pressurization cycles along with vibration, corrosion, and thermal cycling can cause fatigue cracks to form and propagate.

The following images show case histories of fatigue failures in aircraft.

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de Havilland DH 106 Comet

boac1

boac2
The de Havilland DH 106 Comet was the first production commercial jetliner, beginning service in 1952.

Several catastrophic failures occurred over the next two years.

Investigators eventually determined via testing that aircraft’s square windows had a “stress concentration factor” which generated levels of stress two or three times greater than across the rest of the fuselage. The window corners where thus prone to fatigue crack initiation, propagation, and fracture, particularly at the rivet holes.

As a result, the Comet was extensively redesigned with oval windows, structural reinforcement and other changes.

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Aloha Airlines Flight 243

aloha

Aloha Airlines Flight 243 between Hilo and Honolulu in Hawaii suffered extensive damage after an explosive decompression in flight, on April 28, 1988. The aircraft was a Boeing 737-297. It was able to land safely at Kahului Airport on Maui. There was one fatality — a flight attendant was swept overboard.

Fatigue cracks occurred due to disbanding of cold bonded lap joints and hot bonded tear joints in the fuselage panels. This caused the rivets to be over-stressed. A large number of small cracks in the fuselage may have joined to form a large crack. Corrosion was also a related factor.

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Southwest Airlines Flight 812

SW_Yuma

Southwest Airlines Flight 812 suffered rapid depressurization at 34,400 ft near Yuma, Arizona, leading to an emergency landing at Yuma International Airport, on April 1, 2011.

Inspection of the 5 feet long tear revealed evidence of pre-existing fatigue along a lap joint.

The National Transportation Safety Board has concluded that “the probable cause of this accident was the improper installation of the fuselage crown skin panel at the S-4L lap joint during the manufacturing process, which resulted in multiple site damage fatigue cracking and eventual failure of the lower skin panel.”

* * *

Qantas Flight 32

aus_rr

Qantas Flight 32 suffered an uncontained engine failure on 4 November 2010 and made an emergency landing at Singapore Changi Airport. The aircraft was an Airbus A380 with Rolls-Royce Trent 900 engines.

The Australian Transport Safety Bureau concluded that “fatigue cracking” in a stub pipe within the No. 2 engine resulted in oil leakage followed by an oil fire in the engine. The fire led to the release of the Intermediate Pressure Turbine (IPT) disc.

Shrapnel from the exploding engine punctured part of the wing and damaged the fuel system causing leaks and a fuel tank fire, disabled one hydraulic system and the anti-lock brakes and caused No.1 and No.4 engines to go into a ‘degraded’ mode, damaged landing flaps and the controls for the outer left No.1 engine.

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Landing Gear

landing_gear_fatigue

Landing gears are designed to absorb the loads arising from taxiing, take-off, and landing. Hard landing shock is a particular concern. Vibration is another concern. Fatigue cracks can form in the struts and trunnion arms as a results of these loads. Again, corrosion can be a related factor.

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See also:

FAA FR Doc No: 2013-23456

Aircraft Acoustics & Hard Landings

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- Tom Irvine

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Fatigue Exponent Q & A

Question:

What is meant exactly by “fatigue exponent”. I generally input a value between 3 (for notched parts) and 6 (for (unnotched ones). Is it right?…I’ve found confusing and contrasting definitions about b and m exponent (among MIL-STD-810 G and various other documents)

Answer:

The fatigue exponent is the slope of the SN curve in log-log format. It is also the greatest unncertainty factor.

The slope can be affected by many factors including stress concentration, notches, mean stress, residual stress, surface roughness, temperature, corrosion, etc.

Steel with a welded joint has a slope of 3 to 3.5.

Steinberg’s text recommends 6.4 for electronic components.

For bare aluminum, I would use 9 or 10.

A good approach would be to run three cases using lower, nominal, and upper estimates for the fatigue exponent.

Damping is another uncertainty factor. So you should probably also vary the Q value.

So now you will have permutations for both the fatigue exponent and Q.

Best wishes,
Tom Irvine

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A number of methods have been derived for performing rainflow cycle counting for a response PSD. Note that they tend to be conservative.

The Dirlik method is an example of a semi-empirical method for cycle identification.

