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Archive for the ‘Fatigue’ Category

NASA-STD-5019, Fracture Control Requirement for Spaceflight Hardware (excerpt)

4.1.1.12 Low-Risk Part

This section addresses parts that can be classified non-fracture critical because of large structural margins and other considerations that make failure from a pre-existing flaw extremely unlikely.

a. For a part to be classified low risk, it shall be constructed from a commercially available material procured to an aerospace standard or equivalent.

b. Aluminum parts shall not be loaded in the short transverse direction if this dimension is greater than 7.62 cm (3 in).

c. A part whose failure directly results in a catastrophic hazard shall be excluded from being classified low risk, except when the total (unconcentrated) stresses in the part at limit load are less than 30 percent of the ultimate strength for the material used and requirements (1) through (3) and either (4) or (5) are met.

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Thus fatigue and fracture analyses are not required for parts with peak stress less than 0.3*ultimate.

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- Tom Irvine

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sdof_base_image

Rainflow fatigue cycles can be easily calculated for a single-degree-of-freedom subjected to a sine or sine sweep base input.  The reason is that each pair of consecutive positive and negative response peaks forms a half-cycle.

The relative fatigue damage can then be calculated from the rainflow cycles.

Here are Matlab scripts for performing the rainflow and damage calculations.  rainflow_sine.zip

rainflow_sine.m is for the case where the natural frequency is known.

rainflow_sine_fds.m gives the fatigue damage spectrum for a family of natural frequencies.

The remaining scripts are supporting functions.

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See also: 

Rainflow Cycle Counting

ramp_invariant_base.pdf

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- Tom Irvine

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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)

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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:

Matlab script: Vibrationdata Signal Analysis Package

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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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