# Presentation: 108884

## Fatigue Life Assessment

- William O. Hughes/7735
- Mark E. McNelis/7735
- July 22, 2004

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## Introduction:  Fatigue Life Assessment

- Vibration of space-flight hardware, from either ground random vibration testing or launch, fatigues the hardware.  Every additional test or launch reduces the remaining fatigue life of that hardware.
- A methodology to provide guidance on establishing the qualification-test “demonstrated fatigue life” of a hardware design and estimating the remaining vibration fatigue life in identically-designed flight acceptance hardware units was provided in the Lewis Management Instruction (LMI) 8070.2, March 19, 1993.  That methodology may be used to demonstrate that sufficient useful life remains in the flight hardware unit for (re)test and subsequent flight.
- This methodology is derived from the “Inverse Power Law Model” and the “Fatigue Damage Model Based upon the S-N Curve”
- However, the relationship between exposure duration, amplitude and fatigue damage inflicted on hardware is non-linear and material dependent, and one needs to use caution in judging the flightworthiness of hardware exposed to high frequency random vibration environments.

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## Notes taken from “Dynamic Environmental Criteria”NASA-HDBK-7005, March 13, 2001

- Inverse Power Law Model (time-to-failure related to rms dynamic loading)

- Equivalency Equation for two rms dynamic loads and times

- Idealized S-N Curve for Structural Materials

- Special case of the inverse power law describing the S-N curve (ignoring the fatigue limit)
- N = number of loading cycles to failure
- S = peak stress
- b and c are material constants

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## Fatigue Life Assessment Requires Prototype Hardware Program

- _Prototype_ programs allows an assessment to be made of remaining “fatigue life”:
- Qualification testing of the qualification hardware establishes the “test demonstrated fatigue life” for the hardware design.
- The identically-designed flight hardware may confidently be acceptance tested and launched, if these events do not extend beyond the previously demonstrated fatigue life.
- Any remaining fatigue life can be “allotted” to additional ground tests, reflights, etc.
- _Protoflight_ programs have no test demonstrated fatigue life.
- Unknown remaining fatigue life.

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## “Vibration Life Section” from LMI 8070.2

-   “The following formulation for determining vibration life is offered as guidance to be used when no alternate or preferred method is known by the project.”
-   “(1) The allowable accumulated duration of acceptance test vibration and flight vibration of any flight hardware, for which a vibration qualification test has been performed, shall not exceed 30 percent of the previously demonstrated capability at the equivalent acceptance test amplitude.  Prior demonstration at amplitudes greater than acceptance test amplitudes add to the capability in proportion to the time of exposure and to the ratio of the RMS amplitude raised to the power b, where b is the inverse slope of stress verses number of cycles fatigue curve (i.e., the “S-N” curve) for the most fatigue critical material in the item.  This relationship is formulated as:
- TA = 0.3 [ TO (GO/GA)b + T1 (G1/GA)b ]

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## “Vibration Life Section” from LMI 8070.2 (cont.)

** **TA = 0.3 [ TO (GO/GA)b + T1 (G1/GA)b ]
- Where:
- TA = Maximum time of flight or laboratory vibration at acceptance test amplitudes allowed on flight equipment prior to last flight; that is, one flight remains when TA = 0.
- TO = Minimum time of vibration at qualification amplitudes previously demonstrated without fatigue failure on equipment of identical design.
- T1= Minimum time of vibration at acceptance test amplitudes previously accumulated on the same equipment that was subjected to To.
- GO= Vibration acceleration qualification amplitude (Grms).
- G1= Vibration acceleration acceptance test amplitude (Grms) previously applied to the demonstration unit for the duration T1.
- GA= Vibration acceleration acceptance test amplitude (Grms) to which flight equipment is subjected and which must not exceed G1.”
- b = fatigue exponent
-   “(2) This relationship should be applied on a per axis basis and is appropriate only when the spectral shapes are identical for each vibration acceleration amplitude.  If the value of b is not known, then a value of b = 2.4 shall be used.”

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## Example:  Fatigue Life Calculation 

** **Assume Maximum Expected Flight Environment (MEFL) is 3.0 Grms for a flight launch duration of 0.5 minutes
-  Utilizing the _Prototype_ Hardware Program Test Philosophy (the combining of workmanship test levels with these flight-based levels is ignored for this example):
-   Qualification Unit is tested for 2 minutes at 4.23 Grms                          (MEFL + 3 dB; 2 minutes/axes)
-   Acceptance Flight Unit tested for 1 min at 2.13 Grms                           (MEFL – 3dB; 1 minute/axes)
- Then,
- TO = 2 minutes, GO = 4.23 Grms,
- T1  = 0 (no acceptance level testing on Qualification Unit), G1 = 2.13 Grms,
- GA = 2.13 Grms, b = 2.4 (assume copper wire), and:
**T****A ****= 0.3 [ 2(4.23 / 2.13)****2.4**** + 0(2.13 / 3.0)****2.4 ****] = 0.3 (10.38 minutes)**
**T****A ****= 3.11 minutes**

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## Example:  Fatigue Life Calculation (cont.)

_**Interpretation**__ of __T__A__= 3.11 minutes__:_
-  **Qualification Unit has demonstrated that Acceptance Flight Unit (design) can survive vibration at the acceptance test level (of 2.13 Grms) for 3.11 minutes. **
** ****Fatigue Life Remaining on Acceptance Flight Unit **_**at acceptance test levels**_** (**_**after**_** accounting for performing normal acceptance vibration test of flight unit and launching flight unit) = 0.97 minutes, since:**
- Fatigue Life Remaining = TA –  1 acceptance test – 1 flight                                                                                                                                                                                                                                            	                                =  (3.11 – 1.00  – 1.14) minutes = 0.97 minutes
- Since 1 acceptance test = 1.0 minute at the 2.13 Grms acceptance test level
- Since 1 flight (at 3.0 Grms for 0.5 minute) = 1.14 minutes (TAe) at the 2.13 Grms acceptance level, derived from the (inverse power law) equivalency equation:
- TAe=Tf (Gf/GA)b, where TAe= the equivalent acceptance test time for one flight, Tf= flight duration, Gf=vibration acceleration flight amplitude (Grms), GA=vibration acceleration acceptance test amplitude (Grms)

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## Additional Notes on Fatigue Life

- Hardware may have more (unknown) life than indicated (beyond what was demonstrated in qualification test)
- The fatigue exponent “b” will vary depending upon the material under stress.  Some possible values include:
- b=2.4 for electronic equipment (assumes copper wire)
- b=4.0 for complex electrical and electronic equipment items
- b=8.0 for un-notched steel and aluminum alloys structures,                                                     	    under random vibration loading
- Other types of failure modes besides “fatigue based on S-N curve” are possible (such as first passage critical threshold failures, or fatigue based on crack growth).

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