A Matlab script for performing this method is given at: Dirlik_rainflow.zip

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The following script calculates the Dirlik fatigue cycles for a single-degree-of-freedom (SDOF) system subjected to a base input PSD: sdof_ran.zip

The natural frequency and damping value for the system are required inputs.

The immediate output of the Dirlik method is a “Cumulative Histogram of Range (peak-valley).”

This can readily be converted into individual cycles with their respective amplitudes, where: amplitude=(peak-valley)/2

* * *

The following script calculates the Dirlik fatigue damage spectrum for an array of degree-of-freedom (SDOF) systems subjected to a base input PSD: VRS.zip

The natural frequency is an independent variable. The damping value is required. The fatigue exponent from the S-N curve slope is also required.

The calculation can be performed faster using a C++ program. Here is the source code for a C++ vibration response program which has a fatigue damage spectrum option: vrs.cpp

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Reference papers:

T. Irvine, Experimental Verification of the Dirlik Fatigue Cycle Method. Download

Halfpenny & Kim, Rainflow Cycle Counting and Acoustic Fatigue Analysis Techniques for Random Loading. Download

Halfpenny, A frequency domain approach for fatigue life estimation from Finite Element Analysis, nCode International Ltd., Sheffield UK. Download
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See also:

Rainflow Fatigue Cycle Counting

Fatigue Damage Spectrum, Time Domain

- Tom Irvine

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Consider a single-degree-of-freedom system subjected to base excitation where the input is an arbitrary time history.

The response of the system can be calculated via a digital recursive filtering relationship, which is the numerical engine embedded in the SRS calculation.   This is done for each natural frequency and amplification factor Q of interest.

Next, a rainflow cycle count can be performed for each time history response permutation.

Then a relative damage index can be calculated for each fatigue exponent b case of interest using a Miners-type summation.

The damage index can then be plotted as a function of natural frequency, with separate curves for each Q and b pairs.  This is a Fatigue Damage Spectrum (FDS).

The fatigue damage spectrum is useful for comparing the relative damage potential between two different base inputs, particularly for the case of a nonstationary input.

* * *

An FDS program in C/C++ is:

fds.cpp
fds.exe

Note that C/C++ is the optimum language to use for speed because the rainflow calculation requires deleting intermediate rows from the amplitude array.

* * *

An alternative would be to use a Matlab MEX script that calls a C/C++ program. A script set is posted at: Matlab MEX

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The following presentation gives further information on Fatigue Damage Spectra:  SAVE_conference_2013_Irvine_fatigue

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See also:

Rainflow Cycle Counting

Dirlik Rainflow Counting Method from Response PSD

Fatigue Damage Spectra, Frequency Domain

Shock Response Spectrum

Sine Vibration Rainflow & Fatigue Damage

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- Tom Irvine

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I will be teaching two tutorial sessions at:

84th Shock & Vibration Symposium
November 3-7, 2013
Atlanta, GA

The sessions are:

Shock Response Spectra and Time History Synthesis
Rainflow Cycle Counting for Random Vibration Fatigue Analysis

You are invited to participate.

Further information is given at:

http://www.savecenter.org/

Thank you,
Tom Irvine

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sdof_base_image

Consider a single-degree-of-freedom system subject to base excitation.

Assume a case where the base input is a sine tone which must be converted to an “equivalent” narrowband PSD.

The narrowband PSD must be greater than or equal to the sine tone in terms of peak response and fatigue damage.

A conversion technique is given in:  A Method for Converting a Sine Tone to a Narrowband PSD

A Matlab script which performs the conversion calculation is:  sine_to_narrowband.m

Here is a C/C++ version:
sine_to_narrowband.cpp
sine_to_narrowband.exe

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A converse method is given in:  A Method for Converting a Random PSD to a Sine Tone

A Matlab script which performs the conversion calculation is: psd_to_sine.zip

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See also:

Extending Steinberg’s Fatigue Method

Fatigue Damage Spectrum

- Tom Irvine

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I am going to present:

Extending Steinberg’s Fatigue Analysis of Electronics Equipment to a Full Relative Displacement vs. Cycles Curve

at the Dynamic Environments Workshop in El Segundo, California, June 4-6, 2013.

I know that travel budgets are very tight, but I hope to meet a few of you at the conference.

See also: Extending Steinberg’s Fatigue Method

Thank you,
Tom Irvine

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